by a constant and parallel course of the WGR curve. The increase in the phase permeability of reservoir rocks to the formation water is characterised by a sudden and rapid increase in the water ratio. During about 1500 days of production, the WGR increased to a value of about 2300 g/m3, and the WGR' curve is characterised by an analogous and almost parallel course (Figure 5a). Changes in the gas and formation water production curves fully correlate with the changes in the ratio and its derivative. The increase in the production of formation water very quickly manifests itself in the decreasing volume of the exploited gas. The P-6 well is a typical example of a channel mechanism for inflow of formation water to a production well.

#### The Z-1K well

The Z-1K well provides the production horizon with an 18 m long perforation. The analysis of data from the determined curves (Figure 6a) indicates a constant and low level of the water ratio, not exceeding 4 g/m3 up to about the 730th day of operation. During this period, based on the analysis of the course of the water ratio derivative, it should be concluded that there is a conical mechanism of the inflow of formation water. The water cone increases vertically and radially, thereby increasing the water saturation in its zone. In the next stage, there is a sudden and rapid increase in the WGR value to about 4000 g/m3, followed by an almost immediate stabilisation of the ratio at a similar level. The course of the WGR' curve for the growth period is parallel to the course of the water ratio curve. The information contained in the curves of the production of formation water and gas confirm a significant change in the amount of gas produced when the volume of exploited formation water increases (Figure 6b). This nature of the course of changes in the value of the water ratio clearly indicates the inflow of water to the well through a fracture or behind the pipe. Based only on the above data, it is not possible to clearly determine which of these mechanisms occurred in the Z-1K well.

#### **4. The Use of Well Logging Data to Estimate the Permeability Profile of the Reservoir Horizons in Production Wells**

The problem of estimating the permeability of porous materials has a long research history, dating back to the beginning of the 20th century. Of fundamental importance are the theoretical works by Kozeny [33] and Carman [34,35], which allowed for the development of a very general Kozeny–Carman (KC) formula for the calculation of permeability, linking many structural and textual parameters of the rock medium with the parameters of the migrating fluid. In practical terms, this approach is difficult to apply due to the general lack of information about the values of specific parameters, and especially their effective values in the case of polymineral media with a complex system of double porosity. At the same time, empirical models developed for a specific research area were developed based on macroscopic parameters determined from drill core samples, including: porosity (*ϕ*), irreducible water content (*Swi*), capillary water content (*Swirr*) and electrical parameters. Models: Tixier [36], Timur [37], Coates and Dumanoir [38] and Coates [39] are useful tools for the continuous estimation of changes in rock medium permeability along the well profile. However, the cited solutions require each time to take into account the specificity of the studied region and the application of the procedure of calibrating the results on representative data for the current analysed rock formations.

As a part of the project to select the optimal well for the WSO treatment, the most useful approach was the approach using the existing quantitative solutions of clay mineral content (*Vil*), mineral composition (*Vm*i), porosity (*PHI*) and saturation (*Sw),* and available geophysical profiling of natural potentials (*SP*), diameter (*CALI*) and nominal diameter (*BSM*). The developed methodology integrates the qualitative approach, based on the analysis of anomalies registered by individual logs and their mutual relations, with a purely quantitative approach based on the Zawisza model developed for Polish conditions [40]. For obvious reasons, such an approach is needed only in causes when the Production Log (PL) measurements are impossible to perform due to technical or financial reasons, because the interpretation of PL would significantly help in the selection of a well for the planned treatment.

#### *4.1. Assessment of Relative Changes in Permeability—Methodological Aspects*

The methodology for determining the permeable and impermeable zones was based on the qualitative analysis of profiling the diameter in relation to the nominal diameter. The presence of permeable zones is manifested by the presence of a narrowing of the diameter, i.e., the appearance of the so-called mud cake, which manifests its presence in the zones of intensive filtration of the drilling mud deep into the rock mass. Thus, a criterion can be constructed:

*CALI* ≤ *BSM* − potential permeable zones;

*CALI* > *BSM* − potential sealing zones.

The above criterion is rather of a qualitative nature and cannot be used alone except where no other option is available.

The second possibility is a strict quantitative interpretative approach based on the absolute permeability estimation according to the Zawisza model. This model allows the calculation of the irreducible water content (*Swi*) according to Formula (1) and the absolute permeability according to Formula (2):

$$Swi = V\mathcal{H}^a (1 - \varphi)^b \tag{1}$$

$$Kzaw = Aq^{\varepsilon}(1 - Swi)^d\tag{2}$$

where:

*Vil*—volumetric content of clay minerals;

*ϕ* —porosity;

*A, a, b, c, d*—calibration constants.

The calibration constants in the above equations are determined each time for the region and formation in which the estimation is carried out and modified to best reflect the trends of changes in permeability in the available laboratory tests of drill cores, or the average values of this parameter determined on the basis of data from performed well tests.

The results of the permeability estimation allow the definition of another criterion of division into permeable and sealing layers, assuming the limit value *Kgr* = 1 mD for water inflow to the well. This condition will be as follows:

*Kzaw* ≥ *Kgr* − potential permeable zones; *Kzaw* < *Kgr* − potential sealing zones.

The sum of the above criteria is a collective criterion and is the basis for the final division of the profile into:

*CALI* ≤ *BSM* and *Kzaw* ≥ *Kgr* − permeable zones; *CALI* > *BSM* and *Kzaw* < *Kgr* − sealing zones.

The characteristics of the remaining parts of the profile are ambiguous in relation to the above methodological assumptions.

#### *4.2. Analysis Results*

The overall results of the analyses are presented in the figures below (Figures 7–10). The following columns show:

Track 1—profiling of gamma *GR* (API) and natural potentials *SP* (mV);

Track 2—MD depth (m);

Track 3—perforation intervals;

Track 4—borehole diameter (caliper);

Track 5—results of lithological and porosity analysis;

Track 6—results of the analysis of primary saturation with formation media;

Track 7—the results of the absolute permeability estimation according to the Zawisza model (*Kzaw*) (mD);

Track 8—analysis of permeable and sealing zones according to the collective criterion; Track 9—MD depth (m).

**Figure 7.** Results of the interpretation of the profile of permeability changes within the analysed perforation interval in the J-5K well.

**Figure 8.** The results of the interpretation of the permeability change profile within the analysed perforation intervals in the J-8K well.

**Figure 9.** Results of the interpretation of the permeability changes profile within the analysed perforation intervals in the P-6 well.

The description of the results obtained for four of the analysed wells is presented below, with the emphasis on the number of interpreted layers (permeable and impermeable). The J-5K well (Figure 7)

In the interval of the perforation providing access to the 17 m section of the gas horizon profile, an analysis was performed which confirmed the presence of 12 zones with variable filtration characteristics, most of them with unambiguous sealing properties, especially in the bottom part of the horizon.

#### The J-8K well (Figure 8)

Two perforation intervals were analysed in the J-8K well: the 12 m long upper interval profile is characterised by much greater diversity in terms of filtration properties. The lower perforation interval (6 m) almost entirely covers the unambiguously permeable zone. In total, 22 layers with different reservoir parameters were distinguished in this well.

**Figure 10.** Results of the interpretation of the permeability changes profile within the analysed perforation interval in the Z-1K well.

#### The P-6 well (Figure 9)

The subject of the analysis in the P-6 well were two perforation intervals (18 m + 5 m) completed in one gas horizon. These two fragments of the gas horizon profile differ significantly in terms of reservoir characteristics. The lower perforation covers a fairly homogeneous sandstone complex which is practically one permeable formation zone. On the other hand, the part of the profile completed in the upper perforation is characterised by much more variety in terms of reservoir properties, with a large number of unambiguously sealing zones. In this well, it is possible to distinguish a total of 20 zones with different filtration properties.

#### The Z-1K well (Figure 10)

The 18 m long perforation, consisting of the top part of the gas horizon in the Z-1K well, includes the top part of an Upper Devonian carbonate complex and the bottom part of Lower Carboniferous clastic formations, which directly translates into the two-fold nature of the interval provided. The lower part of the perforation interval (carbonate rocks) is a fairly homogeneous zone in terms of filtration properties, while the clastic formations lying above are composed of a large number of layers which are unambiguously and ambiguously sealing. The performed interpretation allowed for distinguishing 27 zones with different filtration properties.

#### *4.3. Ranking of Wells for the Performance of the WSO Treatment Based on the Interpretation of Well Logging Data*

For the purpose of performing a ranking of wells for comparative purposes, a quantitative parameter the called "perforation overlayering index" (*U*) (m−1) was defined, which

specifies the average number of distinguished layers in relation to a running metre of perforation made in the well. The calculations were carried out according to the following Equation (3)

$$
\delta \mathcal{U} = \frac{w}{H} \left[ \mathbf{m}^{-1} \right] \tag{3}
$$

where:

*w*—total number of recognised layers (both unambiguous and ambiguous); *H*—total number of metres of perforation made in the well (m).

The introduced U parameter determines the diversification of the formation in terms of the number of layers with different filtration properties. It was found that the highest values of this parameter would be the most beneficial in terms of performing WSO procedures. Table 1 summarises the systematised results of the *U* parameter estimation for the abovementioned wells. When analysing the compiled values of the *U* parameter for clastic rocks, the first place in the ranking was achieved by the J-8K well (*U* = 1.22), the second by P-6 (*U* = 0.87) and then J-5K (*U* = 0.7). For the Z-1K well, representing carbonate rocks, the *U* parameter value was 1.5.

**Table 1.** Ranking of the wells for the performance of the WSO treatment based on the interpretation of permeability.

#### **5. Well Ranking Based on the Well Evaluation Card**

As part of the project, in the first stage of the ranking, eight wells from the Carpathian Foredeep and the marginal part of the Carpathians were evaluated (Figure 1). The initial selection of these wells was made by the operator. In six wells (C-2, J-5K, J-8K, J-7, P-6, Z-74), gas-bearing horizons related to clastic reservoir levels in Miocene formations were selected for a possible treatment, while in the other two cases (T-3, Z-1K) gas accumulations were located in Palaeozoic carbonate rocks. The ranking of selected wells and reservoir horizons was based on the collected geological, reservoir and exploitation data, as well as a preliminary interpretation of the well logs. As part of the project, a special tool was created, which was called the Well Evaluation Card (WEC). It is a special spreadsheet created in MS Excel, which in a relatively simple technical way allows one to assess the suitability of a given gas well for water shut-off treatment on a 100-point scale. Thus, when evaluating several wells, it is possible to rank them in terms of their suitability for the treatment based on a simple criterion, i.e., the more points the well achieves, the more suited it is for the treatment. It should be emphasised that in the event of failure to meet (or lack of data) one of the so-called "critical conditions" (included in the first part of the card), a well is disqualified as a candidate for water shut off. The interface of this tool is relatively simple. It has been constructed in such a way as to be as easy as possible to use for the user, and at the same time to minimise the possibility of making mistakes by the user, enabling multi-stage evaluation of individual criteria through the use of advanced MS Excel functions.

The category of "critical conditions" necessary to be met includes: water production mechanism, the length of the perforation interval (not more than 50 m), water salinity and the formation temperature. The second group of scored criteria is "other conditions", which include: geometry of the water inflow, presence or absence of impermeable barriers, lithological profile differentiation, type of reservoir, water saturation coefficient, thickness of the gas-bearing horizon and effective permeability. The third group of criteria (not

scored) is "supplementary information", which is intended to facilitate the possible decision regarding the validity of the procedure in the well, if the aforementioned scoring criteria are met. The third group of criteria includes parameters, such as field pressure, water-gas ratio, recovery efficiency, porosity, possibility of acid treatment, possibility of increasing the pressure drawdown and additional tests performed.

From among the eight analysed wells, the four wells with the highest scores were selected in the first stage based on the criteria and scores resulting from the WEC: C-2 (81.3), J-5K (76.6), J-8K (76.6) and P-6 (73.0). The T-3 (53.4) and Z-1K (50.0) wells had the lowest scores, mainly due to the unfavourable mechanism of water inflow through a fracture or behind pipe.

In the next stage of the ranking, only the four above-mentioned wells, which obtained the highest number of points in the previous stage, were considered. The detailed data contained in the geological documentation of the gas fields and the detailed results of the interpretation of the well logs were taken into account. The analysis of these data allowed for obtaining more detailed information on the lithological diversity and the spread of reservoir properties (especially permeability) in the vertical profiles of the selected formation horizons. In three of the four analysed wells (J-5K, J-8K and P-6), the profiles of the interpreted reservoir horizons are characterised by a clear lithological differentiation and the presence of impermeable inserts of fine-clastic rocks within them. In the fourth case (C-2), the reservoir horizons are characterised by lower lithological diversity, and above all by good reservoir properties in the entire intervals completed by pipe perforations. Such horizons should not be taken into account for the test procedure of limiting water production, due to the possibility of cross flows resulting from the homogeneity of the layers completed by perforations. In the final ranking, carried out on the basis of updated information obtained from research and analyses carried out during the project implementation, two wells were considered the most optimal in terms of the planned treatment to reduce water production: P-6 (73.0) and J-8K (68.2). In both of these wells, the reservoir horizons are completed by two perforation intervals with different properties: the upper intervals are characterised by a much greater lithological variability and differentiation of reservoir parameters (within them, a number of permeable and impermeable zones can be distinguished), while the intervals of lower perforations constitute zones with good permeability (Figures 8 and 9).

#### **6. Discussion**

The volume of natural gas consumption in Poland is growing at a much faster pace than production from gas fields that are newly connected for exploitation. An important issue is therefore the idea of implementing secondary methods aimed at increasing the depletion rate over the largest possible area of the field. However, it should be remembered that in the case of small, highly depleted formations, expenses and investment expenditures (OPEX and CAPEX) may exceed the expected returns. In such cases, a more logical decision may be to implement one of the possible methods of improving exploitation efficiency, i.e., the implementation of technologies aimed at the immediate vicinity of production or injection wells, as WSO technologies are. Technologies of this type, including the innovative RCC technology, have been successfully used in Hungary [8,10]. The first treatments performed will provide an answer to the effectiveness of this type of treatment in the Polish part of the Carpathian Foredeep. It should be emphasised that the injection of the treatment fluid into the formation is a relatively simple operation from a technical point of view. However, this type of treatment cannot be performed in every gas well, therefore an extremely important factor for determining the success of the operation is the selection of an appropriate well that meets certain criteria.

This article only discusses the issues related to the selection of wells based on broadly understood geological, reservoir and exploitation data. However, economic factors were not mentioned. Therefore, it should be emphasised that while the assessment of the technological effects of the treatment is relatively simple (by comparing the production of water and gas before and after the treatment), the assessment of the economic effects is not easy or unambiguous. When assessing economic aspects, many factors should be taken into account, such as the costs of sanding, the method of transporting and managing water in specific technical and legal conditions, benefits related to the possibility of continuing operation under unchanged conditions of pressure, etc.

Many authors [1,5,12,41–44] agree that one of the most important criteria for assessing wells is the interpretation of the history of changes in the water ratio and its derivative, leading to the identification of the well water breakthrough mechanism. Correct identification of the water breakthrough mechanism allows the rejection of those wells which do not qualify for any chemical water shut-off treatment. Another important criterion, which significantly determines the possibility of performing the treatment is the vertical lithological differentiation of the profile of perforated interval. Other important criteria include:

However, it is worth noting that as research and technological development progresses, perhaps new solutions will be developed and in the future some of these limitations will no longer be an obstacle to the implementation of water production reduction measures.

Based on the ranking, two wells were finally selected from the eight wells assessed for the water production limitation treatment (P-6 and J-8K). Bearing in mind the procedure of selecting and recommending wells for the possible treatment of limiting water production, it is worth noting that it prefers specific features or specific ranges of values of particular reservoir and exploitation parameters. It can be assumed that the currently proposed technology, based on working fluids prepared on the basis of microemulsions, will be suitable for gas horizons characterised by significant lithological differentiation and located mainly in the middle part of the autochthonous Miocene profile in the Carpathian Foredeep. In practice, this differentiation translates into the presence of a number of permeable and impermeable alternate layers in the profile of the gas interval completed by perforation. The lack of such impermeable barriers disqualifies the well as a candidate for the treatment. The discussed technology will certainly not be used in collectors developed in thick-bedded formations (e.g., amalgamated sandstone beds), massive formations or reservoirs located in stratigraphic traps.

In each case of an attempt to reduce water production in a gas well, it is necessary to assess such a well in terms of water breakthrough mechanisms and its verification based on the Well Evaluation Card. This will help to exclude cases where the procedure cannot be performed, or it will not bring the expected results.

In the case of horizons located in the deeper part of the Miocene profile of the Carpathian Foredeep, as well as natural gas fields located in other petroleum basins, such features as lithological variability, the degree of compaction as well as formation water salinity may be so different that the proposed technology will require significant modification.

#### **7. Conclusions**

Well pre-selection procedure is the first step in the selection of wells for WSO treatment. This was developed to quickly and definitively reject a well as a candidate for WSO treatment. Wells that were not rejected in the pre-selection procedure are not candidates for treatment, yet further verification is required.

In the porous formations, the lack of natural impermeable barriers in the completed interval strongly reduces the probability of WSO treatment success in a given well.

It is important to base the diagnosis on time intervals (so-called diagnostic windows) when assessing the water inflow mechanism, when the well was producing without operator intervention.

Finally, to recommend a well as a candidate for WSO treatment, it is not possible to rely only on one of the criteria, but it is necessary to analyse all available geological, formation and exploitation data for successful outcome.

**Author Contributions:** Conceptualisation: S.F., A.U., M.S. and M.M.; formal analysis: S.F.; investigation and methodology: S.F., A.U., M.S. and M.M.; writing—original draft preparation: S.F., A.U., M.S. and M.M.; writing—review and editing: S.F. and A.U.; visualisation: M.S. and M.M.; supervision: S.F. and A.U. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research leading to these results received funding from the Project titled "Procedure: well selection, water shut-off treatment scenario in gas production wells and preparing microemulsion based treatment fluid", under grant agreement No. DK-4100-190/18.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors express their thanks to the Polish Oil and Gas Company, PGNiG SA, Warsaw, Poland, for granting permission for the use of geological and exploitation data and consent to publish the results.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Influence of Hblock Fine-Grained Material on Selected Parameters of Cement Slurry**

**Marcin Kremieniewski**

Oil and Gas Institute—National Research Institute, 25A Lubicz Str., 31-503 Krakow, Poland<EMAIL_ADDRESS>
**Abstract:** Fine-grained materials are used to seal the microstructure and improve the mechanical parameters of the formed cement sheath. They are used in cement slurries designed to seal casing columns at great depths and in geothermal boreholes to improve thermal conductivity. Such additions shorten the setting time and the transition time from the value of the initial time of the setting to the final of the setting. This allows the shortening of the time needed to bind the slurry and move on to further work. Additionally, it helps to eliminate the possibility of gaseous medium intrusion into the structure of the setting cement slurry. The goal of the work is to determine the influence of the Hblock fine-grained material on selected parameters of the cement slurry. Hblock is used in the research ranging from 1% to 20% (bwoc (bwoc—by weight of cement)), and the two types of cement most commonly used in the petroleum sector. Then the technological parameters of fresh and hardened cement slurries were tested. Research on rheological parameters, determined rheological models and flow curves are performed. On the basis of the obtained test results, the influence of the additive on the technological parameters of the cement slurry is discussed. The research results allow for further work and then the application of the fine-grained material in the petroleum sector.

**Keywords:** cement slurry; fine-grained material; borehole sealing efficiency; technological parameters

**1. Introduction**

The column of casing pipes is sealing a cement slurry, which is a mixture of water, cement and additives or admixtures modifying the technological parameters of the cement slurry. Its properties are adjusted to the geological and technical conditions prevailing in the borehole where the hydration process takes place and the formation of a cement sheath in the annular space [1–3]. In this case, the decisive factor is the type of drilled geological layers, the final drilling depth, dynamic and static temperature, as well as formation pressure and fracturing pressure [4–7]. Therefore, it is necessary to adjust the parameters of the cement slurry properly. For this purpose, various types of chemicals, additives and finegrained material are used, the use of which allows to obtain the parameters required for the given conditions and to obtain the highest possible tightness and durability of the cement sheath formed from the cement slurry [2,8,9]. However, the application of a new type of agent must be preceded by a test cycle, after which it is possible to determine the benefits or the impact of using a given additive [10,11]. Based on the analysis of the obtained results, it is possible to determine the suitability of the tested agent and then modify the slurry recipe for specific borehole conditions. The use of such an advantageously modified cement slurry contributes to the elimination of bad cementing. Such actions are necessary because poor cementation may result in complications and difficulties in liquidating possible outflows of the formation medium from the annular space [12,13]. Due to the high costs of additional works related to sealing, research on the impact and the possibility of using a new type of agents is a necessary element in the continuous improvement of the properties of drilling fluids.

**Citation:** Kremieniewski, M. Influence of Hblock Fine-Grained Material on Selected Parameters of Cement Slurry. *Energies* **2022**, *15*, 2768. https://doi.org/10.3390/en15082768

Academic Editors: Izabela Hager and F. Pacheco Torgal

Received: 18 January 2022 Accepted: 8 April 2022 Published: 9 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### *The Role of Fine-Grained Material in the Technology of Cement Slurries*

The use of hydraulic binders and modification of the properties of the developed cement slurries with the use of additives and mineral admixtures is an issue subject to a wide scope of research [14,15]. It is related to the pursuit of continuous improvement of technological parameters of cement slurries as a result of the use of a new type of agent. Thanks to this, it is possible to seal the matrix of the cement sheath formed in the annular space. Moreover, the modified cement slurry recipe has a more compact structure with a lower porosity value and a much lower gas permeability [2,16,17]. Such conditions make it possible to limit, and most often eliminate, gas migration through the cement sheath. Gas migration is a phenomenon that can occur both during the setting and hardening of the cement slurry, but also during the exploitation of the hole in which the slurry is in the solid state. After binding the cement slurry, the greatest risk of gas migration is in the capillary pore spaces, microcracks in the structure of the cement sheath or in the crevices formed [2,18–20]. Therefore, it is necessary to design a cement slurry recipe that, after setting, will be characterized by a lack of gas permeability. For this purpose, finegrained material and admixtures in the form of mineral dust are used. By increasing the volume of the slurry and hydraulic activity, fine-grained material increases the tightness of the hardened cement slurry [21–23]. It is important because high permeability values of the cement sheath cause corrosion and decrease the mechanical parameters [2,24,25]. The mechanical strength, which is related to the microstructure of the cement sheath and the value of the total porosity, should also be taken into account. When designing the cement slurry recipe, its density is selected depending on the geological and technical conditions, and the mechanical strength decreases in proportion to the reduction in the cement slurry density. Therefore, in order to develop a cement slurry with a well-dense and gas-impermeable microstructure, macropores are filled with a solid substance of finer graining than that of the cement used [26–28]. As a result, it is possible to increase the value of the mechanical strength of the hardened cement slurry and shorten the transition time from the liquid phase to the solid phase. A very important parameter is also the setting time of the cement slurry and the transition time from the point of the beginning of the binding to the point of the end of the binding. It is one of the basic parameters allowing to pre-define whether the liquid cement slurry binds as quickly as possible before gas intrusion into the structure of the liquid cement slurry after being pushed into the cemented annular space,. The shortest possible time between the value of the beginning of the setting and the end of the setting is important [29,30]. Fine-grained materials are commonly used in the building materials industry to improve selected technological parameters of fresh and hardened cement slurries. However, in the technology of cement slurries, these additives are treated with caution. This is due to the much more restrictive parameter values for slurries. The beneficial effect of fine-grained material used to improve the parameters of the hardened cement slurry may adversely affect the rheological parameters of the liquid slurry, which is related to the increase in the water needed for the designed slurry [31–34]. It is important in terms of the pumpability of the cement slurry during the cementing procedure. Therefore, the possibility of using fine-grained material is being investigated in terms of improving the parameters of both the liquid and hardened cement slurry. This is an innovative issue as fine-grain materials from the construction industry are rarely used in the oil industry. Such preliminary work allows to broaden the scientific horizons in this direction and open a new path in the technology of cement slurries.

#### **2. Materials and Methods**

#### *2.1. Materials*

CEM I 42.5R Portland cement was used to prepare slurries. The cement contained 3.22% SO3 and 0.069% Cl−. The cement specific surface was 4200 cm2/g, the specific density was 3.09 g/cm3, and the alkalis content was (eq Na2O) 0.61%. The tap water contained 0.064 mg/L NH4 (ammonia), 2.95 mg/L NO3 (nitrates), 0.048 mg/L NO2 (nitrites), 29.2 μg/L Fe (iron), 5.81 μg/L Mn (manganese), and 344.0 mg/L CaCO3 (calcium carbonate). The second cement used for the tests was the German G class cement (Dyckerhoff). The specific surface area (measured by the Blaine method) is 2800 cm2/g. The alkali content is kept at 0.89%, chloride at 0.061%, and sulphate at 3.23%. The loss on ignition is 3.03%, and the insoluble residue is 0.54%. The volume stability was found to be 0.44 mm.

Hblock is a fine-grained material with the name and chemical composition coded by the manufacturer, in which the dominant oxides are: CaO (35.81–37.53%) and Fe2O3 (26.52–32.45%). The share of MgO is 7.65%, Al2O3 3.62%, MnO 2.87%, and P2O5 1.07%.

#### *2.2. Methods*

To determine the effect of Hblock on selected technological parameters of the fresh cement slurry, the density test, rheological parameters of the cement slurry, and the slurry setting time test along with the transition time from the beginning of setting to the end of the setting are performed. Compressive strength tests and gas permeability tests are carried out for samples of hardened cement slurry.

#### 2.2.1. Slurry Preparation

In order to determine the effect of Hblock on the parameters of the cement slurry, 10 recipes (5 slurries per one type of cement) were tested. The points of reference are two control recipes consisting of cement and water with a constant water-cement ratio. These are samples No. 1 and No. 6. Two types of cement materials are selected for research work: CEM I 42.5R Portland cement with a specific surface area of 4200 cm2/g, and the C3A content in clinker of approx. 7% and class G drilling cement. The specific surface area is 2800 cm2/g, and the C3A content in the clinker is approx. 3%. Modified slurries are 4 recipes containing the tested Hblock fine-grained material, the specific surface of which is 3200 cm2/g. Starters 2 to 5 are made of CEM I 42.5R cement. Starters 7 to 10 were made on the basis of drill cement G. During the preparation of the cement slurry, a certain amount of water is measured with a measuring cylinder. The right amount of Hblock is dosed into the water. Water is poured into the mixer. The speed is then set to 1600 rpm, and mixing takes 5 min. After this time, the cement is poured into the mixing water mixture and mixed for another 25 min. Mixing at low speed is the same as mixing the slurry under the conditions of the well. The basic cement slurry, marked as No. 1 in Table 1, was prepared as a control sample. In order to eliminate the measurement error, the same water-cement coefficient of 0.46 was adopted for all recipes. In subsequent recipes of the cement slurry, increasing concentrations of Hblock in the amount of 1%, 3%, 6%, and 20% (bwoc) were used. Such action is aimed at checking the changes under the influence of the amount of the agent dosed to the starter. The slurry recipes are listed in Table 1 below, while the selected technological parameters are presented in Table 2. Table 3 summarizes the shear rate at 12 speed ranges from 600 rpm to 1 rpm, which corresponds to the shear rate from 1022.040 to 1.703 [1/s]. Table 4 summarizes the apparent viscosity values. On the other hand, Table 5 presents the rheological parameters of the tested slurries, described according to the presented rheological models.

**Table 1.** Recipes of cement slurries with the addition of Hblock agent (water-cement coefficient 0.46).

The share of all measures is given in relation to the weight of cement (bwoc).

**Table 2.** Parameters of the tested cement slurrie.

**Table 3.** Values of the compressive strength measurements for samples P1 to P10.

**Table 4.** Within-subject comparison (comparison of samples to baseline P1) Two-sample *t*-test for the mean.

2.2.2. Density of the Cement Slurry

Density is measured using a Baroid pressure balance (Figure 1) in accordance with EN-PN ISO10426-2 [35]. The balance consists of an arm with a slurry vessel on one side and a calibrated counterweight on the other. The weighing arm is equipped with a sliding weight and has a g/cm3 scale in the range of 0.8–2.75. The weight is read from the position of the sliding weight when the scale is leveled by the appropriate positioning of the bubble on the balance arm.

**Table 5.** Within-subject comparison (comparison of samples to baseline P6) *t*-test: pairwise pairing for the mean.

**Figure 1.** Baroid weight.

#### 2.2.3. Rheological Parameters

The study of rheological properties is based on the determination of shear curves. The tests are performed for the following rotational speeds: 600, 300, 200, 100, 60, 30, 20, 10, 6, 3, 2, and 1 rpm. These values correspond to the shear rates (Y): 1022,04; 511,02; 340.68; ˘ 170.34; 102.20; 51.10; 34.07; 17.03; 10.22; 5.11; 3.41; and 1.70 s−1. The tests are carried out at a temperature of 20 ± 2 ◦C. The dosing liquid is tap water, free from contamination. The viscometer-Model 900 FANN (Figure 2) with coaxial cylinders is used to test rheological properties. To facilitate the calculations (Table 5), the numerical software "Rheo Solution" is used. The software is owned by the Faculty of Drilling, Oil and Gas of the AGH University of Science and Technology and is used in research and development [33,34].

**Figure 2.** Fann model 900 rotary viscometer.

#### 2.2.4. Setting Time

The examination is performed with the use of an automatic six-chamber Vicat apparatus (Figure 3). The test is performed according to IS:4031-PART 4-1988 VICAT APPARA-TUS [36]. The measurement consists of determining the depth of immersion of the needle in the binding cement slurry. The points of the initial time of the setting and the final time of the setting are measured. The test is carried out continuously at the prescribed time. The camera is electronically controlled from a computer using software where the measurement conditions are set. The delay time after which the setting time test is to start is determined, and then the measurement is performed at specified time intervals ranging from 1 min to 20 min. Each subsequent measurement is carried out in a different place on the sample in order to avoid the needle sinking into the same place resulting in an incorrect value.

**Figure 3.** Automated Vicat apparatus.

On the basis of the obtained measurement results, a graph is drawn of the dependence of the depth of the needle plunging into the start of the needle to the binding time of the cement slurry (Figure 4). After each measurement, the needle returns to its base position, where it is cleaned and waits for the next measurement of a given sample or for the next sample. Up to 6 samples of different cement slurries can be measured at the same time. The samples are placed in a water bath that is temperature-controlled from 25 ◦C to 50 ◦C. When the initial time of the setting end is reached, further measurements are stopped, and the results are saved graphically.

#### 2.2.5. Compressive Strength

Measurements are made on beams in accordance with the EN-PN ISO10426-2 [35] standard. The tests are performed using a Chandler Engineering model 4207 testing machine (Figure 5). After the cement slurry is prepared, it is placed in 4 cm × 4 cm × 16 cm molds. The molds are stored in water for 24 h in an autoclave at a temperature of 22 ± 2 ◦C and at atmospheric pressure.

#### 2.2.6. Gas Permeability

The test is performed using a gas permeability meter. The measurement is the basic measure of the ability of a porous medium to transport the liquid and gaseous media it contains. The gas permeability meter (Figure 6) used in the test is used to measure the permeability of core or cement samples one inch in diameter and length (Figure 7). The sample is placed in a "modified Hassler" test cylinder [27]. Nitrogen is then supplied, and the differential pressure is measured at a constant flow velocity obtained. The flow velocity is measured with a calibrated flowmeter. The variables, when substituted for Darcy's law, allow the permeability to be calculated in hardened cement slurry samples.

**Figure 4.** Graph of the dependence of the needle immersion depth in initial time of the setting as a function of time.

**Figure 5.** Chandler Engineering testing machine.

**Figure 6.** OFITE gas permeability meter.

**Figure 7.** A sample of hardened cement slurry for gas permeability testing.

#### **3. Results and Discussion**

The presence of the fine Hblock agent causes the density of the slurry to increase. When analyzing the P1 sample prepared on the basis of CEM I 42.5R cement, the density increased by 10 kg/m3 after adding 1% Hblock compared to the sample without Hblock addition. The addition of 3% Hblock increases the density by 10 kg/m3 compared to the previous sample. The next amount of 6% Hblock in sample P4 is a further increase in density by 10 kg/m3 compared to sample P3, which has 3% Hblock. On the other hand, the use of 20% Hblock in sample P5 causes an increase in density by 40 kg/m3 compared to sample P4.

However, when analyzing the P6 sample prepared on the basis of class G cement, the same trend is visible, but for some time. So 1% Hblock in sample P7 causes an increase in density by 10 kg/m3 compared to the sample without the addition of Hblock, i.e., P6. The addition of 3% Hblock in sample P8 increases the density by 10 kg/m3 compared to sample P7. However, the amount of 6% Hblock in sample P9 increases the density by 20 kg/m3 compared to sample P8, which has 3% Hblock. On the other hand, the use of 20% Hblock in sample P10 causes an increase in density by 60 kg/m3 compared to sample P9.

On the basis of the above, the increase in density is more evident in the formula of the slurry prepared on the basis of G drilling cement than in the case of the CEM I 42.5R Portland cement grout (Figure 8). At the maximum 20% concentration of the Hblock agent in the CEM I 42.5R cement-based slurry, an increase in density by 70 kg/m3 compared to the control recipe can be seen, while in the case of the cement-based slurry, the increase in density is 100 kg/m3 at only a concentration of 20% Hblock (Table 2). This is due to the larger grain diameter of class G drilling cement than CEM I 42.5R class cement, which is related to a better filling of the microstructure of the G cement-based cement slurry.

It should be noted here that the P1 sample has a density of 1890 kg/m3, and the base sample, made on the basis of G cement, has a density of 1870 kg/m3. The difference of 20 kg/m3 more in sample P1 compared to sample P2 results from the greater specific surface area, which for cement in sample P1 is 4200 cm2/g, while cement G used in sample P2 has a specific surface area of 2800 cm2/g.

The addition of 1% Hblock fine-grained material to the composition of the CEM I 42.5R Portland cement-based cement (sample No. 2) accelerates the setting, as shown in Figure 9. The setting time is shortened by 69 min, while the setting time is shortened by 189 min (Table 2). A further increase in Hblock concentration (values 3% and 6%) does not cause a significant difference in the setting time of the slurry; only at a 20% concentration of the agent (sample P5) is an extension of the thickening time visible compared to the previous sample (P4). However, this value is lower than the base sample (P1). When analyzing the slurries based on drilling cement G, it can be seen that the presence of the Hblock agent in the slurry results in an upward trend for the analyzed values of the slurry setting time (Figure 9). This effect is a result of the larger grain diameter of class G cement than CEM I 42.5R cement.

**Figure 8.** Summary of the density of the tested cement slurries.

**Figure 9.** Summary of the setting time values of the tested cement slurries.

The transition time of the tested recipes was significantly shorter in the case of CEM I 42.5R Portland cement slurries than in the case of G cement-based slurries (Figure 10).

The transition from the value of the beginning of the setting to the end of the setting for the base slurry (sample P1) is strongly stretched in both time and amount to 194 min, as shown in Figure 11.

On the other hand, after using the Hblock agent, much shorter values were obtained in the range from 43 min for the P5 sample to 74 min for the P2 sample. The short transition time from the value of the beginning of the setting to the value of the end of the setting for the P5 cement slurry is shown in Figure 12 and Table 2.

In the case of G cement-based slurry, a reduction in the value of the transition time between the initial time of the setting and the final time of the setting is also obtained. However, this change takes place to a lesser extent than in the previous group of slurries. The cement G-based control slurry has a transit time of 217 min, while the Hblock-containing slurries have transition times ranging from 104 min (sample P10) to 145 min (samples P7, P9). When analyzing the changes in the value of the transition time of the slurries containing the Hblock agent (Figure 10), the most favorable change is visible when using the 1% Hblock concentration in relation to the cement mass.

**Figure 10.** Summary of the values of the transition time from the initial time of the setting to final time of the setting of the tested cement slurries.

**Figure 11.** The setting process of the cement slurry based on CEM I 42.5R Portland cement (long transition time); Composition No. 1.

**Figure 12.** The setting process of the cement slurry with the addition of 20% Hblock (short transition time) Composition No. 5.

The addition of Hblock in the tested cement slurries has a beneficial effect on the improvement of the mechanical parameters of hardened cement slurries. When analyzing the results of compressive strength tests after 24 h of hydration for the cement-based CEM I 42.5R slurry, an increase in the range from 17.5 MPa (sample P4) to 25.5 MPa (sample P5) compared to the base value of 15, 5 MPa for the P1 hardened cement slurry (Figure 13, Table 2). For slurries based on G drilling cement, an increase in the value of compressive strength is also visible, but to a lesser extent. From the value of 14.5 MPa for the base cement slurry (sample P6), the strength value increased to 18 MPa for the P8 slurry containing 3% Hblock. A further increase in the concentration of the tested agent does not improve the value of the compressive strength (Figure 13). The most favorable concentration range is visible, ranging from 1% to 3% of Hblock (marked in Figure 13). It significantly improves the compressive strength of the hardened cement slurry based on the analyzed cement.

#### *Statistical Analysis of the Value of Compressive Strength*

Based on the obtained results, a statistical analysis is performed, taking into account the variability of the data. Table 3 presents the measurement values. However, in Tables 4–6 the uncertainties of measurement and calculated values are estimated. They come from direct measurements based on the accuracy of the measuring devices. Value uncertainties are estimated from the calculated standard deviations from the mean, and a pairwise *t*-test for the mean is estimated from the appropriate formulas.

**Figure 13.** Compressive strength values of the samples of hardened cement slurries.

**Table 6.** Among-subject comparison (comparison of samples with the same amounts of Hblock) *t*-test: pairwise pairing with two samples for the mean.

On the basis of the mean equality test for α = 0.05, the T-Student's statistic is calculated and compared with the data from the distribution. When analyzing the within-subject comparison for samples P1 − P6 made on the basis of CEM I 42.5R cement (Table 4), all Tstat values are in the critical area and range from 9.03 to 24.14, assuming a two-sided T-test of 2.78. Therefore, the samples are statistically different.

The second comparison in Table 5 for the samples (P7 − P10) based on drill cement G shows that only sample P9 is statistically similar to the base samples (P9 − P6) null hypothesis. However, the remaining samples are statistically different.

However, in the among-subject analysis (Table 6), where samples prepared on different types of cement are compared, it can be seen that the P1 − P6 base samples and samples with 3% Hblock additive (P3 − P8) show statistical similarity. The 3% Hblock amount may be the optimal dosing value to achieve the required mechanical performance.

The gas permeability of the analyzed cement slurries decreased from 0.245 mD (sample P1) to 0.043 mD (sample P2) after using 1% Hblock in the case of CEM I 42.5R Portland cement slurries and from 0.337 mD (sample P6) to the value of 0.042 mD (sample P8). The obtained values are summarized in Table 2.

Analyzing the influence of the Hblock agent on the rheological parameters of the cement slurry prepared on the basis of CEM I 42.5R Portland cement, an increase in the yield point after the application of the Hblock additive can be seen. The base slurry P1 had the value of the yield point equal to 6.1 Pa, described by the Herschel–Bulkley model; the introduction of 1% Hblock causes the increase in the yield limit HB to 10.08 Pa, while the 3% Hblock reduces the yield limit to 5.8 Pa. Increasingly larger amounts of the tested agent cause an increase in the yield point value, which can be seen in Figure 14,. The addition of Hblock also increases the consistency coefficient according to the Herschel–Bulkley model. The control slurry (P1) has a consistency coefficient HB of 9.59 Pa sn. After introducing Hblock into the cement slurry, the HB consistency coefficient increases in the range from 12.29 Pa sn to 31.21 Pa·sn. Significantly lower values of the discussed rheological parameters were obtained for the cement slurry prepared on the basis of drilling cement G (Figure 15, Tables 7–9).

**Figure 14.** Summary of selected test results for rheological parameters of cement slurries (cement class CEM I 42.5R).

**Figure 15.** Summary of selected test results for rheological parameters of cement slurries (cement class CEM G).

**Table 7.** Results of measurements and calculated values of shear stress for slurries.

**Table 8.** Results of measurements and calculated values of apparent viscosity for slurries.

**Table 9.** Rheological parameters of cement slurries.

**Table 9.** *Cont.*

The P6 base slurry has a 1.9 Pa Herschel–Bulkley flow limit. The presence of Hblock results in an HB flow limit in the range of 2.75 Pa (sample P10) to 4.64 Pa (sample P7). The HB consistency coefficient ranges from 0.89 Pa·sn (sample P7 with 1% Hblock content) to 3.11 Pa·sn (sample P10 with 20% Hblock content). Casson viscosity of slurries prepared on the basis of CEM I 42.5R Portland cement ranges from 0.08 Pa·s (sample P3 with the addition of 6% Hblock) to 0.12 Pa·s (sample P5 with the addition of 20% Hblock) (Figure 16). In turn, the exponent n decreases with the increase in the Hblock addition (Figure 16). In the case of slurries prepared on the basis of drilling cement G, the Casson viscosity values are lower than in the previous group of slurries and range from 0.05 Pa·s to 0.07 Pa·s (sample P10 with 20% Hblock) (Figure 17). The exponent n has an irregular course and does not show a satisfactory correlation with the concentration of the Hblock measure (Figure 17).

For a thorough analysis of the rheological parameters and determination of the effect of the addition of fine-grained Hblock on the rheology of the cement slurry, diagrams of the flow curves of the tested slurries were prepared. The decrease in the dynamic viscosity of the slurry with the increase in the Hblock agent in the range from 1% to 6% (samples P2, P3, P4) in the slurries prepared on the basis of CEM I 42.5R Portland cement is visible from the slope of the curves (Figure 18), i.e., the decreasing tangent of the angle that forms with the line of abscissa. This is confirmed in previous studies of rheological parameters, where the Casson viscosity values and the plastic viscosity described by the Bingham model decrease due to the increasing amount of Hblock in the slurry. Only in the case of the slurry with the highest amount of Hblock (20% bwoc) (sample P5) is the flow curve above the base slurry curve (P1—red line) visible. This proves the increase in the dynamic viscosity of the cement slurry with a significant (20%) concentration of the Hblock agent.

**Figure 16.** Summary of selected test results for rheological parameters of cement slurries (cement class CEM I 42.5R).

**Figure 17.** Summary of selected test results for rheological parameters of cement slurries (cement class CEM G).

A different course of the flow curves takes place during the interpretation of slurries with the addition of the Hblock agent prepared on the basis of drilling cement G (Figure 19). The curve for the base slurry (sample P6—red color) runs almost the lowest, and the recipe of this slurry has the lowest value of dynamic viscosity. A slightly lower course of the flow curve occurred only in the sample with the addition of 1% Hblock agent (sample P7), while successive increasing amounts of Hblock in the range from 3% to 6% caused an increase in viscosity manifested by a smaller slope of the curves. The greatest increase in viscosity is seen at the highest 20% concentration of Hblock (sample 10).

**Figure 19.** Flow curves for cement slurries with the addition of Hblock (cement class CEM G).

When analyzing the flow curves, a significant increase in shear stresses is visible at low shear rates in the group of slurries made on the basis of CEM I 42.5R Portland cement. This result confirms the thixotropic nature of cement slurries, which have high values of the yield point and structural strength (Table 9; Figure 18). In the case of slurries prepared on the basis of G drilling cement, comparable values of shear stresses in the low ranges of shear rates can be seen, which confirms the low values of rheological parameters in this group of slurries (Table 9; Figure 19).

The fine-grained material of Hblock significantly improves the parameters of both fresh and hardened cement slurry. The use of Hblock reduces the time of transition from the PW value to the KW value in all tested cement slurries (Table 2; Figures 9, 11 and 12). Compressive strength increases after 24 h of sample hydration with small (1% to 3%) amounts of Hblock (Table 2; Figure 13). The use of the tested Hblock agent results in the sealing of the cement matrix, which will result in a reduction in the gas permeability value (Table 2). The use of the Hblock fine-grained material is advantageous due to the fact that a compact and impermeable microstructure of the cement sheath is obtained, characterized by a higher value of compressive strength.

#### **4. Conclusions**

Based on the results of the work aimed at determining the effect of the fine-grained Hblock agent on selected parameters of the cement slurry, it is concluded that:

**Funding:** The work was financially supported by Ministry of Science and Higher Education Warsaw (Internal order Oil and Gas Institute—National Research Institute Project No. 0021/KW/21).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The author thanks the anonymous reviewers for their constructive comments and the editor for handling the paper.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Nomenclature**

#### **References**

## *Article* **Strategy of Compatible Use of Jet and Plunger Pump with Chrome Parts in Oil Well**

**Oleg Bazaluk 1, Olha Dubei 2, Liubomyr Ropyak 3, Maksym Shovkoplias 3, Tetiana Pryhorovska 4 and Vasyl Lozynskyi 5,\***

**Abstract:** During oil fields operation, gas is extracted along with oil. In this article it is suggested to use jet pumps for utilization of the associated oil gas, burning of which causes environmental degradation and poses a potential threat to the human body. In order to determine the possibility of simultaneous application of a sucker-rod pump, which is driven by a rocking machine, and a jet pump (ejector) in the oil well, it is necessary to estimate the distribution of pressure along the borehole from the bottomhole to the mouth for two cases: when the well is operated only be the sucker-rod pump and while additional installation of the oil-gas jet pump above its dynamic level. For this purpose, commonly known methods of Poettman-Carpenter and Baksendel were used. In addition, the equations of high-pressure and low-pressure oil-gas jet pumps were obtained for the case, when the working stream of the jet pump is a gas-oil production mixture and the injected stream is a gas from the annulus of the well. The values which are included in the resulting equations are interrelated and can only be found in a certain sequence. Therefore, a special methodology has been developed for the practical usage of these equations in order to calculate the working parameters of a jet pump based on the given independent working parameters of the oil well. Using this methodology, which was implemented in computer programs, many operating parameters were calculated both for the well and for the jet pump itself (pressures, densities of working, injected and mixed flows, flow velocities and other parameters in control sections). According to the results of calculations, graphs were built that indicate a number of regularities during the oil well operation with such a jet pump. The main result of the performed research is a recommendation list on the choice of the oil-gas jet pump location inside the selected oil well and generalization of the principles for choosing the perfect location of such ejectors for other wells. The novelty of the proposed study lays in a systematic approach to rod pump and our patented ejector pump operation in the oil and chrome plating of pump parts. The result of scientific research is a sound method of determining the rational location of the ejector in the oil well and the calculation of its geometry, which will provide a complete selection of petroleum gas released into the annulus of the oil well. To ensure reliable operation of jet and plunger pumps in oil wells, it is proposed to use reinforcement of parts (bushings, plungers, rods, etc.) by electrochemical chromium plating in a flowing electrolyte. This has significantly increased the wear resistance and corrosion resistance of the operational surfaces of these parts and, accordingly, the service life of the pumps. Such measures will contribute to oil production intensification from wells and improve the environmental condition of oil fields.

**Keywords:** jet pump; oil; well; sucker-rod pump; gas-water-oil mixture; chrome coating

**Citation:** Bazaluk, O.; Dubei, O.; Ropyak, L.; Shovkoplias, M.; Pryhorovska, T.; Lozynskyi, V. Strategy of Compatible Use of Jet and Plunger Pump with Chrome Parts in Oil Well. *Energies* **2022**, *15*, 83. https://doi.org/10.3390/en15010083

Academic Editor: Marcin Kremieniewski

Received: 13 November 2021 Accepted: 21 December 2021 Published: 23 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

It is almost impossible to avoid associated gases extraction during the operation of oil field. These associated gases consist of gas mixture, which contains methane and propanebutane fraction. It requires separation into fractions in special gas processing plants, which are not always present near oil producing areas. Therefore, in oil fields these gases are often burnt in flares and the products of their combustion are a potential threat to the human body.

The practice of associated oil gas utilization using flare units is very dangerous for the environment [1]. For each ton of extracted oil there is from 25 m3 to 800 m3 of associated gas [2]. During the combustion of oil gas, a large amount of mutagenic and toxic substances (carbon oxides, nitrogen oxides, sulfur dioxide, hydrocarbons, soot) are released into the environment, which, when they enter the living organism, lead to the development of irreversible changes caused by the bioaccumulation effect [3–5]. In particular, in the regions that are influenced by the combustion plants, the population is suffering from an increased disease incidence of circulatory, respiratory, digestive and endocrine systems. The effect from combination of several compounds is synergistically upset while the response from the influence of several pollutants is greater than the summation of separate effects [6–9].

Oil producing countries and companies have created a partnership association "Global Gas Flaring Reduction Partnership" GGFR. The purpose of this association is to reduce the environmental impact from gas combustion at flare units through the creation of an appropriate legislative framework and expansion of markets for the disposal of associated gases [10]. Additionally, the promising method of associated gas utilization is using jet pumps for its capturing. The potential energy of the associated oil gas, when properly used, can serve to raise the production fluid to the surface [11–14]. Due to the gas adding to the water–oil mixture of the well, it is possible to reduce the fluids density to such level that it will even reduce the minimum required outlet pressure of the sucker-rod pump, which is used for oil well operation [15,16]. The paper in [17] describes the fundamental possibility of joint operation of the ground jet pump in the conditions of sinusoidal change of the working flow and the rod pump.

A perspective solution for the creation of a gas–water–oil mixture inside the well is inserting of a jet pump in it. Such jet pump, due to the flow of production fluid that will pass through it, will offtake free oil gas from the annulus, mix it with fluid and such mixture of a significantly lower density will be pumped to the mouth of the well. Jet pump can be installed either inside the tubing or in the annulus. With a correctly selected location for such an oil–gas jet pump in the well it will reduce the tubing load and decrease the electric energy consumption of the plunger pump. In addition, to ensure efficient operation of wells, it is necessary to increase the service life of pumps, as their replacement requires significant resources and leads to the cessation of oil production.

Analysis of the method of calculating the pressure distribution in the well, as well as its improvement proposed to clarify the results by the methods of Poettman-Carpenter and Baksendel was given by the authors in the previously published article [18].

#### *1.1. State of the Current Development of the Problem and Formulating a Research Task*

Oil and gas equipment, plunger, centrifugal and jet pumps are operated in extreme conditions during oil production. They are subject to high alternating loads in aggressive environments with the content of solid abrasive particles of rock at elevated temperatures [19]. The action of these factors leads to intensive corrosion and mechanical wear and destruction of machine parts, so the design, materials for their manufacture and technologies for strengthening parts are subject to increased requirements. Jet pumps are widely spread in different areas of modern technology. In recent decades, they have been used directly in oil production. For many cases, during oil wells operation with electrical submersible pump (ESP), additional jet pump usage ensured the stabilization of the ESP work. At the same time, this allowed to use the energy of free petroleum gas, which is

always present in the injected flow and, to a certain extent, this provides an increase in the well's flow rate [20]. In this case the jet pump was installed directly above the ESP.

To create reliable and efficient jet pumps for oil production, it is necessary to develop a theory of their operation. Theoretical issues related to the operation of jet pumps in oil wells were considered in the works in [21,22]. Practical issues related to the efficiency and reliability of pumping equipment are considered in [23–25]. A case of placing the jet pump above the dynamic level of the well is also used in order to extract gas from its annulus, which made it possible to stabilize the dynamic level and increase the reliability of the ESP system [26]. In this case, the injected flow of the jet pump is oil gas, which is accumulated in the annulus.

After this technology showed its effectiveness, such oil-gas jet pumps were proposed to be used together with sucker-rod pumps [27] or individually in complicated production conditions [28,29]. It should be noted here that a sucker rod string could be subjected to abnormal static and dynamic loads [30–32] especially for complex profile wells. Some authors [33–35] consider vibration reduction of oil equipment as a guarantee of dynamic stability of pump rod strings and ensuring the stability of submersible pumps. Actual problems of anti-vibration device designing for long structures (rod strings, pipe strings, etc.) were considered in [36–38], recommendations for over-loaded pump reliability are given in [39–41].

The high profitability of oil-gas jet pumps was also proven in case of their application for gas-lifting operation of wells [42–44]. In general, jet pumps can improve the operation of the equipment they work with, extend its overhaul period and increase oil recovery. Due to such a list of advantages, jet pumps are installed in different places inside of oil wells (near the bottomhole, above and below the dynamic level, on the surface and near the mouth) [45].

A technique for selection of the geometrical parameters for the downhole ejection system's body with an external placement of several jet pumps is presented [46]. To assess the strength of the jet pump's bodies, the theory of membrane-free shells with via openings or cutouts is used [47,48]. The presence of technological openings, designed to attach jet pumps, contributes to the uneven distribution of stresses and, as a result, reduce the fatigue life of such structures. The problems of stress concentration in shell systems under conditions of contact interaction while complex loading were considered in [49–51]. When designing such equipment, engineers pay special attention to the accuracy and tightness of threaded joints [52–54], increasing thread [55–57] and preventing self-unscrewing of threaded joints [58,59].

Concerning the features of the design of modern ejection systems that are operated under aggressive conditions, some authors suggest the use metallic ceramics or ceramic coatings to provide the required operational life of the nozzle [60–62]. Recommendations have been made on the technology of forming, optimal design and calculation of the operational properties of single layer [63,64], flexible [65,66] or multilayer ceramic coatings [67–69]. Thermoplastic composite materials are also widely used [70–73]. For surface hardening of parts of elite models of downhole ejection systems, chromium plating in a flowing electrolyte is used, as well as functionally gradient coatings of required parts of surfaces [74–76]. New technological schemes for hydrocarbon development from used wells to use additionally non-commercial and closed deposits and extend mining enterprise operation are presented in [77–80].

Therefore, one of the most important tasks before the implementation of jet pump technologies in production was the development of a methodology for calculating their working and geometric parameters, as well as technologies to strengthen their parts. Literature review, analyses of patents and regulations on electrochemical chromium plating of parts in quiet and flowing electrolytes showed that chromium plating in quiet electrolyte does not provide a uniform thickness of coatings, and the formation of coatings in flowing electrolyte occurs at higher current densities [62]. This ensures uniform application of the coating layer with low roughness, as well as achieving high coating performance

and increased current yield of chromium. Increasing the service life of pumps can be achieved through the use of reinforcing technologies in the manufacture of their parts by chrome plating.

The issues of obtaining theoretical dependences and their usage for practical calculations of jet pumps are described in [81]. Since the theory of jet devices, installed above the dynamic level of oil wells, which are operated by sucker-rod pumps, has already been developed [82], it is possible to proceed directly to determining the rational location of such jet pumps in wells and calculating their geometry with strengthening of their details.

#### *1.2. Purpose and Tasks of Research*

Thus, the purpose of this article is to determine such location of the oil-gas jet pump inside of the oil well, which will provide the maximum possible reduction of outlet pressure for the sucker-rod pump and decrease the tubing load; as well as being used in development of technology of strengthening of details of jet and plunger pumps by chrome coverings. The formulated purpose can be achieved by solving the following tasks:

#### **2. Materials and Methods**

#### *2.1. Features of Design, Manufacture and Strengthening by Chrome Plating of Details of Pumps*

To strengthen the parts of jet and plunger pumps, an installation for electrochemical chromium plating in a flowing electrolyte and a technological process of coating the parts of these pumps were developed. The installation for electrochemical chrome plating of pump parts in a flowing electrolyte contains interchangeable electrochemical cells used for coating the outer surfaces of the plunger or rod, respectively, or the inner surfaces of the plunger pump sleeve and the jet pump ejector. The electrochemical cell, after mounting the part and the electrode in it, was sealed and connected by means of current leads to the power supply, and by pipes—to the system of electrolyte supply to the annular cavity between the electrodes of the cell. The unit is equipped with an automated control system for electrochemical chromium plating in the flow electrolyte, which allows to maintain independently at a given level the technological parameters of electrolysis: temperature, electrolyte flow rate, electrolysis operating current and the ratio of electrolyte components. Chrome coatings were applied to the working surfaces of pump parts made of steel 40KHN (GOST 4543-2016), which were surface hardened with high frequency currents and subjected to grinding. The anode was an alloy of lead with sulfur and tin. Chrome plating of pump parts (ejectors, bushings, plungers, rods) was performed in a standard electrolyte based on chromic anhydride and sulfuric acid with nano-additives.

To reduce the harmful effects of chromium electrolyte on the environment during the application of electrochemical chrome coating on the pump parts the developed design of the electrochemical sealed cell was used. The system for supplying electrolyte to the annular cavity formed between the electrodes of the electrochemical sealed cell is equipped with a unit for neutralization and purification of gaseous electrolysis products according to our invention [83]. The amount of harmful emissions released into the atmosphere does not exceed the maximum allowable concentration.

#### *2.2. Determination of Rational Placement of the Jet Pump in the Well*

Instead of directing the extracted gas from the well space directly to the flare for its combustion, the article proposes mixing oil gas with well products in the downhole ejector, which allows to use its potential energy of this gas. In the future, this gas is separated at oil treatment plants, and then it can be sent for further use or for the needs of production, or for the current needs of maintenance personnel. The innovation proposed in the article eliminates the combustion of emitted gas during the operation of oil wells, which reduces the amount of emissions of carbon dioxide and other combustion products into the atmosphere. Such measures improve the environmental situation in the oil and gas fields.

In order to determine the rational placement of the oil-gas jet pump in the oil well 753-D Dolyna Oil Field "Dolynanaftogaz" PJSC "Ukrnafta", first of all, it is necessary to calculate the distribution of thermobaric and other operating parameters along its borehole and also to find the daily amount of oil gas, entering its annulus [18].

The scheme of the general layout and the mutual placement of the sucker-rod pump and the oil-gas jet pump is shown in Figure 1 [84].

**Figure 1.** General layout of the tandem installation [84]: 1—rods; 2—separator; 3—tubing string; 4—casing; 5—sucker-rod pump; 6—dynamic level; 7—check valve; 8—oil-gas jet pump.

The wellbore fluid, which is pumped by the sucker-rod pump (5) into the tubing string (3), enters the oil-gas jet pump (8), which is placed in the annulus, where, due to its high velocity, the associated gas from the annular space enters the ejector through the return valve (7). Then this gas–liquid mixture returns back to the tubing and then moves to the mouth of the well. Inside the tubing at the jet pump's level, a separator (2) must be installed to ensure that the ejector's input and output are not connected. More detailed view of the suggested design for the oil-gas jet pump is shown in Figure 2.

In order to determine the location of the jet pump inside the oil well, first of all the range of possible depths of the jet pump placement was selected: from 610 m to 890 m. Low-pressure jet pumps with a ratio of the mixing chamber and the nozzle cross-section areas equal to 6.25. With the help of a created computer program, the outlet pressure for the jet pump was found, as well as a number of its variable parameters (like geometric dimensions), based on the improved Poettman-Carpenter method, which is used for calculation of thermobaric parameters' distribution in wells. In such case, the working flow for the jet pump will be the gas–oil mixture of the well and the injected flow—oil gas from the annulus.

The study [18] considered in details all the values included in the Poettman-Carpenter and Baxendel equation and explains the procedure for implementing this calculation. The scientific novelty of the proposed methods is to solve nonlinear differential equations on which the Poettman-Carpenter and Baxendel methods are based, the Adams-Krylov numerical method, which excludes a number of assumptions made in the original methods (including assumptions about the linear relationship between temperature and pressure). wells). Comparison of the results of the proposed and well-known methods is presented in [86].

The phenomenon of cavitation and ejector efficiency have not been studied by the authors. The work [87] is devoted to obtaining the characteristics of high-pressure and low-pressure ejectors operating in an oil well; this article also presents the curves of characteristics of these jet pumps to represent dependences of dimensionless relative difference of pressure on coefficient of injection are resulted.

As input parameters in this program we have taken: pressure of the working flow before entering the jet pump, its density, consumption gas content, the density of free gas. All of these parameters were equal to the correspondent parameters of considered oil well. In addition, the velocity of the working flow before the nozzle is also known as far as it was previously determined through the average integral velocity of the production liquid in the tubing. Finally, we have values of pressure in the receiving chamber of the jet pump, the finding of which was described in article [61].

The basic parameter of any jet pump, which influences all the rest geometric and working parameters of it, is the cross-section area of the working nozzle. In the course of mathematical transformations, a formula for determining cross-section area of the nozzle was obtained [84]:

$$f\_1 = w\_W f\_w [(1 - \beta\_W)p\_1 + \beta\_W p\_w] \sqrt{\frac{(1 + \xi\_n)\rho\_w}{[2p\_w(1 - \beta\_w) + \rho\_w w\_w^2]p\_1^2 - 2(1 - \beta\_w)p\_1^3}}\tag{1}$$

where *ww* is velocity of the working liquid before entering the nozzle, m/s; *fw* is crosssection area in the outlet of a nozzle, m2; *βw* is consumption gas content under working conditions of a well; *p*1 is pressure of the working liquid at the outlet of a nozzle, Pa; *pw* is pressure of the working liquid before entering the nozzle, Pa; *ξn* is resistance coefficient of the nozzle; *ρw* is density of the working liquid before entering the nozzle, kg/m3.

Based on the found area of the nozzle, the cross-section area of the mixing chamber was calculated (*f* 3 = 6.25 *f* 1) and the diameters of the nozzle *dn* and the mixing chamber *dmc*. The cross-section area in the outlet of the diffuser and its diameter were obtained from the condition that the angle of the diffuser's cone is α = 8◦ and the length of the diffuser is equal to the twelve diameters of the mixing chamber.

First, the Bernoulli equations for the working flow within the nozzle, the receiving chamber and the mixed flow for the diffuser, as well as the equation of change of the amount of motion (pulse conservation) for the working and injected flows in the cylindrical mixing chamber are recorded. In the last equation, all flow rates are expressed in terms of volume costs. From Bernoulli's equations are expressed the pressures at the inlet and outlet of the mixing chamber and substitute in the equation of change in the amount of motion. We express the terms in the right part of the obtained equation, which contain the flow velocities in different sections of the ejector due to the flow of working and injected flows at the entrance to the mixing chamber. The law of conservation of mass is written down and substituted into the previously obtained equation (the product of the cross section at the entrance to the mixing chamber at the expense of the workflow). As a result, we obtain the equation of the oil and gas ejector. This derivation is given in more detail in [84,87].

The variable parameters of the jet pump were determined in a certain sequence and as a result of solving characteristic equations for jet pumps [58] and to find the outlet pressure the equation of a low-pressure oil-gas jet pump was used:

$$\begin{split} \frac{2f\_1^2 \rho\_1^2}{(1+\xi\_n^\*)\rho\_w f\_3} \left( p\_w - p\_1 \frac{\rho\_w}{\rho\_1} + \frac{\rho\_{\overline{n}} w\_w^2}{2} \right) &\times \left\{ \frac{1}{f\_1 \rho\_1} + \frac{\rho\_{\overline{n}2}}{\rho\_1^2 f\_{\overline{n}2}} u\_2^2 \left[ 1 - \frac{k-1}{2\xi} (1 + \xi\_{\overline{n}n}) \right] - \right\} \\ &- \left( \zeta\_d + \xi\_{\overline{n}c} + 1 \right) \frac{1}{2f\_3 \rho\_3} \left( 1 + \frac{\rho\_{\overline{n}2}}{\rho\_1} u\_2 \right)^2 \right\} - p\_m \frac{\rho\_3}{\rho\_m} - \frac{\rho\_3 w\_m^2}{2} + p\_1 \times \\ &\times \left[ 1 - \left( 1 - \frac{\mathcal{C}\_{\text{in2}}}{\mathcal{P}\_{\text{in}}} \right) \frac{f\_{\text{in2}}}{f\_3} \right] + \frac{k-1}{2k} \frac{f\_{\text{in2}}}{\mathcal{P}\_3} \rho\_{\text{in2}} w\_{\text{in}}^2 = 0, \end{split} \tag{2}$$

where *f* 1 is cross-section area in the outlet of a nozzle, m2; *ρ*1 is density of the working liquid at the outlet of a nozzle, kg/m3; *f* 3 is cross-section area at the outlet of a mixing chamber, m2; *ρin*2 is density of the injected gas before entering the mixing chamber, kg/m3; *fin*2 is cross-section area of the injected gas before entering the mixing chamber, m2; *u*2 is injection ratio before entering the mixing chamber; *k* is adiabatic exponent; *ξin*, *ξmc*, *ξd* are resistance coefficients for the inlet of injected gas to the mixing chamber, in the mixing chamber and diffuser; *ρ*3 is density of the mixed flow at the outlet of the mixing chamber, kg/m3; *ρm* is density of the mixed flow at the outlet of the diffuser, kg/m3; *pm* is pressure of the mixed flow at the outlet of the diffuser, Pa; *wm* is velocity of the mixed flow at the outlet of the diffuser, m/s; *ρin* is density of the injected gas while entering the mixing chamber, kg/m3; *win* is velocity of the injected gas while entering the mixing chamber, m/s.

Equation (2) was obtained based on Bernoulli equation and mass conservation law. It can be used for jet pumps, where the working and mixed flows are compressible two-phase liquids [84].

In order to establish the pressure distribution between the jet pump and the mouth based on the known parameters of the mixed flow after the jet pump, a computer program was created, where the Baksendel method was applied [61].

After building up the pressure distribution curves along the wellbore, taking into account the presence of the jet pump, it is necessary to analyze the obtained value of the wellhead pressure. If the wellhead pressure is higher than technologically required, that means that it is allowed to reduce the pressure in every point of the wellbore starting from the outlet of the sucker-rod pump as long as the form of the curve remains the same. However, if the wellhead pressure turned to be lower than technologically required it is essential to consider other installation depth of even another jet pump (means with other geometrical parameters).

In addition to low-pressure jet pumps, which are able to prove high flow rates of liquid and gas but with a great pressure drop in the jet pump, there are high-pressure jet pumps with cross-section areas ratio *f* 3/*f* 1 = 3 and less. These jet pumps have smaller pressure losses but can inhaust less gas.

The methodology of choosing the rational place of such jet pumps in oil well is exactly the same as for the low-pressure jet pumps. The only difference is in the characteristic equation for finding outlet pressure of jet pump:

$$\begin{split} \frac{2f\_1^2 \rho\_1^2}{(1+\underline{\ell}\_n)\rho\_{w}\underline{\ell}\_3} \left(p\_w - p\_1 \frac{\rho\_w}{\rho\_1} + \frac{\rho\_w w\_w^2}{2}\right) &\times \left[\frac{1}{\underline{f}\_{w2}\rho\_{w2}} + \frac{\rho\_{\tilde{m}2}}{\rho\_{w2}^2 \underline{f}\_{\tilde{m}2}} u\_2^2 - \\ -\frac{1}{2} \left(1 + \frac{\underline{\rho\_{\tilde{m}2}}}{\underline{\rho\_{w2}}} u\_2\right)^2 \left(\frac{\underline{\ell}\_d + \underline{\ell}\_{\text{f3C}} + 1}{\underline{f} \underline{\rho} \underline{\ell}\_3} + \frac{f\_3 \underline{\rho\_3}}{\underline{f}\_{\tilde{m}}^2 \underline{\rho\_{\tilde{m}}}}\right) - p\_m \frac{\underline{\rho\_3}}{\underline{\rho\_{\tilde{m}}}} + p\_2 = 0, \end{split} \tag{3}$$

where *fw*2 is cross-section area of the working liquid before entering the mixing chamber, m2; *ρw*2 is density of the working liquid before entering the mixing chamber, kg/m3; *p*2 is pressure of the working liquid before entering the mixing chamber, Pa.

#### **3. Results**

Table 1 shows some of the results obtained using mentioned programs for low-pressure oil-gas jet pumps.

As can be seen from the Table 1, if the inlet parameters of the jet pump (*pw*, *ρw*, *βw*, *ww*) in the cross-section of the well where it is installed were the same as in the well without jet pump, then the pressure at the wellhead would be less than necessary (should be 0.5 MPa). The only exception is the jet pump installed at a depth of 890 m. This jet pump will provide a slightly higher wellhead pressure (*pwh* = 0.52 MPa).

As soon as the pressure at the wellhead should be *pwh* = 0.5 MPa, that requires installation depth of jet pump not less than 890 m.

What is then the cause of this phenomenon? After all, the relation between the flow densities at the inlet and at the outlet of the jet pump it is quite significant (*pw*/*pm* = 2.06–2.246). In addition, outlet pressure of the jet pump is significantly less than the inlet pressure, which leads to a substantial flash gas liberation. Yet, despite this, during the movement of production liquid to the mouth, the pressure is dropping faster in case of jet pump installation compared to the option without it.

Figure 3 shows the pressure distribution between jet pumps, placed in different depth, and the wellhead for the case when the inlet pressure of jet pumps would be equal to the pressure in the corresponding cross-sections of the well before jet pumps installation (curves 2, 3, 4 and 5).

**Table 1.** Input and calculated parameters of the oil well and the jet pump when it is installed at different depths.

**Figure 3.** Pressure distribution along the wellbore between jet pumps and wellhead: 1—wellbore pressure distribution; 2, 3—pressure distribution after using jet pump with *f* 3/*f* 1 = 6.25; 4, 5—pressure distribution after using jet pump with *f* 3/*f* 1 = 4.

Curves 2 and 3 correspond to jet pumps with the cross-sections ratio *f* 3/*f* 1 = 6.25 and curves 4 and 5 correspond to jet pumps with the cross-sections ratio *f* 3/*f* 1 = 4. In addition, the pressure distribution in oil well between the sucker-rod pump and the wellhead (curve 1) without using jet pump is additionally depicted. The pressure in all four cases decreases almost linearly and much more slowly than in the well without jet pump. The only exception is for the part of the wellbore (approximately 200 m) straight below the mouth, where the pressure drop with and without jet pump is almost the same.

A smaller pressure change gradient is caused by the presence of a significant amount of free gas from the annulus in the tubing. The actual constancy of the pressure change gradient can be explained by the fact that, on the one hand, an increase in the amount of gas in the production liquid should cause a decrease in the pressure change gradient, and, on the other hand, as the amount of gas in the mixture increases, its velocity also increases and this causes the growth in friction losses. These two variable losses almost compensate each other.

The reason for the small wellhead pressure, which low-pressure jet pumps with crosssection areas ratio *f* 3/*f* 1 = 6.25 can provide, when the depth of their placement in the well changes in the range from 610 m to 890 m, is a significant pressure drop between inlet and outlet of the jet pump. In Figure 3, these pressure drops are represented by the segments *ab* and *a'b'*. Jet pumps with cross-section areas ratio *f* 3/*f* 1 = 4, as it can be seen from Figure 3, allow to obtain significantly greater wellhead pressure than the previous two.

If these jet pumps are installed in the oil well 753-D, then placing the jet pump at a depth of 700 m (*f* 3/*f* 1 = 6.25) will entail a slight increase in inlet pressure compared to the pressure in this cross-section of the well without a jet pump. At the same time, the jet pump, located at a depth of 890 m (*f* 3/*f* 1 = 6.25), on the contrary, will give a slight decrease in inlet pressure compared to the pressure in this cross-section of the well without a jet pump. Jet pumps with cross-section areas ratio *f* 3/*f* 1 = 4 will provide a noticeable decrease in pressure in front of the jet pump, and, consequently, a substantial decrease in outlet pressure of the sucker-rod pump.

Thus, it follows from the above that an increase of the installation depth for such jet pumps will have a little affect on the pressure change in front of it. With increasing of jet pump placement depth in the well, the inlet pressure of it will slightly reduce. It turned out that even greater influence on inlet pressure decreasing has the cross-section areas ratio *f* 3/*f* 1.

It would be possible to determine to which level low-pressure jet pumps with the ratio *f* 3/*f* 1 = 4 can reduce the outlet pressure of the sucker rod pump. However, since we have proven that the inlet pressure of the jet pump substantially depends on the value *f* 3/*f* 1, it is necessary to consider installation of high-pressure jet pumps, for which the value of cross-section areas ratio is *f* 3/*f* 1 < 4. Such jet pumps provide the highest possible pressure at their outlet.

Table 2 shows the input and some calculated values for such jet pumps, taking into account that input parameters in this case are equal to the corresponding parameters of the well at depths of 700, 800, 850 and 870 m.

**Table 2.** Input and calculated parameters of the high-pressure oil-gas jet pumps during their installation in oil well at different depths [84].

After that, for these four jet pumps, the pressure distribution between them and the wellhead was determined using previously mentioned computer program for the Baksendel method. In Figures 4 and 5 the dotted line (curves 2) shows the pressure distribution between the jet pump, installed at depths of 700 and 870 m in the well, and its mouth, obtained from the results of this program.

**Figure 4.** Pressure distribution between the sucker-rod pump and the wellhead: 1—without the jet pump; 2—with the jet pump (*f* 3/*f* 1 = 3); 3—with the jet pump after decreasing inlet pressure *pw* = 3.908 MPa.

**Figure 5.** Pressure distribution between the sucker-rod pump and the wellhead: 1—without the jet pump; 2—with the jet pump (*f* 3/*f* 1 = 3); 3—with the jet pump after decreasing inlet pressure *pw* = 5.381 MPa.

As seen in Figures 4 and 5, if the inlet pressure of the jet pump is equal to the pressure that exists in the well in this cross-section (in the figures it is point *b'*), then the pressure at the wellhead will be greater than required *pwh* = 0.5 MPa. Therefore, the next task was to find such inlet pressure of the jet pump, at which the wellhead pressure would be 0.5 MPa. The geometry and all other parameters of the jet pump were determined when its inlet pressure was changing, as well as the pressure distribution along the wellbore from the jet pump to the wellhead.

By successively reducing the inlet pressure of the jet pumps, such values of it were found at which the wellhead pressure are equal to 0.5 MPa. Knowing the inlet pressure of the jet pumps and the temperatures at their installation points, calculations were made to determine the pressure distribution along the wellbore from jet pumps to the sucker-rod pump. According to the results of using created computer programs, pressure distribution curves for the oil well 753-D were built for cases of jet pumps installation at depths of 700 and 870 m respectively (curves 3) (Figures 4 and 5).

Figures 4 and 5 show that the usage of high-pressure jet pumps in the well can significantly reduce the outlet pressure of the sucker-rod pump. This reduction is from 1.32 MPa, for the case of jet pump installing at a depth of 700 m and up to 1.96 MPa, when jet pump is installed at a depth of 870 m. Reducing the outlet pressure of the sucker-rod pump means decreasing the stem load. For the case that is considered, such a reduction in load can reach up to 26% (with a decrease in outlet pressure of sucker-rod pump by 1.96 MPa). In addition, by reducing the load on the beam pumping unit's mechanism, smaller counterbalance can be used [84].

Thus, we may say that it is the most rational to install the high-pressure jet pump with *f* 3/*f* 1 = 3 at depth of 870 m in the oil well 753-D Dolyna Oil Field "Dolynanaftogaz" PJSC "Ukrnafta".

In the general case, it can be claimed that usage of tandem installation, which consists of the sucker-rod pump and oil-gas jet pump is advisable when the gas–oil ratio of the well is around 100 m3/t and higher. However, even then the efficiency of such tandem installation will be determined by many other factors.

It is proposed to use an electrochemical chrome coating formed in a flowing electrolyte to increase the wear and corrosion resistance of the polished rod of the rod pump unit.

The cost of applying the chrome coating on parts in a flowing electrolyte does not exceed the cost of applying a chrome coating on parts in a quiet electrolyte—the traditional way. It should be noted that the application of a thick layer of electrochemical chrome coating in the flowing electrolyte reduces the amount of allowance for diamond grinding of parts compared to the quiet electrolyte [88], which ultimately reduces the cost of manufacturing the suitable chrome parts that have high microhardness to our technology (Figure 6).

**Figure 6.** Change in microhardness according to the thickness of the chromium electrochemical coating formed in the electrolyte: 1—flow; 2—calm.

The use of chromium plating in a flowing electrolyte provides thicker coatings compared to chromium plating in a quiet electrolyte. In this case, the coatings applied in the flowing electrolyte evenly cover the steel base, have a lower surface roughness and higher microhardness (11.8 GPa) compared to chromium plating in the quiet electrolyte (8.1 GPa). This is achieved by creating a stable flow of electrolyte in the annular interelectrode space of the electrochemical cell and intensive removal of gases formed during electrolysis on the

surface of the part and the electrode. In addition, the saturation of the chrome coating and the steel base with hydrogen is reduced.

Tests of samples with chrome coatings were performed on an upgraded installation that simulates the reciprocating motion (reversible friction) of the polished rod of the rocking machine and allows you to continuously record the value of the coefficient of friction. The results are presented in Figure 7.

The results of tests of samples with chrome coatings in reciprocating motion showed that the coating reduces the wear rate of the chrome rod, which is operated in pair with the stuffing box seal of the rod installation. The combination of high microhardness of chrome coatings, as well as the specifics of the structure provide high wear resistance of chrome coatings applied from a flowing electrolyte. Chromium plating in a flowing electrolyte also reduces the coefficient of friction in the metal-polymer friction pair as 20 percent compared to chromium plating in a quite electrolyte. It is established that the minimum wear for reversible friction pair of electrochemical chrome coating—stuffing box seal is provided by the surface roughness of the coating Ra from 0.16 to 0.32 μm. All this ultimately increases the service life of pump parts, reduces the load on the mechanical part of the rod installation of the rocking machine, the cost of electricity to overcome the forces of thorns in the installation for rod production of oil from wells. In addition, the combination of ejector and plunger pumps for joint work increases the energy efficiency of oil production and ensures the rational use of potential energy of oil gas, as well as improving the environmental situation in oil fields, as it eliminates the combustion of oil gas.

The usage of the developed method to specify the rational placement of jet pumps in oil wells allows us to find the optimal operation mode of simultaneous operation of the sucker-rod pumps and the oil-gas jet pumps. This method will provide offtaking of the whole amount of free oil gas to enter the annulus of the well, and in turn it will provide the lowest possible stem load.

Results of this research are formulated in the form of a methodology for calculating the working parameters of a downhole ejection system, which is implemented in OGPD "Dolynanaftogaz" PJSC "Ukrnafta" and the methodology for determining the rational placement of oil-gas jet pumps in oil wells, approved by the PJSC "Ukrnafta", and the main design parameters of suggested jet pump for tandem installation in well 753-D as well as the exact place of its location in the well have been submitted for implementation.

This article does not really mention the effect of non-uniformity of the rod pump supply on the operation of the downhole ejector. We have conducted such studies, and they indicate that even at the minimum speed and flow rate of the working flow in the ejector (corresponding to the movement of the rods up) can suck the injected flow from the annulus of the well. In addition, for some wells it is advisable to use periodic ejector operation. This means that the gas will be removed from the annulus only when a certain critical pressure value is reached there.

The performed hydrodynamic calculations prove the efficiency of the proposed scheme of operation of the downhole jet pump and the rod pump in the well. Of course, the authors understand that this method of operation cannot be used for all oil wells and in each case it is necessary to justify the possibility of joint operation of the rod pump and ejector.

The novelty of the proposed study lays in a systematic approach to rod pump and our patented ejector pump operation in the oil well [85] and chrome plating of pump parts. The result of scientific research is a sound method of determining the rational location of the ejector in the oil well and the calculation of its geometry, which will provide a complete selection of petroleum gas released into the annulus of the oil well.

This will make possible obtaining the positive results, namely:

Especially this technology can show its efficiency in conditions of high gas–oil ratios and in regions with predominantly low ambient temperatures.

The results of industrial tests of jet and plunger pumps with reinforced chrome-plated parts showed an increase in their service life of about 27%.

In further research, the authors plan to provide calculations considering the curvature of wellbores.

#### **4. Conclusions**

The study showed the following: the operation capability and efficiency of oil-gas jet pumps was proved, and the following conclusions were made:

It was established that the usage of low-pressure jet pumps with a cross-section areas ratio *f* 3/*f* 1 = 6.25 cannot provide a significant decrease in the outlet pressure of the suckerrod pump even with an increase in the installation depth due to the large difference inlet/outlet pressure of the jet pumps.

Furthermore, the minimum tubing load is specified by the combination of two factors: the minimum possible cross-section areas ratio *f* 3/*f* 1 and the maximal installation depth. This way, the ratio *f* 3/*f* 1 for the jet pumps is a factor to decrease significantly tubing loads. Depth of installation makes a much smaller effect if increased.

According to studies, the best operation mode for the 753-D oil well lays in the tandem installation (sucker-rod pump and the jet pump; *f* 3/*f* 1 = 3 and placed at depth 870 m). This mode provides decreasing of outlet pressure of the sucker-rod pump up to 1.96 MPa.

This way, the authors recommend the following for the 753-D oil well OGPD "Dolynanaftogaz" PJSC "Ukrnafta":

Electrochemical chromium plating according to the developed technological process using an installation equipped with an automated control system of technological parameters of electrochemical chromium plating process in flowing electrolyte with nanoadditives, provided uniform coating with low surface roughness, high microhardness and wear resistance. The proposed innovations ensure the high quality of the working surfaces of parts and increase the performance of ejector and plunger pumps during oil production.

In addition, the usage of jet pumps will also improve the ecological situation in the oil production fields through the recycling of associated oil gas.

**Author Contributions:** Conceptualization, O.D., L.R. and O.B.; methodology, O.D. and M.S.; software, O.D. and T.P.; validation, O.D., L.R. and M.S.; formal analysis, O.D. and M.S.; investigation, O.D. and V.L.; resources, O.D. and L.R.; data curation, O.D. and M.S.; writing—original draft preparation, O.D., M.S. and V.L.; writing—review and editing, O.D., L.R., M.S. and V.L.; visualization, O.D., M.S., T.P. and V.L.; supervision, O.D. and L.R.; project administration, O.B. and L.R.; funding acquisition, O.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was carried out as part of the project "Belt and Road Initiative Institute for Chinese-European studies (BRIICES)" and was funded by the Guangdong University of Petrochemical Technology.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are contained within the article.

**Acknowledgments:** The team of authors express their gratitude to the reviewers for valuable recommendations that have been taken into account to improve significantly the quality of this paper. The authors are grateful to the Ministry of Science and Education of Ukraine for the grant to implement the project D 8-21-P (RK 0121U109591).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Enzymatic and Oxidizing Agents for the Decomposition of Polymers Used in the Composition of Drilling Muds**

**Małgorzata Uliasz, Grzegorz Zima, Sławomir Błaz and Bartłomiej Jasi ´ ˙ nski \***

Oil and Gas Institute—National Research Institute, 31-503 Krakow, Poland<EMAIL_ADDRESS>(M.U<EMAIL_ADDRESS>(G.Z<EMAIL_ADDRESS>(S.B.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +48-1343-689-41

**Abstract:** The article presents the results of research on the influence of enzymatic and oxidizing agents on polymers used in drilling mud technology. The research used calcium hypochlorite, urea peroxide, sodium persulfate, amylase and cellulase. This allowed us to determine the optimal concentrations of these agents in order to reduce the rheological parameters of drilling muds. The ability of enzymes and oxidants to decompose colloids used in the composition of drilling muds was determined on the basis of measurements of their rheological parameters and the influence of oxidants and enzymes on the properties of filter cakes. The final effect of the presented research was the development of a drilling mud treatment method before the cementing procedure and the development of washer fluids containing enzymatic or oxidizing agents to be used to prepare the borehole for the cementing procedure. The drilling muds selected for the research contained starch and cellulose polymer colloids, which allowed for the selection of appropriate agents depending on the type of polymer set used in the drilling mud. Positive results were obtained regarding the possibility of thinning the drilling mud immediately before cementing, as well as the possibility of using oxidants and enzymes in the composition of washer fluids.

**Keywords:** drilling mud; oxidants; enzymes; filter cake

#### **1. Introduction**

In order to improve the quality of cementing of casing, the drilling mud is treated to lower its rheological parameters. Obtaining low rheological parameters of the drilling mud facilitates displacement of the drilling mud solidified at the wall of the borehole and partial leaching of the clay cake that hinders the contact of the cement grout with the rock. The treatment of drilling muds with thinning agents changes the rheological parameters without significantly changing the properties of the drilling mud [1,2].

The filter cake on the borehole wall is formed by filtering the water phase from the drilling mud. It is a mixture of a polymer solution, weighting agent and finely drilled solid phase. The filter cake produced during drilling increases the stability of the borehole walls and reduces the permeability of the porous layers, therefore there are no major losses of the water phase from the drilling mud, which can significantly reduce the strength of the rocks. When drilling cracked rocks, the filter cake is also deposited in the crevices, binding individual rock fragments, and increasing their strength. In addition, the filter cake contributes to an even distribution of hydrostatic pressure on the borehole wall, which prevents its damage. In weakly compact rocks, the filter cake protects the borehole wall against the erosive impact of the drilling mud stream and ensures a good technological process until the casing is inserted into the borehole [3–6].

The use of agents which decompose colloids, which are components of the drilling mud, thins the drilling mud and removes clay deposits stuck by these colloids. Polymers can be decomposed in several ways, by biological, mechanical, chemical or radiation decomposition [7,8].

**Citation:** Uliasz, M.; Zima, G.; Błaz, ˙ S.; Jasi ´nski, B. Enzymatic and Oxidizing Agents for the Decomposition of Polymers Used in the Composition of Drilling Muds. *Energies* **2021**, *14*, 5032. https:// doi.org/10.3390/en14165032

Academic Editor: Vijay Kumar Thakur

Received: 2 July 2021 Accepted: 12 August 2021 Published: 16 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Water-soluble polysaccharides used as components of drilling muds have unique, stable rheological properties in drilling operations, but their structure and properties also have a decisive influence on the formation of a polymer film on the surface of the borehole walls, which in combination with the solid phase becomes difficult to remove from the walls of the borehole. Polysaccharides contain many glycosidic bonds (acetals). Glycoside bonds are sensitive to hydrolysis which leads to degradation of the polymer. The chemical decomposition process of the polymer must be properly designed for specific borehole conditions: temperature, pH, salinity, and exposure time. On the basis of laboratory tests, the most optimal and balanced conditions for polymer decomposition should be determined. Chemical degradation of polymers can be carried out by the action of oxidants and enzymes [3,7,9,10].

Oxidizing agents decompose the polymers contained in the filter cake. Oxidation processes take place as a result of the exchange of electrons between the oxidizing substance and the reducing substance, as a result of which the atoms of the elements taking part in the reaction change their oxidation state. According to the electron interpretation of oxidation-reduction processes, oxidants are atoms, ions, or molecules capable of accepting electrons, i.e., receiving them from other atoms or groups of atoms, thus causing their oxidation. Thus, oxidants are themselves reduced by oxidizing other substances. The most popular oxidants are the most electronegative elements, i.e., fluorine F2, chlorine Cl2, bromine Br2 and oxygen O2. Among chemical compounds, oxidants are those with certain elements in the highest oxidation states, e.g., potassium permanganate KMnO4, potassium dichromate K2Cr2O7, hydrogen peroxide H2O2, potassium nitrate KNO3, nitric acid HNO3 and others [11–14].

The principle action of oxidants is based on the gradual interaction of compounds with high electronegativity on the main polymer chains, breaking them into smaller fragments and, consequently, a decrease in the molecular weight of the polymer. The advantage of oxidants is their wide range of action at a pH of 3 to 14. Oxidizers react quickly with the polymer at high temperatures. Oxidizers cannot be used in an acidic environment as it is possible to oxidize H2S to elemental sulfur and clog the pores of reservoir rock [12].

Enzymes are another type of agent used to decompose the filter cake. Enzymes are biological catalysts, classified as proteins, which accelerate specific chemical reactions as a result of lowering their activation energy. Due to their protein nature, the activity of enzymes depends on the physical and chemical parameters of the environment, i.e., temperature, pH. The rate of enzymatic reactions rises with increasing temperature. After exceeding the optimal temperature, the thermal denaturation of enzymes progresses, and their activity drops sharply. Most enzymes also have an optimal operating pH. The pH optimum, next to the temperature optimum, is the second most important environmental parameter characterizing the activity of enzymes. Enzymes are most active in their optimal pH range and the activity declines with increasing or decreasing pH beyond this range. In most cases, the effects of enzymes heavily depend on their substrates [15–20].

In the case of using an invert drilling mud [21], a different approach should be applied to the problem of filter cake removal prior to cementing. The main task of the washer fluid is to remove the hydrophobic sediment and make the borehole wall hydrophilic, which requires the use of specially selected surfactants, which can possibly be combined with enzymes.

Enzymes such as cellulase can also be used to modify the properties of cellulose without decomposing it, for example to increase the amount of the crystalline phase in it [22], which may find application in the design of nanocomposites containing cellulose fillers.

The article presents the results of research carried out at the Oil and Gas Institute—National Research Institute, which aim to improve the quality of casing cementing. Due to insufficient quality of cementation manifested by the occurrence of gas exhalation, research is being carried out on the development of a methodology for the use of oxidants and enzymatic agents that break down polymers used in the composition of drilling muds. These results can be used in the preparation of the borehole prior to cementing to re-

move filter cake which contribute to reducing the bond between the cement stone and the borehole wall. Most of the research carried out in various research centers concerns the use of enzymes or oxidants in treatment fluids, the purpose of which is to remove drilling mud residues from rock pores in order to reduce damage to rock permeability. The authors [8–11,15,20] use enzymatic agents in their research to remove mud sediments from the pore space of rocks. For the same purpose, ultrasound was used in [13]. Part of the work carried out [15,16,19] concerns the evaluation of enzyme activity under various conditions of temperature, pH, and salt content (chlorides, bromides, formates). The activity of the enzymes was assessed on the basis of the degree of their degradation. The paper [18] presents the results of research on the efficiency of filter cake removal with fluids containing enzymatic, oxidizing, and chelating agents depending on the used weighting agent.

#### **2. Materials and Methods**

#### *2.1. Raw Materials*

In the laboratory tests, natural and semi-synthetic polymers used in the drilling mud technology as well as enzymes and chemical compounds with an oxidizing effect were used. The chemicals and drilling mud materials used in the tests were:

#### *2.2. Research Methodology*

The research was carried out on muds with different density, salinity, and a set of colloids and polymers used for their preparation. To determine the efficiency of oxidants and enzymes in the drilling mud environment, three fluid compositions were selected for drilling holes in the Carpathian Foredeep and the Polish Lowlands. The efficiency of oxidizing agents and enzymes was assessed on the basis of changes in rheological parameters, filtrate volume, and changes in the pH value.

The drilling muds prepared according to the compositions used by the drilling mud services were used for the tests. The drilling muds marked as A and B correspond to the compositions of the drilling muds used in the Carpathian Foredeep. These drilling muds differ in the type of polymers used for their preparation. Drilling mud A contains a starch agent and a biopolymer, drilling mud B contains a cellulose agent, a biopolymer and a PHPA encapsulating polymer. The drilling muds marked with symbols A and B also differed in densities, which were, respectively, 1130 kg/m3 and 1330 kg/m3. The drilling mud marked as C corresponded to the compositions of drilling muds in the area of the Polish Lowlands, therefore it contained NaCl in its composition in the amount corresponding to the concentration of the saturated solution. A biopolymer, a cellulose agent and a PHPA polymer were used to prepare drilling mud C. Drilling mud C has a density of 1535 kg/m3. All drilling muds used in the test (A, B, C) additionally comprised of milled Miocene shale imitating cuttings, selected muds contained barite as a material for adjusting the density, and chemical contamination in the form of calcium and magnesium chlorides was additionally introduced into drilling mud C.

The efficiency of polymer decomposition by particular agents (oxidants and enzymes) in the drilling mud environment was assessed on the basis of changes in the rheological parameters of the drilling muds after the introduction of a given oxidant or enzyme. The tests were carried out in various temperature conditions enabling the assessment of the efficiency of the tested agents in borehole conditions. The efficiency of the enzymes was tested at the temperatures of 20 ◦C, 40 ◦C, 60 ◦C and 80 ◦C due to the decrease in their activity at temperatures above 65 ◦C. The optimal temperature for the application of the tested enzymes is determined in the range of 50–65 ◦C.

The efficiency of the filter cake removal was determined by the percentage loss of the filter cake due to the treatment fluid used, which differed in the type of the measures used. Filter cakes were formed on ceramic filter discs (OFITE No. 170–530) with a defined pore size of 50 μm and a fixed permeability of 15 D using a dynamic High Temperature High Pressure (HTHP) filter press. The weight method was used to assess the efficiency of cake removal.

#### 2.2.1. Weight Method of the Efficiency of Removing Filter Cake from Ceramic Discs Cake Formation

For 15 min the ceramic disc was soaked in a salt solution corresponding to the salinity of the tested drilling mud. The soaked ceramic disc was weighed, and its mass was determined as *W*1. Then, the drilling mud filtration was measured on a dynamic HPHT filter press on a previously soaked ceramic disc, at a pressure of 0.7 MPa of N2 gas, a set temperature, and the speed of the stirrer in the filtration chamber at 200 rpm. After reaching the set temperature, the drilling mud filtration and formation of the cake were measured for a period of 1 h.

#### Removal of Cake with Fluids of Various Compositions

After cooling, the measuring chamber was disassembled and the ceramic disk with the cake was carefully removed and washed with water. Then the disc with the cake was weighed and the mass was recorded as *W*2. The previously prepared treatment fluid was slowly poured into the filtration chamber and the ceramic disc with the cake was placed back in the filtration chamber. At the pressure of 0.7 MPa, the set temperature was achieved and the stirrer's rotation in the filtration chamber was set to 500 rpm. Then, the filtration of the treatment fluid was measured for a period of 30 min. After cooling, the ceramic disc was removed and, after washing with water, weighed and the mass was determined as *W*3. The efficiency of filter cake removal was calculated from the following formula:

$$E\_{Ll} = \frac{\mathcal{W}\_2 - \mathcal{W}\_3}{\mathcal{W}\_2 - \mathcal{W}\_1} \cdot 100 \ (\text{\textquotedblleft})\tag{1}$$

where:

*EU*—efficiency of filter cake removal

*W*1—the weight of a ceramic disc soaked with a salt solution corresponding to the salinity of the tested drilling mud (g)

*W*2—the weight of the ceramic disc with the generated filter cake (g)

*W*3—the weight of the ceramic disk after the effect of the treatment fluid (g).

#### **3. Results and Discussion**

#### *3.1. Influence of Oxidants and Enzymes on the Properties of Potassium-Polymer Drilling Mud A*

A biopolymer and gelatinized starch were used to prepare potassium-polymer drilling mud A. The drilling mud was salted with 5% KCl and a 7% carbonate blocker was added to it. Then the drilling mud was weighted with barite to a density of 1100 kg/m3 and contaminated with ground Miocene clay simulating cuttings. The drilling mud prepared in this way had a density of 1130 g/cm3 and a plastic viscosity of 18 mPa·s, an apparent viscosity of 28.5 mPa·s and a yield point of 10 Pa.

The research on the influence of oxidants and the enzyme on the properties of drilling mud A are presented in Tables 1 and 2 and in Figures 1–4. Various amounts of oxidants and enzymes were added to the drilling mud in order to select the optimal dose at which the greatest thinning effect of the drilling mud can be achieved.

**Table 1.** The properties of potassium-polymer drilling mud A with the addition of oxidizing agents and amylase.

**Table 2.** The rheological parameters of potassium-polymer drilling mud A with thinning additives at various temperature values.

**Figure 1.** Flow curves of drilling mud A with 1.0% calcium hypochlorite: (**a**) at a temperature of 20 ◦C, (**b**) at a temperature of 40 ◦C, (**c**) at a temperature of 60 ◦C, (**d**) at a temperature of 80 ◦C.

**Figure 2.** Flow curves of drilling mud A with the addition of 1.0% urea peroxide: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

**Figure 3.** Flow curves of drilling mud A with 1.0% sodium persulfate: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

**Figure 4.** Flow curves of drilling mud A with the addition of 0.3% amylase: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

Potassium-polymer drilling mud A at 20 ◦C was resistant to the action of oxidants, the addition of 10 g/dm3 of calcium hypochlorite to the drilling mud caused its plastic viscosity to decrease from 18 to 12 mPa·s, the yield point from 10 to 6.7 Pa, and increased its filtration from 2.4 to 3.2 cm3 (Table 1). The rate of the oxidation reaction at 20 ◦C did

not change significantly over time (Figure 1), the greatest decrease in the viscosity of the drilling mud took place after about 1 h, and the further influence of calcium hypochlorite did not significantly affect a further decrease in rheological parameters. Increasing the temperature to 40 ◦C accelerated the process of decomposition of polymers contained in the drilling mud, the oxidation process was much faster, and the maximum thinning of the drilling mud took place after about 30 min of the effects of calcium hypochlorite. At the temperature of 80 ◦C, the process of decomposition of the polymers contained in the drilling mud was turbulent, after about 5 min the drilling mud thinned as a result of the oxidant and the further extension of the time of the oxidant did not significantly change the rheological parameters.

The effect of a 1% addition of urea peroxide on the properties of drilling mud A was marked by a reduction in the plastic viscosity down to 12 mPa·s and the yield point down to 7.2 Pa. The time required for the process of thinning the drilling mud at room temperature is about 24 h, and at the temperature of 40 ◦C the decomposition of the polymers contained in the drilling mud took place after about 30 min. However, at the temperature of 80 ◦C, the same thinning effect of the drilling mud was achieved after about 5 min.

Sodium persulfate showed a much weaker effect than urea peroxide and calcium hypochlorite. For the effective oxidation of the drilling mud with sodium persulfate, it was necessary to increase the temperature to about 60 ◦C. The drilling mud decomposition process at 60 ◦C was much faster and more effective. After the effect of 15 min of sodium persulfate, the plastic viscosity of the drilling mud decreased to 12 mPa·s, and the yield point to 6.7 Pa.

The action of amylase addition on the properties of the potassium-polymer drilling mud A is shown in Table 1. The decomposition of the polymers contained in the drilling mud A by means of amylase at a temperature of 20 ◦C was very fast, after about 5 min there was almost complete decomposition of the starch component of the drilling mud, which resulted in the reduction of the rheological parameters of the drilling mud. Extending the time of the enzyme's action and increasing the temperature did not significantly increase the decomposition effect of the drilling mud.

#### *3.2. Influence of Oxidants and Enzymes on the Properties of Potassium-Polymer Drilling Mud B*

Drilling mud B XCD on the biopolymer matrix and the cellulose polymer colloid weighted with barite to a density of 1330 kg/m3 has a plastic viscosity of 41 mPa·s, a yield point of 18.2 Pa and a filtration of 4.4 cm3. The influence of oxidants on the rheological parameters of potassium-polymer drilling mud B at 20 ◦C is shown in Tables 3 and 4.

The highest degree of thinning of the drilling mud with calcium hypochlorite was obtained by using its addition in the amount of 10 g/dm3. With such a concentration of calcium hypochlorite in the drilling mud, the plastic viscosity decreased from 41 to 20 mPa·s, and the yield point from 18.2 to 8.1 Pa. The drilling mud filtration increased from 4.4 to 6.2 cm3, and the pH value decreased to a value of 7.5. Under the conditions of elevated temperature, i.e., 40 and 60 ◦C, the oxidation process took place to a greater extent. The best results of the drilling mud thinning were obtained by carrying out the oxidation process at 80 ◦C for 15 min (Figure 5). The plastic viscosity of the drilling mud decreased to 6 mPa·s and the yield point up to 3.3 Pa (Table 4).

The most effective oxidizing action in relation to drilling mud B at the temperature of 20 ◦C was shown by urea peroxide (Figure 6), which, with the addition of 10 g/dm3 after an exposure time of 24 h caused the reduction of its plastic viscosity to 13 mPa·s and the yield point to 5.7 Pa. Increasing the temperature improved the efficiency of the agent in relation to oxidation carried out at room temperature.

**Table 3.** The properties of potassium-polymer drilling mud B with the addition of oxidizing agents and cellulase.

**Table 4.** The rheological parameters of potassium-polymer drilling mud B with thinning additives at various temperature values.

**Figure 5.** Flow curves of drilling mud B with 1.0% calcium hypochlorite: (**a**) at a temperature of 20 ◦C, (**b**) at a temperature of 40 ◦C, (**c**) at a temperature of 60 ◦C, (**d**) at a temperature of 80 ◦C.

**Figure 6.** Flow curves of drilling mud B with the addition of 1.0% urea peroxide: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

The process of oxidating the drilling mud at 20 ◦C with sodium persulfate does not significantly change its rheological parameters (Figure 7). The introduction of 10 g/dm3 of sodium persulfate at 20 ◦C reduces the plastic viscosity of the drilling mud from 41 to 27 mPa·s and the yield point from 18.2 to 11 Pa (Table 3).

The action of cellulase on the drilling mud only partially thins it by decomposing cellulose compounds (Figure 8). The addition of 0.3 vol.% of the enzyme reduces the plastic viscosity from 41 to 13 mPa·s and the yield point from 18.2 to 5.7 Pa (Table 3).

**Figure 7.** Flow curves of drilling mud B with 1.0% sodium persulfate: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

**Figure 8.** Flow curves of drilling mud B with the addition of 0.3% cellulase: (**a**) at 20 ◦C, (**b**) at 40 ◦C, (**c**) at 60 ◦C, (**d**) at 80 ◦C.

#### *3.3. The Influence of Oxidants and Enzymes on the Properties of Salt-Barite Drilling Mud C*

Salt-barite drilling mud C based on the XCD biopolymer and cellulose colloid was salted with 33% of NaCl, weighted with barite to a weight of 1500 kg/m3 and contaminated with calcium and magnesium ions. The prepared drilling mud has a plastic viscosity of 57 mPa·s and a yield point of 23 Pa. The influence of polymer degrading agents on the rheological parameters of the drilling mud at 20 ◦C is shown in Tables 5 and 6.

**Table 5.** The properties of salt-barite drilling mud C, density 1530 kg/m3, with the addition of oxidizing agents and cellulase enzyme.

**Table 6.** The rheological parameters of salt-barite drilling mud C with thinning additives at various temperature values.

After adding calcium hypochlorite in an amount of 1.0 vol.% there is a significant decrease in the rheological parameters of the drilling mud. The plastic viscosity is reduced to 26 mPa·s and the yield point is reduced to 7.2 Pa. The filtration of the drilling mud increased to 2.4 cm3 and the pH value decreased to 6.9. The oxidation reaction at an elevated temperature (Figure 9) is accompanied by a greater reduction in the drilling mud viscosity and the decomposition of polymers contained in the drilling mud occurs much faster than at 20 ◦C. Increasing the temperature of the reaction environment to 40 ◦C accelerates the process of decomposition of the drilling mud. At 60 ◦C, the oxidation process is similar, the maximum thinning of the drilling mud takes place after 15 min of the effect of calcium hypochlorite (Figure 9).

**Figure 9.** Flow curves of drilling mud C with 1.0% calcium hypochlorite: (**a**) at a temperature of 20 ◦C, (**b**) at a temperature of 40 ◦C, (**c**) at a temperature of 60 ◦C, (**d**) at a temperature of 80 ◦C.