**1. Introduction**

Over the past decade, most countries all over the world have taken action towards reducing their polluting emissions by investing in renewable energy sources. Among those sources, particularly, photovoltaic (PV) solar panels and wind power systems have seen a significant growth [1]. However, the increase of renewables goes hand in hand with technical challenges. The stochasticity of both PV and wind power systems causes the maintenance of grid stability to become more di fficult [2,3].

A major stakeholder impacted by the renewable energy transition is the distribution network operator. While end users are becoming increasingly more independent from the grid, the revenue constraint for the grid operator still remains [4]. Under the current tari ff structure, which is primarily based on the energy-volume component, a 'death spiral' phenomenon is imminent [4,5]. Nevertheless, the grid infrastructure costs are mainly dependent on the power capacity of the system. Yet, PV users have reportedly slightly lower peak power than non-PV users [6]. In other words, PV-users pay less than non-PV users even though both of them use the grid almost to the same extent [6]. To counteract such unfairness between di fferent user groups and correctly attribute the costs to their origin, new tari ff structures are being introduced that increase the weight factor for the peak demand component. This (peak demand pricing) will also apply for small user groups such as residential consumers who have been so far excluded from peak power measurements [7,8].

Given these increased peak power costs, peak demand reduction ('peak shaving') has gained much attention in recent years. Peak shaving is not a new concept; industrial users with high peak demand already have been using diesel and gas generators to reduce electricity costs for a long time. Still, those conventional generation methods are expected to be replaced by 'green' technologies, among which energy storage and in particular batteries are the primary candidate.

Battery storage systems have been deployed in the past to provide di fferent types of services, such as (i) increasing the self-su fficiency of PV/wind power installations [9–11], (ii) providing ancillary services to the grid operator [12–14], (iii) peak shaving [15–17], (iv) back-up generators and UPS [18,19]. A common issue, arising particularly in (i), (ii) and (iii), is that due to the high cost of the storage system, battery storage investments are not yet economically feasible. However, we note that in the majority of those studies, the battery is deployed exclusively for one service. Therefore, to accelerate the return of investment, many suggest as a possible solution 'hybridizing' multiple services into a single application instead of providing each one separately [14,20,21]. Before studying how such a hybrid strategy can be applied, we should first identify the technical constraints of the services under consideration. In this paper, we focus specifically on peak shaving and present some insights that reflect its potential for hybridization. In the next paragraph, we review previous research works on peak shaving through battery storage.

In [15], the authors present a sizing methodology for defining the optimal energy and power capacity of battery storage systems used for peak shaving. An economic feasibility study was conducted for two di fferent technologies, lead acid and vanadium redox flow (VRF). A control strategy was proposed, but it assumed that the load profile is perfectly predictable in advance. In [16], the researchers applied peak shaving for residential end users. One of the main conclusions was that the utilization of the lithium-ion battery stays very low, lower than 165 cycles per year. At such a low rate (here, the cycle lifetime is 3000 cycles) the system could be used for more than 20 years unless it exceeded its calendar lifetime. Finally, considering also its calendar lifetime, the battery would have to be replaced approximately after 10–15 years. Furthermore, the researchers suggested adding grid support services next to peak shaving in order to increase the utilization of the system. In [22], the researchers developed a model in Matlab/Simulink where a VRF battery is used to simultaneously provide frequency regulation and peak shaving. It was concluded that the battery storage system can successfully perform both services. However, the experiment was conducted only for a limited time period (30–140 s), thus, in essence, without a ffecting the battery state of charge (SoC) and as a consequence, it was not possible to evaluate the reliability of the control system under unfavorable conditions. In [23], a fuzzy control algorithm was developed for peak shaving in university buildings. The algorithm was tested and compared to two di fferent peak shaving techniques, namely the fixed-threshold and adaptive-threshold controller. The results showed that the proposed algorithm was the best of all. Although the researchers conducted several case studies (with 8 di fferent load profiles), they did not provide su fficient information about the load forecasting method. In [17], a control algorithm is proposed for peak shaving in low-voltage distribution networks based on day ahead aggregated load forecasts. The main novelty of that study is that the algorithm, considering also the inherent forecasting errors, relies solely on historic data; hence there is no need to intervene in real-time and readapt the dis-charging process of the battery. Results from a case study show that peak reduction is achieved for 97% of the time and that for 55% of the time, the peak reduction is at least 10%. In [18,19,24,25], peak shaving is addressed as a secondary application. Here, the primary service of the battery is to provide uninterruptible power supply (UPS) in data centers. The researchers argue that because of the significantly low probability of the peak occurrence (e.g., a Google data center exceeds 90% of its power capacity only for 1% of the time), it is possible to achieve peak reduction without impacting the reliability of the primary service. In [26], a battery sizing methodology and an optimal control algorithm is proposed for peak shaving in industrial and commercial customers. One of the main objectives was to determine an appropriate peak shaving threshold. Three case studies were carried out, each one considering a di fferent daily load profile. The results showed that adapting the peak shaving threshold in real-time leads to higher peak reduction than keeping a fixed threshold based only on a historic data analysis. A drawback of the study might be that when calculating the battery utilization, it is assumed that the battery is equally utilized every weekday of the year, thus omitting possible idle periods on days with low power consumption. In [27], a peak shaving algorithm was proposed for microgrid applications. In contrast to conventional approaches considering only the load consumption, here, the peak threshold applies also for the PV generation. The battery capacity is equally reserved for both positive (injection to the grid) and negative (absorption from the grid) peaks by setting the SoC during normal operation at 50%. The algorithm was tested on a real-time microgrid, implemented in the lab. The researchers used predefined data (load/PV profiles) to carry out the experiment; however, they did suggest in future deploying predictive analytics to improve the reliability of the system.

In this paragraph, we explain three major contribution pillars of the present research work.

	- • How much peak demand reduction can a user achieve for a given battery energy capacity (kWh)?
	- • What is the battery utilization, how much time during the year and how many cycles? Does peak shaving heavily impact the degradation of the battery? Can we hybridize peak shaving with other services?
	- • Which performance metrics should we use and how can these be interpreted from an economic perspective? What are the profitability margins of battery storage for Belgium?

The rest of the paper is structured as follows. In Section 2, the data of the study are presented (Section 2.1). Then, we proceed with the methodology; the power flow model is explained (Section 2.2) and the dichotomy method is proposed as an optimization algorithm (Section 2.3). Section 2 closes with the definition of performance metrics (Section 2.4). Next, Section 3 shows the results of the simulation (Section 3.1) and explains how to interpret those from an economic perspective (Section 3.2). Finally, Section 4 summarizes the most important conclusions and makes suggestions for future research objectives.

## **2. Materials and Methods**


*Edited by Abbas Moustafa*

This book sheds lights on recent advances in Geotechnical Earthquake Engineering with special emphasis on soil liquefaction, soil-structure interaction, seismic safety of dams and underground monuments, mitigation strategies against landslide and fire whirlwind resulting from earthquakes and vibration of a layered rotating plant and Bryan's effect. The book contains sixteen chapters covering several interesting research topics written by researchers and experts from several countries. The research reported in this book is useful to graduate students and researchers working in the fields of structural and earthquake engineering. The book will also be of considerable help to civil engineers working on construction and repair of engineering structures, such as buildings, roads, dams and monuments.

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3. Graphene oxide (GO)/cobalt oxide (Co3O4) nanoparticles

### 3.1 Synthesis procedure

The GO/Co3O4 composite nanoparticles were synthesized and used for various applications. Liang et al. [22] synthesized Co3O4/N-doped graphene hybrid nanoparticles as catalyst for oxygen reduction. They prepared GO sheet using the modified Hummers method; after the Co3O4/rmGO hybrid was synthesized using a Co(OAc)2 aqueous solution dispersed in GO/ethanol at room temperature and stirred for 10 h at a temperature of 80°C, then NH4OH was added to the solution. They used the GO/Co3O4 composite nanoparticles for catalytic activity. Syam Sundar et al. [18] synthesized the GO/Co3O4 hybrid nanoparticles using the chemical coprecipitation method. Their procedure involved first the preparation of GO sheets using modified Hummers method, after that, 0.2 g of GO-COOH nanosheet dispersed in 100 mL of distilled water and added the solution to 0.4 g of CoCl26H2O dispersed in 20 mL of distilled water and added 0.2932 g of NaBH4, which was accompanied by the formation of a black precipitate. They prepared GO/Co3O4 hybrid nanofluids and observed higher values of thermal conductivity and viscosity when particle concentration and temperature increase. The synthesis method and TEM results are shown in Figure 6. The XRD, FTIR, and VSM results are presented in Figure 7a–c. The XRD patterns of GO/Co3O4 nanoparticles contain

> both the peaks of Co3O4 and GO. The 2θ position of GO/Co3O4 nanoparticles is 11.68, 19.2, 31.2, 36.9, 44.8, 55.43, 59.4, and 65.2° which can be indexed as (002) plane for GO and (111), (220), (311), (400), (511), and (440) planes for Co3O4 nanoparticles (Figure 7a). The IR spectra of GO nanoparticle (Figure 7c) show the GO peak at 1622 cm1 is the aromatic C=C group, the peak at 1727 cm1 is the C=O

> The Cobalt Oxide-Based Composite Nanomaterial Synthesis and Its Biomedical and Engineering…

DOI: http://dx.doi.org/10.5772/intechopen.88272

GO/Co3O4 nanoparticles: (a) XRD patterns, (b) FTIR spectra, and (c) M-H curves [18].

1410 cm1 are contributed to C▬O▬C vibration of epoxy or alkoxy group. The IR spectra of Co3O4 nanoparticle show the strong band peak at 584 cm1 and 671 cm1 is due to the Co▬O vibration of Co3O4 nanoparticles, which shows that Co2+ has been oxidized into Co3O4 nanoparticles. The IR spectra of GO/Co3O4 nanoparticles show the peaks at 1622, 1727, 1045, 1220, and 1410 cm1 reflect C=C, C=O, and C▬O▬C groups related to GO and the peaks at 584 and 671 cm1 reflect the Co▬O groups related to Co3O4 nanoparticles. The total saturation magnetization of GO/ Co3O4 (Figure 7c) is 4.67 emu/g and pure Co3O4 nanoparticles is 14.23 emu/g. The weight percentages of GO and Co3O4 nanoparticles present in the GO/Co3O4 nanocomposite particles were 67 and 33%, respectively. Shi et al. [20] prepared different concentrations of Co3O4/GO such as 20% Co3O4/GO, 30% Co3O4/GO, 50% Co3O4/GO, 70% Co3O4/GO, 90% Co3O4/GO, 95% Co3O4/GO, and pure Co3O4, and they studied their catalyst activity; the highest catalytic activity was observed when the Co3O4 loading was about 50% in the catalyst. Xiang et al. [21] synthesized 20-nm-sized Co3O4 nanoparticles, which were in situ grown on the chemically reduced graphene oxide (rGO) sheets to form an rGO/Co3O4 composite during hydrothermal processing; they were used as the pseudocapacitor electrode in the

, 1220 cm1

, and

vibration of carboxylic group, and the peaks at 1045 cm1

Figure 7.

37

Figure 6. GO/Co3O4 nanoparticles: (a) synthesis method and (b) TEM image [18].

The Cobalt Oxide-Based Composite Nanomaterial Synthesis and Its Biomedical and Engineering… DOI: http://dx.doi.org/10.5772/intechopen.88272

Figure 7. GO/Co3O4 nanoparticles: (a) XRD patterns, (b) FTIR spectra, and (c) M-H curves [18].

both the peaks of Co3O4 and GO. The 2θ position of GO/Co3O4 nanoparticles is 11.68, 19.2, 31.2, 36.9, 44.8, 55.43, 59.4, and 65.2° which can be indexed as (002) plane for GO and (111), (220), (311), (400), (511), and (440) planes for Co3O4 nanoparticles (Figure 7a). The IR spectra of GO nanoparticle (Figure 7c) show the GO peak at 1622 cm1 is the aromatic C=C group, the peak at 1727 cm1 is the C=O vibration of carboxylic group, and the peaks at 1045 cm1 , 1220 cm1 , and 1410 cm1 are contributed to C▬O▬C vibration of epoxy or alkoxy group. The IR spectra of Co3O4 nanoparticle show the strong band peak at 584 cm1 and 671 cm1 is due to the Co▬O vibration of Co3O4 nanoparticles, which shows that Co2+ has been oxidized into Co3O4 nanoparticles. The IR spectra of GO/Co3O4 nanoparticles show the peaks at 1622, 1727, 1045, 1220, and 1410 cm1 reflect C=C, C=O, and C▬O▬C groups related to GO and the peaks at 584 and 671 cm1 reflect the Co▬O groups related to Co3O4 nanoparticles. The total saturation magnetization of GO/ Co3O4 (Figure 7c) is 4.67 emu/g and pure Co3O4 nanoparticles is 14.23 emu/g. The weight percentages of GO and Co3O4 nanoparticles present in the GO/Co3O4 nanocomposite particles were 67 and 33%, respectively. Shi et al. [20] prepared different concentrations of Co3O4/GO such as 20% Co3O4/GO, 30% Co3O4/GO, 50% Co3O4/GO, 70% Co3O4/GO, 90% Co3O4/GO, 95% Co3O4/GO, and pure Co3O4, and they studied their catalyst activity; the highest catalytic activity was observed when the Co3O4 loading was about 50% in the catalyst. Xiang et al. [21] synthesized 20-nm-sized Co3O4 nanoparticles, which were in situ grown on the chemically reduced graphene oxide (rGO) sheets to form an rGO/Co3O4 composite during hydrothermal processing; they were used as the pseudocapacitor electrode in the

(BEAS-2B) cells exposed to 1 40 μg=mL. In A549 cells, they found no cytotoxicity; however, BEAS-2B cells presented viability reduction at 40 μg=mL and early membrane damage at 1, 5, and 40 μg=mL. The results related to toxicity study are presented in Figures 3 and 4. Alarifi et al. [17] investigated the toxicity of Co3O4 nanoparticles in HepG2 cells and observed cytotoxicity and genotoxicity in HepG2 cells through ROS and oxidative stress, and their results are presented in Figure 5.

The GO/Co3O4 composite nanoparticles were synthesized and used for various

3. Graphene oxide (GO)/cobalt oxide (Co3O4) nanoparticles

applications. Liang et al. [22] synthesized Co3O4/N-doped graphene hybrid nanoparticles as catalyst for oxygen reduction. They prepared GO sheet using the modified Hummers method; after the Co3O4/rmGO hybrid was synthesized using a Co(OAc)2 aqueous solution dispersed in GO/ethanol at room temperature and stirred for 10 h at a temperature of 80°C, then NH4OH was added to the solution. They used the GO/Co3O4 composite nanoparticles for catalytic activity. Syam Sundar et al. [18] synthesized the GO/Co3O4 hybrid nanoparticles using the chemical coprecipitation method. Their procedure involved first the preparation of GO sheets using modified Hummers method, after that, 0.2 g of GO-COOH nanosheet

dispersed in 100 mL of distilled water and added the solution to 0.4 g of

GO/Co3O4 nanoparticles: (a) synthesis method and (b) TEM image [18].

CoCl26H2O dispersed in 20 mL of distilled water and added 0.2932 g of NaBH4, which was accompanied by the formation of a black precipitate. They prepared GO/Co3O4 hybrid nanofluids and observed higher values of thermal conductivity and viscosity when particle concentration and temperature increase. The synthesis method and TEM results are shown in Figure 6. The XRD, FTIR, and VSM results are presented in Figure 7a–c. The XRD patterns of GO/Co3O4 nanoparticles contain

3.1 Synthesis procedure

Cobalt Compounds and Applications

Figure 6.

36

2 M KOH aqueous electrolyte solution, and the measured specific capacitance was 472 F=g at a scan rate of 2 mV=s.

#### 3.2 Thermal properties

The water- and ethylene glycol-based GO/Co3O4 nanocomposite nanofluid's thermal properties were measured by Syam Sundar et al. [18], and the results are shown in Figures 8 and 9 at different volume concentrations and temperatures. It is noticed that the thermal conductivity of nanofluids increases linearly with the increase of particle volume concentrations and temperatures. Similarly, the viscosity of nanofluids increases with an increase of particle volume concentrations and decreases with an increase of temperature. The thermal conductivity of 0.05% nanofluid is enhanced by 2.82% and 8.58% at temperatures of 20 and 60°C, respectively, as compared to water. The thermal conductivity of 0.2% nanofluid is enhanced by 7.64 and 19.14% at temperatures of 20 and 60°C, respectively, as compared to water (Figure 8, left side). The viscosity of 0.05% volume concentration of nanofluid is enhanced by 1.075 times and 1.166 times; the viscosity of 0.2% volume concentration of nanofluid is enhanced by 1.49 times and 1.70 times at temperatures of 20 and 60°C compared to water (Figure 8, right side).

The thermal conductivity of 0.05% nanofluid is enhanced by 2.71 and 4.44% at temperatures of 20 and 60°C, respectively, as compared to EG. The thermal conductivity of 0.2% nanofluid is enhanced by 5.81 and 11.85% at temperatures of 20 and 60°C, respectively, as compared to EG (Figure 9, left side). The viscosity enhancement of 0.05% volume concentration of nanofluid is 1.028 times and 1.096 times; the viscosity enhancement of 0.2% volume concentration of nanofluid is 1.22 times and 1.42 times at temperatures of 20 and 60°C compared to EG (Figure 9, right side).

3.3 Electrical properties

DOI: http://dx.doi.org/10.5772/intechopen.88272

Figure 9.

39

Xiang et al. [21] measured the electrical properties of GO/Co3O4 using pseudocapacitor electrode in 2 M of KOH aqueous electrolyte solution. Figure 10 depicts the galvanostatic charge discharge curve of rGO and the rGO/Co3O4 composite electrodes between 0 and 0.85 V at different current densities. Both the samples of rGO and rGO/Co3O4 electrodes exhibited good symmetric shape with the coulomb efficiency close to 1. The rGO/Co3O4 composite electrode presented longer charge discharge time than the rGO electrode, indicating larger specific capacitance (Figure 10a and b). The specific capacitance of the rGO/Co3O4 electrode was investigated with a progressively increasing current density (Figure 10c). The specific capacitance decreases from 458 to 416 F=g with an increase in the current density from 0.5 to 2.0 A=g, respectively. The long-term stability of the rGO/Co3O4 electrode was observed at the current density of 2.0 A=g. The specific capacitance of the rGO/Co3O4 electrode increased during the first 100 cycles, which was due to an activation process in the super capacitor electrode. About 95.6% of the specific capacitance of rGO/Co3O4 electrode was retained at the current density of 2.0 A=g after 1000 cycles (Figure 10d), which demonstrated its high cycling stability. Lai et al. [23] synthesized Co3O4 nanoparticles grown on nitrogen-modified microwave-exfoliated graphite oxide (NMEG) with weight ratio controlled from 10 to 70%; due to their electrochemical performance, they are used as Li-ion battery anode, and they exhibit improved cycle stability. Seventy percent of the Co3O4/NMEG composite has an initial irreversible capacity of 230 mAh=g (first cycle efficiency of 77%), and 910 mAh=g of capacity is retained after 100 cycles. Seventy percent of Co3O4/tRG-O delivers a reversible capacity of 750 mAh=g, and the irreversible capacity loss during the first cycle is 700 mAh=g. It is noted that the composite material synthesized with Co3O4 exhibits larger specific capacitance than rGO material when they are used as electrode. The Co3O4/NMEG composite material shows higher capacitance when they are used as Li-ion battery

Ethylene glycol-based GO/Co3O4 nanofluids: thermal conductivity (left side) and viscosity (right side) [18].

The Cobalt Oxide-Based Composite Nanomaterial Synthesis and Its Biomedical and Engineering…

The Cobalt Oxide-Based Composite Nanomaterial Synthesis and Its Biomedical and Engineering… DOI: http://dx.doi.org/10.5772/intechopen.88272

Figure 9. Ethylene glycol-based GO/Co3O4 nanofluids: thermal conductivity (left side) and viscosity (right side) [18].

### 3.3 Electrical properties

2 M KOH aqueous electrolyte solution, and the measured specific capacitance was

The water- and ethylene glycol-based GO/Co3O4 nanocomposite nanofluid's thermal properties were measured by Syam Sundar et al. [18], and the results are shown in Figures 8 and 9 at different volume concentrations and temperatures. It is noticed that the thermal conductivity of nanofluids increases linearly with the increase of particle volume concentrations and temperatures. Similarly, the viscosity of nanofluids increases with an increase of particle volume

concentrations and decreases with an increase of temperature. The thermal conductivity of 0.05% nanofluid is enhanced by 2.82% and 8.58% at temperatures of 20 and 60°C, respectively, as compared to water. The thermal conductivity of 0.2% nanofluid is enhanced by 7.64 and 19.14% at temperatures of 20 and 60°C, respectively, as compared to water (Figure 8, left side). The viscosity of 0.05% volume concentration of nanofluid is enhanced by 1.075 times and 1.166 times; the viscosity of 0.2% volume concentration of nanofluid is enhanced by 1.49 times and 1.70 times at temperatures of 20 and 60°C compared to water

The thermal conductivity of 0.05% nanofluid is enhanced by 2.71 and 4.44% at temperatures of 20 and 60°C, respectively, as compared to EG. The thermal conductivity of 0.2% nanofluid is enhanced by 5.81 and 11.85% at temperatures of 20 and 60°C, respectively, as compared to EG (Figure 9, left side). The viscosity enhancement of 0.05% volume concentration of nanofluid is 1.028 times and 1.096 times; the viscosity enhancement of 0.2% volume concentration of nanofluid is 1.22 times and 1.42 times at temperatures of 20 and 60°C compared to EG (Figure 9,

Water-based GO/Co3O4 nanofluids: thermal conductivity (left side) and viscosity (right side) [18].

472 F=g at a scan rate of 2 mV=s.

Cobalt Compounds and Applications

3.2 Thermal properties

(Figure 8, right side).

right side).

Figure 8.

38

Xiang et al. [21] measured the electrical properties of GO/Co3O4 using pseudocapacitor electrode in 2 M of KOH aqueous electrolyte solution. Figure 10 depicts the galvanostatic charge discharge curve of rGO and the rGO/Co3O4 composite electrodes between 0 and 0.85 V at different current densities. Both the samples of rGO and rGO/Co3O4 electrodes exhibited good symmetric shape with the coulomb efficiency close to 1. The rGO/Co3O4 composite electrode presented longer charge discharge time than the rGO electrode, indicating larger specific capacitance (Figure 10a and b). The specific capacitance of the rGO/Co3O4 electrode was investigated with a progressively increasing current density (Figure 10c). The specific capacitance decreases from 458 to 416 F=g with an increase in the current density from 0.5 to 2.0 A=g, respectively. The long-term stability of the rGO/Co3O4 electrode was observed at the current density of 2.0 A=g. The specific capacitance of the rGO/Co3O4 electrode increased during the first 100 cycles, which was due to an activation process in the super capacitor electrode. About 95.6% of the specific capacitance of rGO/Co3O4 electrode was retained at the current density of 2.0 A=g after 1000 cycles (Figure 10d), which demonstrated its high cycling stability. Lai et al. [23] synthesized Co3O4 nanoparticles grown on nitrogen-modified microwave-exfoliated graphite oxide (NMEG) with weight ratio controlled from 10 to 70%; due to their electrochemical performance, they are used as Li-ion battery anode, and they exhibit improved cycle stability. Seventy percent of the Co3O4/NMEG composite has an initial irreversible capacity of 230 mAh=g (first cycle efficiency of 77%), and 910 mAh=g of capacity is retained after 100 cycles. Seventy percent of Co3O4/tRG-O delivers a reversible capacity of 750 mAh=g, and the irreversible capacity loss during the first cycle is 700 mAh=g. It is noted that the composite material synthesized with Co3O4 exhibits larger specific capacitance than rGO material when they are used as electrode. The Co3O4/NMEG composite material shows higher capacitance when they are used as Li-ion battery

Figure 10.

GO/Co3O4 nanomaterial: (a) charge-discharge curves at the current density of 0.5 A=g, (b) charge-discharge curves at different current densities (0.5, 1.0, and 2.0 A=g), (c) cycling stability at varying the current density, and (d) long-term stability at a current density of 2.0 A=g [21].

anode. So, it is understood that the composite material exhibits synergistic (superior electrical) properties compared to the single-phase nanoparticles.


**HAIR AND SCALP DISORDERS**

Edited by **Zekayi Kutlubay** and **Server Serdaroglu**

#### **Hair and Scalp Disorders**

http://dx.doi.org/10.5772/63002 Edited by Zekayi Kutlubay and Server Serdaroglu

#### **Contributors**

Safvet Örs, Anton Yuryev, Anastasia Nesterova, Selda Pelin Kartal, Emin Ozlu, Ayse Serap Karadag, Murat Küçüktaş, Arzu Kilic, Melike Kibar Ozturk, Goknur Ozaydin Yavuz, Ibrahim Halil Yavuz, Serap Gunes Bilgili, Shin-Ichi Osada, Ekaterina Kalabusheva, Vasily Terskikh, Elina Chermnykh, Ekaterina Vorotelyak, Khitam Al-Refu, Burhan Engin, Eduard Vsevolodov, Hilal Gokalp, Filiz Cebeci, Melek Aslan Kayıran, Burak Tekin, Tugba Kevser Uzuncakmak, Gurkan Yardimci, Filiz Canpolat, Bilgen Erdoğan, Zekayi Kutlubay

#### **© The Editor(s) and the Author(s) 2017**

The moral rights of the and the author(s) have been asserted.

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#### **Notice**

Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

First published in Croatia, 2017 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

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**6. Numerical approach description**

The treatment of permeable natural fractures is a part of UFM model. It is possible to model leakoff from HF into the NF form UFM in different ways, depending on the importance of required accuracy, numerical stability and CPU time.

The most computationally expensive but at the same time most accurate is a fully coupled numerical approach. The fully coupled approach means to discretise different parts of the invaded NFs and numerically solve the pressure as a part of total system of equations for the fracture network using iterative solution scheme. Another, more CPU efficient approach, is a decoupled numerical approach, where pressure and width along the invaded but closed part of NF are calculated separately based on the results from previous time step calculations along the HFN and corresponding pressure at HF/NF intersections (inlets).

Two approaches have been considered to model interaction of hydraulic fracture with permeable natural fractures.

#### **6.1. Decoupled numerical approach**

**•** Save elements information (volume, pressure, flow rates) for the next time step

#### **6.2. Fully coupled numerical approach**

If some elements in closed not disturbed part of NF are sliding then the corresponding shear stress is involved in the stress shadow calculations and thus influences simulations results.

The treatment of permeable natural fractures is a part of UFM model. It is possible to model leakoff from HF into the NF form UFM in different ways, depending on the importance of

The most computationally expensive but at the same time most accurate is a fully coupled numerical approach. The fully coupled approach means to discretise different parts of the invaded NFs and numerically solve the pressure as a part of total system of equations for the fracture network using iterative solution scheme. Another, more CPU efficient approach, is a decoupled numerical approach, where pressure and width along the invaded but closed part of NF are calculated separately based on the results from previous time step calculations along

Two approaches have been considered to model interaction of hydraulic fracture with

**•** When NF is intercepted by HF, create elements along whole NF to be used at next time step **•** Evaluate initial guess of flow rate into the NF based on the pressure at the intersection and

**•** Check for a possibility of frictional sliding along the closed parts of NFs to evaluate pressure-

**•** Iteratively calculate pressure, hydraulic width, flow rate and length of each zone along NF with using corresponding equations (for filtration and pressurized zones) by marching from intersection till the end of NF until condition (27) is satisfied indicating final results and final

**•** Track the end of filtration zone for each pressure and flow rate iterations by checking the

**•** Save invaded volume for volume balance, influx for mass balance, pressure at intersection,

**•** Track the pressure at intersections and/or tips of opened HF part in NF to capture opened

**•** If intersection is opened, use the pressure at the tip of opened HFN part along invaded NF

**6. Numerical approach description**

304 Effective and Sustainable Hydraulic Fracturing

permeable natural fractures.

positions of zones' fronts

zones.

**6.1. Decoupled numerical approach**

old pressure profile along closed NF

dependent permeability and conductivity along NF

volume of fluid injected into NF at given time step

for calculations along corresponding closed NF part

**•** Apply rules to treat special situations (intersecting NFs, etc)

and time step to be used at the next time step

required accuracy, numerical stability and CPU time.

the HFN and corresponding pressure at HF/NF intersections (inlets).

**Figure 5.** The proposed algorithm to account for leakoff from HF into the permeable NFs (*i=N* indicates the end of NF)

Figure 5 The proposed algorithm to account for leakoff from HF into the permeable NFs (*i=N* indicates the end of NF)

12

**•** Calculate the flow rate and volume of fluid injected to NFs at each pressure iteration, and update/calculate pressure along HFN using existing scheme for opened elements and new equations (described above) for elements in closed invaded and pressurized NF parts

[2] Chuprakov, D, Melchaeva, O, & Prioul, R. Hydraulic Fracture Propagation Across a

Hydraulic Fracturing in Formations with Permeable Natural Fractures

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The fully coupled NF modeling approach is heavier and more CPU expensive than decoupled approach. The Decoupled Numerical Approach has been selected as basic approach and it is described schematically on Figure 5 as a part of total solution