**3. Ongoing Work and Future Directions**

To ensure that EuroFIR AISBL resources remain valuable to user communities, it is important not only to update, expand, and enhance databases, but also to do these in standardized and harmonized ways among organizations and countries, considering existing and emerging food sources, and adding new descriptors and markers as necessary. To this end, engagement with networks and research infrastructures is a priority, creating synergies necessary to generate high-quality data and develop tools for the production, management, and exploitation of food data. In line with the European Strategy Forum on Research Infrastructures (ESFRI), the research infrastructure METROFOOD-RI and the European Open Science Cloud (EOSC), strategies leading to reliable and comparable analytical measurements in foods along food chains, from primary producers to consumers and beyond (food waste) and increasingly FAIR data [81] are valuable for researchers, food producers, and consumers. However, continued cooperation and sharing of data between compilers and users, within an integrated approach for agro-food, nutrition, and health, are key to success. Management of data at agro-food, nutrition, and health interfaces is a priority, but integrating FCDBs and infrastructures (interoperability) can only be achieved if approaches are applied based on metrological principles [81–86].

In this context, EuroFIR AISBL is involved in Member and Client activities and EU or otherwise-funded projects considering a range of relevant topics. The Food Nutrition Security Cloud (FNS-Cloud, Grant Agreement ID: 863059, www.fns-cloud.eu, accessed on 26 October 2022) aims to support integration of existing and emerging food research data and tools to address diet and health research questions across agro-food, nutrition and lifestyle, and non-communicable disease and healthy diet domains [87].

EuroFIR AISBL is also active in the proposed Food Nutrition Health Research Infrastructure (FNH-RI), which aims to link food production (agriculture and food technology) and food consumption (food determinants, intake, nutrition, and health) domains. To this end, a prototype *Determinants and Intake Platform*, harmonizing and linking consumer food behaviors, was formulated based on EuroDISH (Study on the need for food and health research infrastructures in Europe, Grant Agreement ID: 311788) and RICHFIELDS (Research infrastructure on consumer health and food intake using e-science with linked data sharing, Grant Agreement ID: 654280) outputs [88].

With the food environment undergoing vast changes, the need to study the nutritional variation in processed foods has driven an international move for branded food composition databases (BFCDBs). EuroFIR AISBL is working with its members to create a platform for collaboration and advocacy around BFCDBs, addressing user needs and gaps surveyed in 2020–2021. During the EuroFIR Food Forum 2021, a workshop was dedicated to BFCDBs, discussing advances at the European level and open access issues.

**Author Contributions:** Conceptualization, A.D. and P.F.; writing—original draft preparation, A.D., S.A., M.K., H.S.C., A.M.-V., L.P., L.B., M.G., K.P. and P.F. All authors have made substantial, direct, and intellectual contributions to the work and approved it for publication. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

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


**GASTRIC CANCER - AN UPDATE**

Edited by **Hajime Orita, Hiroshi Maekawa** and **Michael Gibson**

#### **Gastric Cancer - An Update**

http://dx.doi.org/10.5772/intechopen.71704 Edited by Hajime Orita, Hiroshi Maekawa and Michael Gibson

#### **Contributors**

Nebojsa S. Stanoje Ignjatovic, Tomislav Randjelovic, Miroslav Stojanovic, Goran Stanojevic, Miodrag Djordjevic, Byoung Jo Suh, Tamer Saafan, Shunsuke Sakuraba, Satoshi Kanda, Tetsu Fukunaga

#### **© The Editor(s) and the Author(s) 2019**

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First published in London, United Kingdom, 2019 by IntechOpen eBook (PDF) Published by IntechOpen, 2019 IntechOpen is the global imprint of INTECHOPEN LIMITED, registered in England and Wales, registration number: 11086078, The Shard, 25th floor, 32 London Bridge Street London, SE19SG – United Kingdom Printed in Croatia

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Gastric Cancer - An Update Edited by Hajime Orita, Hiroshi Maekawa and Michael Gibson p. cm. Print ISBN 978-1-78985-745-0 Online ISBN 978-1-78985-746-7 eBook (PDF) ISBN 978-1-83962-095-9


Sweetness potency is the ratio of the concentration of sucrose to that of a sweetener at equivalent sweetness intensities (Equation (3)). A sweetness potency of >1 indicates that a smaller concentration of a sweetener is required to achieve the same sweetness intensity at a particular sucrose concentration and, therefore, the sweetener could be considered as 'more potent' than sucrose. Sweetness potency is often quoted as a single value e.g., 'acesulfame-K is 120 times sweeter than sucrose', however this value should always be reported with the concentration of sucrose at which it was calculated, since sweeteners often have different sweetness growth rates to sucrose.

#### 2.5.4. Statistical Analysis

A two-way analysis of variance (ANOVA) was run to confirm absence of first-order and carryover effects. A one-way repeated measures ANOVA analysis was used to test the effect of sweetener type and effect of concentration and statistical significance was set at 5% (α = 0.05). Post hoc pairwise comparisons, using Bonferroni corrections, were used to compare differences in sweetness intensity scores across sweeteners (16 levels) and concentration of sweeteners (6 levels) using the statistical analysis software SPSS (IBM SPSS Statistics for Windows, Version 22.0, IBM Corporation, Armonk, NY, USA).

#### **3. Results**

The dose-response for all sweeteners are illustrated on semi-log curves (Figure 1A–C) and fitted with the Hill equation (Equation (1)) with *r*2 ≥ 0.95 for all sweeteners. The fitting parameters are listed in Table S2. Repeated-measures ANOVA confirmed that all sweeteners exhibited a concentration dose-dependency for sweetness intensity (*F*5,39 = 142.12, *p* < 0.001). Sweetener type had a significant effect on sweetness intensity as concentrations increased (*F*15,39 = 18.05, *p* < 0.001) and this was confirmed as a significant interaction between concentration and sweetener type (*F*75,39 = 4.20, *p* < 0.001).

#### *3.1. Concentration Dose-Response of Sweeteners*

The sweetness intensity of sucrose ranged from 'barely detectable' (3) to 'strong' (33) on the gLMS for the concentration range of 3.8 to 25% *w*/*v*. Nutritive saccharide and polyol sweeteners sucrose, dextrose, allulose, palatinose, maltitol, sorbitol, mannitol, xylitol and erythritol exhibited sigmoidal dose-response functions. By contrast, fructose displayed a more linear response and had a higher sweetness intensity than sucrose and other nutritive sweeteners, across all sucrose concentrations (Figure 1A,B). The sucrose–allulose mixture, maltitol and xylitol had dose-response curves closely matched to sucrose within the range of 3.8 to 25% *w*/*v* sucrose. The dose-response curve for xylitol was similar to sucrose at lower concentrations but had higher sweetness intensity above 11.7% *w*/*v*. Allulose was perceived as less sweet than sucrose at equivalent concentrations, but when allulose and sucrose were blended in a 1:1 mixture, this blend achieved a near identical dose-response curve to sucrose. Palatinose required the highest concentration to match the sweetness intensity of sucrose, and only produced a noticeable rise in sweetness intensity as the concentration went above 10% *w*/*v*. Dextrose, erythritol, sorbitol and mannitol all had lower sweetness intensities than sucrose across the concentration range tested.

Non-nutritive sweeteners exhibited sigmoidal dose-response functions (Figure 1C) and stevia (rebA) and acesulfame-K had flatter responses at low and high concentrations, where increased concentration produced smaller increments in perceived sweetness intensity. In addition, maximum sweetness for these sweeteners peaked below sucrose at 'moderate' (25). Sucralose had a higher peak sweetness intensity (35) compared to sucrose (33) at the highest concentration, and was higher than the other non-nutritive sweeteners across equivalent concentrations. Aspartame and *luo han guo* both had similar peak sweetness to sucrose, and their dose-response curves were similar to each other. Their sweetness intensities were weaker than stevia (rebA) at low concentrations (0.01–0.1% *w*/*v*) but stronger at higher concentrations (>0.1% *w*/*v*) when the sweetness intensity of stevia (rebA) plateaued.

**Figure 1.** Sweetness intensity with concentration for (**A**) saccharide, (**B**) polyol and (**C**) non-nutritive sweeteners (sucrose is plotted using the secondary x-axis below (0.1–100% *w*/*v*)).

#### *3.2. Comparison of Sweetness Growth Rates across Sweeteners*

The sweetness growth rate is represented by the slope of the log-log sweetness intensity concentration curves (% *w*/*v* basis) (Figure 2 and Table 3). Sucrose had a sweetness growth rate of 1.31 whereas saccharide sweeteners (dextrose, palatinose, fructose, allulose, sucrose–allulose mixture,) had sweetness growth rates >1, ranging from 1.08 (fructose) to 1.46 (sorbitol). The bulk polyol sweeteners (sorbitol, xylitol, mannitol and erythritol) had sweetness growth rates with similar slopes to sucrose (~1.3–1.4), indicating a similar growth rate to sucrose such that changes in concentration produce similar changes in sweetness intensity. Palatinose and fructose yielded much flatter sweetness growth rates (slopes ≈ 1) amongst the nutritive sweeteners, with 1.10 and 1.08 respectively. By contrast, non-nutritive sweeteners had compressed sweetness growth rates < 1, ranging from 0.65 (sucralose) to 0.84 (aspartame).

**Figure 2.** Log sweetness intensity vs. log concentration for 16 sweeteners.

**Table 3.** Slope and y-intercept values of linear fit between log sweetness intensity and log concentration (% *w*/*v*).

‡ 1:1 sucrose–allulose mixture (weight basis).

#### *3.3. Sweetness Potency of Sweeteners Relative to Sucrose*

Sweetness potency as well as the concentration of sweetener required to achieve equivalent sweetness intensity to sucrose concentrations at 5%, 10% and 15% *w*/*v* are summarised in Table 4. Saccharide and polyol sweeteners had sweetness potencies <1, with the exception of xylitol (at 15% *w*/*v* sucrose) and fructose. Sweetness potency values for allulose increased from 5% to 15% *w*/*v* sucrose respectively, whereas the sweetness potency for maltitol, xylitol and sucrose–allulose mixture were closer to sucrose across sucrose concentrations, emphasising the similarity of their dose-response functions (Figure 1). Non-nutritive sweeteners had decreasing sweetness potencies at increasing sucrose concentrations. Sucralose has the highest sweetness potency across all sweeteners, but also the largest decline, from sweetness potency of 521 at 5% *w*/*v*, to 201 at 15% *w*/*v* sucrose. Aspartame had the smallest decline in sweetness potency among the non-nutritive sweeteners at higher sucrose concentrations.

**Table 4.** Concentrations matching for equi-sweetness and sweetness potency of 15 sweeteners to 5%, 10% and 15% *w*/*v* sucrose.

‡ 1:1 sucrose–allulose mixture (weight basis).

#### *3.4. Potential for Calorie Reduction across Sweeteners*

Figure 3 shows the caloric value across the different nutritive sweeteners at sweetness intensities ranging from weak (6) to strong (35). The equivalent sweetness intensity to sucrose per unit calorie provides a summary of the calorie saving potential across the different sweeteners. With the exception of dextrose and palatinose, all of the other nutritive sweeteners enable calorie saving at an equivalent perceived sweetness intensity to 10% sucrose (indicated by red line on Figure 3). Allulose and erythritol have the lowest energy densities (0.2 kcal/g) and can achieve an equivalent sweetness intensity to 10% sucrose with very few calories (~95% reduction). For example, a product with 10% *w*/*v* sucrose could potentially be reduced from 40 kcal to <5 kcal/100ml by substituting with allulose or erythritol. Mannitol, sucrose–allulose mixture, xylitol, fructose, maltitol and sorbitol provide about 5–20 kcal/100 mL savings in terms of energy required to achieve equivalent sweetness to 10% sucrose.

**Figure 3.** Energy content (kcal/100 mL) of nutritive saccharide and polyol sweeteners to achieve sweetness intensities ranging from weak (6) to strong (35).

#### **4. Discussion**

In order to support sugar reduction, sweeteners must first match the sweetness intensity of sucrose across the range of perceived intensities commonly encountered in foods and beverages. From a public health perspective, the reduction in sucrose should also support calorie reduction while maintaining consumer appeal beyond sensory-matching perceived sweetness. In addition to their sweetening capacity, sweeteners that can confer additional functionality such as acting as bulking agents, supporting clean labelling or providing an additional anti-glycaemic effect are also highly desirable. A wide variety of sweeteners are currently available and the present study sought to evaluate the sweetening capabilities of these sweeteners in comparison to sucrose based on their dose-response behaviour, sweetness growth rate, sweetness potency and potential calorie savings at equal sweetness intensities.

All sweeteners exhibited sigmoidal dose-response behaviours although fructose displayed a more linear response across the concentration range tested. This sigmoidal relationship between concentration and perceived intensity is the result of the binding kinetics of the sweetener molecules to taste receptors, which plateaus at higher concentration when receptors become saturated [32,33]. From the dose-response curves, all sweeteners were found to match the perceived sweetness intensity of a 10% *w*/*v* sucrose solution, which represents a 'moderate' sweetness associated with 10% sugar that is frequently found in many commercially available sweetened and carbonated beverages (e.g., Arizona Ice Tea 10.1 g/100 mL) [34]. This aligns with similar findings from other studies, where the sweetness intensity of ~10% *w*/*v* sucrose was also found to be of 'moderate' intensity with rating scores approximately 15 to 20 on the gLMS [23–25]. Interestingly, the perceived sweetness intensity of the sucrose–allulose mixture (1:1) was nearly identical to that of sucrose by weight basis, although allulose on its own had consistently lower sweetness intensity than sucrose across the concentrations tested. Previous research has demonstrated that the sweetness intensity of binary

mixtures of sweeteners is often an intermediate of the two compounds when tasted alone and at the same total molarity as the mixtures [35,36]. Since the weight of allulose (monosaccharide) is half that of sucrose (disaccharide), the dose-response behaviour of the sucrose–allulose mixture was expected to be between that of sucrose and allulose when expressed in terms of total molarity. Other nutritive sweeteners with smaller molecular weights than sucrose, such as fructose or xylitol, would be relatively even less sweet than sucrose on a molarity basis as compared to weight basis [37]. Nonetheless, for purposes of sweetener application to product re-formulation and interpretation of the calorie reduction potential, the dose-response behaviour of the sweeteners were expressed on a weight basis in the current study, in line with previous reports [18,21,24]. Fructose, xylitol and sucralose were the only sweeteners which had greater peak sweetness intensities than sucrose at the highest concentrations tested, and this has previously been demonstrated across a range of previous studies [23,38,39]. This suggests that 'high-intensity' sweeteners such as aspartame and sucralose may be more accurately described as 'high-potency' sweeteners, as proposed previously by Antenucci and Hayes [23]. The peak sweetness intensities for the non-nutritive sweeteners acesulfame-K and stevia (rebA) were markedly lower than that of sucrose, reaffirming that these high-intensity sweeteners are not necessarily higher in perceived sweetness intensity than sucrose. Further concentration increments of acesulfame-K, stevia (rebA) and sucralose have been shown to produce a further decrease in sweetness intensity [23,24], which was likely due to bitter taste antagonism at higher concentration among these sweeteners [40]. This decrease in sweetness was not observed for any sweeteners at the concentrations used in the current study. The low peak sweetness of acesulfame-K and stevia (rebA) could limit their use in foods where higher sweetness intensities are required. Nevertheless, it is difficult to determine the true peak sweetness achievable unless a plateau in sweetness can be clearly observed [21], on the condition that the intensity scaling method is not limited by a ceiling effect [29,41]. The concentration ranges for the sweeteners were selected prior to the study based on literature and preliminary experiments, although we acknowledge that further concentration increments would likely result in greater perceived sweetness for some sweeteners. In this case, comparing the sweetness growth rate would be a better indicator of the dose-response trajectory rather than the peak sweetness of each sweetener, to understand whether they are likely to match or surpass the sweetness of sucrose.

The sweetness growth rate is the Stevens' power law exponent or slope of the log relationship between changing concentration and the perceived sweetness. It should be noted that the sweetness growth rate obtained in this study is a product of the concentration ranges from which they are derived. These range effects mean that sweetness growth rates can change to be higher or lower depending on the range of concentrations tested, and a higher sweetness growth rate is obtained with a smaller concentration range [42]. Sucrose had a sweetness growth rate of 1.3 which is consistent with previous findings which reported sweetness growth rates of 1.15 to 1.3 [18–20,24]. The sweetness growth rates of sucralose, stevia (rebA), dextrose and mannitol were also found to be comparable to those previously reported [18,24] and collectively these findings highlight that sucrose, and other nutritive sweeteners exhibit sweetness growth rates greater than non-nutritive sweeteners. This appears counterintuitive since only a small quantity of non-nutritive sweetener is required to impart an intense sweetness, which should be perceived as a higher growth rate. However, sweetness growth rates are based on sweetness intensity changes *per* unit log-concentration, and in relative terms greater quantities of non-nutritive sweeteners are required to achieve a proportional increment in perceived sweetness. This may also be due to the emergence of bitter side-tastes and taste–taste antagonism at higher concentrations [40], or different binding mechanisms across sweeteners, which often remain poorly understood [43]. Sweeteners with lower sweetness growth rates to sucrose are capable of matching the sweetness intensity, albeit over a limited concentration range. The implication is that sweetness growth rates should be considered when estimating the predicted sweetness intensity of a sweetener at concentrations beyond those reported in the dose-response curves. For example, sucralose matched the sweetness intensity of sucrose to an upper concentration of 25% *w*/*v*, but displayed a smaller growth rate, suggesting that the peak sweetness intensity for sucralose would be lower than that of sucrose. This is further supported by the flatter dose-response curve for sucralose at higher concentrations (0.172–0.350% *w*/*v*).

Sweeteners with the same growth rate as sucrose will increase in perceived sweetness intensity with equal increases per unit concentration. Sweetness potency or relative concentration of sweetener required to produce an equi-intense sweetness to sucrose would, therefore, be similar across a range of different concentrations. By contrast, sweeteners with growth rates that differ significantly from sucrose would have sweetness potencies that vary with sucrose concentration, as demonstrated previously [19,20,24,44]. While sweetness growth rate and sweetness potency are closely related indices, sweetness potency is more often used as a quick indication of the quantity required to achieve an equi-intense sweetness to sucrose at a given concentration. Non-nutritive sweeteners have growth rates significantly lower than sucrose, and therefore their sweetness potency is also highly concentration-dependent. The sweetness potency values reported for non-nutritive sweeteners in the current trial were not fully consistent those reported previously. For example, aspartame was found to be 128 and 185 times more potent than sucrose at 5 and 10% sucrose equivalence by Tunaley, Thomson and McEwan [45], and Cardello et. al. [20] respectively, as compared to the 173 (5% *w*/*v*) and 121 (10% *w*/*v*) found in our study. Differences were also found for sweetness potencies of stevia (rebA) and sucralose [24]. Sucrose–allulose mixture, xylitol and maltitol have sweetness potencies closest to 1, indicating that the quantities required to achieve an equivalent sweetness intensity on a weight basis are similar to sucrose. This is an important consideration when the replacement sweetener is also required to substitute some of the bulking properties of the removed sucrose. When calorie reduction without the addition of bulk is the main goal of sucrose reduction, low calorie and/or high potency sweeteners may be more effective, particularly among certain products (i.e., beverages) as lower concentrations are required to match sweetness intensity.

With the inclusion of several low-calorie nutritive sweeteners in the study, it is still possible to achieve calorie reduction while maintaining sweetness, even when sweetness potency was not equivalent or higher than sucrose. With the exception of dextrose and palatinose, the nutritive sweeteners profiled supported reductions in total calories to varying extents while meeting the equivalent sweetness intensity of a 10% sucrose solution. Allulose and erythritol in particular have the lowest calories at a sweetness intensity equivalent to 10% sucrose, and could be used to support substantial calorie savings. When allulose was mixed 1:1 to partially replace sucrose, the sucrose–allulose mixture showed very similar sweetening properties to sucrose, while supporting significant reduction in overall calories. Considering the sweetness intensity, sweetness growth rate, sweetness potency and potential calorie reduction together, the sucrose–allulose mixture, maltitol and xylitol were most similar to sucrose, across the concentrations studied. All three sweeteners can provide bulk, support a clean label, reduce total calories for equivalent sweetness intensity and in the case of sucrose–allulose mixture, also impart an additional anti-glycaemic effect post-ingestively [12,14]. When selecting the appropriate sweetener for use in sugar reduction, the sensory, physical, nutrient and metabolic impact of the selected sweetener should be considered, and in some cases sweeteners will have desirable characteristics for some properties but not others. For example, palatinose has an anti-glycaemic benefit which is desirable for products that support the management of glucose homeostasis, but it is required at a greater concentration and energy content to achieve an equi-intense sweetness intensity to sucrose [13]. Non-nutritive sweeteners are calorie-free but may have certain undesirable side-taste attributes, especially at higher concentrations [23,24,40,46] which may limit their usage. With these factors considered, it may be judicious to blend sweeteners with sucrose to optimise the sensory profile and sweetening capacity, and compromise on some elements of the nutrient or metabolic profile. Results from the current study demonstrate that blends like the sucrose–allulose mixture provide encouraging results with excellent sweetness characteristics in line with sucrose, at a fraction of the calories and a potential post-consumption anti-glycaemic benefit.

Findings from the current study are aligned with previously reported differences in sweetness dose–response, growth rate and potency, although some subtle differences were observed in the absolute values reported. These are likely to be due to differences in methodological approach, individual variability, sweetener source, matrix effects, concentration range used, pH and temperature [20,21,23,25,47]. Our findings are most closely aligned with those previously reported by Antenucci and Hayes which were collected using the same standardised gLMS approach to rate sweetness intensity. This approach minimises ceiling effects and produced comparable intensity ratings for many of the same sweeteners [23]. There is currently no official standardised approach to quantify the perceived sweetness intensity of a sweetener, although the comparability of results would be greatly enhanced if future efforts adopt a consistent objective approach, such as used in the current and previous studies [23–25].

In choosing to focus on sweetness intensity alone, we have not accounted for other temporal and qualitative taste differences between the sweeteners reported elsewhere [46]. In addition, perceived sweetness intensity rated in water does not account for matrix effects or taste–taste interaction that would occur when these same sweeteners and concentrations are used in foods and beverages [48,49]. The current findings present an overview of the psychophysical dose-response behaviour of a wide range of different sweeteners, and provides guidance on the similarity of various sweeteners to sucrose and the likely calorie savings that could be achieved if they are used to reduce or replace sugar. Future research should aim to extend this further by profiling the temporal and qualitative differences between sweeteners and characterising their performance in food and beverages.

#### **5. Conclusions**

The current paper characterized the psychophysical dose-response behaviour of 16 sweeteners and identified differences in the peak sweetness, sweetness potency and sweetness growth rate. Sucrose—allulose mixture, maltitol and xylitol exhibited similar psychophysical behaviours to sucrose in terms of peak sweetness intensity, sweetness growth rate and sweetness potency, and showed the greatest potential to match the sweetness of sugar, for significantly fewer calories. Non-nutritive sweeteners offer significant calorie savings, but had lower peak sweetness intensities and lower sweetness growth rates, which may not limit their ability to match sweetness intensity over a wider range of sucrose concentrations. Differences in the psychophysical relationships identified in the current paper should be considered when selecting sweeteners to support sucrose reduction or replacement, and offer significant opportunities to match the perceived sweetness of sugar, while supporting energy density reductions.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2072-6643/10/11/1632/ s1, Table S1: Concentrations tested for each of the sweetener tastant series in molarity (mmol/L), Table S2: Fitting parameters for dose-response of sweeteners using the Hill equation.

**Author Contributions:** C.F. conceived and planned the experiments. M.W. and V.T. collected the data. M.W. and C.F. analysed the data and prepared the manuscript. All authors approved the final version of the manuscript.

**Funding:** Research supported by Biomedical Science Institute Strategic Positioning Fund Grant (G00067; BMSI/13-80048C-SICS: (Sensory Nutritional Science; PI: C. Forde).

**Acknowledgments:** We would like to thank the following companies for providing some of the sweetener samples for this study: Roquette, Matsutani and Beneo. The Compusense Cloud software was also used as part of the Compusense Academic Consortium (Compusense Inc., Guleph, ON, Canada).

**Conflicts of Interest:** C.F. has received reimbursements for speaking at conferences sponsored by companies selling food ingredients and nutritional products, and currently serves on the scientific advisory council of a commercial ingredient manufacturer. None of these organizations had any influence on the design or interpretation of the findings in the current study. All other authors declare no conflicts of interest.

#### **References**

1. Drewnowski, A.; Mennella, J.A.; Johnson, S.L.; Bellisle, F. Sweetness and Food Preference–3. *J. Nutr.* **2012**, *142*, 1142S–1148S. [CrossRef] [PubMed]

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).


*Article* **Analysis of Outburst Coal Structure Characteristics in Sanjia Coal Mine Based on FTIR and XRD**

**Anjun Jiao 1, Shixiang Tian 1,2,\* and Huaying Lin 1**

**Abstract:** In order to reveal the distribution characteristics of functional groups and the difference of microcrystalline structure parameters between outburst coal and primary coal, the coal samples inside and outside the outburst holes of the Sanjia coal mine were examined. The functional groups and microcrystalline structure parameters of outburst coal and primary coal in the Sanjia coal mine were studied by infrared spectroscopy, X-ray diffraction (XRD) experiment and peak-splitting fitting method. The results showed that the substitution mode of the benzene ring in an aromatic structure was mainly benzene ring tri-substituted, with primary coal of 32.71% and outburst coal of 31.6%. The primary coal contained more functional groups, from which hydrogen bonds can easily be formed, meaning that gas is not easily adsorbed by coal. The aromatic hydrogen rate (*fHa*) of the outburst coal was 0.271, the aromatic carbon rate (*ƒC*) was 0.986, the aromaticity *I*1 was 0.477, *I*2 was 0.373 and the length of the aliphatic branched chain (*ACH*2/*ACH*3) was 0.850. Compared with the primary coal, the aromatic hydrogen rate, aromatic carbon rate and the aromaticity of the outburst coal were higher, indicating that the hydrogen and carbon elements in the aromatic functional groups of outburst coal were higher and that the aliphatic functional group was higher than the aromatic structural functional group. *ACH*2/*ACH*3 and maturity (*Csd*) were slightly lower than those of primary coal, indicating that the coal has more straight chains than side chains, while aliphatic hydrocarbons are mostly short chains and have high branched degree. There were obvious 002 and 100 peaks in the XRD pattern. The *d*002 and *d*100 of outburst coal were 3.570 and 2.114, respectively, while the number of effective stacking aromatics was 3.089, which was lower than that of primary coal, indicating that the structure of the dense ring in the coal saw certain changes.

**Keywords:** outburst coal; primary coal; structural parameters; infrared spectrum; XRD


**Abstract**

This chapter draws attention on the different ways of colonisation, Islamisation and the decolonization of gender and sexuality amongst the transgender communities called Khawaja Sara and Hijra in contemporary Pakistan. The literature describes that during British colonialism the communities of Khawaja Sara and Hijra have been regulated and they were declared criminals with Criminal Tribal Act and Section-377, that produced rigorous repercussion on the living life of trans folks in colonial, postcolonial and contemporary periods. They are now and then were discriminated, oppressed, and marginalised, but this was not the case in precolonial periods where their lives were considered honourable, and they were given respectable positions in the Mughal Harems and other princely palaces. To investigate the contemporary marginalisation and then the survival practices of Khawaja Sara and Hijra as decolonial practice, this chapter engages with 10 members from Khawaja Sara and Hijra communities in a faceto-face direct interview and 04 photovoice interviews in Peshawar city. The findings highlight that Khawaja Sara and Hijra communities has the capacity to resist against the colonised and Islamised policies and to advocate for their rights and to get their voices heard across in their communities. This process is named as the decolonization of gender and sexuality in contemporary Pakistan.

**Keywords:** Khawaja Sara, Hijra, Guru, Cheela, Dera, Islamisation, Marakh, Murata


**7. Conclusion**

Vascular remodeling encompasses a series of complex biological pathways and involves the phenotype change of VSMCs, EC dysfunction, as well as macrophage activation. The alteration of VSMCs, ECs, and macrophage cellular functions is related to the various extracellular stimulus-dependent changes in transcriptional regulation, which is regulated by miRNAs. Thus, the identification of stimuli-dependent vascular remodeling which affects miRNA expression in different vascular cell types is imperative. The augmenting or inhibiting of the expression levels of specific miRNAs may provide opportunity for the development of miRNA-based therapeutic application to treating diverse vascular pathologies. In addition, extracellular circulating miRNAs have been reported to be altered under specific pathologic conditions, implicating their usage as biomarkers for specific diseases including cardiovascu‐ lar disease. Although there are unsolved issues of the efficiency and safety of using miRNAs in diagnosis and therapy, accumulating evidence indicate that continuous research on the functions and mechanisms of miRNAs and the identification of a network between miRNAs and their targets is highly recommended and the results will expand our understanding of vascular remodeling and diseases.


**4. Cloud based solutions**

The term "*cloud computing*"1 has become popular since October 2007 when Google and IBM jointly announced their collaboration (IBM website announcement, 2010 cited in Vouk, 2008) due to its main benefits such as reduced IT overhead and flexibility in offering cheaper user access. Fitzgerald and Dennis (2010) described cloud based design as a "*circuit-switched service architecture*" that is easier to implement for organisations because "*they move the burden of*

1 Cloud computing refers to a computing platform in which users have options to use lease connection points into a network for establishing a temporary operation between computers (Fitzgerald & Dennis, 2010). Hayes (2008) described cloud computing as a software application migration from local PCs "to distant Internet servers, users and developers alike go along for the ride" (p.9).

*network design and management inside the cloud*" (p. 297). As such, Cloud computing provision has been used as a modern architecture of shared computing services. These services are mainly elevated through computing utility rental by service providers on the Internet.

After the introduction of web-based utility services by Amazon.com, many service providers became increasingly interested in utilising the cloud computing platform for launching new services that met their client group demands, including minimising labour and implementation expenses (Santos, Gummadi & Rodrigues, 2009). It is therefore surprising that the use of cloud based services for the effective communication and decision making of multiple parties is still largely overlooked given the potential benefits. As such we provide a conceptual approach of cloud provision to improve communication in event risk management contexts. In theory our concept represents a convergence of communication and decision making through the use of cloud based services.


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**Meet the editors**

monitoring. During his activities he has developed skills in GIS, land surveying with GPS or Laser Scanners and data analysis by R programming. He is a member of NATRISK - Research Centre on Natural Risks in Mountain and Hilly Environments, in the same University. He acts as a freelance consultant, in the same topics, for other research bodies, training agencies and professionals, too. Outside his research and professional activities, he carries on his passion for mountain by practising hiking, snowshoeing and climbing. Additionally, he is a, martial arts and self-defence, instructor.

University. She is actively involved in outreach and soil awareness raising activities targeting kids and the large public, and in international training

activities focusing on mountain development and management.

Danilo Godone holds a PhD in "Agriculture, Forest and Food Sciences", doctorate's topic was cryosphere's phenomena monitoring by geomatic methodologies. Currently he is a PostDoc grant holder, at Turin University, studying geomatic contribution in land management and analysis. His main research interests are, however, landslide, glacier and, more generally, natural disasters

Silvia Stanchi holds a PhD in "Agriculture, Forest and Food Sciences", with a focus on fractal theory approaches for the study of soil aggregation and structure. Currently, she is a PostDoc at Turin University working on soil hazards and vulnerability in mountain areas. Silvia Stanchi is a member of NATRISK - Research Centre on Natural Risks in Mountain and Hilly Environments, in the same


3. Previous results revisited

The system-associated matrix (MP-matrix) is

�ð Þ Φ12 þ Φ13 þ Φ14 =V1 0 0 00

Hereafter, we will call MP-matrix to any ODE system-associated matrix related to a given MP,

In the previous example, the MP-matrix obviously depends on the numbers given to the different containers. In that example it was possible to enumerate the compartments such that the flux always goes from the ith compartment to the jth one, where . For instance, a

In general, if in a given MP it is possible to enumerate the containers such that the flux always goes from the ith compartment to the jth one, with , then the MP will be considered as a

Now, let us analyze a different problem, where a couple of tanks are linked by all possible connections between them, including recirculation from the second tank back to the first one, as in Figure 2. This problem represents an interesting variation of an MP analyzed by Zill [7] in his textbook, where the main difference is that this new MP has no incoming and/or outgoing

If in a given MP we have that PΦi ¼ 0, being Φi all the system incoming fluxes, and PΦk ¼ 0, being Φk all the system outgoing fluxes, then it will be named MP closed system (MP-CS).

Taking into account the abovementioned nomenclature, the example considered in Figure 2 corresponds to an MP-CS, while the MP analyzed in Zill's textbook [7] is an MP-OS, and both

possible enumeration for this purpose is the one illustrated in Figure 1.

mixing problem without recirculation (MP-WR).

Otherwise, it will be an open system (MP-OS).

Figure 2. Two tanks with recirculation and no incoming or outgoing fluxes.

Φ12=V2 �Φ25=V2 0 00 Φ13=V3 0 �Φ35=V3 0 0 Φ14=V4 0 0 �Φ45=V4 0

0 Φ25=V5 Φ35=V5 Φ45=V5 �Φ0=V5

1

CCCCCCCCCA

(6)

A ¼

like matrix A of Eq. (6).

flux, i.e., it is a closed system.

are systems with recirculation.

0

44 Matrix Theory-Applications and Theorems

BBBBBBBBB@

In order to give some general results, it is convenient to consider two different situations: MP without recirculation and MP with recirculation.

Considering again the example in Figure 1, it is possible to enumerate the compartments, such that the flux always goes from the ith container to the jth one, being i < j, shown in brackets.

Analyzing the system (Eq. (4)), it is easy to observe that for the jth container, the ODE right hand side is a linear combination of a subset of , and this result can be extended straightforward. In fact, in a previous book chapter [6], it was proved that if in a given MP the compartments can be enumerated such that there is no recirculation (i.e., if there is no flux from compartment to compartment ), then the ODE corresponding to the jth compartment will be of the form:

$$\mathcal{W}\_{i}\frac{dC\_{j}}{dt} \quad \alpha\_{i1}C\_{i1} + \alpha\_{i2}C\_{i2} + ... + \alpha\_{ik}C\_{ik} \tag{7}$$

being and

As a consequence, under the previous conditions, the corresponding ODE system has an associated upper matrix.

Revisiting the ODE system (Eq. (4)), corresponding to Figure 1, it can be rewritten as

$$\begin{cases} \frac{d\mathbf{C}\_1}{dt} = \frac{\Phi\_0}{V\_1}\mathbf{C}\_0 - \frac{(\Phi\_{12} + \Phi\_{13} + \Phi\_{14})}{V\_1}\mathbf{C}\_1\\ \frac{d\mathbf{C}\_2}{dt} = \frac{\Phi\_{12}}{V\_2}\mathbf{C}\_1 - \frac{\Phi\_{25}}{V\_2}\mathbf{C}\_2\\ \frac{d\mathbf{C}\_3}{dt} = \frac{\Phi\_{13}}{V\_3}\mathbf{C}\_1 - \frac{\Phi\_{35}}{V\_3}\mathbf{C}\_3\\ \frac{d\mathbf{C}\_4}{dt} = \frac{\Phi\_{14}}{V\_4}\mathbf{C}\_1 - \frac{\Phi\_{45}}{V\_4}\mathbf{C}\_4\\ \frac{d\mathbf{C}\_5}{dt} = \frac{\Phi\_{25}}{V\_5}\mathbf{C}\_2 + \frac{\Phi\_{35}}{V\_5}\mathbf{C}\_3 + \frac{\Phi\_{45}}{V\_5}\mathbf{C}\_4 - \frac{\Phi\_0}{V\_5}\mathbf{C}\_5 \end{cases} \tag{8}$$

It follows that for the jth compartment, the coefficient corresponding to can be written as

, where represents the sum of outgoing fluxes. This situation can be easily

generalized, since concentration only appears in the right hand side of the corresponding ODE when a certain flux is leaving the tank. Combining this result with the previous one about the upper matrix—it is easy to observe that the ODE system has only negative eigen-

$$\text{values of the form } \mathcal{A}\_j = \frac{-\sum\_{k} \Phi\_{jk}}{V\_j} < 0 \text{ for all } j = 1, 2, \dots, n$$

However, not all of these results can be extended to MPs with recirculation as will be analyzed in the following subsection.

In previous works [4, 5], a "black box" system was analyzed (see Figure 3), in order to obtain a necessary condition to be satisfied by any MP-matrix with any number of compartments and unknown internal geometry. In Figure 3 and represent flux and concentration at the input, and is also the output flux (since tanks neither fill up nor empty with time), and is the final concentration. In this system there are compartments inside the black box with volumes and concentrations , and recirculation fluxes may exist or not.

If all volumes remain constant, by performing a mass balance, it can be proved that.

$$\sum\_{i=1}^{n} V\_i \frac{dC\_i}{dt} = \Phi\_0 \left( C\_0 - C\_n \right) \tag{9}$$

dC1

8 >><

>>:

Operating with these equations, it can be proved that V1

by Eq. (9) is satisfied.

dition Eq. (9) since is zero.

It is easy to observe that

and A the MP-matrix.

dC2 dt ¼ Φ12 V2

A ¼

0

BB@

This equation can be written as VT A ¼ 0, being V the volumes' vector.

ð Þ V1 V2

matrix corresponding to Figure 1, the result will be

dt ¼ � Φ12 V1 C1 þ Φ21 V1 C2

> dC1 dt þ V2

dC2

Square Matrices Associated to Mixing Problems ODE Systems

http://dx.doi.org/10.5772/intechopen.74437

CCA ¼ ð Þ 0 0 (12)

dt ¼ 0, which satisfies con-

(10)

47

(11)

C1 � Φ21 V2 C2

The previous result can be generalized as follows: in a given MP—with or without recirculation—with input and output concentrations and , respectively, and being the incoming and outgoing flux, then, independently of the internal geometry, the condition given

An analogous condition may be used to know if a given matrix may or may not be an MP-matrix. For this purpose, let us consider the MP-matrix , associated to the ODE system given by Eq. (10):

> � Φ12 V1

0

BB@

� Φ12 V1

> Φ12 V2

Φ12 V2

Φ21 V1

1

CCA

VT A ¼ ð Þ 0000 �Φ0 (13)

VT A ¼ ð Þ 0 ⋯ 0 �Φ0 (14)

� Φ21 V2

1

Φ21 V1

� Φ21 V2

If there exists an incoming (and outgoing) flux , the last result will change. For instance, if we compute VT A, being V ¼ ð Þ V1 V2 V3 V4 V5 the volumes' vector and A the MP-

It can be noted that Eq. (12) and Eq. (13) are particular cases of the following result: in a given MP—with or without recirculation—with an incoming and outgoing flux , the condition VT A ¼ ð Þ 0 ⋯ 0 �Φ0 is satisfied, being V ¼ ð Þ V1 V2 ⋯ Vn the volumes' vector

Then, independently of the internal geometry of the system, the following condition is satisfied:

Then, Eq. (9) is obtained without any consideration of the internal geometry of the tank system and can be easily verified in the previous example (see Figure 1). In fact, by adding the equations of the ODE system (Eq. (4)), it follows straightforward that the condition given in Eq. (9) is satisfied. The same conclusion can be drawn from other possible examples, corresponding to open or closed MPs, with or without recirculation. For instance, in the case schematized in Figure 2, the ODE system can be written as follows:

Figure 3. A "black box" tank system.

Square Matrices Associated to Mixing Problems ODE Systems http://dx.doi.org/10.5772/intechopen.74437 47

$$\begin{cases} \frac{d\mathbb{C}\_1}{dt} = -\frac{\Phi\_{12}}{V\_1}\mathbb{C}\_1 + \frac{\Phi\_{21}}{V\_1}\mathbb{C}\_2\\ \frac{d\mathbb{C}\_2}{dt} = \frac{\Phi\_{12}}{V\_2}\mathbb{C}\_1 - \frac{\Phi\_{21}}{V\_2}\mathbb{C}\_2 \end{cases} \tag{10}$$

Operating with these equations, it can be proved that V1 dC1 dt þ V2 dC2 dt ¼ 0, which satisfies condition Eq. (9) since is zero.

The previous result can be generalized as follows: in a given MP—with or without recirculation—with input and output concentrations and , respectively, and being the incoming and outgoing flux, then, independently of the internal geometry, the condition given

$$\text{by Eq. (9)} \sum\_{i=1}^{n} V\_i \frac{dC\_i}{dt} = \Phi\_0 \left( C\_0 - C\_n \right) \text{is satisfied.}$$

An analogous condition may be used to know if a given matrix may or may not be an MP-matrix. For this purpose, let us consider the MP-matrix , associated to the ODE system given by Eq. (10):

$$\mathbf{A} = \begin{pmatrix} -\frac{\Phi\_{12}}{V\_1} & \frac{\Phi\_{21}}{V\_1} \\ \frac{\Phi\_{12}}{V\_2} & -\frac{\Phi\_{21}}{V\_2} \end{pmatrix} \tag{11}$$

It is easy to observe that

ð9Þ

It follows that for the jth compartment, the coefficient corresponding to can be written as

generalized, since concentration only appears in the right hand side of the corresponding ODE when a certain flux is leaving the tank. Combining this result with the previous one about the upper matrix—it is easy to observe that the ODE system has only negative eigen-

However, not all of these results can be extended to MPs with recirculation as will be analyzed

In previous works [4, 5], a "black box" system was analyzed (see Figure 3), in order to obtain a necessary condition to be satisfied by any MP-matrix with any number of compartments and unknown internal geometry. In Figure 3 and represent flux and concentration at the input, and is also the output flux (since tanks neither fill up nor empty with time), and is the final concentration. In this system there are compartments inside the black box with

volumes and concentrations , and recirculation fluxes may exist or not.

schematized in Figure 2, the ODE system can be written as follows:

If all volumes remain constant, by performing a mass balance, it can be proved that.

Then, Eq. (9) is obtained without any consideration of the internal geometry of the tank system and can be easily verified in the previous example (see Figure 1). In fact, by adding the equations of the ODE system (Eq. (4)), it follows straightforward that the condition given in Eq. (9) is satisfied. The same conclusion can be drawn from other possible examples, corresponding to open or closed MPs, with or without recirculation. For instance, in the case

values of the form , for all

in the following subsection.

46 Matrix Theory-Applications and Theorems

Figure 3. A "black box" tank system.

, where represents the sum of outgoing fluxes. This situation can be easily

$$
\begin{pmatrix}
(V\_1 \ V\_2) \begin{pmatrix} -\frac{\Phi\_{12}}{V\_1} & \frac{\Phi\_{21}}{V\_1} \\ \frac{\Phi\_{12}}{V\_2} & -\frac{\Phi\_{21}}{V\_2} \end{pmatrix} = \begin{pmatrix} 0 & 0 \end{pmatrix} \tag{12}
$$

This equation can be written as VT A ¼ 0, being V the volumes' vector.

If there exists an incoming (and outgoing) flux , the last result will change. For instance, if we compute VT A, being V ¼ ð Þ V1 V2 V3 V4 V5 the volumes' vector and A the MPmatrix corresponding to Figure 1, the result will be

$$\mathbf{V}^{\mathsf{T}}\mathbf{A} = \begin{pmatrix} 0 & 0 & 0 & 0 & -\boldsymbol{\Phi}\_{0} \end{pmatrix} \tag{13}$$

It can be noted that Eq. (12) and Eq. (13) are particular cases of the following result: in a given MP—with or without recirculation—with an incoming and outgoing flux , the condition VT A ¼ ð Þ 0 ⋯ 0 �Φ0 is satisfied, being V ¼ ð Þ V1 V2 ⋯ Vn the volumes' vector and A the MP-matrix.

Then, independently of the internal geometry of the system, the following condition is satisfied:

$$\mathbf{V}^{\mathsf{T}}\mathbf{A} = \begin{pmatrix} 0 & \cdots & 0 & -\Phi\_0 \end{pmatrix} \tag{14}$$

Now, let us consider again the MP-matrix , corresponding to the system of Figure 2:

$$\mathbf{A} = \begin{pmatrix} -\frac{\Phi\_{12}}{V\_1} & \frac{\Phi\_{21}}{V\_1} \\ \frac{\Phi\_{12}}{V\_2} & -\frac{\Phi\_{21}}{V\_2} \end{pmatrix} \tag{15}$$

If is slightly changed only in its first entry, we have the following matrix:

$$\mathbf{A}\_{\ell} = \begin{pmatrix} -\frac{\Phi\_{12}}{V\_1} + \varepsilon & \frac{\Phi\_{21}}{V\_1} \\ \frac{\Phi\_{12}}{V\_2} & -\frac{\Phi\_{21}}{V\_2} \end{pmatrix} \tag{16}$$

the system and it also has an outgoing flux Φ0 that leaves the tank system. It should be noted

Square Matrices Associated to Mixing Problems ODE Systems

http://dx.doi.org/10.5772/intechopen.74437

49

Another interesting example was proposed by Boelkins et al. [8]. The authors considered a three-tank system connected such that each tank contains an independent inflow that drops salt solution to it, each individual tank has a separated outflow, and each one is connected to the rest of them with inflow and outflow pipes. In this case, all tanks are input and output

It is important to mention that those types of tanks or compartments play different roles in the ODE-associated system and also—as a consequence—in the corresponding MP-matrix. In order to show this fact, let us examine a three-tank system with all the possible connections

As a first remark, Figure 5 system has recirculation—unless Φ21 ¼ Φ32 ¼ Φ31 ¼ 0, which represents a trivial case—and consequently, an associated upper MP-matrix will not be expected

In the mass balance for the first tank—which is an input one—a term Φ0C0 must be considered. In the same way, in the mass balance of the third tank—which is an output one—a term Φ0C3 will appear. These two terms will not be part of the second equation of the ODE system, which

ð17Þ

that in Figure 4, the second tank is an internal one.

Figure 4. A tank system with recirculation and with incoming and outgoing fluxes.

ones, and there is no internal tank.

among them, as in Figure 5.

can be formulated as follows:

for this problem.

It is easy to observe that this new matrix will not satisfy the condition given by Eq. (14). Moreover, there is no MP associated to this matrix , since this condition must be satisfied independently of the internal geometry of the system.

As a first consequence, not every square matrix is an MP-matrix. A second observation is that if a given MP-matrix is slightly changed, the result is not necessarily a new MP-matrix.

Furthermore, if volumes and fluxes are multiplied by a scale factor, then the MP-matrix Eq. (11) remains unchanged, and so, a scale factor in geometry, not in concentrations, produces exactly the same mathematical model.

After interpreting the previous results, we note that when working with MP-matrices, existence, uniqueness, and stability questions for the inverse-modeling problem have negative answers.

The same situation can be observed in many other inverse problems [2], and it is not an exclusive property of compartment analysis.


**4.10 Post-flood work**

Often when a flood has passed, leaving a lasting mark on people's lives and the environment, yet not as much attention is paid to post-flood work as it should be. The post-flood work involves rehabilitation, restoration, reconstruction, timely delivery of resources, and anxiety management.


**1. Introduction**

Multistage fracturing of horizontal wells is widely used in the exploration and development of shale gas. It typically takes tens of thousands of square meters of fracturing fluids and thousands of tons of sand to fracture a shale gas horizontal well, and the flowback of the fracturing fluids directly affects shale gas production. Hence, the flowback curve of fracturing fluids is a key issue in shale gas exploration [1]. The pores and fractures in shale gas reservoirs have different scales [2], and new multiscale pore-split systems are created by multistage fracturing. Thus, the shale gas flow mechanism is very complex, including pressure sensitivity, adsorption, diffusion, slip, imbibition, and seepage [3–6]. Currently, no consensus has been reached on this flow mechanism. Moreover, there is gas–water two-phase flow in the formation after large-scale fracturing. At present, there is no commercial software to realize the numerical simulation of flowback curve. It may take

**Citation:** Guo, W.; Zhang, X.; Kang, L.; Gao, J.; Liu, Y. Investigation of Flowback Behaviours in Hydraulically Fractured Shale Gas Well Based on Physical Driven Method. *Energies* **2022**, *15*, 325. https://doi.org/ 10.3390/en15010325

Academic Editor: Maxim Tyulenev

Received: 10 November 2021 Accepted: 23 December 2021 Published: 4 January 2022

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

**Copyright:** © 2022 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/).

several years to develop such software because, when developing such calculation programs, the solutions of the flow equations, unstructured meshing, equation discretization, and large-scale irregular sparse matrix are very complex. The gas flow equation for shale gas involves many flow mechanisms. The solution of this equations requires many known parameters which are difficult to obtain directly or measure experimentally. For example, shale gas is a multicomponent mixture containing hydrocarbons and nonhydrocarbon gases (CO2 and N2) [7], and its molecular free path at a high temperature and pressure cannot be obtained for unknown component proportions. Even if there is a perfect numerical simulation program, inaccurate parameters will affect the reliability of the results.

In recent years, with the development of big-data-related technology, researchers began to introduce machine learning into the research of oil and gas development and have mainly used it as a prediction tool. Kohli et al. [8] took well-log data as input parameters and trained the multilayer forward neural network by using the least square Levenberg–Marquardt optimization algorithm to predict the formation permeability; the predicted permeability is consistent with field data. Jia et al. [9] studied the water channel problem resulting from long-term water injection. A density peak clustering algorithm based on streamline clustering was used to quantify the flow area for water flooding in the oil reservoir and thereby effectively identify the invalid water injection circulation channels between the injection and production wells, as well as areas with development potential. Adibifard et al. [10] carried out a Chebyshev polynomial interpolation of pressure derivative data and input the results to an artificial neural network to estimate reservoir parameters. Ghaffarian et al. [11] processed the pseudo pressure of gas wells and used the pseudo pressure derivative data as the input of single and coupled multilayer perceptron network to identify the condensate gas reservoir model. Tian et al. [12] used recurrent neural network learning to train the data collected by permanent downhole pressure gauge (PDG) for the inversion of reservoir permeability and other parameters and production prediction. Hung et al. [13] introduced the application of Gaussian process regression (GPR), support vector machine (SVM), and random forest (RF) to predict CO2 trapping efficiency in saline formations.

As the fracturing fluids flowback is influenced by many factors, big data technology has attracted increasing attention. Bai et al. [14] used exponential and harmonic functions to fit the water production in the flowback stage and produced the water stages of 32 wells and developed a prediction tool for accumulated water production based on the fitting results. Zhou et al. [15] used various binary and multivariate methods to analyse the data from 187 wells in the Marcellus block in the USA. The flowback rate during the first three weeks of data collection was found to increase with the thermal maturity and decrease with increasing strata thickness. Lin et al. [16] used a back propagation neural network to model the static data and flowback rate for 74 wells in Sichuan Province, China. The flowback rate and gas production in the first month were estimated using six parameters with relatively high weights in the model. Liu et al. [17] developed two neural networks with different structures to predict the flowback rate at specific time points and compared the predictions. In summary, current big data-based methods used to determine the flowback pattern focused on static or dynamic data of many wells for a given block, and a combined analysis of static and dynamic data has not been conducted. Some studies have been performed by using a fixed data point or a periodic average of dynamic data, which is a static data methodology in essence. All these lead to incomplete data utilization and limited application scope of the method.

In order to simplify the time-dependent flowback curve into simple parameters, as the target parameters of big data analysis and flowback influencing factor analysis, this paper combined the flowback dynamic data and static data of shale gas fracturing horizontal wells to study the flowback curve. The approaches and processes used in this study are shown in Figure 1. The first part of this paper briefly introduces the geological background of the research area and the relevant data collected. In the second part, the multi-stage fracturing physical model of shale gas horizontal wells was established. The flow equation in Laplace

space was obtained from the convolution formula, and the time-dependent flowback rate was obtained. In the third part, the flowback data of 214 horizontal wells in the Weiyuan block were fitted to obtain the characteristic parameters. The calculation formula of characteristic coefficient including characteristic parameters was established. Then, the correlation analysis was carried out by using a flowback characteristic coefficient, and the influencing factors of the flowback characteristic coefficient were comprehensively studied. Through the method established in this paper, the shale gas flowback curve containing complex flow mechanism can be abstracted into simple characteristic parameters and characteristic coefficients, and the relationship between static data and dynamic data is established, which can help to establish a machine learning method for predicting the flowback curve of shale gas horizontal wells.

**Figure 1.** Schematic diagram of the approach used in the study 2. Research area background and analysis data.

Weiyuan shale gas block is located in the southwest of Sichuan Basin of China. The whole Weiyuan block has a monoclinic structure inclined to the southeast. The Longmaxi Formation (LF) is the main exploration target layer. The LF can be divided into two layers: L1 and L2. The first layer of L1 can be subdivided into two sublayers, namely, L11 and L12. The L11 sublayer can be further subdivided into four layers, namely, L111, L112, L113 and L114, from bottom to top. The middle and lower parts of L111 have the best reservoir quality.

Table 1 shows the data from the study area. A total of 20 different types of data were collected from 282 wells in Weiyuan shale gas block, including the fracturing lateral length, the number of fracturing stages, first-year average daily production rate, vertical depth, TOC, porosity, high-quality reservoir thickness, gas saturation, pressure coefficient, brittle mineral content, average fracturing stage interval, fracturing fluid intensity, proppant intensity, average hydraulic fracturing fluid displacement, drilling length in high-quality reservoir, EUR (Estimated Ultimate Recovery), 30 day flowback rate, 90 day flowback rate, 180 day flowback rate, 360 day flowback rate, and peak gas production flowback rate. The data volume ranges from 214 to 282. The minimum data volume is 214, and the corresponding data of these 214 wells is used in subsequent analysis. The 30 day flowback rate, 90 day flowback rate, 180 day flowback rate, 360 day flowback rate, peak gas production flowback rate, and first-year average daily production rate are taken from the daily production reports of the horizontal wells. The fracturing lateral length, number of fracturing stages, average fracturing stage interval, fracturing fluid intensity, proppant intensity, and average hydraulic fracturing fluid displacement are taken from the drilling and completion reports of horizontal wells. The vertical depth, TOC, porosity, high-quality reservoir thickness, gas saturation, pressure coefficient, brittle mineral content and drilling length in high-quality reservoirs are taken from well logging interpretation.

**Table 1.** Statistical tables of data for the study area. Copyright permission: The copyright of Table 1 belongs to the publisher and authors.

#### **2. Basic Theory**

The time-dependent daily flowback volume curve for the Weiyuan shale gas block in southern Sichuan Province, China, shows that the daily flowback volume is large during the early stages of continuous production and decreases to a stable value during the late stage of production. The daily flowback volume during early-stage production is two to three orders of magnitude higher than that during the later stage, and the relationship between daily flowback and time is generally exponential. The flowback of a fracturing fluid after large-scale fracturing is essentially the seepage of fluid from the stimulated reservoir volume (SRV) area to the wellbore. The corresponding law can also be obtained from the seepage equation of fracturing fluid.

#### *2.1. Bottomhole Flow Equation*

The formula derivation in this paper considers single-phase liquid seepage, assumes constant flowing bottom hole pressure (FBHP) and continuous production, and is based on the multi-stage fracturing seepage equation of horizontal well [18]. The following dimensionless parameters are defined:

Dimensionless pressure:

$$P\_D = \frac{2\pi k h [p\_i - p(r, t)]}{qB\mu} \tag{1}$$

Dimensionless time:

$$t\_D = \frac{kt}{\phi \mu \mathbf{C}\_t L^2} \tag{2}$$

Dimensionless distance:

$$\mathbf{x}\_D = \frac{\mathbf{x}}{L} \tag{3}$$

$$y\_D = \frac{y}{L} \tag{4}$$

where *K* denotes the permeability, m2; *φ* denotes the porosity; *μ* denotes the viscosity, Pa.s; *Ct* denotes the comprehensive compressibility coefficient, 1/Pa; *xfi* denotes the half-length oftheithfracture,m;and*L*= *n* ∑*xfi*denotes thesumoverthehalf-lengthsofnfractures,m.

*i*=1 For multistage fractured horizontal wells, the total flowback volume is the sum of the flowback volumes of all the individual fractures. The flowback volume can be related to the FBHP in Laplace space as follows:

$$\sum\_{j=1}^{n} \overline{q}\_{Dj} = \frac{1}{s} \tag{5}$$

$$\overline{\mathcal{P}}\_{\text{WDi}}(f(\mu)) = \sum\_{j=1}^{n} s \overline{\eta}\_{Dj} \overline{\mathcal{P}}\_{Di^j}(f(\mu)) \tag{6}$$

where:

$$\overline{P}\_{Dij}(f(u)) = \pi \int\_0^\infty P\_D(t\_D) e^{-f(u)t\_D} dt\_D \tag{7}$$

$$P\_{\rm D}(t\_{\rm D}) = \int\_{0}^{t\_{\rm D}} \mathbf{G}\_{\rm xD}(\tau\_{\rm D}) \mathbf{G}\_{\rm yD}(\tau\_{\rm D}) d\tau\_{\rm D} \tag{8}$$

The expressions for *GxD* and *GyD* vary with the external boundary conditions. For enclosed strata with rectangular boundaries, *GxD* and *GyD* are defined as follows [19]:

$$G\_{\rm xD}(\tau\_{\rm D}) = \frac{1}{\chi\_{\rm eD}} \left[ 1 + 2 \sum\_{n=1}^{\infty} \exp\left( \frac{-n^2 \pi^2 (\tau\_{\rm D})}{2 \chi\_{\rm eD}^2} \right) \cos \frac{n \pi \chi\_{\rm wD}}{\chi\_{\rm eD}} \cos \frac{n \pi \chi\_{\rm D}}{\chi\_{\rm eD}} \right] \tag{9}$$

$$\mathcal{G}\_{yD}(\tau\_{\rm D}) = \frac{2}{y\_{\rm eD}} \left[ 1 + \frac{2y\_{\rm eD}}{\pi} \sum\_{n=1}^{\infty} \frac{1}{n} \exp\left(\frac{-n^2 \pi^2 (\tau\_{\rm D})}{2y\_{\rm eD}^2}\right) \sin\frac{n\pi}{y\_{\rm eD}} \cos\frac{n\pi y\_{\rm wD}}{y\_{\rm eD}} \cos\frac{n\pi y\_{\rm D}}{y\_{\rm eD}} \right] \tag{10}$$

Equations (5) and (6) can be used to obtain the following linear equation:

$$\begin{bmatrix} f(u)\overline{\mathcal{P}}\_{D1,1}f(u)\overline{\mathcal{P}}\_{D1,2}f(s)\overline{\mathcal{P}}\_{D1,3}\cdots f(u)\overline{\mathcal{P}}\_{D1,n} \\ f(u)\overline{\mathcal{P}}\_{D2,1}f(u)\overline{\mathcal{P}}\_{D2,2}f(s)\overline{\mathcal{P}}\_{D2,3}\cdots f(u)\overline{\mathcal{P}}\_{D2,n} \\ \vdots \\ f(u)\overline{\mathcal{P}}\_{Dk,1}f(u)\overline{\mathcal{P}}\_{Dk,2}f(u)\overline{\mathcal{P}}\_{Dk,3}\cdots f(u)\overline{\mathcal{P}}\_{Dk,n} \\ \vdots \\ f(u)\overline{\mathcal{P}}\_{Dn,1}f(u)\overline{\mathcal{P}}\_{Dn,2}f(u)\overline{\mathcal{P}}\_{Dn,3}\cdots f(u)\overline{\mathcal{P}}\_{D,n} \\ \end{bmatrix} \begin{bmatrix} \overline{q}\_{1D} \\ \overline{q}\_{2D} \\ \vdots \\ \overline{q}\_{kD} \\ \overline{q}\_{nD} \\ \overline{\mathcal{P}}\_{\overline{\mathcal{P}}\_{\overline{\mathcal{P}}\_{\overline{\mathcal{P}}}}} \\ \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ \dots \\ 0 \\ \dots \\ 0 \\ 0 \\ 1 \end{bmatrix} \tag{11}$$

The solution of Equation (11) without considering the wellbore storage and the skin factor yields the FBHP as the dimensionless pressure *PWD*. The dimensionless pressure *PCWD* is obtained considering the skin factor and wellbore storage for multistage fracturing of horizontal wells in low permeability reservoirs as:

$$\overline{P}\_{\rm CWD} = \frac{f(u)\overline{P}\_{\rm WD}(f(u)) + S}{\mu \{1 + \mathcal{C}\_{\rm D} f(u) S \overline{P}\_{\rm WD}(f(u)) + S\}} \tag{12}$$

where *C* is the wellbore storage constant, Pa/m3; *CD* = *C* 2*πφCthL*2 denotes the dimensionless wellbore storage constant; *S* is the total skin factor of the fracture system; *u* is the Laplace transform variable; and *f*(*u*) is a function that characterizes the properties of the strata. For a homogeneous stratum, *f*(*u*) *= u*.

For production wells with a variable flowback volume, the dimensionless pressure can be expressed in the following convolution form:

$$P\_D(\mathbf{x}\_D, y\_D, z\_D, t\_D) = \int\_0^{t\_D} Q\_D(t\_D - \tau) \frac{\partial P\_{\rm u}(\mathbf{x}\_D, y\_D, z\_D, \tau)}{\partial \tau} d\tau \tag{13}$$

where *Pu*(*xD*, *yD*, *zD*, *t*) denotes the dimensionless pressure of multistage fractured horizontal wells per unit flowback volume; *QD*(*tD*) = *q*(*t*) *qI* denotes the dimensionless flowback volume; and *qI* represents the unit flowback volume.

Using the properties of Laplace transform for convolutions yields the relationship between the pressure and flowback volume in Laplace space:

$$
\overline{\mathcal{P}}\_{\mathcal{D}}(\mathbf{x}\_{\mathcal{D}}, y\_{\mathcal{D}}, z\_{\mathcal{D}}, u) = \overline{\mathcal{Q}}\_{\mathcal{D}}(u) u \overline{\mathcal{P}}\_{u}(\mathbf{x}\_{\mathcal{D}}, y\_{\mathcal{D}}, z\_{\mathcal{D}}, u) \tag{14}
$$

Equation (14) can be used to obtain the flowback volume in Laplace space:

$$\overline{Q}\_{D}(u) = \frac{\overline{P}\_{D}(x\_{D}, y\_{D}, z\_{D}, u)}{\overline{\mu}\_{\text{\textquotedblleft}}(x\_{D}, y\_{D}, z\_{D}, u)}\tag{15}$$

Equation (15) can also be expressed in terms of the FBHP as follows:

$$\overline{\mathcal{Q}}\_D(u) = \frac{\overline{P}\_{wfD}(u)}{\overline{\mu}\_{wfu}(u)}\tag{16}$$

where *Pwfu*(*u*) is the *PWD* obtained by solving Equation (11) for a unit flowback using *GxD* and *GyD*, which are both exponential functions of time. Therefore, the flowback can be simplified to *Ql*(*t*) = *αexp*(−*βt*). Thus, the time-dependent flowback curve is defined by two characteristic parameters, *α* and *β*. Figure 2 shows the flowback volume versus time for horizontal segments of a 1000-m horizontal well with 20 stages, an effective fracture half-length of 40 m, and an effective fracture permeability of 0.25 mD. Fitting the curve yields the following equation for the flowback volume:

$$q(t) = 10\theta.23 \exp(-0.007t) \tag{17}$$

where *t* denotes the flowback time, (d); and *q*(*t*) is the daily flowback volume, (m3/d).

**Figure 2.** Theoretical flowback curve for multistage fracturing of horizontal wells.

Equation (9) accurately describes the characteristics of the flowback curve of horizontal wells, which indicates that α and β can be effectively used to parametrize the dynamic flowback curves. In addition, the flowback pattern is consistent with field measurements (Figure 3). The field data in Figure 3 are from one of the 282 Wells in Table 1. The abscissa is production days, the ordinate is daily fracturing fluid flowback volume, and the blue dot represents the daily flowback volume of a specific day.

**Figure 3.** Field flowback curve for multistage fracturing of horizontal wells.


2.2.1. Blue Light Effects on Shoot Proliferation

The effects of BL are often reported to be antagonistic of RL ones, although the studies reported in literature concerning the role played by BL on new meristem formation are not always consistent. The positive effects of BL on the stimulation of shoot production and growth of *Nicotiana tabacum* during in vitro culture were reported, but at a higher light intensity [67], and the authors hypothesized photoinactivation of IAA. Five weeks of exposure to BL induced the highest shoot production from *Nicotiana tabacum* callus [159].

Monochromatic BL increased shoot number in *Ficus benjamina* [94], the number of shoots and nodes in *Vitis vinifera* L. *hybrid* [68,70], the number of adventitious buds in *Hyacinthus orientalis* L. [160] and the percentage of organogenesis and the mean number of buds per explant in *Curculigo orchioides* [103]. Higher percentages of BL in the light spectrum were also effective on in vitro shoot induction and proliferation of *Anthurium andreanum* [49], *Gerbera jamesonii* 'Rosalin' [107], *Remnania glutinosa* [65] and *Saintpaulia ionantha* [69]. In various species, positive results on proliferation from adding different ratios of B to the R spectrum have been described and will be widely discussed in sub-paragraph 2.3.1. The proliferation rate was greater in *Brassica napus* plantlets when cultured under monocromatic BL and BL plus RL [51]. In lavandin, on a BA-free medium, shoot number was enhanced under BL, WL and RL at low photon fluence rates [72]. In *Oryza sativa* [121] under B-LED illumination, the time required for callus proliferation, differentiation and regeneration was the shortest and the frequency of plantlet initiation, differentiation and regeneration was the highest. Concerning orchids, in *Dendrobium officinale*, the monochromatic BL and RL:BL (1:2) emitted by LEDs determined a higher percentage of protocorm-like bodies (PLBs) producing a higher number (1.5 fold) of shoots [92], in *Cattleya intermedia* × *C. aurantiaca* the number of shoots regenerated from PLBs was enhanced by BL [161]. In *Oncidium*, RL promoted PLB induction from shoot apex and the higher content of carbohydrate but the lowest differentiation rate, while the highest differentiation rate and protein content were observed under B-LED [87]. BL increased node and total shoot number as compared to RL, FRL and dark in *Prunus avium* cv 'Hedelfinger' and one of its somaclones [127]. In contrast, on *Begonia erythrophylla* petiole explants, RL played a role in meristem initiation and BL and FRL were antagonistic to meristem formation, but BL was important for primordia development [79]. In *Gerbera jamesonii* [118], inhibition of shoot multiplication and a reduced plant height was observed under BL compared to what resulted from all other light treatments, and a decrease of lateral shoots number was observed on *Malus domestica* [135] as compared to RL. The same study demonstrated that BL inhibited the rate of proliferation, increasing the apical dominance. Inhibition of meristematic tissue proliferation by BL has also been observed for the embryogenic tissue of Norway spruce [162]. The conflicting reports found in the literature might not only be attributed to species effects, but also to the different types of explants and to the stage of the organogenic process. Hunter and Burritt [81], working on different *Lactuca sativa* L. genotypes, observed a significant decrease under monochromatic BL in shoot proliferation as compared to RL or WL. They argued that RL is required for the formation of shoot primordia, whereas BL is inhibitory to primordia initiation. The effects of RL and BL on this species depended on the stage of the organogenic process in which *Lactuca sativa* plantlets were exposed to the different lights. Exposure to BL during the critical first few days of culture, when meristems are being initiated, results in a significant reduction in the number of shoots produced as compared to exposure to RL and WL. Furthermore, this suppression of meristem initiation is permanent and not reversible afterward by culturing plants under RL. Observations with a scanning electron microscope (SEM) clarified that the lowest shoot development under BL was attributable to the production of much more callus as compared to those cultured under WL or RL, demonstrating that rapid cell division occurred, although the organized center of cell division required for primordia formation was reduced.  Based on the literature, they stated that the stimulatory effects of RL as compared to WL is genotype dependent, but the inhibitory effect of BL is more widely diffused. Callus formation as affected by continuous BL illumination was observed also in *Pyrus communis*, where callus weight doubled as compared to BL plus RL and BL plus FRL [59]. In *Ficus benjamina*, BL induced a huge formation of callus at the basal section of shoots [94]. Other studies have shown that the timing of exposure to different light regimes is also critical for shoot development *in vitro*. For example, at least 2 wks under RL were required to improve shoot numbers from *Pseudotsuga menziesii* callus, and the length of time in which

RL promoted shoot production lasted only 2–3 wks [122]. It was suggested that PHY plays an inductive role in organogenesis of *Lactuca sativa* L., as suggested by Kadkade and Seibert [137], in contrast to antagonistic role of BL, probably via CRYs.

In a series of research projects carried out with different rootstocks of *Malus domestica*, *Prunus domestica* and *Prunus persica*, M9, MM106, Mr.S.2/5, and GF677, respectively [125,128,142,163], it was demonstrated that BL induced, in the starting explant and in the developed shoots, a greater number of nodes with shorter internodes than those observed in RL and in dark. It should be noted that the percentage of nodes that formed lateral shoots was higher in the presence of RL as compared to the BL one. In the *Malus domestica* M9 rootstock, the percentage of sprouted buds under RL was double that under BL [135].

Based on these results, shoot multiplication can be defined as the result of two events: the induction and formation of new buds from the apical meristem and their sprouting through the reduction or the suppression of apical dominance [2,36]. BL would increase the number of axillary buds but, in contrast, it exerts an inhibitory action on buds sprouting (increase in apical dominance). RL, on the other hand, would reduce the apical dominance even though it reduces the formation of new axillary buds. The lower outgrowth of buds in the presence of BL compared to RL would indicate a role in a specific photoreceptor(s) of BL, which would act as an antagonist of the PHY. Photomorphogenetic events detected in the presence of RL and BL would agree with an antagonistic model of stem branching, modulated by light through the PHYs and the photoreceptors of BL, which would interact with each other according to a dynamic model. Moreover, Muleo et al. [142] also showed that the internode extension inhibition under BL exposure and the concomitant positive effect of BL in enhancing axillary bud formation (neoformed nodes) was dependent on the photon fluence rate, but not on PHY photoequilibrium or on concomitant exposure to RL. A quantitative BL threshold was found near 30 µmol m−2 s −1 (400–500 nm); up to this value, internode extension decreased [142].

Plants, thus, possess a complex and dynamic light response and memory system that involves reactive oxygen species and hormonal signaling, which are used to optimize light acclimation and immune defenses [164]. Thus, regulating the spectral quality, particularly by the B-LED, improves the antioxidant defense line and is directly correlated with the enhancement of phytochemicals in *Rehmannia glutinosa* [65]. Mengxi et al. [90] found higher values of superoxide dismutase (SOD), peroxidase (POD) and catalase (CAT) activities in leaves under B-spectrum irradiance and concluded that B-LED may be more satisfactory for activating different defensive systems to reduce excessive amounts of reactive oxygen species. However, in two important *Dianthus caryophyllus* cultivars, 'Green Beauty' and 'Purple Beauty', RL treatment also increased the activities of antioxidant enzymes and nutrient contents [165]. The B-LED illumination also significantly increased the antioxidant enzyme activities in leaves and roots in *Amaranthus tricolor* and *Brassica rapa* L. subsp. *oleifera* [166]. In the in vitro cultured *Pyrus communis* plantlets, it was detected that the gene encoding the pathogenesis-related protein PR10 is regulated daily by the body clock of a plant, while *PR1* was expressed without clear evidence of circadian regulation [167]. In the same studies, a specific function was played by PHYB and CRY1 photoreceptors, considering that in transgenic plants the first photoreceptor enhanced the gene expression of *PR1* 5- to 15-fold, and CRY1 enhanced plant resistance to the *Erwinia amylovora* bacterial infection [167]. *Prunus avium* rootstock plantlets, overexpressing the PHYA gene and grown in vitro, displayed a strong resistance to bacterial canker (*Pseudomonas syringae* pv. morsprunorum), highlighting a role of light quality and quantity in the regulation of plant resistance to bacterial disease [168]. Therefore, light quality through the regulative network of photoreceptors plays a relevant role in the endogenous rhythms of gene expression and pathogen attacks.