This paper focuses on establishing the trilinear fuzzy seepage model with multiple fuzzy parameters for shale gas reservoirs. Different from the conventional seepage models of shale gas reservoirs, the multiple fuzzy parameters seepage model uses fuzzy numbers to describe some parameters with uncertainty. Firstly, the multiple fuzzy parameters seepage model is constructed based on fuzzy concepts. The fuzzy structure element method and the centroid method are used to solve the fuzzy seepage model and defuzzifier, respectively. Secondly, the advantages of the development fuzzy model over the conventional seepage model are discussed and illustrated through numerical examples and simulations. Finally, to further study the seepage laws inside shale gas reservoirs, this paper explores the sensitivity of relevant main control parameters to gas production based on the development model.
RogersJ.H., Natural gas from shale formation – The evolution, evidences and challenges of shale gas revolution in United States, Renewable and Sustainable Energy Reviews, 2014.
RossD.J.K. and BustinR.M., The importance of shale composition and pore structure upon gas storage potential of shale gas reservoirs, Marine and Petroleum Geology26(6) (2009), 916–927.
4.
VengoshA., JacksonR.B., WarnerN., et al., A critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the United States, Environmental Science and Technology48(15) (2014), 8334–8348.
5.
JacksonR.B., VengoshA., DarrahT.H., et al., Increased Stray Gas Abundance in a Subset of Drinking Water Wells near Marcellus Shale Gas Extraction, Proceedings of the National Academy of Sciences110(28) (2013).
6.
BarenblattG.I., MonteiroP.J.M. and RycroftC.H., On a boundary layer problem related to the gas flow in shales, Journal of Engineering Mathematics84(1) (2014), 11–18.
7.
LeeS.T. and BrockenbroughJ.R., A New Approximate Analytic Solution for Finite-Conductivity Vertical Fractures, SPE Formation Evaluation1(01) (1986), 75–88.
8.
OzkanE., BrownM.L., RaghavanR., et al., Comparison of Fractured-Horizontal-Well Performance in Tight Sand and Shale Reservoirs, SPE Reservoir Evaluation and Engineering14(02) (2011), 248–259.
9.
ZhaoY.L., ZhangL.H., ZhaoJ.Z., et al., “Triple porosity” modeling of transient well test and rate decline analysis for multi-fractured horizontal well in shale gas reservoirs, Journal of Petroleum Science and Engineering110 (2013), 253–262.
10.
QiuD., LuC., ZhangW., et al., Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mare? equivalence relation, Fuzzy Sets and Systems245 (2014), 63–82.
11.
Avner, Vengosh, Robert, et al.,
A Critical Review of the Risks to Water Resources from Unconventional Shale Gas Development and Hydraulic Fracturing in the United States, Environmental Science and Technology: ES and T48(15) (2014), 8334–8348.
12.
BedeB. and GalS.G., Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems151(3) (2005), 581–599.
13.
HaiS., GongZ. and LiH., Generalized differentiability for n-dimensional fuzzy-number-valued functions and fuzzy optimization, Information Sciences2016, 374.
14.
AllahviranlooT. and ChehlabiM., Solving fuzzy differential equations based on the length function properties, Soft Computing19(2) (2015), 307–320.
15.
SongS. and WuC., Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems110(1) (2000), 55–67.
16.
BedeB. and StefaniniL., Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems230(Complete) (2013), 119–141.
17.
ChehlabiM. and AllahviranlooT., Positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability, Applied Soft Computing70 (2018), 359–370.
18.
WuC., SongS. and LeeE.S., Approximate Solutions, Existence, and Uniqueness of the Cauchy Problem of Fuzzy Differential Equations, Journal of Mathematical Analysis and Applications202(2) (1996), 629–644.
19.
VorobievD. and SeikkalaS., Towards the theory of fuzzy differential equations, Fuzzy Sets and Systems125(2) (2002), 231–237.
20.
Chalco-CanoY. and Román-FloresH., Comparation between some approaches to solve fuzzy differential equations, Fuzzy Sets and Systems160(11) (2009), 1517–1527.
21.
LozanoC. and WangP.P., Fuzzy Set Theory Applied to Accounting Sciences, New Mathematics and Natural Computation (NMNC), 2020, 16.
22.
AryaV. and KumarS., A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKOR– TODIM approach, Computational and Applied Mathematics39(3) (2020), 1–24.
23.
Yan, Zhijia, Yang, et al.,
A Reputation-Enhanced Hybrid Approach for Supplier Selection with Intuitionistic Fuzzy Evaluation Information, Mathematics, 2019.
24.
ZhangD., ShuL. and LiS., Fuzzy structural element method for solving fuzzy dual medium seepage model in reservoir, Soft Computing2020(3).
25.
ZhangD., YuZ., ShuL., et al., Fuzzy Structural Element Method for Solving Nonlinear Fuzzy Seepage Model of Shale Gas Reservoir, 2019 IEEE 14th International Conference on Intelligent Systems and Knowledge Engineering (ISKE), IEEE, 2019.
26.
YiF., LiangB. and GuoY.H., The Fuzzy Seepage Theory Based on Fuzzy Structuring Element Method, International Conference on Fuzzy Information and Engineering, Liaoning Technical University, 123000, Fu-xin, Liao-ning, China, 2007.
27.
NOVAKOVI, Aleksandar, RANKOVI, et al.,
DEVELOPMENT OF NEURO-FUZZY MODEL FOR DAM SEEPAGE ANALYSIS, Annals of the Faculty of Engineering – Hunedoara International Journal of Engineering12(2) (2014), 133–136.
28.
ChongshiG.U., ZhangZ., CaiX., et al., Application of entropy-based fuzzy matter-element analysis in seepage monitoring of RCC dam, Frontiers of Architecture and Civil Engineering in China5(001) (2011), 105–111.
29.
LiL.G. and PengD.H., Interval-Valued Hesitant Fuzzy Hamacher Synergetic Weighted Aggregation Operators and Their Application to Shale Gas Areas Selection, Mathematical Problems in Engineering2014 (2014), 1–25.
30.
ZhangD., QiuD. and ShuL., Fuzzy Structure Element Method for Solving Fuzzy Trilinear Seepage Model of Shale Gas Reservoir, International Journal of Fuzzy Systems21(5) (2019), 1597–1612.
31.
XieW., LiX., ZhangL., et al., Two-phase pressure transient analysis for multi-stage fractured horizontal well in shale gas reservoirs, Journal of Natural Gas Science and Engineering21 (2014), 691–699.
32.
ChenP., JiangS., ChenY., et al., Pressure response and production performance of volumetric fracturing horizontal well in shale gas reservoir based on boundary element method, Engineering Analysis with Boundary Elements87(feb.) (2018), 66–77.
33.
Wei-YangX., Xiao-PingL., Lie-HuiZ., et al., Production Decline Analysis for Two-Phase Flow in Multifractured Horizontal Well in Shale Gas Reservoirs, Journal of Chemistry 2015, (2015-9-27), 2015 (2015), 1–10.
34.
TavassoliS., YuW., JavadpourF., et al., Well Screen and Optimal Time of Refracturing: A Barnett Shale Well, Journal of Petroleum Engineering 2013, (2013-4-18), 2013 (2013), 1–10.
35.
OlmsteadS.M., MuehlenbachsL.A., ShihJ.S., et al., Shale gas development impacts on surface water quality in Pennsylvania, Proceedings of the National Academy of Sciences of the United States of America110(13) (2013), 4962–4967.
36.
SangY., ChenH., YangS., et al., A new mathematical model considering adsorption and desorption process for productivity prediction of volume fractured horizontal wells in shale gas reservoirs, Journal of Natural Gas Science and Engineering19 (2014), 228–236.
