Fuzzy structural element method for solving fuzzy dual medium seepage model in reservoir
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METHODOLOGIES AND APPLICATION
Fuzzy structural element method for solving fuzzy dual medium seepage model in reservoir Duo Zhang1 · Lan Shu1 · Shunchu Li2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study primarily introduces fuzzy set theory in the reservoirs modeling to enhance the accuracy of the model. The conventional seepage models of dual medium in reservoirs have several limitations. To be specific, it considers the complexity of the model during the modeling process and idealizes certain reservoir parameters to be constant. By adopting fuzzy set theory to study reservoir seepage theory, on the one hand, the seepage model is capable of fully considering the complex and variability of the reservoir; on the other hand, it can avoid parameter errors attributed to laboratory measurements. A numerical example is given in this study to illustrate the accuracy and superiority of the fuzzy seepage model. Studies suggest that fuzzy set theory is capable of effectively addressing the limitations in conventional seepage models. Keywords Partial differential equations · Oil and gas reservoir · Fuzzy permeability · Fuzzy differential equation · Fuzzy double medium model · Fuzzy structural element
1 Introduction Insights should be gained into the seepage situation of the reservoir to exploit the reservoir efficiently in a large scale. In recent years, numerous studies on the seepage theory of oil and gas reservoirs have emerged (Deng et al. 2014; Zeng et al. 2013; Civan et al. 2011; Lian et al. 2013; Zhang et al. 2012; Daniel and Bustin 2007; Craig et al. 2009). Li et al. (2017) established the seepage model of a triple media shale gas reservoir and taken the adsorption and desorption process into account. This had a profound influence on the development of well testing analysis software. Li et al. (2017) and Zhang et al. (2017) established a comprehensive mathematical model by pseudo-quadruple porosity medium conception, coupling the effects of slippage flow, Knudsen diffusion, surface diffusion, adsorption/desorption and gas transferring from kerogen to nanopore system, while fluid flow in fracCommunicated by V. Loia.
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Duo Zhang [email protected]
1
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, People’s Republic of China
2
School of Science of Xihua University, Chengdu 610039, Sichuan, People’s Republic of China
tures/macropores is described by Darcy’s law. The study can not only help us understand fluid flow mechanisms in nanopores from microscopic perspective, but also enable us to analyze production performance and determine key operational parameters from macroscopic perspective. However, the idealized assumptions made by the conventional models have led to a significant reduction in the accuracy of some models. For example, irregular fracture media space is regarded as a homogeneous porous medium space, and even in ample space, the permeability of the medium is regarded as constant (Afanasyev 2
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