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Journal of Hydrodynamics 2012年第3期24卷 332-338页

作者： LI Wei LI Xiao-ping LI Shun-chu LI Quan-yong State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum UniversityChengdu 610500 China Institute of Applied Mathematics Xihua University Chengdu 610039 China

When the classical nonlinear partial differential equations are used to model the fractal reservoir, based on the assumption of low compressibility fluids, the effects of the quadratic gradient term are ignored, which would be questionable for mixed gas reservoirs and low permeability reservoirs. To consider the influence of the wellbore storage, the nonlinear mathematical flow model of the fractal multilayer reservoir is built in this paper, with three kinds of outer boundaries （infinite boundaries, constant pressure boundaries and closed boundaries）. Using the Laplace transform method, the solutions for the dimensionless reservoir pressure and the bottom hole pressure in the Laplace space are obtained. An analysis shows that the solutions involve similar structures even for three different kinds of outer boundaries, and can be unified as a continuous fraction. The unified expression would make it more convenient to analyze the formation parameters, which greatly facilitates the development of the well test analysis software.

关键词： fractal multilayer reservoir quadratic gradient wellbore storage similar structure

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Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

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Chinese Physics B 2016年第2期25卷 262-270页

作者：刘文超刘曰武牛丛丛韩国锋万义钊 Institute of Mechanics Chinese Academy of Sciences

The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.

关键词： threshold pressure gradient stress-sensitive effect wellbore storage skin effect

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Non-Darcian Flow Toward a Finite-Diameter Vertical Well in a Confined Aquifer

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Pedosphere 2008年第3期18卷 288-303页

作者： WEN Zhang HUANG Guan-Hua ZHAN Hong-Bin College o.f Water Conservancy and Civil Engineering China Agricultural University Beijing 100083 （China） Chinese-Israeli International Center for Research and Training in Agriculture Beijing 100083 （China） Department of Geology and Geophysics Texas A＆M University College Station Texas 77843-3115 （USA）

Non-Darcian radial flow toward a finite-diameter, fully penetrating well in a confined aquifer was analyzed on the basis of the Izbash equation with consideration of the wellbore storage effect. We derived semi-analytical solutions of drawdown by using the Boltzmann transform, and obtained approximate analytical solutions of the drawdown at early and late times. MATLAB programs were developed to facilitate computation of the semi-analytical solutions. The turbulence factor v which was directly related to the pumping rate appeared to have negligible influence upon the wellbore well function at early times, but imposed significant influence at intermediate and late times. However, the turbulence factor v imposed non-negligible influence upon the aquifer well function during the entire pumping period, provided that the observation point was not sufficiently close to the wellbore. Sensitivity analysis indicated that the power index n in the Izbash equation had less influence on the type curves at the face of the pumping wellbore, but had much greater influence upon the well function in the aquifer. As the n values increased, the drawdown in the aquifer decreased at early times and increased at late times. The Boltzmann transformation could only be used in an approximate sense for radial non-Darcian flow problems. This approximation would provide accurate solutions at early times, and introduce small but consistent discrepancies at intermediate and late times for the wellbore well function.

关键词： finite-diameter well non-Darcian flow' type curves well function wellbore storage

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Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

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Journal of Groundwater Science and Engineering 2022年第4期10卷 311-321页

作者： Yi-jie Zong Li-hua Chen Jian-jun Liu Yue-hui Liu Yong-xin Xu Fu-wan Gan Liang Xiao College of Civil Engineering and Architecture Guangxi UniversityNanning 530004China Guangxi Key Laboratory of Disaster Prevention and Engineering Safety Guangxi UniversityNanning 530004China Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education Guangxi UniversityNanning 530004China Department of Earth Sciences University of the Western CapeCape Town 8000South Africa

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge *** mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s *** solutions are derived by Boltzmann and dimensionless ***,the non-Darcian effect and wellbore storage are especially investigated according to the proposed *** results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of *** higher the degree of non-Darcian,the smaller the drawdown.

关键词： Non-Darcian effect Bounded aquifer wellbore storage Izbash’s equation Analytical solution

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