Exact solution of Poisson’s equation with an elliptical boundary

Liemert, André; Kienle, Alwin

doi:10.1016/j.amc.2014.04.003

Cited by 4 publications

(2 citation statements)

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“…Introducing the Joukowski function , defines the transform as follows where z = x + i y and w = u + i v = M e iθ , and based on Euler formula, we can get …”

Section: Mathematical Model Of Multiregion Coupling Flowmentioning

confidence: 99%

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Study on Pressure Propagation in Tight Oil Reservoirs with Stimulated Reservoir Volume Development

Zhu

Liu

Li³

et al. 2021

ACS Omega

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The stimulated reservoir volume fracturing development in tight oil reservoirs is characterized by multiscale flow of the reservoir matrix, fracture network, and hydraulic fracture. Therefore, the flow field structure is extremely complex. Multiscale flow characteristics have been revealed through the systematical experiments including the threshold pressure gradient and the stress sensitivity. Based on the theory of elliptical flow, a comprehensive and practical mathematical model of multiregion coupling flow is established to characterize the multiscale flow, and the pressure distribution equation is derived. The calculation method of moving boundary is established to simulate the dynamic supply boundary and the dynamic pressure distribution by using the steady-state sequential replacement method. The characteristics of multiscale flow, multistage development state, and stress sensitivity are considered, especially the different stress sensitivity characteristics in different regions. Finally, the pressure propagation in tight reservoirs is clarified and the influence of matrix permeability, stress sensitivity characteristics, and drawdown pressure on the distance at the dynamic supply boundary are revealed. The research results provide theoretical basis for the development effect evaluation.

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“…Introducing the Joukowski function , defines the transform as follows where z = x + i y and w = u + i v = M e iθ , and based on Euler formula, we can get …”

Section: Mathematical Model Of Multiregion Coupling Flowmentioning

confidence: 99%

“…43,44 An analytic function is introduced which transforms from the elliptic domain to circular domain (Figure 5), and the original problem is solved by using the inverse transformation. Introducing the Joukowski function 45,46 defines the transform as follows…”

Section: Mathematical Model Of Multiregionmentioning

confidence: 99%