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Development, analysis and numerical methods for multicomponent, multiphase flow in porous media.

機(jī)譯：多孔介質(zhì)中多組分多相流的開發(fā)，分析和數(shù)值方法。

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In my scientific research I have concentrated on numerical methods for partial differential equations and their applications to multiphase, multicomponent flows in porous media. A fractured porous medium has throughout its extent a system of interconnected fractures dividing the medium into a series of essentially disjointed blocks of porous rock, called matrix blocks. It has two main length of scales of interest: the microscopic scale of the fracture thickness about (10-4 m) and the macroscopic scale of the average distance between fracture planes, i.e., the size of the matrix blocks(about 0.1-1 m). Since the entire porous medium is about (10 3-104m) across, flow can be mathematically simulated only in some averaged sense. The concept of dual porosity (and dual porosity/permeability) has been utilized to model the flow of fluids on its various scales. In this concept, the fracture system is treated as a porous structure distinct from the usual porous structure of the matrix itself. The fracture system is highly permeable, but can store very little fluid, while the matrix has the opposite characteristics. When developing a dual-porosity model, it is critical to treat the flow transfer terms between the fracture and matrix systems.;In the first part of this thesis we have worked on multiphase, multicomponent flow with mass interchange between phases in porous media. The governing equations of a compositional model for three-phase multicomponent fluid flow in multi-dimensional petroleum reservoirs have been cast in terms of a pressure equation and a set of component mass balance equations in this project. The procedure is based on a pore volume constraint for component partial molar volumes, which is different from earlier techniques utilizing an equation of state for phase fluid volumes or saturations. The present technique simplifies the pressure equation, which is written in terms of various pressures such as phase, weighted fluid, global, and pseudo-global pressures. The different formulations resulting from these pressures have been numerically solved; the numerical computations use a scheme based on the mixed finite element method for the pressure equation and the finite volume method for the component mass balance equations. A qualitative analysis of these formulations have been also carried out. The analysis shows that the differential system of these formulations is of mixed parabolic-hyperbolic type, typical for fluid flow equations in petroleum reservoirs. Numerical experiments based on the benchmark problem of the third comparative solution project organized by the society of petroleum engineers(SPE)have been presented.;In the second part we have derived well flow models for various numerical methods used in the discretization of fluid flows and transport in porous media. Numerical simulation of fluid flow and transport processes in the subsurface must account for the presence of wells. The pressure at a grid block that contains a well is different from the average pressure in that block and different from the flowing bottom hole pressure for the well. Various finite difference well models had been developed to account for the difference. This part has been concerned with a systematical derivation of well models for other numerical methods such as standard finite element, control volume finite element, and mixed finite element methods. Numerical results for a simple well example illustrating local grid refinement effects and the seventh comparative solution project organized by the society of petroleum engineers(SPE) have been given to validate these well models. The well models have particular applications to groundwater hydrology and petroleum reservoirs.;Therefore, my dissertation will include the derivation of flow models, their qualitative analysis, the development of numerical methods, and their analysis. Future research will involve the development of computational codes and their parallel versions, and extensions of the mathematical modeling, numerical methods, scientific computing, computer simulation, and the supporting mathematical analysis from ordinary porous media to fractured porous media.
機(jī)譯：在我的科學(xué)研究中，我專注于偏微分方程的數(shù)值方法及其在多孔介質(zhì)中多相，多組分流動(dòng)中的應(yīng)用。破裂的多孔介質(zhì)在其整個(gè)范圍內(nèi)具有相互連接的裂縫系統(tǒng)，將這些介質(zhì)分為一系列基本分離的多孔巖石塊，稱為基質(zhì)塊。它具有兩個(gè)主要的感興趣尺度長度：裂縫厚度的微觀尺度（約10-4 m）和裂縫平面之間平均距離的宏觀尺度，即基質(zhì)塊的大?。s0.1-1 m）。 ）。由于整個(gè)多孔介質(zhì)的寬度約為（10 3-104m），因此只能在某種平均意義上對(duì)流量進(jìn)行數(shù)學(xué)模擬。雙重孔隙率（和雙重孔隙率/滲透率）的概念已被用來模擬各種規(guī)模的流體流動(dòng)。在這個(gè)概念中，將斷裂系統(tǒng)視為不同于基質(zhì)本身通常的多孔結(jié)構(gòu)的多孔結(jié)構(gòu)。裂縫系統(tǒng)具有高滲透性，但只能儲(chǔ)存很少的流體，而基質(zhì)具有相反的特征。開發(fā)雙孔隙度模型時(shí)，處理裂縫和基質(zhì)系統(tǒng)之間的流動(dòng)傳遞條件至關(guān)重要。在本論文的第一部分中，我們研究了多孔介質(zhì)中各相之間質(zhì)量交換的多相，多組分流。在該項(xiàng)目中，根據(jù)壓力方程和一組組分質(zhì)量平衡方程，建立了多維多相油藏中三相多組分流體組成模型的控制方程。該程序基于對(duì)組分部分摩爾體積的孔體積約束，這與早期的技術(shù)相比，后者采用了狀態(tài)流體相或體積飽和度的狀態(tài)方程。本技術(shù)簡化了壓力方程式，該方程式是根據(jù)各種壓力（例如相壓力，流體加權(quán)壓力，全局壓力和擬全局壓力）編寫的。由這些壓力產(chǎn)生的不同公式已得到數(shù)值解決；數(shù)值計(jì)算使用基于混合有限元法的壓力方程式和基于有限體積法的成分質(zhì)量平衡方程式的方案。還對(duì)這些制劑進(jìn)行了定性分析。分析表明，這些配方的微分系統(tǒng)是混合拋物線-雙曲線型的，通常用于石油儲(chǔ)層的流體流動(dòng)方程?；谑凸こ處焻f(xié)會(huì)（SPE）組織的第三個(gè)比較解決方案項(xiàng)目的基準(zhǔn)問題，進(jìn)行了數(shù)值試驗(yàn)。第二部分，我們導(dǎo)出了用于流體離散化的各種數(shù)值方法的井流模型。在多孔介質(zhì)中運(yùn)輸。地下流體流動(dòng)和傳輸過程的數(shù)值模擬必須考慮井的存在。包含井的網(wǎng)格模塊上的壓力不同于該模塊中的平均壓力，也不同于該井的流動(dòng)井底壓力。已經(jīng)開發(fā)了各種有限差分井模型來解釋差異。這部分涉及系統(tǒng)地推導(dǎo)其他數(shù)值方法（例如標(biāo)準(zhǔn)有限元，控制體積有限元和混合有限元方法）的油井模型。給出了一個(gè)簡單的油井實(shí)例的數(shù)值結(jié)果，該油井實(shí)例說明了局部網(wǎng)格的細(xì)化效果，并給出了由石油工程師協(xié)會(huì)（SPE）組織的第七個(gè)比較解決方案項(xiàng)目，以驗(yàn)證這些油井模型。井眼模型在地下水水文和石油儲(chǔ)層中具有特殊的應(yīng)用。因此，本文的研究內(nèi)容包括流動(dòng)模型的推導(dǎo)，定性分析，數(shù)值方法的發(fā)展及其分析。未來的研究將涉及計(jì)算代碼及其并行版本的開發(fā)，以及數(shù)學(xué)建模，數(shù)值方法，科學(xué)計(jì)算，計(jì)算機(jī)仿真的擴(kuò)展，以及從普通多孔介質(zhì)到破裂多孔介質(zhì)的輔助數(shù)學(xué)分析。

著錄項(xiàng)

  • 作者

    Zhang, Youqian.;

  • 作者單位

    Southern Methodist University.;

  • 授予單位 Southern Methodist University.;
  • 學(xué)科 Mathematics.
  • 學(xué)位 Ph.D.
  • 年度 2007
  • 頁碼 93 p.
  • 總頁數(shù) 93
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類
  • 關(guān)鍵詞

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