Boundary Element Method For Porous Media Flow

الموضوعات

علوم بحتة وطبيعية

الملخص

The focus point of this study is to develop BEM formulation to overcome thedifflculties caused by nonlinearity and heterogeneity in the solution of partialdifferential equations governing the porous media flow .This dissertation consist oftwo major parts ,theory of BEM , and applications of BEM to two important fields ofporous media ,water flow in aquifers and oil flow in reservoirs.The contribution done in the theory sections is mainly a mathematical derivation ofthe standard boundary element method for Lapiace's equation and the step by stepformulation to the BEM , starting from its correspondence differential equation,beside the developed form of BEM based on GEM and DRBEM that has presented. tohandle both heterogeneous and nonlinearity. In the applications section a novelboundary integral solution was applied for determining :(1) Water table elevation in an unconfined homogeneous aquifer subjected torecharge and dewatering from a stream as well as fluctuations induced by constantand continuous recharge in a two stream unconfined-aquifer system.(2) Changes in water table exposed to a transient boundary condition and space-dependent recharge. This technique was compared with the closed form solutionobtained in [111] and excellent results were obtained.(3) Characteristics of the flow through heterogeneous unsaturated porous aquifer .(4) Solution of reservoir engineering problems.This work adapted the most recent developments in boundary element methods toreservoir engineering problems. The transient pressure (diffusion) and convection-diffusion equations were solved in heterogeneous media using the Dual ReciprocityBoundary Element Method (DRBEM) and the Green Element Method (GEM). Numericalexperiments showed that DRBEM is more accurate than a standard finite differencemethod. However like finite difference methods, DRBEM is subject to spuriousoscillation at high Peclet numbers.DRBEM also requires the solution of a dense system of equations. GEM, which is ahybrid boundary elementlfinite element method, overcomes these disadvantages.The method was found to produce very accurate solutions to convection-diffusionproblems and only shows small oscillations in the solution at very high Pecletnumbers. A further important advantage is the sparse nature of the matrix system.GEM is also amenable to solving transient nonlinear problems, which makes it thebasis for a new technique for multiphase flow simulation.This work explores the advantages of a hybrid boundary element method known asthe Green element method for modeling pressure transient tests. Boundary elementmethods are a natural choice for the problem because they are based on Green'sfunctions, which are an established part of well test analysis. The classical boundaryelement method is limited to single phase flow in homogeneous media. This workspresents formulations which give computationally efflcient means to handleheterogeneity. Comparisons of the proposed Green element approach to standardfinite difference simulation show that both methods are able to model the pressurechange in the well over time. When pressure derivative is considered however thefinite difference method produces very poor results which would give misleadinginterpretations. The Green element method in conjunction with singularityprogramming reproduces the derivative curve very accurately. Boundary elementmethod was applied for solving Stokes flow equations on multi particle system. Also,the method is modified for estimating flow parameters for a specified porous media.A new method for the so/ut/‘an of the unsteady incompressible Navier-Sta/resequations was presented

روابط وملفات

التعريف والنوع

رقم الوثيقة

0824c65a-dee6-4e6f-a461-41e6b94f93de

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

62938_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"ازهري احمد عبدالله","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"محمد الصاوي","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

English

المصدر والدورية

اسم المصدر

Boundary Element Method For Porous Media Flow

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

محمد الصاوي

الإعداد

ازهري احمد عبدالله

الاقتباسات الببليوغرافية