A Novel Method for Verifying the Performance of an Analytical Solution Governing the Fluid Flow From a Perforated Cylinder to Confined Porous Medium with Dirichlet Boundary Using the Test Data of Neumann Boundary Problem

2015 ◽  
Vol 6 (2) ◽  
pp. 164
Author(s):  
A. K. Vashisht ◽  
S. K. Shakya
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Boundary Problem ◽  
Test Data ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Perforated Cylinder ◽  
Novel Method

scholarly journals Analytical Solution of Magnetohydrodynamics(MHD) Squeezing Fluid Flow in Porous Medium

2020 ◽  
Vol 15 (2) ◽  
pp. 215-230
Author(s):  
Thanon Korkiatsakul ◽  
Khomsan Neamprem ◽  
Sanoe Koonprasert
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Analytical Solution

A Discrete, Arbitrarily Oriented 3D Plane-Source Analytical Solution to the Diffusivity Equation for Modeling Reservoir Fluid Flow

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1609-1623 ◽  
Author(s):  
Anqi Bao ◽  
Randy D. Hazlett ◽  
D.. Krishna Babu
Keyword(s):  
Fluid Flow ◽  
Analytical Solution ◽  
Fluid Transport ◽  
Field Experiments ◽  
Neumann Boundary ◽  
Plane Source ◽  
Multiple Fractures ◽  
Fracture Intersection ◽  
Neumann Function ◽  
Diffusivity Equation

Summary A highly accurate and efficiently computable analytical solution to the diffusivity equation is presented for modeling fluid flow into a 3D, arbitrarily oriented plane sink within a box-shaped, anisotropic medium with Neumann boundary conditions. The plane sink represents a gathering system for a well stimulated by means of hydraulic fracturing. Our plane-source Neumann function arises from analytic double integration of the point-source solution to the diffusivity equation along two vectors, forming a parallelogram. A Neumann boundary condition is achieved by means of the method of images, resulting in triple infinite summations that are reduced with mathematical identities to a combination of closed-form expressions and infinite sums with exponential damping. Our solution forecasts time-dependent behavior of fractured wells, useful in interpreting field experiments for the characterization of fracturing efficacy, reservoir size, and matrix fluid-transport properties. We demonstrate our model with two applications. One is pressure-transient analysis with identified flow regimes from a pressure vs. time plot. The other is pseudosteady-state (PSS) pressure mapping, simulating inflow from multiple fractures along the trajectory of a single horizontal well, which is achieved with superposition theory and adjustment of flux strength of each plane source to achieve a common pressure at each well/fracture intersection.

scholarly journals Modeling of Grouting Penetration in Porous Medium with Influence of Grain Distribution and Grout–Water Interaction

Processes ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 77
Author(s):  
Mengmeng Zhou ◽  
Fengshuai Fan ◽  
Zhuo Zheng ◽  
Chenyang Ma
Keyword(s):  
Grain Size ◽  
Porous Medium ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Stokes Equations ◽  
Linear Trend ◽  
Injection Pressure ◽  
Navier Stokes ◽  
Two Phase ◽  
Grain Distribution

In this study, a numerical model of grouting penetration in a porous medium is established. The fluid flow in the interstices of the porous medium is directly modeled by Navier–Stokes equations. The grouting process is considered as a two-phase flow problem, and the level set method is used to characterize the interaction between grout and groundwater. The proposed model has considered the nuances for each grain during grouting penetration, instead of representing the fluid flow as a continuum process. In the simulation, three kinds of porosity (0.3; 0.4; 0.5) and two kinds of grain size distribution (0.5~1 mm; 1~2 mm) are used. Results show that: the pressure drop along penetration distance is approximately in a linear trend. The variation of filling degree along grouting distance approximately obeys a quadratic polynomial function. The injection pressure is influenced by the porosity and grain size of the porous medium, especially by the former. A theoretical analysis is carried out to propose an analytical solution of the grouting penetration. The analytical solution gives a good estimation when the grain amounts in the porous medium are small, and the difference becomes larger as the grain amounts increase.

scholarly journals Fluid Flow Model with Mean Microtubule Pressure through Porous Media

2020 ◽  
pp. 38-44
Author(s):  
A. T. Ngiangia ◽  
P. O. Nwabuzor
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Flow Model ◽  
Perturbation Technique ◽  
Regular Perturbation ◽  
Fractional Model

We discussed in this paper a fractional model arising in flow of three different incompatible fluids through a porous medium with mean microtubule pressure. The method adopted for obtaining the solution is the regular perturbation technique for the analytical solution and for the transformation of the boundary conditions. The results are in decent agreement with the findings of researched work reviewed in this paper.

scholarly journals Fluid flow in a medium distorted by a quasiconformal map can produce fractal boundaries

1996 ◽  
Vol 7 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Olli Martio ◽  
Bernt Øksendal
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Elliptic Boundary ◽  
Homogeneous Medium ◽  
Moving Boundary Problem ◽  
Fractal Boundary ◽  
Elliptic Boundary Value ◽  
Quasiconformal Map

Physical experiments indicate that when an expanding fluid flows through a porous rock then the boundary between the wet and the dry region can be very irregular (e.g. see [OMBAFJ] and the references therein). In fact, it has been conjectured that this boundary is a fractal with Hausdorff dimension about 2.5. The (one-phase) fluid flow in a porous medium can be modelled mathematically by a system of partial differential equations, which, under some simplifying assumptions, can be reduced to a family of semi-elliptic boundary value problems involving the (unknown) pressure p(x) of the fluid (at the point x and at t) and the (unknown) wet region Ut at time t. (See equations (1.5)–(1.7) below). This set of equations, called the moving boundary problem involves the permeability matrix K(x) of the medium at x. A question which has been debated is whether this relatively simple mathematical model can explain such a complicated fractal nature of ∂Ut. More precisely, does there exist a symmetric non-negative definite matrix K(x) such that the solution Ut of the corresponding (expanding) moving boundary problem has a fractal boundary? The purpose of this paper is to prove that this is indeed the case. More precisely, we show that a porous medium which produce fractal wet boundaries can be obtained by distorting a completely homogeneous medium by means of a quasiconformal map.

THE INHOMOGENEOUS DAM PROBLEM WITH LINEAR DARCY’S LAW AND DIRICHLET BOUNDARY CONDITIONS

1996 ◽  
Vol 06 (08) ◽  
pp. 1051-1077 ◽  
Author(s):  
A. LYAGHFOURI
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Dirichlet Boundary Conditions ◽  
Flow Through

In this paper we study a fluid flow through a porous medium with Dirichlet boundary conditions and a general permeability. We establish the continuity of the free boundary and the uniqueness of the S3-connected solution.

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