Two-Phase Flow in Random Network Models of Porous Media

Author:

Koplik J.1,Lasseter T.J.1

Affiliation:

1. Schlumberger-Doll Research

Abstract

Abstract To explore how the microscopic geometry of a pore space affects the macroscopic characteristics of fluid flow in porous media, we have used approximate solutions of the porous media, we have used approximate solutions of the Navier-Stokes equations to calculate the flow of two fluids in random networks. The model pore space consists of an array of pores of variable radius connected to a random number of nearest neighbors by throats of variable length and radius. The various size and connectedness distributions may be arbitrarily assigned, as are the wetting characteristics of the two fluids in the pore space. The fluids are assumed to be incompressible, immiscible. Newtonian, and of equal viscosity. In the calculation, we use Stokes flow results for the motion of the individual fluids and incorporate microscopic capillary force by using the Washburn approximation. At any time, the problem is mathematically identical to a random electrical network of resistors, batteries, and diodes. From the numerical solution of the latter, we compute the fluid velocities and saturation rates of change and use a discrete timestepping procedure to follow the subsequent motion. The scale of the computation has restricted us so far to networks of hundreds of pores in two dimensions (2D). Within these limitations, we discuss the dependence of residual oil saturations and interface shapes on network geometry and flow conditions. Introduction A significant limitation to our understanding of the dynamics of multiphase fluids in porous media is the inability to connect the physics at the microscopic scale to the macroscopic phenomena observed in the laboratory and in the field. Within individual pores, the motion of fluids and menisci can be discussed, at least approximately, in terms of the microgeometry and the physical characteristics of the liquids. gases, and solids present. On the macroscopic scale, the multiphase Darcy equations involving several empirical parameters-relative permeabilities and average capillary pressures permeabilities and average capillary pressures conventionally are used. The connection between these two levels of description, if there is one, has never been elucidated despite years of effort (as reviewed by Scheidegger ). In consequence, it is difficult to predict the behavior of oil reservoirs in advance, and considerable waste of money, effort, and resources can ensue. Economic issues aside, this situation provides another example of a pervasive problem in physics: macroscopic averaging of a random problem in physics: macroscopic averaging of a random microscopically disordered medium to predict large-scale behavior from a knowledge of small-scale dynamics. In optimal circumstances, existing methods in the physics literature (i.e., Ziman ) can be used to carry out physics literature (i.e., Ziman ) can be used to carry out the averaging. For fluid problems, for example, percolation theory has been applied to the spatial distribution of percolation theory has been applied to the spatial distribution of fluids in a pore space, both in static situations and in quasistatic displacement. Another set of ideas, effective medium theories, has been applied to electrical conductivity and its fluid analog, absolute permeability. The general fluid displacement problem, when both permeability. The general fluid displacement problem, when both capillary and viscous forces are present, is related to a class of physics problems that are as yet unresolved, such as crystal growth, surface evolution, and dynamic percolation. In this situation, we are forced to resort to percolation. In this situation, we are forced to resort to brute-force numerical modeling, both as a means of obtaining statistical information and as a guide to approximations that may permit future analytical work. In this paper, we describe our initial efforts to calculate the motion of two fluids in porous media from the microscopic scale up, starting from the Stokes equations and boundary conditions in this pore space. As usual, we model the porous medium as a network of similarly shaped, but randomly sized, elements. The key to the calculation is the mathematical analogy between the fluid problem and an appropriate electrical network of random problem and an appropriate electrical network of random resistors, batteries, and diodes. The calculation is a very difficult one, numerically speaking, and to date we have been restricted to fairly small 2D networks of hundreds of pores. We expect, however, that with more sophisticated programming methods our approach can be applied to three-dimensional (3D) networks of thousands of pores. pores. After this work was in progress, we came across a paper of Singhal and Somerton where a similar calculational framework was used but with a different emphasis. Those authors considered a single realization of a small network of triangular channels of random sizes with flow regimes randomly assigned in each channel and compute the relative permeabilities and capillary pressure curves of the network. Our emphasis in this paper is on time-dependent phenomena and statistical averaging of flow quantities. We also note the somewhat related work by Payatakes et al., who considered a square lattice of Payatakes et al., who considered a square lattice of converging/diverging tubes meeting at point nodes and simulate the dislodgement of blobs of trapped oil. Subsequently, Dias and Payatakes used the same geometry and calculational rules similar to those employed here to study fluid displacement. SPEJ P. 89

Publisher

Society of Petroleum Engineers (SPE)

Subject

General Engineering

Cited by 97 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3