# A circuit-based algorithm for two-phase flow at the pore scale in porous media

#### Abstract

Models of two-phase flow in porous media are of practical interest in many fields of science and engineering such as in oil recovery and hydrology. For this class of problem, an immiscible fluid is injected into a single-phase, porous medium to evict its valuable, native fluid. Because the aim is to amass as much of the indigenous fluid as possible, models attempt to output reliable flow regime patterns depicting how well the invading fluid displaces the native fluid. Flow regime patterns generally depend upon the geometry of the domain, stimulation at the boundaries, and properties of the invading and native fluids. However, solving for the displacement using the set of differential equations known as the Navier-Stokes equations is not guaranteed at the pore scale. As an attempt to make the problem tractable, the void space of a porous medium where fluid resides is often viewed as an interconnection of simple geometries. The medium then reduces to a graph of nodes and edges, ideally allowing simulators to model flow behavior in larger domains with less computational effort compared to other approaches. Due to the nature of the simplification, flow in these networks resembles flow in electric circuits. Consequentially, the boundary conditions and simple geometries comprising the system are analogous to electric circuit components. Motivated by the prospect of handling time-varying and/or position dependent boundary conditions, a simulator based upon these electrical equivalents is presented. Because the resulting fluid circuit abides by the conservation laws of electric circuits, a commonly employed method to solve electric circuits in simulation software becomes the basis for an algorithm to arrive at the flow regime patterns. After providing relevant background information and establishing the translation between a porous medium and its boundary conditions into a circuit equivalent, this work documents all aspects of a two-phase model such that the algorithm is replicable. Such aspects include the network data structure, a set of algorithmic flow rules, a time stepping mechanism, and nodal pressure solver. Attempting to replicate known flow regime patterns for a specific problem where the qualitative behavior is known, this work concludes by outlining the aspects of the model that need refinement according to the results from testing.

#### Subject Area

Mechanical engineering|Petroleum engineering

#### Recommended Citation

Dorethy, Todd Wayne, "A circuit-based algorithm for two-phase flow at the pore scale in porous media" (2014). *ETD Collection for University of Texas, El Paso*. AAI1557754.

https://digitalcommons.utep.edu/dissertations/AAI1557754