Multiphase non-Darcy Flow Research Articles

Non-Darcy displacement by a non-Newtonian fluid in porous media according to the Barree-Conway model

An analytical solution for describing the non-Darcy displacement of a Newtonian fluid by a non-Newtonian fluid in porous media has been developed. The two-phase non-Darcy flow is described using the Barree-Conway model under multiphase conditions. A power-law non-Newtonian fluid, whose viscosity is a function of the flow potential gradient and the phase saturation, is considered. The analytical solution is similar to the Buckley-Leverett theoretical solution, which can be regarded as an extension of the Buckley-Leverett theory to the non-Darcy flow of non-Newtonian fluids. The analytical results revel how non-Darcy displacement by a non-Newtonian fluid is controlled not only by relative permeabilities but also by non-Darcy flow coefficients as well as non-Newtonian rheological constitutive parameters and injection rates. The comparison among Darcy, Forchheimer and Barree-Conway models is also discussed. For application, the analytical solution is then applied to verify a numerical simulator for modeling multi-phase non-Darcy flow of non-Newtonian fluids.

Simulation of Non-Darcy Porous Media Flow According to the Barree and Conway Model

Non-Darcy porous media flow has been traditionally handled using the Forchheimer equation. However, recent experimental studies have shown that the Forchheimer model is unable to fit laboratory results at high flow rates. On the other hand, the non-Darcy flow model, proposed by Barree and Conway, is capable of describing the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through proppant packs. In this paper, we present a numerical model by incorporating the Barree and Conway model into a general-purpose reservoir simulator for modeling single-phase and multiphase non-Darcy flow in porous and fractured media. The numerical formulation is based on the TOUGH2 methodology, i.e., spatial integral-finite-difference discretization, leading to an unstructured grid, followed by time discretization carried out with a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly by Newton iteration. In the numerical approach, flow through fractured rock is handled using a general multi-continuum approach, applicable to both continuum and discrete fracture conceptual models. In an effort for model validation, we use analytical solutions to verify our numerical model results for both single-phase and multiphase non-Darcy flow. In addition, the numerical model is applied for well testing analysis of transient non-Darcy flow toward a well.

Analysis of Multiphase Non-Darcy Flow in Porous Media

Recent laboratory studies and analyses (Lai et al. Presented at the 2009 Rocky Mountain Petroleum Technology Conference, 14–16 April, Denver, CO, 2009) have shown that the Barree and Conway model is able to describe the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through porous media. A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the Barree and Conway model. The comparison between Forchheimer and Barree and Conway non-Darcy models is discussed. We also present a general mathematical and numerical model for incorporating the Barree and Conway model in a general reservoir simulator to simulate multiphase non-Darcy flow in porous media. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids with the Barree and Conway model. The results show how non-Darcy displacement is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, and injection rates. Overall, this study provides an analysis approach for modeling multiphase non-Darcy flow in reservoirs according to the Barree and Conway model.

Multiphase Non-Darcy Flow in Proppant Packs

Summary This paper builds on a model for single-phase, non-Darcy flow in porous media presented in by Barree and Conway (2004). In this work, the generalized equation for single-phase non-Darcy flow is extended to multiphase-flow conditions. Laboratory measurements of gas/water flow were conducted in several flow cells to determine relative permeability curves and the nonlinear relationship between individual-phase flow rate and induced potential gradient over a wide range of input fractional-flow conditions and over a range of Reynolds numbers (Re). A model is presented to predict multiphase non-Darcy flow in porous media that is applicable to high-deliverability reservoirs and hydraulically fractured wells.

Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs

A numerical method as well as a theoretical study of non-Darcy fluid flow through porous and fractured reservoirs is described. The non-Darcy behavior is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The non-Darcy flow through a fractured reservoir is handled using a general dual-continuum approach. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in petroleum and geothermal reservoirs.