Jennifer Niessner

Black-Oil Simulations for Three-Component - Three-Phase Flow in Fractured Porous Media

Discrete-fracture modeling and simulation of two-phase flow in realistic representations of fractured reservoirs can now be used for the design of IOR and EOR strategies. Thus far, however, discrete fracture simulators fail to include a third compressible gaseous phase. This hinders the investigation of the performance of gas-gravity drainage, water alternating gas injection, and blow-down in fractured reservoirs. Here we present a new numerical method that expands the capabilities of existing Black-Oil models for threecomponent – three-phase flow in three ways: (i) It utilizes a finite element - finite volume discretization generalized to unstructured hybrid element meshes. (ii) It employs higher-order accurate representations of the flux terms. (iii) Flash calculations are carried out with an improved equation of state allowing for a more realistic treatment of phase behavior. We illustrate the robustness of this numerical method in several applications. First, quasi-1D simulations are used to demonstrate grid convergence. Then, 2D discrete fracture models are employed to illustrate the impact of mesh quality on predicted production rates in discrete fracture models. Finally, the proposed method is used to simulate three-component – three-phase flow in a realistic 2D model of fractured limestone mapped in the Bristol Channel, U.K. and a 3D stochastically generated discrete fracture model.

Multiphase Processes in Porous Media

Models for multiphase flow in porous media are widespread today and can be found in many places in science and engineering. More complex multiphase-multicomponent models that even allow phase changes to occur need sophisticated numerical algorithms. Research in this area has been very successful with a versatile result.

Multiphase flow and transport modeling in heterogeneous porous media

We focus on the inter-related roles of scale and heterogeneity of porous medium properties for fluid flow and contaminant transport in isothermal and non-isothermal multiphase systems across a range of scales. Multiscale network and macro-scale continuum models, and detailed laboratory experiments are used to support the investigation. We demonstrate the critical role of scale in determining the dominant forces in a porous medium system, the importance of heterogeneity across a range of scales, and the dominant role of block heterogeneities on macro-scale fluid flow and non-isothermal contaminant remediation. We give special attention to the numerical approximations of pressure-saturation-conductivity relations in heterogeneous systems, and we show the effects of interface approximation schemes on both the ability to resolve phenomena of concern and on the efficiency of the numerical simulator.

Multi‐scale modelling of two‐phase–two‐component processes in heterogeneous porous media

This work deals with flow and transport phenomena in porous media, which occur on different space and time scales. Additionally, the porous medium itself is heterogeneous where the heterogeneities occur on all spatial scales. We consider a large domain with randomly distributed heterogeneities where complex two-phase–two-component processes are relevant only in a small (local) subdomain. This subdomain needs fine resolution as the complex processes are governed by small-scale effects. For a comprehensive fine-scale model taking into account two-phase–two-component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is high. Therefore, we developed a multi-scale concept where on the one hand, the global flow field influences the local two-phase–two-component processes on the fine scale. On the other hand, a coarse-scale saturation equation is solved where the effects of the fine-scale two-phase–two-component processes in the subdomain are captured by source/sink terms and the effects of fine-scale heterogeneities by a macrodispersion term. Copyright

Recent advances in finite element methods for multi-phase flow processes in porous media

In this paper, we will focus on three essentially important issues considering the modeling of multi-phase flow in heterogeneous porous media. Depending on the governing processes, the multi-phase flow equation system can show either predominant advection or diffusion/dispersion. Numerical methods have to be able to capture both cases. Furthermore, realistic porous media are always heterogeneous. The physically correct description of the interfacial behaviour is numerically very challenging, as discontinuities in primary variables may occur. In this paper, we review these issues and present the box scheme, a control volume finite element method, including an interface condition as one numerical method capable of tackling the three problems. In the end, we will give the results of a 3D simulation.

Multi-scale modeling of two-phase--two-component processes in heterogeneous porous media

Flow and transport phenomena in porous media are the governing processes in many natural and industrial systems. Not only do these flow and transport phenomena occur on different space and time scales, but it is also the porous medium itself which is heterogeneous where the heterogeneities are present on all spatial scales. We consider a large domain with randomly distributed heterogeneities where complex two-phase--two-component processes are relevant only in a small (local) subdomain. This subdomain needs fine resolution as the complex processes are governed by small-scale effects. For a comprehensive fine-scale model taking into account two-phase--two-component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is high. Therefore, we developed a multi-scale concept where on the one hand, the global flow field influences the local two-phase--two-component processes on the fine-scale. On the other hand, a coarse-scale saturation equation is solved where the effects of the fine-scale two-phase--two-component processes in the subdomain are captured by source / sink terms and the effects of fine-scale heterogeneities by a macrodispersion term. The overall algorithm as well as results will be discussed for simplified applications.

Horizontal Redistribution of Two Fluid Phases in a Porous Medium: Experimental Investigations

Classical models for flow and transport processes in porous media employ the so-called extended Darcy’s Law. Originally, it was proposed empirically for one-dimensional isothermal flow of an incompressible fluid in a rigid, homogeneous, and isotropic porous medium. Nowadays, the extended Darcy’s Law is used for highly complex situations like non-isothermal, multi-phase and multi-component flow and transport, without introducing any additional driving forces. In this work, an alternative approach by Hassanizadeh and Gray identifying additional driving forces were tested in an experimental setup for horizontal redistribution of two fluid phases with an initial saturation discontinuity. Analytical and numerical solutions based on traditional models predict that the saturation discontinuity will persist, but a uniform saturation distribution will be established in each subdomain after an infinite amount of time. The pressure field, however, is predicted to be continuous throughout the domain at all times and is expected to become uniform when there is no flow. In our experiments, we also find that the saturation discontinuity persists. But, gradients in both saturation and pressure remain in both subdomains even when the flow of fluids stops. This indicates that the identified additional driving forces present in the truly extended Darcy’s Law are potentially significant.

Modeling Two-Phase Flow in Porous Media Including Fluid-Fluid Interfacial Area

We present a new numerical model for macro-scale two-phase flow in porous media which is based on a physically consistent theory of multi-phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy’s law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid–fluid interfaces. An alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We show how parameters can be obtained for the alternative model using experimental data from a new kind of flow cell and present results of a numerical modeling study.© 2008 ASME

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling

1.1 Motivation This chapter focusses on the description and modeling of mass transfer processes occurring between two fluid phases in a porous medium. The principle underlying physical process comprises a transport of particles from one phase to the other phase. This process takes place across fluid–fluid interfaces (see Fig. 1) and may constitute evaporation, dissolution, or condensation, for example. Such mass transfer processes are crucial in many applications involving flow and transport in porous media. Major examples are found in soil science (where the evaporation from soils is of interest), soil and groundwater remediation (like thermally-enhanced soil vapor extraction where dissolution, evaporation, and condensation play a role), storage of carbon dioxide in the subsurface (where the dissolution of carbon dioxide in the surrounding groundwater is a crucial storage mechanism), CO2-enhanced oil recovery (where after primary and secondary recovery, carbon dioxide is injected into the reservoir in order to mobilize an additional 8-20 per cent of oil), and various industrial porous systems (such as certain types of fuel cells). Let us have a closer look at a few of these applications and identify where interphase mass transfer is relevant. Four specific examples are shown in Fig. 2 and briefly described.

Interface condition and exact linearization in the newton iterations for two-phase flow in heterogeneous porous media

Modelling multiphase flow and transport in porous media is an important tool for the preparation of remediation strategies for non-soluble pollutants in the hydrosystem groundwater, and thus helps to preserve the essential source drinking water. Macroscale block heterogeneities, and especially the interfaces between the different materials, have a strong influence on these flow and transport processes. In particular, the physically correct approximation of the saturations at the interface is essential and a pre-condition for the effective planning and application of remediation strategies. We apply different numerical approximation schemes, in one of which we explicitly implement an interface condition that guarantees the physically correct representation of saturations at the interface. In order to improve the efficiency of the Newton solver in the numerical simulator MUFTE_UG, which is generally worsened by the implementation of the interface condition, different schemes of linearizing the partial differential equations are compared. Whereas numerical linearization leads to better efficiencies for all considered realistic sets of constitutive relationships for natural soils, principle parameter studies showed that an exact linearization of the partial differential equations can improve the efficiency only in special “academic” cases, i.e., for steep relative permeability—saturation relationships under certain conditions. In the end, we show the applicability of the scheme with interface condition to the migration of gas in a fractured-medium system as an example for a “real-life” problem.