The purpose of this study is to formulate a coupled fluid-flow/geomechanics model of a naturally fractured reservoir. Fluid flow is modeled within the context of dual-porosity (more generally, overlapping-continuum) concept while geomechanics is modeled following Biot's isothermal, linear poroelastic theory. The development follows along the line of the conventional and existing porous fluid-flow modeling. The commonly used systematic fluid-flow modeling is therefore preserved. We show how the conventional fluid-flow dual-porosity formulations are extended to a coupled fluid flow/geomechanics model. Interpretation of the pore volumetric changes of the dual continua, fractures and matrix-blocks, and the associated effective stress laws are the most difficult and critical coupling considerations. New relations describing the dual rock volumetric changes are presented. These relations allow a smooth and consistent transition between single-porosity and dual-porosity concepts and are in terms of measurable quantities. Reduction to the single-porosity is presented to demonstrate the conceptual consistency of the proposed model. Introduction Geomechanics is particularly important in petroleum reservoir management of naturally fractured reservoirs [Teufel et al., 1993]. Economical petroleum production from most naturally fractured reservoirs relies on the fracture permeability (including magnitude and orientation of an isotropy). Natural fractures basically are the product of evolving rock stress state. Therefore any disturbance of the stress field, such as due to fluid production/injection, can affect the existing fractures (e.g., opening, closure, reorientation) and the associated reservoir performance. A coupled fluid-flow/geomechanics model thus provides a rational tool for a better understanding and management of a naturally fractured reservoir. The theory describing fluid-solid coupling was first presented by Biot [1941, 1955, 1956] in which mechanical issues were emphasized over the fluid flow issues. Because of this, Biot's theory is less compatible with the conventional fluid-flow models (without geomechanics considerations) in terms of concept understanding, physical interpretation of parameters involved (e.g., rock compressibilities), and computer code upgrading. These issues, however, can be resolved if Biot's theory is reinterpreted and reformulated along the line of conventional fluid-flow modeling as done by Geertsma [1957] and Vermijt [1969], and recently by Chen et al. [1995]. In essence, these reformulations provide better "compatibility" and "expandability" to the existing fluid-flow knowledge and models. The original Biot's theory is a single-fluid/single-solid model, i.e., a single-porosity type of model from a fluid-flow point of view. Naturally fractured reservoirs are often modeled by the dual-porosity (overlapping continuum) type of concept developed by Barenblatt et al. [1960] (also Warren and Root [1963]). Models incorporating both Biot's poroelastic theory and Barenblatt et al's dual-porosity concept have been studied by several authors. These models can be classified into two types based on the approach taken. The first approach is based on mixture theory and was adopted by Wilson and Aifantis [1982], Beskos and Aifantis [1986], and Bai et al.'s [1993]. Two related features of the resulting formulations are:all the fluid-flow equations in a "mixture" have the same functional form as that of a single- porosity if the fluid exchange term is dropped, andphenomenological coefficients are proposed firstly and their physical interpretations are deduced, if necessary, after the completion of the formulation. Item (i) implies that the stress- dependent rock properties in one continuum are independent of the other mixing continua. This in turn may cause difficulty for the later physical interpretation (i.e., item (ii)) and even inconsistency with the geomechanical equations adopted. P. 419^
This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February 1999.
Five proteases designated as A ', A 2 , B, C and D were isolated from Euphausia superba by the succesive steps o f ammonium sulfate fractionation, acetone precipitation, gel filtration and DEAESephadex A-50 chromatography. A l , B, C and D were purified to homogeneity in disc gel electrophoresis by means of rechromatography on the DEAE-Sephadex A-50 column. Studies on substrate specificity of these enzymes revealed that A 2 , B, C and D were trypsin-like enzymes and A , a carboxypeptidase A . A ' , B, C and D had molecular weights of about 24,000, 24,000, 28,000 and 27,000; optimal pH a t 9.0, 8.0, 7.5 and 7.5-8.0; and optimal temperature at 48, 50, 55-60 and 55"C, respectively. The actiuity of B, C and D were not inhibited by sulfhydryl reagents and N-a-tosyl-L-phenylalanylchloro-methyl ketone, but inhibited by reducing agents, N-a-tosyl-L-lysylchloromethyl ketone and soybean trypsin inhibitor. The activity of protease A l was stimulated 3.5 fold by cobalt, but inhibited by 3-indolepropionate and D -p hen y la la n in e. vation of fresh krill and utilization of the enzymes. Noguchi et al.
This paper presents a 3D finite-difference, fully implicit model to represent the physical phenomena that occur during the production from tight-gas reservoirs with stress-sensitive permeability. The reservoir is treated as a multiphase poroelastic system consisting of a deforming solid skeleton and a moving compressible pore fluid. The governing equations describing the deformation of the solid part of the rock and the motion of the pore fluid are fully coupled. The model takes into account the effect that rock deformation has on reservoir-rock properties. This feature, and the pressure dependence of the gas properties, leads to a highly non-linear system of finite-difference equations. Simulation results show that the permeability reduction due to changes in the stress state and pore pressure can significantly affect the production of tight-gas reservoirs. Introduction Variation of the pore pressure and the stress state associated with the production of fluids from an oil/gas reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock depends on the mechanical properties of the rock material and the magnitude of the changes in pore pressure and stress state. In some cases, the volumetric deformation of the rock has appreciable effects on some of the physical properties of the reservoir rock, such as porosity and permeability. In conventional reservoir simulation, the permeability is considered to remain constant with time. However, published laboratory works indicate that the permeability of tight-gas reservoirs may be strongly stress-sensitive. Vairogs et al. concluded that low-permeability rocks are affected by stress to a greater degree than those having higher levels of permeability. This agrees with the results published earlier by McLatchie et al. A study by Thomas and Ward showed that the permeability of cores from the Pictured Cliffs and Fort Union formations were affected significantly by confining pressure. Jones and Owens performed laboratory tests on more than 100 tight-gas-sand core samples from five formations. They found that the confining pressure simulating the reservoir effective stress reduces permeability of tight-gas sands two to more than 10 times, depending on the permeability and rock type. Warpinski and Teufel studied the permeability and deformation behavior of low-permeability, gas-reservoir rocks and provided laboratory results showing that tight-gas-sand cores can lose up to 90% or more of their permeability when subjected to the reservoir effective stress. These laboratory studies show that the permeability of gas-reservoir rocks may change significantly with variation of the pore pressure and the stress state. On the other hand, field observations show that the stress state changes throughout the reservoir as well as with time. These two evidences suggest that it is necessary to consider permeability variation in reservoir simulation. The mechanisms causing the dependence of permeability on the pore pressure and the stress state can be summarized as follows:fluid production/injection causes changes in the pore pressure;pore pressure changes cause variations in the in-situ stresses and rock deformation, and vice-versa; andin-situ stress changes and rock deformations cause variations in the reservoir permeability. The simultaneous interaction of these mechanisms leads to the coupling of two different physical processes:motion of the pore fluid, anddeformation of the rock solid skeleton.
The objective of this paper are:to summarize a recently developed coupled fluid-flow/geomechancs, dual-porosity model intended to describe the behaviour of naturally fractured reservoirs, andto analyze and compare four other existing models. Conceptual consistency is examined for each model within the concept of dual-porosity. The comparison provides important understanding and interpretation to the complex model parameters. Introduction Geomechanics is particularly important in petroleum reservoir management of naturally fractured reservoirs [Teufel et al., 1993]. Economical petroleum production from most naturally fractured reservoirs relies on the fracture permeability (including magnitude and orientation of anisotropy). Natural fractures basically are the product of evolving reservoir stress state. Therefore any disturbance of the stress field, such as due to fluid production/injection, can affect the existing fractures (e.g., opening, closure, reorientation) and the associated reservoir performance. A coupled fluid-flow/geomechanics model thus provides a rational tool for a better understanding and management of a naturally fractured reservoir. There are five coupled fluid-flow/geomechanics dual-porosity models in the literature. The concept of dual-porosity introduces some difficulties in parameter interpretation and measurement. In this paper, we summarize our model [Chen and Teufel, 1997], and analyze/compare the other four earlier models. Three main purposes of this comparison:To identify and compare the physical interpretations of the rock volumetric changes;To check the internal model consistency within the adopted principles and assumptions of a given model; andTo check the model continuity between the single-porosity and dual-porosity concepts. Background Theory of Coupled Fluid-Flow and Geomechanics. The theory describing fluid-solid coupling was first presented by Biot [1941, 1955] in which mechanical issues were emphasized over the fluid flow issues. Because of this, Biot's theory is less compatible with the conventional fluid-flow models (without geomechanics considerations) in terms of concept understanding, physical interpretation of parameters (e.g., rock compressibilities), and computer code upgrading. These issues, however, can be resolved if Biot's theory is reinterpreted along the line of conventional fluid-flow modeling, as done by Geertsma [1957] and Verruijt [1969], and Chen et al. [1995]. In essence, these reformulations provide better compatibility, continuity, and expandability to the existing fluid-flow knowledge and models. The original Biot's theory is a single-fluid/single-solid model, i.e., a single-porosity model from a fluid-flow point of view. Naturally fractured reservoirs are often modeled by the dual-porosity-type of concept to be described next. Concept of Dual-Porosity. The concept of dual-porosity (overlapping-continuum) involves two overlapping continua: matrix-blocks (primary pores) and fractures (secondary pores) [Barenblatt et al., 1960] (also Warren and Root [1963]). Each continuum possesses its own fluid-pressure field. We will use subscript n=1 to denote the matrix-block (primary pores) while n=2 for the fractures (secondary pores), and the subscript s for the solid phase. A bulk fractured medium, Vb, thus is viewed to comprise three components/phases: Vb=Vp 1+Vp2+Vs, . . . . . . . . . (1) Theory of Coupled Fluid-Flow and Geomechanics. The theory describing fluid-solid coupling was first presented by Biot [1941, 1955] in which mechanical issues were emphasized over the fluid flow issues. Because of this, Biot's theory is less compatible with the conventional fluid-flow models (without geomechanics considerations) in terms of concept understanding, physical interpretation of parameters (e.g., rock compressibilities), and computer code upgrading. These issues, however, can be resolved if Biot's theory is reinterpreted along the line of conventional fluid-flow modeling, as done by Geertsma [1957] and Verruijt [1969], and Chen et al. [1995]. In essence, these reformulations provide better compatibility, continuity, and expandability to the existing fluid-flow knowledge and models. The original Biot's theory is a single-fluid/single-solid model, i.e., a single-porosity model from a fluid-flow point of view. Naturally fractured reservoirs are often modeled by the dual-porosity-type of concept to be described next. Concept of Dual-Porosity. The concept of dual-porosity (overlapping-continuum) involves two overlapping continua: matrix-blocks (primary pores) and fractures (secondary pores) [Barenblatt et al., 1960] (also Warren and Root [1963]). Each continuum possesses its own fluid-pressure field. We will use subscript n=1 to denote the matrix-block (primary pores) while n=2 for the fractures (secondary pores), and the subscript s for the solid phase. A bulk fractured medium, Vb, thus is viewed to comprise three components/phases: Vb=Vp 1+Vp2+Vs, . . . . . . . . . (1)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.