Modeling Gas-Phase Mass Transfer Between Fracture and Matrix in Naturally Fractured Reservoirs

SPE Journal ◽  
2011 ◽  
Vol 16 (04) ◽  
pp. 795-811 ◽  
Author(s):  
A.. Jamili ◽  
G.P.. P. Willhite ◽  
D.W.. W. Green
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Fractured Reservoirs ◽  
Porous Matrix ◽  
Naturally Fractured Reservoirs ◽  
Gravity Drainage ◽  
Liquid Phases ◽  
The Matrix ◽  
Diffusion And Convection

Summary Gas injection in naturally fractured reservoirs maintains the reservoir pressure and increases oil recovery primarily by gravity drainage and to a lesser extent by mass transfer between the flowing gas in the fracture and the porous matrix. Although gravity drainage has been studied extensively, there has been limited research on mass-transfer mechanisms between the gas flowing in the fracture and fluids in the porous matrix. This paper presents a mathematical model that describes the mass transfer between a gas flowing in a fracture and a matrix block. The model accounts for diffusion and convection mechanisms in both gas and liquid phases in the porous matrix. The injected gas diffuses into the porous matrix through gas and liquid phases, causing the vaporization of oil in the porous matrix, which is transported by convection and diffusion to the gas flowing in the fracture. Compositions of equilibrium phases are computed using the Peng-Robinson EOS. The mathematical model was validated by comparing calculations to two sets of experimental data reported in the literature (Morel et. al. 1990; Le Romancer et. al. 1994), one involving nitrogen (N2) flow in the fracture and the second with carbon dioxide (CO2) flow. The matrix was a chalk. The resident fluid in the porous matrix was a mixture of methane and pentane. In the N2-diffusion experiment, liquid and vapor phases were initially present, while in the CO2 experiment, the matrix was saturated with liquid-hydrocarbon and water phases. Calculated results were compared with the experimental data, including recovery of each component, saturation profiles, and pressure gradient between matrix and fracture. Agreement was generally good. The simulation revealed the presence of countercurrent flow inside the block. Diffusion was the main mass-transfer mechanism between matrix and fracture during N2 injection. In the CO2 experiment, diffusion and convection were both important.

A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part I

2009 ◽  
Vol 12 (02) ◽  
pp. 200-210 ◽  
Author(s):  
Benjamin Ramirez ◽  
Hossein Kazemi ◽  
Mohammed Al-kobaisi ◽  
Erdal Ozkan ◽  
Safian Atan
Keyword(s):  
Mass Transfer ◽  
Oil Recovery ◽  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Gas Injection ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fine Grid ◽  
Matrix Block ◽  
The Matrix

Summary Accurate calculation of multiphase-fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to account accurately for fluid exchange resulting from capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks. The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water/oil and gas/oil systems were compared with results obtained with transfer functions. In both water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil, depending on the wettability of the matrix. In gas injection, the thermodynamic phase equilibrium, aided by gravity/capillary interaction and, to a lesser extent, by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow, the fracture/matrix mass transfer is less complicated because there are no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil. Using the transfer functions presented in this paper, fracture- and matrix-flow calculations can be decoupled and solved sequentially--reducing the complexity of the computation. Furthermore, the transfer-function equations can be used independently to calculate oil recovery from a matrix block.

scholarly journals Interpolation of Boundary Condition at Time-Interval of Unknown Lenghth for the Problem of Convective Diffusion in a Three-Layered Water Filter

2019 ◽  
pp. 25-28
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Convective Diffusion ◽  
Lower Boundary ◽  
Time Interval ◽  
Water Filter ◽  
The Right

On the basis of mathematical model of convectivediffusion in a three-layered filter it is formulated a contactinitial-boundary value problem for description of mass transferof pollution accompanying the sorption processes. It is proposedthe algorithm for establishing the estimation of values of soughtfunction (concentration of pollution) at the lower boundary of thefilter on the basis of the interpolation of experimental data. It istaken into account that the right end of the interpolation segmentis unknown. It is determined the exact solutions of contact-initialboundaryvalue problems of mass transfer with provision forboth diffusive and convective mechanisms of transfer as well assorption processes, which is based on integral transformationsover space variables in the contacting regions. Is it designedsoftware and established regularities of convective diffusionprocess in the three-layered filter.

Unsteady-State Behavior of Naturally Fractured Reservoirs

1965 ◽  
Vol 5 (01) ◽  
pp. 60-66 ◽  
Author(s):  
A.S. Odeh
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Unsteady State ◽  
Fractured Reservoir ◽  
State Behavior ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix ◽  
Porosity And Permeability ◽  
Bulk Volume

Abstract A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs from pressure build-up and/or drawdown plots. Introduction The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard, Freeman and Natanson, and Samara. The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results. Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a factured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. To understand the behavior of the pressure build-up and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions:1. The matrix blocks act like sources which feed the fractures with fluid;2. The net fluid movement toward the wellbore obtains only in the fractures; and3. The fractures' flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures' bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady-state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. SPEJ P. 60ˆ

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