Advective–diffusive mass transfer in fractured porous media with variable rock matrix block size

2012 ◽  
Vol 133 ◽  
pp. 94-107 ◽  
Author(s):  
Amin Sharifi Haddad ◽  
Hassan Hassanzadeh ◽  
Jalal Abedi
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Block Size ◽  
Fractured Porous Media ◽  
Rock Matrix ◽  
Diffusive Mass Transfer ◽  
Matrix Block

A Proposed Model for Multiphase Flow Through Naturally Fractured Reservoirs

1982 ◽  
Vol 22 (05) ◽  
pp. 669-680 ◽  
Author(s):  
Ronald D. Evans
Keyword(s):  
Porous Media ◽  
Fractured Rock ◽  
Fractured Reservoirs ◽  
Fractured Porous Media ◽  
Naturally Fractured Reservoirs ◽  
Fracture Flow ◽  
Rock Matrix ◽  
Porous Rock ◽  
Matrix Blocks ◽  
Flow Through

Abstract A general mathematic model is derived that may be used to describe fluid movement through naturally fractured reservoirs. The model treats the reservoir as a double-porosity medium consisting of heterogeneous isotropic primary rock matrix blocks and an anisotropic. heterogeneous fracture matrix system. The fractured are assumed to have a general distribution in space and orientation called the fracture matrix function to represent their statistical nature. Simplifying assumptions are made concerning flow in individual fractures and a hemispherical volume integration of microscopic fracture flow equations is performed to arrive at a generalized Darcy-type equation, with a symmetric permeability tensor evolving to describe the flow in the fracture evolving to describe the flow in the fracture matrix. For flow in the primary rock matrix blocks. Darcy's law for an isotropic medium is assumed. Time-dependent porosity equations for the primary rock matrix and the fractures are derived and coupled with the conservation of mass principle for each system to arrive at a governing set of continuity equations. Each resulting continuity equation is coupled further by a fluid interaction term that accounts for fluid movement that can take place between rock matrix blocks and fractures. The resulting equations of continuity and the equations of motion are generalized for multiphase flow through the fractured medium with variable rock and fluid properties. To complete the model formulation, a general set of auxiliary equations are specified, which can be simplified to fit a particular application. Introduction Flow of fluid in fractured porous media was recognized first in the petroleum industry in the 1940's. Since that time, many researchers have added to the volume of literature on fractured media. An extensive bibliography on flow in fractured porous media is given in Ref. 1. When attempting to model fluid flow through any type of medium, the researcher must decide which kinds of fluids and the type of flow to model. In the case of fractured porous media where most of the flow takes place through fractures, the flow can become truly turbulent. However, as demonstrated for many encounters with fracture flow, the laminar flow regime probably prevails. The development of fracture flow models has proceeded along two different approaches: the statistical and the fractured rock mass is considered a statistically homogeneous medium consisting of a combination of fractures and porous rock matrix. The fractures are considered ubiquitous, and the system is called statistically homogeneous because the probability of finding a fracture at any given point in the system is considered the same as fining one an any other point. In the enumerative approach, a fractured rock medium is studied by attempting to mode the actual geometry of fractures and porous rock matrix. The locations, orientation, and aperture variations for each individual fracture must be considered in this approach. Statistical Approach Many researchers have developed models with the statistical approach. Elkins and Skov used this approach to study anisotropic fracture permeability associated with Spraberry field, TX. Considering the extensive system of orthogonal vertical joints as an anisotropic medium, from a number of drawdown tests they were able to construct permeability ellipsoids whose axes were aligned reasonably well with the observed fractured system. This is called a "one-medium statistical model" because flow in the porous rock matrix was not considered. A two-medium statistical model for transient flow in a fractured rock medium was developed by Barenblatt et al. SPEJ P. 669^

Transport of reactive tracers in rock fractures

1999 ◽  
Vol 378 ◽  
pp. 335-356 ◽  
Author(s):  
V. CVETKOVIC ◽  
J. O. SELROOS ◽  
H. CHENG
Keyword(s):  
Mass Transfer ◽  
Flow Equation ◽  
Transfer Reactions ◽  
Fracture Plane ◽  
Fracture Aperture ◽  
Rock Fractures ◽  
Advective Transport ◽  
Rock Matrix ◽  
Cubic Law ◽  
Diffusive Mass Transfer

Transport of tracers subject to mass transfer reactions in single rock fractures is investigated. A Lagrangian probabilistic model is developed where the mass transfer reactions are diffusion into the rock matrix and subsequent sorption in the matrix, and sorption on the fracture surface as well as on gauge (infill) material in the fracture. Sorption reactions are assumed to be linear, and in the general case kinetically controlled. The two main simplifying assumptions are that diffusion in the rock matrix is one-dimensional, perpendicular to the fracture plane, and the tracer is displaced within the fracture plane by advection only. The key feature of the proposed model is that advective transport and diffusive mass transfer are related in a dynamic manner through the flow equation. We have identified two Lagrangian random variables τ and β as key parameters which control advection and diffusive mass transfer, and are determined by the flow field. The probabilistic solution of the transport problem is based on the statistics of (τ, β), which we evaluated analytically using first-order expansions, and numerically using Monte Carlo simulations. To study (τ, β)-statistics, we assumed the ‘cubic law’ to be applicable locally, whereby the pressure field is described with the Reynolds lubrication equation. We found a strong correlation between τ and β which suggests a deterministic relationship β∼τ3/2; the exponent 3/2 is an artifact of the ‘cubic law’. It is shown that flow dynamics in fractures has a strong influence on the variability of τ and β, but a comparatively small impact on the relationship between τ and β. The probability distribution for the (decaying) tracer mass recovery is dispersed in the parameter space due to fracture aperture variability.

Numerical Modeling of Steam Injection Into Saturated Porous Media

2000 ◽  
Author(s):  
Scott F. Kaslusky ◽  
Kent S. Udell ◽  
Glenn E. McCreery
Keyword(s):  
Porous Media ◽  
Organic Contaminants ◽  
Local Equilibrium ◽  
Block Size ◽  
Steam Injection ◽  
Fractured Porous Media ◽  
Grid Spacing ◽  
Steam Condensation ◽  
Condensation Front ◽  
Non Equilibrium

Abstract The Steam Enhanced Extraction (SEE) process is being considered for removal of volatile organic contaminants contained in the fractured basalt rocks which lie above the Snake River aquifer at the Idaho National Engineering and Environmental Laboratory (INEEL). In this work the computer code M2NOTS (Multiphase Multi-component Non-isothermal Organic Transport Simulator) was used to simulate an experiment which tracked the movement of a steam condensation front through glass blocks separated by glass beads. The experiment was designed to represent steam injection into highly fractured basalt. For grid spacing equal to the block size heat transfer from the fractures to the blocks was severely under predicted, resulting in an over prediction of the condensation front velocity. A method was developed to accurately simulate the propagation of a steam condensation front through a fractured porous media using grid spacing equal to the block dimension. The method accounts for non-equilibrium conduction within a grid node, allowing the grid spacing to be increased well beyond the local equilibrium restriction. Simulation results compare well with the experimental results, validating the non-equilibrium model, and also indicating that M2NOTs can be effectively used to model the steam enhanced extraction process in fractured porous media.

Diffusive mass transfer in island films

1978 ◽  
Vol 125 (7) ◽  
pp. 489-525 ◽  
Author(s):  
Ya.E. Geguzin ◽  
Yu.S. Kaganovskii
Keyword(s):  
Mass Transfer ◽  
Diffusive Mass Transfer ◽  
Island Films
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