Theoretical Analysis of Miscible Displacenllent In Fractured Porous Media By a One-dinneIllsional Model: Part II - Features
Authors: Tan C.T. , Firoozabadi A. 
Published: March 2010

Abstract
The efficiency of miscible displacement in fractured porous media is strongly influenced by two parameters:gravity number, Ngr, andfracture density. An important feature of miscible fluid injection is the early breakthrough, but the solvent cut remains small, provided either Ngr or the fracture density is high.
Such a characteristic makes miscible displacement in fractured porous media an efficient process. A key assumption of our model is the crossflow equilibrium. Numerical simulation results show that this is an appropriate assumption.

Introduction
In part I of this study, in one-dimensional model was formulated to describe miscible displacement in fractured porous media(1). The basic equation for the fracture (medium I) and the matrix (medium 2) in dimensionless form are:
Equation. (Available In Full Paper)
In Equations (1) and (2). q1D and q2D are the rates (volume/time) in the fracture and the matrix. respectively. These rates can be obtained from the expression, provided in Reference (I) for both no crossflow (NC) and crossflow equilibrium (CE) cases. For a single block system, the initial and boundary condition are:
Equation. (Available In Full Paper)
All symbols are defined in rile nomenclature. The above system was solved analytically in Reference (1)
Four parameters. characterized miscible displacement in fractured porous media(1). These are: normalized fracture Capacity. Equation (Available In Full Paper)compare the result from theory to the experimental data Thompson and Mungun(2).examine the effect of different parameters on the displacement efficiency andstudy the effect of fracture density on the displacement performance. Iin the following we will first study the features of miscible displacement in fractured media comprised of a fracture and a matrix. The effect of fracture density on miscible displacement will be presented next. Finally, we will provide justification for some of the assumption that we made in our model.

Single Block Features
Thompson and Mungun(2) have conducted experiments to study miscible displacement in fractured porous media. In their experiments, liquid soltrol 130 was used as the condition of the experiments are 0.163 and 1.2 cp and 0.575 and 0.753 g/cm3 respectively. Lets us select core/fracture system I/F of Reference (2) fun which R1= 0.012, S1= 0.0023, and B=4.03 (K1= 1066 darey and butane is 6.3 and Ngr values are 0.42, 0.70 . 1.05, 1.68 and 8.41. The five Ngr value are calculated from the V/V of Thompsn and Mungun that equal to 2.0, 1.2, 0.8, 0.5 and 0.1 respectively. V is the displacement rate and Ve is the critical rate of instability (viscous fingering) defined by Slobod and Howled for miscible displacement in vertical homogeneous media.
Equation. (Available In Full Paper)
Thus Ngr approaches Vc/V for large M.
The five flowrates for the core/fracture system 11F of Thompson and Mungun are in the gravity crossflow region. The criterion for strong gravity crossflow and moderate gravity crossflow are Ngr0.543 and 0.168 Ngr ≤0.543, respectively [see reference (1)].