Simulation of Miscible Displacement in Full-Diameter Carbonate Cores

Abstract

Miscible gas displacement data obtained from full-diameter carbonate reservoir cores have been fitted to a modified miscible flow dispersion-capacitance model. Starting with earlier approaches, we have synthesized an algorithm that provides rapid and accurate determination of the three parameters included in the model: the dispersion coefficient, the flowing fraction of displaceable volume, and the rate constant for mass transfer between flowing and stagnant volumes. Quality of fit is verified with a finite-difference simulation. The dependencies of the three parameters have been evaluated as functions of the displacement velocity and of the water saturation within four carbonate cores composed of various amounts of matrix, vug, and fracture porosity. Numerical simulation of a composite core made by stacking three of the individual cores has been compared with the experimental data. For comparison, an analysis of Berea sandstone gas displacement also has been provided. Although the sandstone displays a minor dependence of gas recovery on water saturation, we found that the carbonate cores are strongly affected by water content. Such behavior would not be measurable if small carbonate samples that can reflect only matrix properties were used. This study therefore represents a significant assessment of the dispersion-capacitance model for carbonate cores and its ability to reflect changes in pore interconnectivity that accompany water saturation alteration. Introduction Miscible displacement processes are used widely in various aspects of oil recovery. A solvent slug injected into a reservoir can be used to displace miscibly either oil or gas. The necessary slug size is determined by the rate at which deterioration can occur as the slug is Another commonly used miscible process involves addition of a small slug within the injected fluids or gases to determine the nature and extent of inter well communication. The quantity of tracer material used is dictated by analytical detection capabilities and by an understanding of the miscible displacement properties of the reservoir. We can develop such understanding by performing one-dimensional (1D) step-change miscible displacement experiments within the laboratory with selected reservoir core material. The effluent profiles derived from the experiments then are fitted to a suitable mathematical model to express the behavior of each rock type through the use of a relatively small number of parameters. This paper illustrates the efficient application of the three-parameter, dispersion-capacitance model. Its application previously has been limited to use with small homogeneous plugs normally composed of intergranular and intencrystalline porosity, and its suitability for use with cores displaying macroscopic heterogeneity has been questioned. Consequently, in addition to illustrating its use with a homogeneous sandstone, we fit data derived from previously reported full-diameter carbonate cores. As noted earlier, these cores were heterogeneous, and each of them displayed different dual or multiple types of porosity characteristic of vugular and fractured carbonate rocks. Dispersion-Capacitance Model The displacement efficiency of one fluid by a second immiscible fluid within a porous medium depends on the complexity of rock and fluid properties. SPEJ P. 647^

Enhanced gas recovery with CO2 sequestration: The effect of medium heterogeneity on the dispersion of supercritical CO2–CH4

“…Those results revealed that the stagnant portion of the fluid was relatively constant as flow rate was increased, whereas the velocity profile in the individual (mobile) pores increased and flattened, consistent with an increased value of . Figure 7b indicates that the mass transfer coefficients obtained in this study were comparatively consistent with the ones described in literature (Baker, 1977;Batycky et al, 1982;Bretz and Orr Jr., 1987;Orr Jr. and Taber, 1984;Spence Jr. and Watkins, 1980). The resultant corrected dispersion coefficients (K corr ) and their corresponding experimental conditions (T, p and u m ) for the Estaillades and Ketton carbonates, as well as new high velocity data obtained for the Donnybrook sandstone, are listed in Table 2.…”

“…This model has been used for several dispersion studies on carbonate rocks (Baker, 1977;Batycky et al, 1982;Bretz and Orr Jr., 1987;Bretz et al, 1988;Brigham, 1974;Spence Jr. and Watkins, 1980). Equation (4) and (5) may be analytically solved for a pulse input where semi-infinite initial-boundary conditions were assumed (Goltz and Roberts, 1986;van Swaaij, 1967;Villermaux and Van Swaaij, 1969):…”

“…Even though the flow of incompressible fluids through carbonate rocks has been broadly investigated, very few dispersion measurements have been conducted on gas-gas systems in carbonates (Batycky et al, 1982;Legatski and Katz, 1967;Mamora and Seo, 2002;Seo, 2004). Legatski and Katz (1967) initiated the gas-gas dispersion measurements in carbonate cores by conducting pulse dispersion experiments at ambient conditions and various interstitial velocities.…”

“…The dispersion was larger for the carbonates than the ones measured for sandstone samples; however the obtained dispersion values contained uncertainties of about 30%, based on the error bars shown explicitly in the reported figures. Batycky et al (1982) performed supercritical N 2 -CH 4 displacement experiments on five carbonate cores at a pressure of 6.9 MPa and temperature of 23°C. Similar to other investigators, long tailed and early breakthrough profiles were detected during the course of their work, and were hypothesized to be the effect of stagnant pores.…”

Effect of Pore Structure on Miscible Displacement in Laboratory Cores

“…The CoS model is the simplest differential model that reflects typical observations of corefloods in which breakthrough occurs before 1 PVI and hence has been used extensively to interpret miscible displacements in laboratory cores. 10,11,[13][14][15][16][17] The CoS model equations are first order in time and second order in space and hence require one initial condition and two boundary conditions for solution. For the experiments described here, the initial condition is and where C' is the exit concentration.…”