Interpretation of Miscible Displacements in Laboratory Cores
- Robert E. Bretz (New Mexico Inst. of Mining and Technology) | Franklin M. Orr Jr. (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1987
- Document Type
- Journal Paper
- 492 - 500
- 1987. Society of Petroleum Engineers
- 5.6.5 Tracers, 5.4.9 Miscible Methods, 2.5.2 Fracturing Materials (Fluids, Proppant), 5.3.4 Reduction of Residual Oil Saturation, 5.3.2 Multiphase Flow, 5.3.1 Flow in Porous Media, 1.6.9 Coring, Fishing, 5.2 Reservoir Fluid Dynamics, 4.3.4 Scale, 5.2.1 Phase Behavior and PVT Measurements
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Summary. Results of stable, first-contact miscible displacements are presented for three San Andres carbonate cores from west Texas and eastern New Mexico. All three cores showed evidence of significant heterogeneity at the core scale. Effluent composition measurements were interpreted with two relatively simple models of mixing during flow in heterogeneous porous media: the Coats-Smith (CS) model, which represents the pore space as flowing and stagnant fractions with mass transfer between them, and a porous sphere (PS) model, which describes flow between an assemblage of porous spheres with diffusive interchange of material in the spheres with fluid flowing past them. Parameters for the two models are reported and compared. Direct measurements of some parameters from thin-sections agreed well with least-error parameters for one sample for which comparisons were possible. PS model fits showed less error than CS model fits. The form of the PS model is then used to examine how mixing effects change with change in flow velocity, displacement length, the length scale associated with heterogeneity, and the rate of exchange of material between flowing and stagnant zones. We conclude that for reservoirs with scales of heterogeneity larger than those present in core samples, laboratory core displacements do not provide evidence about mixing behavior at field scale.
In a typical miscible displacement experiment, a core is filled with one fluid, and a second fluid containing a tracer is used to displace the first. The composition of fluids leaving the core is then measured. When the pore space is uniform, typical effluent composition data can be represented well by the convection-dispersion (CD) equation. When the rock sample is not uniform, breakthrough of injected fluid occurs well before I PV has been injected, and the effluent composition curve exhibits a long tail. To represent that behavior, Deans proposed a simple model of the effects of heterogeneity in which the pore space is represented as flowing and stagnant fractions with mass transfer between them. Coats and Smiths extended Deans' model to include the effects of dispersion in the flowing fraction. The CS model has been used extensively to interpret miscible displacements in laboratory cores.
Miscible displacement behavior is of interest because mixing effects influence the performance of EOR processes, such as CO2 flooding and surfactant injection processes in which process performance depends on the composition of mixtures that form in situ as injected fluid encounters reservoir fluids. For example, Gardner et al. showed that high dispersion reduces local displacement efficiency in CO2 floods. In an extensive set of CO2 floods in reservoir core samples, Spence and Watkins found that heterogeneities that can be modeled with a stagnant fraction in the CS model also produce higher residual oil saturations. On the basis of simulations of the coupling of the effects of phase behavior with mass transfer between flowing and stagnant fractions, Dai and Orr] concluded that mixing of nearly pure CO2 in the flowing stream with oil in the stagnant fraction causes the formation of the larger residual oil saturation observed by Spence and Watkins. Gardner and Ypma reported that a similar mechanism increases residual saturations in flows in which viscous instability and phase behavior interact. Thus, there is considerable evidence that mixing affects CO2 flood performance, at least on the laboratory core scale.
While it is clear that laboratory CO2 floods are influenced by mixing behavior, it is less clear how such effects affect field-scale displacements. Part of the uncertainty results because the lumped parameters of the CS model cannot be estimated independently; hence they must be determined by fitting experimental results to the model. That procedure is also routinely used to determine dispersion coefficients with the simpler CD equation. As Arya et al. pointed out. however. measured dispersion coefficients increase with the length scale of the displacement, a reflection of the fact that larger-scale local variations in permeability can be present as the scale of the system grows. While representation of mixing in terms of the dispersion coefficient may still be useful, it is clear that a coefficient appropriate to the scale of the displacement must be used in any assessment of the effects of dispersive mixing at field scale. The parameters of the CS model have the same limitations. They are likely to be scale-dependent; hence parameter values determined in laboratory corefloods are not likely to be appropriate for description of displacements at larger scales.
In this paper, we use a comparison of the CS model with a slightly more complex model, the PS model, to evaluate the effects of changes of scale in the CS model. In the PS model, flow occurs between spheres, which are themselves porous. Fluid in the pores of the spheres is assumed to exchange with that flowing between spheres only by diffusion. Thus, the model is quite similar to the CS model except that there is an explicit representation of the length scale of the low-permeability (stagnant) regions. To evaluate the performance of the PS model, we compare model calculations with effluent composition measurements for three carbonate core samples, one of which showed pore structures very similar to that envisioned in the PS model. Results of CS model fits for the same cores are also reported, and scaling behavior with changes in displacement velocity is compared for parameters of the two models. Finally, we use the PS model to estimate how CS parameters change for displacements at larger scale.
The CS model has the form
In the calculations described below, the CS model was solved by a fully explicit finite-difference model in which a correction was made to compensate for the effects of numerical dispersion. 14 plots that show the dependence of solutions to the CS model on the three model parameters-the flowing fraction', f, the Peclet number Npe = vL/Kd, and the Damkohler number, NDa = Km/Lv-are available elsewhere.
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