Simulation of Miscible Displacement in Full-Diameter Carbonate Cores

Capacitance Effects in Porous Media

Summary.

The velocity dependence of parameters in the Coats-Smith model for tracer dispersion and tailing in porous media was investigated. An axisymmetric pore with a step change in cross-sectional area was used as a model system to determine whether the stagnant zone resulting from variations in flow cross sections contributes to the observed capacitance (i.e., tailing) at the pore level. Numerical simulations show that eddies with recirculation flow are formed in the pockets as a result of flow separation. The tracer transport between the eddies in the dead zones and the main channel was found to be diffusion-limited. The simulations reveal that in the Stokes flow regime, the mass-transfer coefficient between the two regions is independent of the interstitial velocity, in contradiction to earlier theories.

Coreflood experiments were performed with radioactive tracers to verify the hypothesis that the capacitance effects are not the result of a change in flowing fraction. The experimental results confirm that tracer tailing is a function of the ratio of the molecular diffusivity to the flow rate. In light of these findings, we investigated the validity of the Coats-Smith model to predict dispersion and tailing in a porous medium. Our studies show that the Coats-Smith model may be used; however, certain restrictions, described in this paper, apply to the procedure for estimation of parameters.

Introduction

EOR processes generally involve injection of relatively small amounts of chemicals like polymers, surfactants, and CO2 into a reservoir. These slugs are then displaced by a chase fluid, which is usually immiscible with the in-place fluid. An important design criterion for miscible slug injection is the slug size required for optimum oil recovery. In a reservoir flow process, the degradation of the miscible slug is caused primarily by hydrodynamic dispersion and, to a smaller extent, by tracer tailing. This study focuses on the tailing phenomenon that arises from stagnant or dead-end pore spaces in the porous medium for miscible systems. The dead-end pores also trap oil because of capillary forces, and this mechanism, along with the formation of oil ganglia, contributes to the residual oil saturation. Thus, a detailed understanding of the tailing phenomenon is of fundamental importance to the EOR process.

Hydrodynamic dispersion in porous media has been extensively studied in the past and is caused by variation of the flow paths in a porous medium. Previous works indicates that an effective dispersion coefficient can be used to represent the tracer residence time distribution (RTD) in a porous medium. However, a skewed Gaussian RTD has also been observed that is a consequence of tracer tailing. Tailing, also known as the capacitance effect, is caused by the dead-end pore spaces in porous media. The tracer transport between the flowing fraction and the dead-end space (stagnant fraction) is thought to be governed by molecular diffusion alone. It has been shown that the RTD for a purely diffusive process is also Gaussian, and the resultant diffusion coefficient is scaled by a tortuosity factor. Hence, the tracer RTD in a consolidated porous medium should be a summation of two normal distributions corresponding to dispersion in bulk flow and molecular diffusion into and out of the stagnant pockets. Because of the time lag between the two normal RTD's and exchange of the tracer molecules between the two regions, however, the resultant RTD for the tracer is skewed, leading to the described tailing phenomenon.

The tailing phenomenon was first studied by Turner in 1959. He viewed the porous medium as consisting of main channels of pores through which the fluid flows and dead-end pockets (Turner structures) distributed uniformly along the length of the pores. There was no flow within the pockets and the only mechanism of tracer transport between the channels and the dead-end pockets is molecular diffusion. Aris extended Turner's model by varying the size of the stagnant pockets and found that the dispersion coefficient increases up to a factor of 11, if the dead-end PV is included. Gill and Ananthakrishnan used a numerical analysis to predict the effect of Turner structures on the tracer RTD. They solved the convective-diffusion equation to simulate tracer transport in a cylindrical pore with a stagnant pocket having an arbitrary depth. The assumed parabolic velocity in the pore, zero velocity in the stagnant pocket, and diffusion-limited tracer transport between the bulk and the Turner structure.

Previous studies show that the RTD of the tracer molecules with large diffusion coefficients are identical to nominal distribution. In other words, an effective diffusion coefficient can be used to predict the tracer effluent concentrations. However, no analysis was carried out to analyze the effect of the stagnant zones on the extent of tailing observed in the effluent concentration profiles.

Azzam and Dullien numerically solved the complete Navier-Stokes equations to determine flow patterns for Turner structures of various sizes, and their results reveal that the flow in the dead-end pockets is not stagnant. Thus, Gill and Ananthakrishnan's assumption of stagnant flow in the dead-end pockets may not be valid for all pockets.

The dispersion model developed by Coats and Smith is used extensively in the petroleum industry for quantifying dispersion and tailing in consolidated porous media. This model extends the Deans model by incorporating hydrodynamic dispersion. The void space occupied by the fluid in the porous medium is divided into two regions: a flow region having a tracer concentration of C and a stagnant region of tracer with concentration C'. The volume fraction of the flowing region is called the flowing fraction, f. For one-dimensional miscible systems, the following equations describe the process of tracer transport through porous media for both regions:

(1)

and

(2)

with the following boundary conditions:

(3)

(4) and(5)

SPERE

P. 1207^

Experimental Investigation of the Interaction of Phase Behavior With Microscopic Heterogeneity in a CO2 Flood

Summary

This paper reports results of an experimental investigation of the effects of microscopic heterogeneity on local displacement efficiency in a CO2 flood. Flow-visualization experiments for first-contact miscible displacements are described and compared with effluent composition measurement for the same models. High-pressure flow-visualization experiments for multicontact miscible CO2 floods are also described. The displacements were performed in two-dimensional (2D) etched glass models made from thin-sections of San Andres carbonate core from the Maljamar field. Techniques used in preparation of the models are described briefly. Observations of first-contact miscible displacements in heterogeneous models indicate that early breakthrough and a long transition zone occur when preferential flow paths exist in the pore structure. This behavior corresponds to a flowing fraction less than 1 in the Coats-Smith model. Because the 2D models contained no dead-end PV, the results presented indicate that a low flowing fraction can occur if flow velocities in different portions of the pore space differ significantly. Coats-Smith parameters obtained for models were comparable with values obtained in parameters obtained for models were comparable with values obtained in floods performed in reservoir samples. Visual observations of the CO2/crude-oil displacements indicate that there is an interaction between phase behavior and microscopic heterogeneity. Mixing of nearly pure CO2 in the preferential flow path with oil in adjacent regions leads to a residual oil saturation (ROS) that forms in the preferential path after oil initially present has been displaced.

Introduction

Dense CO2 can displace oil very efficiently if the pore space is uniform and the effects of viscous instability are suppressed. For example, oil recoveries in excess of 95% are commonly observed in slim-tube displacements at pressures above the minimum miscibility pressure (MMP). Many reservoir rocks do not have uniform pore structures, however, and viscous instabilities will occur in most CO2 floods. Thus, a question of some importance in the interpretation of CO2 floods in laboratory cores and in the prediction of the performance of larger-scale CO2 floods is the prediction of the performance of larger-scale CO2 floods is the following: to what extent is CO2 flood displacement efficiency influenced by interactions of phase behavior, viscous instability, and local heterogeneity of the pore structure? Local displacement efficiency in a CO2 flood is sensitive to the composition path of fluid mixtures that are created as injected CO2 encounters crude oil in the pore space. Composition path is determined partly by the phase behavior of the CO2/crude-oil mixtures and partly by the mixing that takes place within the pore structure. Theoretical results suggest that both viscous instability and heterogeneity at the pore level affect local displacement efficiency by altering local mixing and hence changing composition path. For example, Gardner and Ypma predicted, on the basis path. For example, Gardner and Ypma predicted, on the basis of numerical simulations of the growth of a viscous finger, that mixing of nearly pure CO2 in the finger with crude oil from adjacent unswept regions creates a higher ROS in zones first penetrated by a finger. Dai and Orr also used simulation results penetrated by a finger. Dai and Orr also used simulation results to argue that microscopic heterogeneity has a similar effect. Mixing between CO2 in fast-flowing regions of the pore space and oil in other regions causes phase compositions to fall deeper into the two-phase region, with the result that ROS's exceed those obtained in simulations for uniform pore structures. Experimental evidence concerning those interactions is limited. Campbell and Orr described flow visualization experiments that confirmed qualitatively the predictions of Gardner and Ypma, who also reported results of coreflood experiments that supported their arguments. Spence and Watkins performed stabilized CO2 floods in reservoir core samples in which ideal miscible displacements were also performed. They interpreted the miscible displacements in terms of the Coats-Smith model, in which represents the pore space as a flowing fraction in which dispersion occurs and pore space as a flowing fraction in which dispersion occurs and a stagnant fraction with mass transfer between the two fractions. They found that cores for which Coats-Smith flowing fractions were less than one showed higher ROS's than did more uniform cores. Thus, there is experimental evidence that supports the interpretations of Gardner and Ypma and Dai and Orr, but there has been no previous attempt to observe directly the effects of heterogeneity previous attempt to observe directly the effects of heterogeneity at the pore level. In this paper, we report results of flow-visualization experiments that provide additional evidence concerning the interplay of phase behavior, microscopic heterogeneity, and viscous instability. The displacement experiments were performed in etched-glass pore networks made from thin-sections of carbonate reservoir core material. We describe preparation of the micromodels and then compare results of both stable and unstable first-contact miscible displacements with multicontact miscible CO2/crude-oil displacements. We also report results of effluent composition measurements for stable miscible displacements in the same models, along with interpretations of those displacements in terms of the Coats-Smith model. Finally, we discuss the connection between heterogeneities observed at the scale of thin-sections with displacements at laboratory core scale. The experiments described here are part of an investigation of mixing behavior in reservoir core samples. In the course of that study, miscible displacements were performed in several sandstone and carbonate cores, and the resultant effluent composition data were fit to the Coats-Smith model. In addition, thin-sections from each core were examined in an attempt to determine whether features of the pore space observable at the scale of a thin-section correlate with mixing behavior obtained in the core displacements.