Anthony R. Kovscek

Fundamentals of foam transport in porous media

Foam in porous media is a fascinating fluid both because of its unique microstructure and because its dramatic influence on the flow of gas and liquid. A wealth of information is now compiled in the literature describing foam generation, destruction, and transport mechanisms. Yet there are conflicting views of these mechanisms and on the macroscopic results they produce. By critically reviewing how surfactant formulation and porous media topology conspire to control foam texture and flow resistance, we attempt to unify the disparate viewpoints. Evolution of texture during foam displacement is quantified by a population balance on bubble concentration, which is designed specifically for convenient incorporation into a standard reservoir simulator. Theories for the dominant bubble generation and coalescence mechanisms provide physically based rate expressions for the proposed population balance. Stone-type relative permeability functions along with the texture-sensitive and shear-thinning nature of confined foam complete the model. Quite good agreement is found between theory and new experiments for transient foam displacement in linear cores.

Computed tomography in petroleum engineering research

Abstract Imaging the distribution of porosity, permeability, and fluid phases is important to understanding single and multiphase flow characteristics of porous media. X-ray computed tomography (CT) has emerged as an important and powerful tool for non-destructive imaging because it is relatively easy to apply, can offer fine spatial resolution and is adaptable to many types of experimental procedures and flow conditions. This paper gives an overview of CT technology for imaging multiphase flow in porous media, the principles behind the technology and effective experimental design. By critically reviewing prior work using this important tool, we hope to provide a better understanding of its use and a pathway to improved analysis of CT-derived data. Because of the wide variety of image processing options, they are discussed in some detail.

Spontaneous imbibition characteristics of diatomite

Abstract A systematic investigation of fluid flow characteristics within diatomite (a high porosity, low permeability, siliceous rock) is reported. Using an X-ray computerized tomography (CT) scanner, and a novel, CT-compatible imbibition cell, we study spontaneous cocurrent water imbibition into diatomite samples. Air–water and oil–water systems are used and the initial water saturation is variable. Mercury porosimetry and a scanning electron microscope (SEM) are employed to describe diatomite pore structure and the rock framework. Diatomite exhibits a fine pore structure and significant pore-level roughness relative to sandstone thereby aiding the flow of imbibing water. Despite a marked difference in permeability and porosity as compared to sandstone, we find similar trends in saturation profiles and dimensionless weight gain vs. time functions. Although diatomite is roughly 100 times less permeable than sandstone, capillary forces result in a strong imbibition potential for water such that imbibition rates rival and surpass those for sandstone

A mechanistic population balance model for transient and steady-state foam flow in Boise sandstone

Foam in porous media is discontinuous on a length scale that overlaps with pore dimensions. This foam-bubble microstructure determines the flow behavior of foam in porous media and, in turn, the flow of gas and liquid. Modeling of foam displacement has been frustrated because empirical extensions of the conventional continuum and Newtonian description of fluids in porous media do not reflect the coupling of foam-bubble microstructure and foam rheology. We report a mechanistic model for foam displacement in porous media that incorporates pore-level mechanisms of foam generation, coalescence, and transport in the transient flow of aqueous foams. A mean-size foam-bubble conservation equation, along with the traditional reservoir/groundwater simulation equations, provides the foundation for our mechanistic foam-displacement simulations. Since foam mobility depends heavily upon its texture, the bubble population balance is both useful and necessary, as the role of foam texture must be incorporated into any model which seeks to predict foam flow accurately. Our model employs capillary-pressure-dependent kinetic expressions for lamellae generation and coalescence, and incorporates trapping of lamellae. Additionally, the effects of surfactant chemical transport are included. All model parameters have clear physical meaning and, consequently, are independent of flow conditions. Thus, for the first time, scale up of foam-flow behavior from laboratory to field dimensions appears possible. The simulation model is verified by comparison with experiment. In situ, transient, and steady aqueous-phase liquid contents are garnered in a 1.3 μm2 Boise sandstone using scanning gamma-ray densitometry. Backpressures exceed 5 MPa, and foam quality ranges from 0.80 to 0.99. Total superficial velocities range from as little as 0.42 to 2.20 m/d. Sequential pressure taps measure flow resistance. Excellent agreement is found between experiment and theory. Further, we find that the bubble population balance is the only current means of describing all flow modes of foam self-consistently.

SCREENING CRITERIA FOR CO2 STORAGE IN OIL RESERVOIRS

ABSTRACT Oil fields are likely to the first category of geologic formation where carbon dioxide (CO2) is injected for sequestration on a large scale, if geologic sequestration proves feasible. About 1.4 BCF per day (69 300 tonnes/day) of CO2 are currently injected for oil recovery in the U.S. Replacing this naturally occurring CO2 with anthropogenic CO2 would have a minor, but measurable, effect on overall CO2 emissions. However, CO2 is injected into only a small fraction of reservoirs and it is estimated that upwards of 80% of oil reservoirs worldwide might be suitable for CO2 injection based upon oil recovery criteria alone. These facts combined with the generally extensive geologic characterization of oil reservoirs and the maturity of CO2–oil recovery technology make oil reservoirs attractive first targets as CO2 sinks. This paper lays the groundwork necessary to evaluate whether an oil reservoir might be suitable for CO2 storage. As such, a series of criteria for injection into currently producing, depleted, or inactive reservoirs are proposed. Aspects considered include the reservoir depth, storage capacity, water and oil volumes in place, formation thickness, and permeability. Importantly, the effect of oil production on reservoir properties, especially fault movement and induced fractures must be gauged and included in assessments. It is demonstrated that CO2 density with depth alone is not a sufficient criterion for choosing candidate sites. It is necessary to consider also porosity and the amount of water and oil that are displaceable. The end result is a criteria table for rapid screening of candidate reservoirs.

Scaling of counter-current imbibition processes in low-permeability porous media

Oil recovery from low permeability reservoirs is strategically important because of the large resources locked in such formations. Imbibition is fundamental to oil recovery from such reservoirs under most secondary and improved recovery processes of practical interest. It is also characteristic of porous medium wettability. The rate and the extent of imbibition depend critically on the viscosity of the wetting and nonwetting phases. In this study, recent work is presented regarding imaging imbibition in low permeability porous media (diatomite) with X-ray computed tomography. The viscosity ratio between nonwetting and wetting fluids is varied over several orders of magnitude yielding different levels of imbibition performance. A mathematical analysis of counter-current imbibition processes is performed and a modified scaling group is developed that incorporates the mobility ratio. This modified group is physically based and appears to improve scaling accuracy of countercurrent imbibition significantly.

Experimental and analytical study of multidimensional imbibition in fractured porous media

Abstract Capillary imbibition is an important mechanism during water injection and aquifer influx in fractured porous media. Better understanding of matrix–fracture interaction and imbibition in general is needed to model effectively these processes. Using an X-ray computerized tomography (CT) scanner and a novel CT-compatible core holder, a series of experiments to study air and oil expulsion from rock samples by capillary imbibition of water in a three-dimensional (3-D) geometry were conducted. The air–water system was useful because a relatively large number of experiments could be conducted to delineate physical processes. Different injection rates and fracture apertures were utilized. Two different fracture flow regimes were identified. The “filling fracture” regime shows a plane source that grows in length due to relatively slow water flow through fractures. In the second regime, the “instantly filled fracture” regime, the time to fill the fracture is much less than the imbibition time and the imbibition performance scales as the square root of time. In the former regime, the mass of water imbibed scales linearly with time. A new analytical model is proposed for filling fractures incorporating implicit matrix/fracture coupling. Good agreement is found between experiments and calculation. This analytic coupling was obtained by solving the saturation diffusion equation with appropriate initial and boundary conditions. The solution provides the location of the wetting phase front in the fracture and the saturation distribution in the matrix. The solution is analogous to that obtained by Marx and Langenheim [Trans. AIME 216 (1959) 312] for the areal extent of an equivalent heated zone in thermal recovery methods. Analogous terms among flow and heat transfer in porous media were found and are also presented.

A technique for measuring two-phase relative permeability in porous media via X-ray CT measurements

Abstract A novel method for computing two-phase relative permeability curves from the results of spontaneous imbibition experiments is presented. Using a specially constructed imbibition cell and an X-ray Computed Tomography (CT) scanner, we obtain accurate measurement of saturation profiles along the length of cores as a function of time. The saturation profile history allows direct computation of the relative permeability for both phases from a single experiment when used in combination with a previously measured capillary pressure curve. Results are unique within experimental error. The proposed procedure works equally well for spontaneous and forced cocurrent imbibition. It was tested thoroughly using synthetic and experimental spontaneous imbibition data, for water–air and water–oil systems. Study showed that the pressure-gradient history can be neglected during calculations of air–water relative permeability; however, pressure-gradient data improves the accuracy of measurement for viscous oil flowing at high water saturation. Test results are described within the paper. Advantages include the incorporation of capillary forces and no requirement for steady-state conditions. This method is useful to measure imbibition relative permeability curves, especially in low permeability rocks at relatively low wetting phase saturations. In such systems, it is laborious to reach multiple steady states and capillary forces are significant so that classical unsteady-state techniques do not apply.

Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries

A model for snap-off of a gas thread in a constricted, cornered pore is developed. The time for wetting liquid to accumulate at a pore throat into an unstable collar is examined, as is the time for the resulting pore-spanning lens to be displaced from the pore so that snap-off may repeat. A corner-flow hydrodynamic analysis for the accumulation rate of wetting liquid due to both gradients in interfacial curvature and in applied liquid-phase pressure reveals that wetting-phase pressure gradients significantly increase the frequency of liquid accumulation for snap-off, as compared to liquid rearrangement driven only by differences in pore-wall curvature. For moderate and large pressure gradients, the frequency of accumulation increases linearly with pressure gradient, because of the increased rate of wetting liquid flow along pore corners. Pore topology is important to the theory, because pores with relatively small throats connected to large bodies demonstrate excellent ability to snap off gas threads even when the initial capillary pressure is high or equivalently when the liquid saturation is low. A macroscopic momentum balance across the lens, resulting from snap-off, reveals that lens displacement rates are not linear with the imposed pressure drop. Instead, the frequency of lens displacement scales with powers between 0.5 and 0.6 for pores with dimensionless constriction radii between 0.15 and 0.40. Statistical percolation arguments are employed to form a generation rate expression and connect pore-level foam generation events to macroscopic pressure gradients in porous media. The rate of foam generation by capillary snap-off increases linearly with the liquid-phase pressure gradient and according to a power-law relationship with respect to the imposed gas-phase pressure gradient.

Mechanistic Foam Flow Simulation in Heterogeneous and Multidimensional Porous Media

Gases typically display large flow mobilities in porous media relative to oil or water, thereby impairing their effectiveness as displacing fluids. Foamed gas, though, is a promising agent for achieving mobility control in porous media. Because reservoir-scale simulation is a vital component of the engineering and economic evaluation of any enhanced oil recovery (EOR) or aquifer remediation project, efficient application of foam as a displacement fluid requires a predictive numerical model. Unfortunately, no such model is currently available for foam injection in the field where flow is multidimensional and the porous medium is heterogeneous. We have incorporated a conservation equation for the number density of foam bubbles into a fully implicit, three-dimensional, compositional, and thermal reservoir simulator and created a fully functional, mechanistic foam simulator. Because foam mobility is a strong function of bubble texture, the bubble population balance is necessary to make accurate predictions of foamflow behavior. Foam generation and destruction are included through rate expressions that depend on saturations and surfactant concentration. Gas relative permeability and effective viscosity are modified according to the texture of foam bubbles. In this paper, we explore foam flow in radial, layered, and heterogeneous porous media. Simulations in radial geometries indicate that foam can be formed deep within rock formations, but that the rate of propagation is slow. Foam proves effective in controlling gas mobility in layered porous media. Significant flow diversion and sweep improvement by foam are predicted, regardless of whether the layers are communicating or isolated.