Modeling and investigation of the influence of capillary heterogeneity on multiphase flow of CO₂ and brine [electronic resource]
Keywords: Energy Resources Engineering

Coreflooding experiments are routinely used in many applications pertaining to multiphase flow of fluids. These experiments can be used to study qualitative behavior of fluid displacement, or more quantitatively to derive fluid properties and flow parameters such as relative permeability and capillary pressure. Whatever the application however, it is clear that an accurate description of core properties is necessary to determine these properties and parameters accurately. While past investigators were limited in their ability to observe and describe sub-core scale flow behavior, recent coreflooding applications often include the use of a Computed Tomography (CT) scanner to view fluid and rock property distributions within the core (Akin and Kovscek 2003). This advance enables a whole new level of observational detail with which to gain insight into the influence of rock properties on fluid interactions in porous media. Despite this significant experimental advance in the study of multiphase flow, its true potential remains unrealized due to a fundamental limitation in the ability to characterize sub-core scale permeability and capillary pressure heterogeneity accurately. Characterization of these heterogeneous properties would enable high resolution, direct numerical simulation of coreflooding experiments. Whether for qualitative analysis or quantitative derivation of fundamental parameters, the ability to simulate the core-flooding process provides a natural theoretical complement to physically explain experimental observations at the same level of detail. However, due to limited ability to characterize sub-core scale heterogeneity accurately, simulation of sub-core scale displacement behavior has remained primarily qualitative in nature. To address this fundamental limitation, this work has focused on developing an accurate and practical method for characterizing sub-core scale heterogeneity. To accomplish this we bring together four principle concepts. First, it can be easily shown that sub-core scale saturation distributions are principally determined by capillary forces (Chang and Yortsos 1992). Secondly, Leverett et. al. (1942) showed that capillary pressure curves in correlated rock types scale according to local porosity and permeability variations. Thirdly, we rely on sub-core scale saturation distributions measured via CT scanning to provide sub-core scale heterogeneity information. Finally, it will be demonstrated that the sub-core scale capillary pressure distribution corresponding to a given experimentally measured sub-core scale saturation distribution may be accurately approximated. With these four principals firmly established, it will be demonstrated in this work that it is possible to determine the sub-core scale permeability distribution within a rock core accurately, and that this may be used to characterize the sub-core scale capillary heterogeneity. This will be demonstrated in this work using a variety of rock cores, fluid pairs, and experimental measurements. The basic approach developed in this work was first demonstrated in Krause (2009), however at the conclusion of that work, it was clear that a number of issues remained to be resolved. Most importantly, the quality of the results required improvement, more specifically, as measured saturation distributions are used as input to calculate permeability, this input must be very accurately reproduced numerically to demonstrate that both the calculated permeability distribution, as well as the simulation procedure are correct. Second, simulations using the calculated permeability distribution must be capable of predicting independent experimental measurements not used as input. Third, while Krause (2009) demonstrated the basic permeability calculation procedure for a single Berea Sandstone core under ideal experimental conditions, it must be demonstrated to be accurate for less ideal cores and under less ideal experimental conditions. Finally, the significance of this technique to characterize sub-core scale heterogeneity should be demonstrated by application to practical research questions. In this work here, these issues are systematically addressed to demonstrate that the conceptual approach from Krause (2009) is both valid and accurate. A more generalized approach than Krause (2009) is first presented, whereby regions of capillary equilibrium within the core may be user defined, this approach results in a significantly improved ability to match experimental measurements numerically. This approach is then generalized to remove the restrictive assumption of capillary equilibrium. To achieve this, numerical simulations are iteratively conducted to approximate the actual sub-core scale capillary pressure distributions. This approach provides only modest improvement to when working with ideal cores, such as Berea Sandstone, under ideal experimental conditions where the assumption of sub-core scale capillary equilibrium is accurate. However, when working with cores that have a significant degree of heterogeneity, or under complicated flow conditions (e.g. gravity override), this approach provides significant improvement. While this approach is able to very accurately replicate the saturation distribution used as input to calculate permeability, its ability to predict other saturation distributions is often limited by the degree of experimental measurement error. A simplified approach to quantify the effect of measurement error on the calculated permeability distribution is presented, and it is shown that errors in the predicted saturation distribution lie within these bounds. More importantly however, two straightforward methods to reduce the effect of measurement errors are presented. First, one may reduce the degree of experimental measurement error within measured sub-core scale porosity and saturation distributions, and second, one may optimize the selection of permeability within several measured saturation distributions so as to reduce error propagation. When using this optimal selection procedure, independently measured sub-core scale observations can be predicted to a high degree of accuracy. Finally, while development of such a technique to characterize sub-core scale heterogeneity may be a fundamental scientific achievement, it may ultimately be of little value if its practical application cannot be demonstrated. To achieve this, we investigate the apparent flow-rate dependency of effective relative permeability as first reported by Leverett (1939). Findings reveal that in heterogeneous cores, it is sub-core scale capillary heterogeneities, not capillary end-effects which are the primary mechanism responsible for apparent flow-rate dependency of effective relative permeability. It is then demonstrated that it is possible to derive the flow rate-independent characteristic relative permeability from apparent flow-rate affected data using numerical simulation if the sub-core scale heterogeneity is accurately parameterized using methods described in this work. Another important conclusion from this investigation is that it may not be possible to directly measure the flow rate-independent characteristic relative permeability using high flow rates in laboratory experiments as capillary heterogeneities continue to influence flow behavior even at the practical maximum laboratory-scale injection rates. Finally, this work demonstrates that heterogeneous cores cannot be accurately approximated as homogeneous and one-dimensional when using numerical simulation to derive the characteristic relative permeability, even when high injection rates are used.