A Steady-State Upscaling Approach for Immiscible Two-Phase Flow

The paper presents a model for computing rate-dependent effective capillary pressure and relative permeabilities for two-phase flow, in 2 and 3 space-dimensions. The model is based on solving the equations for immiscible two-phase flow at steady-state, accounting for viscous and capillary forces, at a given external pressure drop. The computational performance of the steady-state model and its accuracy is evaluated through comparison with a commercial simulator ECLIPSE. The properties of the rate-dependent effective relative permeabilities are studied by way of computations using the developed steady-state model. Examples presented show the dependence of the effective relative permeabilities and capillary pressures, which incorporate the effects of fine scale wettability heterogeneity, on the external pressure drop, and thereby on the dimensionless macro-scale capillary number. The effective relative permeabilities converge towards the viscous limit functions as the capillary number tends to infinity. Special cases, when the effective relative permeabilities are rate-invariant, are also studied. The applicability of the steady-state upscaling algorithm in dynamic displacement situations is validated by comparing fine-gridded simulations in heterogeneous reservoirs against their homogenized counterparts. It is concluded that the steady-state upscaling method is able to accurately predict the dynamic behavior of a heterogeneous reservoir, including small scale heterogeneities in both the absolute permeability and the wettability.     

Coarse Scale Capillary Pressure in Heterogeneous Reservoirs

The problem of capillary pressure upscaling and generation of initial water saturation data on the simulation scale consistent with the underlying geological model is addressed analytically. The approach is based on the concept of random spatial variations of permeability and porosity. We have revised the previously published expression for the coarse scale capillary pressure (Desbarats, Water Resour Res 31, 281–288) and rigorously derived a new one avoiding the unnecessary assumptions. Both expressions are evaluated by their comparison to the directly averaged realizations of the corresponding random fields. Generally, the new expression is superior to the one previously published. The important features of the analytical coarse scale capillary pressure expression are the dependence of the endpoint water saturation on the drainage pressure, or equivalently, on the elevation over the free water level and an additional multiplier taking into account the variation of rock properties within the coarse scale grid-block. George A. Virnovsky was the main editor of this article and we, the co-writers, want to honour his memory. He died suddenly on 12 March 2008 before this article was published. George was an internationally recognized scientist especially in the areas of multi-phase upscaling, interpretation of special core analysis and pore scale modelling.     

Mechanisms Involved in Microbially Enhanced Oil Recovery

Microbial enhanced oil recovery (MEOR) represents a possible cost-effective tertiary oil recovery method. Although the idea of MEOR has been around for more than 75 years, even now little is known of the mechanisms involved. In this study, Draugen and Ekofisk enrichment cultures, along with Pseudomonas spp. were utilized to study the selected MEOR mechanisms. Substrates which could potentially stimulate the microorganisms were examined, and l-fructose, d-galacturonic acid, turnose, pyruvic acid and pyruvic acid methyl ester were found to be the best utilized by the Ekofisk fermentative enrichment culture. Modelling results indicated that a mechanism likely to be important for enhanced oil recovery is biofilm formation, as it required a lower in situ cell concentration compared with some of the other MEOR mechanisms. The bacterial cells themselves were found to play an important role in the formation of emulsions. Bulk coreflood and flow cell experiments were performed to examine MEOR mechanisms, and microbial growth was found to lead to possible alterations in wettability. This was observed as a change in wettability from oil wet (contact angle 154°) to water wet (0°) due to the formation of biofilms on the polycarbonate coupons.