Relative permeability is a key input for multiphase reservoir simulations. Challenges related to the validation and interpretation of the laboratory core measurements are associated with the restoration processes and resulting wettability states, the heterogeneities and multi-scale aspects of complex rocks, as well as the limitations of core flooding experiments. Moreover, the relative permeability curves from several samples can be scattered and their correlation with wettability and reservoir-rock types not directly apparent. Grouping, averaging, end-point scaling and assessing the data uncertainty are crucial steps in relative permeability data processing. To improve these processes, a new workflow is proposed, based on the water fractional flow concept (fw), which is an effective representation of the behavior of oil displacement by water injection, combining both relative permeability curves to oil and water into a single, equivalent curve. First, the water fractional flow curve, obtained from a relative permeability core flooding test, is normalized according to saturation end-points at a constant viscosity ratio equal to one. Such normalization allows the separation of the fw plot area into two regions according to the wettability state of the samples. Fractional flow curves for the same sample but at opposite wettability conditions, i.e. strongly oil-wet or water-wet, present a remarkable symmetry, from which a wettability index is calculated. This proposed new wettability index may then be compared to other indexes like Amott-Harvey or USBM for validation. Additionally, the shape of the normalized water fractional flow curves is influenced by rock-pore sizes. Subsequently, the normalized fractional flow curves are grouped by wettability and by reservoir-rock type, supporting the validation of the relative permeability data and identifying associated trends and uncertainties. The average, lower and upper-bound normalized fractional flow curves are obtained for each group. Likewise, relative-permeability and saturation end-points are correlated with reservoir-rock-type index or other rock properties. Finally, average, lower and upper-bound normalized relative permeability sets of curves and corresponding end-points may be used for reservoir simulation. Alternatively, de-normalized relative permeability curves can be obtained. By varying wettability, a controlled relative permeability dataset is obtained using direct-hydrodynamic (DHD) simulations on 3D digital rock model of a carbonate core sample. The proposed workflow is applied to such a dataset. The results confirm the ability of the method to correctly identify the different wetting states and to group the fractional flow curves accordingly. The proposed wettability index, directly obtained from relative permeability data, may be complementary to other industry wettability indexes and better represent the expected displacement behavior. The proposed workflow, although simple and widely applicable, considerably improves the relative permeability analysis process. It can be integrated with other core analysis, well-log analysis and digital-rock analysis workflows.

Heterogeneities of carbonate core plugs can be assessed by different measurements resulting in different interpretations. In this study, dielectric spectroscopy, NMR, and tracer displacement method performed on the same cores reflect different aspects of heterogeneity related to their own characteristic length scales and physics of the measurements, which complement each other in a multiphysical interpretation. The complex dielectric permittivity measured on carbonate core samples in the reflection mode in the range of 1 MHz to 1 GHz, exhibits a strong difference between the two extremities of the plugs when turning them upside down. The difference between the two extremities is a result of heterogeneity in the rock plug. It can be due to chemical composition, density, porosity, water saturation, presence of cavities, vugs and micro-fractures, crystalline structure and rock lithology, and, distribution of components inside the rock, which is a complex process need to be fully understand. The dielectric heterogeneity is compared with the NMR porosity profile which, in certain cases, indicates cross section averaged porosity heterogeneities along the core-plug axis and correlated with tracer displacement measurement, which characterizes the pore system hydraulic connection and its related heterogeneity. To complete this "multiphysics" approach, a numerical forward model of the electromagnetic propagation in the core-plugs was performed, focusing on the effect of artificial vugs at different locations inside the core-plug on the electromagnetic propagation patterns. From dielectrics and NMR profiles, quantitative heterogeneity indexes are proposed and compared, and correlated with tracer displacement measurement. This results in a better characterization of pore system (such as size, distribution, connectivity). A preliminary carbonate rock model taking into account the pore size effect is developed. The cementation factor is inverted from dielectrics dispersion curve measurements, a good match between inversion and laboratory measurements indicates the importance of pore partitioning in carbonates. These laboratory measurements on core plugs can be applied to well-bore measurements combining for instance Array Dielectric Scanner and NMR downhole tools.

In formation evaluation and reservoir engineering, resistivity index, relative permeability, and capillary pressure are crucial parameters for estimating oil reserves and planning a production scenario. They can be determined in the laboratory using Special Core Analysis, or SCAL techniques. Since they are all functions of fluid saturation, correlations between them may exist; but the literature on their inter-relationships is lacking. In this paper, experimental relative permeabilities and relative permeabilities obtained from resistivity measurements using Li’s model (2007) are compared for different immiscible brine-oil displacements. An experimental study on a water-wet grainstone rock was initiated in order to measure its resistivity response during different ambient water-oil flow displacements. Three different flooding techniques were performed and compared. The most popular technique is the resistivity porous plate Pc-RI method where resistivity and capillary pressure are measured at equilibrium. The steady-state flooding method was also tested; resistivity and steady-state relative permeability were measured at the equilibrium state. Finally the fastest yet least reliable method is the transient technique or unsteady-state flooding method where resistivity and unsteady-state relative permeability are measured under transient conditions. A comparison between resistivity index obtained from the three flooding techniques showed that the unsteady-state technique cannot give reliable resistivity index curve, and so should be avoided to infer Kr from resistivity measurements. The Pc-RI method provides the most reliable resistivity index curve but relative permeability can only be derived from the capillary pressure curve. Finally, the steady-state displacement was found to be the best method to compare experimental relative permeability with relative permeability inferred from resistivity. In spite of an acceptable match between them, an improvemnent of Li’s model is proposed. Additional investigations such as effects of wettability and rock heterogeneities on these results will be necessary to validate the generality of the overall workflow.

In formation evaluation, resistivity logs are used to calculate the reservoir water saturation using the well known Archie's law. When high degree of heterogeneity exists, like when vuggy structures are present, the interpretation of electrical logs can be complex. In order to highlight the effect of a vug on a two-phase oil and water flow displacement, a laboratory apparatus was designed. The system employs the 4-contact electrode method to monitor the resistivity response of a rock slab during primary drainage and imbibition cycles. The effect of frequency on the saturation exponent n was also investigated. Two rock slab models were cut from a strongly water-wet Indiana limestone block: one slab was left untouched while the other one was drilled at its center to simulate the presence of a cylindrical vug (vuggy model). Two transparent windows were placed at both ends of the vug to allow a direct visualization of the fluids distribution with a video camera. The resistivity change was monitored during primary drainage and imbibition cycles on both homogeneous (without hole) and vuggy models. Petrophysical properties of the rock matrix were measured on the homogeneous model (without hole) from the same block. The visual cell was helpful in understanding the difference of flow behavior between primary drainage and imbibition on the vuggy model. A comparison between the electrical response of the homogeneous and vuggy rock models showed a difference between the two respective saturation exponents at constant frequency. The experimental setup also helped to study the dependence of Archie's saturation exponent n on frequency for the vuggy sample. Because resistivity tools operate at different frequencies (LWD versus wireline), this observation is crucial for the resistivity logs calibration and interpretation for heterogeneous oil reservoirs.

When an active aquifer encroaches into a gas bearing reservoir or when an oil rim sweeps gas during late depletion of the gas cap, gas displacement by liquid is important for estimating the gas recovery. In the water displacing gas condition, the viscosity ratio is extremely favorable, resulting in a sharp waterfront in the reservoir matrix: it results that changing the relative permeability Kr shape has negligible effect, while endpoints water relative permeability Krw Max and residual gas saturation Sgr are much more important to understand gas flow performance for estimation of gas recovery with active aquifer or productivity decline after water breakthrough. Three main methods are used to determine water/gas relative permeability curves: imbibition unsteady-state, imbibition steady-state or indirect approaches such as co-current spontaneous imbibition if transient data are available. One of the other popular indirect methods is called Brooks-Corey approach: by measuring the drainage Pc curve using centrifuge or porous plate methods, it is possible to calculate a pore size distribution index c. This coefficient is used in a Brooks-Corey model to determine the drainage Kr curve. It is also required to measure and determine the relationship between the residual gas saturation Sgr and the initial gas saturation Sgi relationship. Finally, it is accepted that there is no hysteresis on the water relative permeability Krw curve, as water is always the wetting phase in the gas/water couple. As non-wetting phase, gas exhibits strong hysteresis between drainage and imbibition curves: it is therefore necessary to apply a correction on the drainage Krg curve to build the imbibition one using correcting models. The aim of this paper is to compare gas/water relative permeability of clastic rocks using direct waterflooding information and indirect approach using Brooks-Corey model. It is shown that using the indirect approach leads to results like those experimentally obtained. Also, additional numerical simulations are proposed to discuss the relevance of measuring the entire water-gas imbibition relative permeability curve using the steady-state approach.