Innovative Workflow for Grouping, Averaging, End-Point Scaling and Assessing Uncertainty of Water-Oil Relative-Permeability Curves, Considering Corresponding Normalized Water-Fractional-Flow Curves, Reservoir-Rock Types and Wettability Indexes

Abstract

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.

Wettability of Carbonate Reservoir Rocks: A Comparative Analysis

“…Ferreira et al [39] presented another qualitative method to determine wettability from relative permeability curves, based on the concept of fractional flow Equation (6), called the normalized water fractional flow curve.…”

“…where q w is the water flow rate, q o is the oil flow rate, and q t is the total flow rate, µ w is the water viscosity, µ o is the oil viscosity, k ro is the oil relative permeability, and k rw is the water relative permeability. Ferreira et al [39] assumed an equal viscosity for oil and water (viscosity ratio equal to 1) to eliminate the influence of the viscosity ratio on water fractional flow (f w ) and proposed changing Equation ( 6) into…”

“…standard USBM [36], and modified USBM [37] have been widely applied in the oil industry. In addition, relative permeability-based techniques including Craig's triple rules of thumb [38], the normalized water fractional flow curve [39], Lak [15], and modified Lak [13] were proposed to deduce knowledge of wettability in rocks. There exist other wettability indicators, such as the relative pseudo work of imbibition [40], MPMS (MPMS stands for Mirzaei-Paiaman, Masihi and Standnes) [41,42], relative imbibition rate [43], rise in core [44], and NMR-based techniques [45][46][47][48][49][50] that require additional experiments.…”