Modeling Imbibition Capillary Pressure Curves

Abstract

Abstract Although spontaneous imbibition capillary pressures are relevant in all reservoirs having undergone or undergoing gravity stable water displacement, they are not commonly measured nor considered for reservoir modelling. Imbibition is particularly important when establishing initial hydrocarbons in place for reservoirs already having residual hydrocarbon columns prior to production commencement. As part of a saturation-height study, an empirical model relating imbibition capillary pressure curves to their drainage precursors was created. Drainage saturation-height functions could then be used to create imbibition equivalents based upon the saturation history of the reservoir rock. Calibration was carried out using laboratory measurements of both drainage and imbibition capillary pressure curves. This "imbibition from drainage" (IFD) model was verified against log derived water saturations from wells in the initial study area. The match was excellent in those wells considered to have reliable petrophysical evaluations. The IFD model was even able to describe imbibition capillary pressure curves for sections of reservoir in drainage transition zones prior to the commencement of water imbibition. The model has since been further verified in other hydrocarbon accumulations found in different basins. The IFD model developed represents the first publication of a technique for creating meaningful spontaneous imbibition capillary pressure curves and imbibition saturation-height functions through reservoirs with significant capillary transition zones. The technique should be widely used to describe water saturations in reservoirs with residual hydrocarbon columns, providing better estimates of initial hydrocarbons in place than with more commonly used drainage data. Iteration of the model also allows determination of both original and current day Free Water Level locations in systems having residual hydrocarbon columns from either leakage prior to production or from gravity controlled water sweep during production. Introduction There are a number of oil and gas accumulations worldwide that cannot be adequately described using conventional drainage capillary pressure curves. In many of these cases, the transition zone described by the capillary pressure curves is much longer than that suggested by the wireline log evaluation. In these situations, and if there are residual hydrocarbons evident below the pressure-derived Free Water Level (FWL), the hydrocarbon saturations are better modelled using imbibition capillary pressure curves. This paper backgrounds the type of imbibition capillary pressure curves available and how they are measured. It then details how to create mathematical expressions to efficiently describe these curves for use in reservoir modelling and reserves determinations. Unlike techniques previously used to describe reservoirs in imbibition mode1, the model presented here will also describe short hydrocarbon columns i.e. those columns which never reached irreducible water saturation, so imbibition has occurred into the drainage capillary pressure transition zone. Investigations have found no references to any techniques to model such situations in the literature. Note that although the technique presented herein has not previously been described in the literature, results of the first model developed using the technique have been presented2. Drainage and Imbibition Figure 1 illustrates the difference between drainage and imbibition capillary pressure curves. It shows how saturations in a reservoir can alter such that imbibition rather than drainage curves provide a better description. Initially the reservoir is charged with hydrocarbons down to a point A (typically a spill point, unless hydrocarbon charge is limited). The hydrocarbon saturation profile at this stage is best represented by drainage capillary pressure curves. These curves are measured by gradual displacement of the wetting fluid in rock samples with a non-wetting fluid i.e. a process mirroring the displacement of water with hydrocarbons in the reservoir.