A novel method for computing two-phase relative permeability curves from the results of spontaneous imbibition experiments is presented. Using a specially constructed imbibition cell and an X-ray Computed Tomography (CT) scanner, we obtain accurate measurement of saturation profiles along the length of cores as a function of time. The saturation profile history allows direct computation of the relative permeability for both phases from a single experiment when used in combination with a previously measured capillary pressure curve. Results are unique within experimental error. The proposed procedure works equally well for spontaneous and forced cocurrent imbibition. It was tested thoroughly using synthetic and experimental data, for water-air and water-oil systems. Test results are described within the paper. Advantages include the incorporation of capillary forces and no requirement for steady-state conditions. This method is useful to measure imbibition relative permeability curves, especially in low permeability rocks. In such systems, it is laborious to reach multiple steady states and capillary forces are significant so that classical unsteady- state techniques do not apply.
Simulation of multiphase flow in porous media requires knowledge of relative permeability functions. These functions are necessary to make estimates of productivity, injectivity, and ultimate recovery from oil reservoirs for evaluation and planning of production operations1. Therefore, measurements of relative permeability in the laboratory and/or empirical and theoretical models are an important subject in reservoir modeling.
The laboratory methods used to calculate relative permeability functions are grouped into centrifuge, steady- and unsteady-state techniques. The centrifuge method has been improved, however, concerns regarding the replacement of viscous forces with a range of centrifugal forces still remain for unsteady state2 displacement processes that are rate dependent. Steady-state methods offer disadvantages, especially in the case of low permeability rocks, in which it is laborious to reach multiple steady states and, capillary forces and capillary end effects are significant3,4. Steady-state techniques have been improved in order to make corrections for capillary effects5 but they still require successive measurements for different total flow rates. Capillary pressure has a significant effect on saturation distribution and recovery, and capillary forces dominate multiphase flow in low-permeability rocks and fractured reservoirs. In developing unsteady-state methods for low-permeability systems, it is necessary to account for capillary pressure when obtaining the relative permeability curve. Thus, most unconventional unsteady techniques do not apply.
There are also methods that measure relative permeability by history matching observable parameters such as fluid production, pressure drop, and saturation profile history. These methods assume that the relative permeability and capillary pressure curves behave according to a pre-determined function. The limitation imposed on the description of the actual shape of the relative permeability curve causes a bias error and a variance error6. When the number of parameters in the functional representation increases, the bias error tends to decrease. However, because more parameters are estimated on the basis of the same amount of information, the variance error tends to increase.
In the method we propose, each relative permeability value at a particular saturation is treated independently. Fitting to a pre-determined functional shape is not necessary. Two-phase relative permeability curves are computed from experimental in-situ, saturation profiles obtained from spontaneous imbibition experiments for cases where the water saturation profile shows an advancing front. This is the case observed for experiments with low or zero initial water saturation. For experiments where the core is partially saturated with water initially, the water saturation increases almost uniformly in time throughout the core. In this event, the imbibition method becomes quite similar to that proposed by Sahni et al7 for gravity drainage in three-phase systems. Synthetic cases are used to first verify the technique before application to experimental data. In all cases, the relative permeability curve obtained is input for numerical simulation and the agreement between input and computed saturation profiles checked.