Implementation of Multirate Technique to Measure Relative Permeabilities Accounting for Capillary Effects

Abstract

A practical implementation of the multi-rate steady-state technique to determine relative permeabilities from steadystate floods and its comparison with the standard steady-state technique is the main subject of the paper. The multi-ra~e technique is based on the theory of two-phase flow, and facilitates analytical corrections of relative permeabilities to account for capillary end effect. This is especially of practical importance if the experiment is performed at low rates when the relative role of capillary forces increases. NormaIIy, it is recommended to perform flooding experiments at high rates ancl/or on long cores to suppress capillary effects. Though this approach ensures simplicity in the interpretation procedure it disregards several factors one of which is that the relative permeabilities may depend on the rate. Proper account for capillary effects makes usage of long cores and high rates unnecessary, A number of steady-state core floods have been performed at different rates varying from a high rate typically used in the lab experiments to a low rate approaching the range of typical reservoir rates. The experimental results, i.e. a set of relative permeabilities depending on the rate, have been interpreted both without and with account for capillary end effect. The previously developed analytical corrections for capillary effects were implemented in the interpretation, The results of analytical interpretation are quality controlled by numerical simulation of the experiments. It is shown that much of the difference observed in relative permeability curves and residual saturations measured at different rates can be explained by the influence of capillary end effect. Introduction The steady-state technique is one of conventional methods applied in special core analysis to determine relative perrneabilities. Since the classical paper [10] it is recognized that capillary forces significantly affect laboratory experiments though neglected in the standard interpretation procedures. In order to avoid inaccuracies resulting from capillary effects neglect generally 2 options exist: either to avoid them by using sufficiently high total rates (which is not always possible in case of low permeable rocks), or to introduce the corrections taking into consideration capillary pressure. An analytical approach to correct the steady-state measurements of relative permeabilities taking into account capillary forces has been developed and tested against simulated data in [13], [14], [15]. The method employs self-similarity of the steady-state twophase flow with respect to flow rate. The same idea was used to determine capillary pressure and relative permeability of the non-wetting phase in [9], [ 6] for a more restricted model, only the non-wetting phase is flowing. In the present paper the analytical corrections are applied to real experimental data. It is shown how the measured data a corrected step by step using EXCEL work sheet. Experimental planning To ensure measurable capillary end effects the injection rates for the flooding experiments have to be planned based on the parameters of the core plug, capillary pressure, and the estimates of the unknown relative permeabilities. Input data. To guide in planning the experiments, simulations of the steady-state experiments have been performed, using the core flood simulator CENDRA. Steady-state drainage experiments at 2 different total rates have been simulated. Capillary pressure was measured by centrifuge method on a plug cut from the same core. The measurements were interpreted by Hassler-Brunner method, see Figure 1. The length of the core is 25 cm. The grid is 150x1x1, of which the 50 blocks close to the core outlet have a length of 1 mm, while the length of the rest is 2 mm. The relative perrneabilities functions used in the simulations, see Figure 2, were taken from literature, Ref. [12].