Considerable amount of resources are spent by the petroleum industry on laboratory measurements of relative permeability. The technique used in most of these measurements is based on the interpretation of core displacement results, i.e. the unsteady-state method. Often core displacements for relative permeability tests are carried out at high flow rates and involve unfavorable mobility ratios. Although it is well known that such displacements can suffer from viscous instabilities, usually little or no attention is paid to the consequences of such instabilities. This may be one of the reasons why laboratory-measured relative permeability data are often found to be unreliable in reservoir simulation studies. It is, therefore, important to understand how viscous instabilities affect the measurements of relative permeability.
The objective of this study was to experimentally determine the relationship between the extent of viscous instability and the measured relative permeability. Oil displacement experiments were carried out in a triaxially confined core packed with silica sand. The extent of viscous instability was varied by using mineral oils of different viscosities as well as by using different flow rates. Relative permeabilities were calculated by using both a history-matching technique and an explicit technique similar to the JBN method.
Results of this study show that the two techniques of calculating relative permeabilities from unsteady-state displacement data provide essentially similar results, and that viscous instability affects relative permeability measurements significantly. Further, this study demonstrates that breakthrough recovery, end-point water permeability and residual oil saturation are co relatable with a dimensionless number characterizing the extent of viscous instability.
The importance of reliable relative permeability data in reservoir engineering studies is well recognized in the petroleum industry. Such data are often obtained by using either steady-state or unsteady-state methods. Because a long time is needed to obtain a single relative permeability curve when using the steady-state method, the unsteady-state method, also referred to as the external-drive method, is often preferred in laboratory studies as it facilitates a much faster data acquisition process. Moreover, the unsteady-state method is applicable to displacements where saturation gradients exist, while the steady-state method is not. As a consequence, the difference between relative permeabilities estimated by using the two methods can be significant for the same sand-fluid system [l,2].
Use of the unsteady-state method is limited to displacements in which the assumptions underlying the Buckley-Leverett theory are met . This implies that the displacement used for measuring relative permeabilitles must be stabilized and strictly one-dimensional so that the pressure and saturation are uniform in any cross-section. Therefore, ideally, the unsteady-state method is applicable only when the displacement is both stable and stabilized.
Usually, one of the two approaches -- explicit or implicit is taken to estimate relative permeabilities from laboratory displacement data. The implicit approach is advantageous when the displacement is unstabilized and/or the end-point mobility ratio is near one [6,7,8,9]. In this approach a reservoir simulator is used and the differentiation of laboratory data is not required.