A Simple Statistical Method for Calculating the Effective Vertical Permeability of a Reservoir Containing Discontinuous Shales

Abstract

Abstract This paper describes a quick, a simple, easy to use method of calculating the effective vertical permeability of a reservoir region containing discontinuous shales. The method, which is derived in both two and three dimensions, can be applied to a layered medium in which the sand permeability anisotropies (in three mutually permeability anisotropies (in three mutually perpendicular directions) and the shale frequencies perpendicular directions) and the shale frequencies and dimensions can vary from layer to layer. The method is validated for specific cases by using numerical simulation and an analogue model of a real outcrop. The latter consists of conducting paper with slits cut in it to represent impermeable paper with slits cut in it to represent impermeable shales. Although strictly the method is only applicable to impermeable shales we show that it would appear to be generally valid when the real shale permeability is more than about two orders of magnitude lower than the effective permeability derived by assuming impermeable shales. Introduction The major inhomogeneity in many reservoirs may frequently by permeability barriers (on scale less than the typical well spacing) embedded in the porous medium. Such permeability barriers are often referred to as stochastic shales. We use the term "shales" since these are probably the most common type of barriers. however they could arise from other sources such as carbonate cementation. Whilst continuous correlatable shales can be handled with relative ease in reservoir simulation models these stochastic shales historically have presented a difficult reservoir engineering problem, both in terms of their description and in accounting for their effects in fluid flow. Some important effects which they may have are given below:The presence of shales above/below the perforations can provide protection from gas/water coning.Shales may decrease viscous, capillary or gravitational cross-flow and increase dispersive cross-flow.In reservoir simulators several physical parameters can be adjusted to yield the same response to observed pressure and production ratios. A good shale description could increase confidence in the uniqueness of the history match.Any EOR process relying on the injection of a gas into the reservoir will be very sensitive to the presence of shales. In horizontal drives they may be advantageous by increasing the vertical sweep and retarding gas breakthrough at the producer. In vertical drives they may be a disadvantage due to decreased vertical sweep.Shales may affect gravity drainage by:-uneven advancement of gas-oil contact-hold-up of oil on top of shales-inhibiting upward segregation of liberated solution gas.