On the Modelling of Vertical Permeability Barriers in Single-Well Simulation Models;a Hybrid Approach

Abstract

ABSTRACT This paper presents stochastic descriptive schemes for explicit and implicit modelling of vertical permeability barriers in single-well simulation studies. The drainage volume of the well to be simulated is first partitioned into two regions; one explicit region (termed explicit because actual barriers such as shales of varying sizes are placed within the grid) and one implicit region (termed implicit because the effects of the discontinuous shales are averaged into an effective vertical permeability). Secondly, the shales are converted into vertical transmissibility modifiers and included in the data input stream along with the effective vertical permeabilities calculated for the implicit regions. The paper describes in detail procedures which: -Generate lateral dimensions of shales observed in a well (shale shape and length/width statistics supplied by geologists, shale positions in wells and thicknesses of shales in wells from cores and logs).-Maintain the sand/shale sequence observed in the well.-Generate additional shales in the defined explicit shale region around the well until an overall desired vertical shale density (number of shales/vertical foot) is achieved. The placement of these shales which are not "hit" by the well-bore is subject to conditioning and constraints.-Make all shales "conform" to a pre-set areal and vertical grid system.-Plot out pictures of the resulting shale descriptions.-Estimate an effective large-scale vertical permeability for use in large grid-blocks far away from the well (in the implicit region).-Convert shales into subdomains over which the vertical transmissibility between model layers K and K+1 is modified (written out to tape for direct inclusion in simulator data input stream). The methodology developed is illustrated by applying it to a North Sea reservoir with a thin oil column sandwiched between a gas cap and an active aquifer. In this reservoir, trustworthy predictions of oil, gas and water production rates through time are of fundamental importance. In fact, the field development decision may be swayed one way or the other depending on how long the gas and water production may be suppressed (aided by shales) for a reasonably high (and sustainable) oil production rate.