An Improved Method For Matching Field Performance In The Simulation Of Complex Low Permeability Reservoirs
Authors: Arthur Kenneth Bismark , Morgan David Keith 
Published: December 2007

Abstract
For a high permeability reservoir with relatively uniform rock properties the matching of field performance, derived from buildup curves, to simulated performance is not a very difficult operation. When permeability is low and the reservoir is complex, the matching process is less straight forward. Difficulties can arise from two sources. The local variations of rock properties around the well can distort the buildup curves, and the coarse mesh used in field-wide simulations cannot reproduce individual well behaviour correctly. The method described generalizes and extends published methods for unified pressure analysis and derives data for matching purposes by filtering out unwanted short-term transients. The process also corrects for the effects of mesh size which is of importance when mesh block size is large. The principles underlying the method have been proved in field application over a considerable period of time, during which the methods themselves have been refined.

INTRODUCTION
A number of published papers (e.g. References 1 and 2) have shown that automatic matching of simulator performance to field performance is now economically feasible. The question that we wish to consider in this paper is how an optimum 'field performance' may be defined. We intend, for the sake of simplicity, to limit our discussion to single-phase, or effectively single-phase, flow.
If 'field performance" is defined as the assembly of measurements of pressure and of flowrates on all wells, then a simulator would have to have a very fine mesh spacing around each well if it were to reproduce faithfully the measured performance. While technically feasible, such a course would be unduly costly.
Another approach, described by Peaceman3, is to derive from each buildup an average block pressure. This approach assumes that the reservoir around the well has uniform properties and it can therefore be expected to work well when this assumption holds. In his paper Peaceman bases his derivation on the following equation which defines a 'block productivity index' as:Equation 1
This result is derived by comparison of the steady-state analytic solution for a repeated five-spot with that obtained from an equivalent mesh.
We ourselves carried out a similar numerical experiment some years ago, but made the comparison using an unsteady-state solution. We obtained effectively the same formula when steady conditions were attained but found that the mesh and analytic solutions did not give comparable results until a time of the order ofEquation 2
had elapsed. Figure 1 illustrates the time dependence of block productivity behaviour and is a plot of both the block productivity ratio and the log slope ratio against the dimensionless block time.
A formula, equivalent to that of Peaceman, for block PI was used in the work reported in References 4 and 5 and in all other simulators that we have since constructed. We thus agree with Peaceman's block PI, but would point out that it is derived for steady state conditions, i.e. for t &gt; tpssb and by assuming constant reservoir parameters.
We have therefore concentrated our attention on cases where variations of reservoir properties do not permit the unambiguous application of standard well analysis techniques, and where average permeabilities are too low to permit stabilized buildup pressures to be reached in an economic time. Our first attempts to analyse this type of reservoir4, while reasonably successful, proved difficult to apply and accuracy was limited by flow rate measurement errors.