Journal of Canadian Petroleum Technology, Vol.46, No.7, 49-54, 2007
An improved pseudo-time for gas reservoirs with significant transient flow
The use of semi-analytic methods for correcting flow equations to accommodate changing gas properties with pressure has become increasingly common. It is a mainstay of modem production decline analysis, as well as gas deliverability forecasting. The use of pseudo-time is one method which enables a time-based correction of gas properties, honouring the gas material balance within the time-based flow equation. By using pseudo-time, the analytical well/reservoir models, derived for the liquid case (slightly compressible fluid), can be modified for gas by re-evaluating the gas properties as the reservoir pressure depletes. These gas correction procedures are well documented in the literature. Also well documented is the iterative nature of the gas properties correction methods, as original gas-in-place is a required input into the equations. The pseudo-time correction is based on the average reservoir pressure and works very well for boundary dominated flow. However, when transient flow prevails, the pseudo-time concept is not valid and its use can create anomalous responses. This will occur in low permeability systems or in reservoirs with irregular shapes, especially where some of the boundaries are very distant from the well. The semi-analytic gas correction has a 'representative pressure' at its root, which, in the existing models, is always the average reservoir pressure. We propose a straightforward modification to the determination of this pressure as follows. The representative pressure ought to be based on a 'radius of investigation' or 'region of influence' (in the case of non-radial systems), rather than the average reservoir pressure. In the case of a depleting system, the representative pressure would be the same as the average reservoir pressure. The following paper outlines the proposed procedure and illustrates its advantages over the existing method by using synthetic and field data examples.