This paper describes a new method for combining pressure decline data and production rates to determine original gas volumes for gas reservoirs. The method is illustrated by application to actual field data. The new method is similar to the classical analysis which extrapolates a plot of p/z vs. cumulative production to the original gas in place. However, it allows for the influx of water into the original reservoir volume in a more rigorous manner than previous methods. It also provides an estimate of the reliability of the predicted original-gas-in-place values.
Pressure decline analysis has become a basic reservoir engineering tool, particularly for gas reservoirs. It is readily apparent from the gas law of physical chemistry that the reservoir-pressure/gas-deviation factor ratio (p/z) should decline linearly with cumulative reservoir production, provided the reservoir is highly permeable and has a constant volume. Unfortunately, many reservoirs do not have a constant volume as a result of water influx that occurs with declining reservoir pressure. Most methods of accounting for this complication are based on the early work of van Everdingen and Hurst. Van Everdingen and Hurst used the Laplace transform to solve the partial differential equation governing single-phase radial flow in porous media and were able to relate production at an internal reservoir boundary to the pressure at that boundary. Many investigators have used this solution to account for water influx at the edge of a reservoir. These include the well-known techniques of van Everdingen et al., Hurst, Carter and Tracy, and Odeh and Havlena. The literature abounds in applications and variations of these methods.These methods can be visualized as modeling reservoirs as large tanks which gradually fill with water as the tank pressures decrease. Many workers have questioned the validity of such a model. In particular, Chierici et al. and McEwen have investigated the errors in the predicted hydrocarbon volumes that result from the unavoidable errors in the pressure measurements. Furthermore, Bruns et al. have shown that the effects of water influx on the nature of the pressure decline curve are diverse. Water influx can cause a concave upward pressure history, a concave downward pressure history, or an S-shaped curve. Pressure decline with strong water influx also can resemble closely the straight-line pressure decline of a depletion-type reservoir.This work is an attempt to overcome the short- comings of previous methods. The improvements are twofold. First, the model includes a moving water/hydrocarbon interface. In analogy with previous models, this allows a nonconstant tank volume. Second, the method provides not only a best estimate of the hydrocarbons in place but also an estimate of the accuracy of these results.
This work involves the development and use of a model that predicts reservoir pressure as a function of cumulative production and time. A schematic of the model is shown here.
JPT
P. 2261^
