A Reservoir Simulator for Studying Productivity Variation and Transient Behavior of a Well in a Reservoir Undergoing Gas Evolution
Authors: Kazemi H. 
Published: December 2007

A gas-oil reservoir simulator was developed to study the productivity behavior of a well from the time the reservoir is above bubble-point pressure until abandonment. The studies include the effect of wellbore pressure until abandonment. The studies include the effect of wellbore shut in on subsequent oil productivity and the role of nonuniform gas distribution on the pressure buildup curve.

Introduction
in some instances, average reservoir pressure is above the bubble point of the in-place oil, but the in-situ pressure distribution in the vicinity of a producing pressure distribution in the vicinity of a producing well is below the bubble point. This situation usually gives rise to the coexistence of oil and gas around the wellbore in a cylindrical region with a diameter of several feet. In the presence of gas, the permeability to oil is reduced; this can cause substantial loss of oil productivity. The local reduction of oil permeability in the vicinity of the wellbore appears as a pseudodamage for the well.
As the reservoir depletes, the outer radius of the gas-oil zone grows. Eventually, the gas-oil zone spans the entire drainage area of the well. The gas saturation distribution is, of course, not uniform; that is, it varies with the radial distance from the well and in the vertical direction. This nonuniformity in gas saturation could affect the oil productivity and the pressure transient responses of a well in a manner different than if the gas saturation were uniform. Other factors, such as reservoir layering with and without crossflow, supersaturation, bubble-point change, residual solubility hysteresis, gravity force, etc., can also affect the reservoir and the well behavior.
To study the interplay of these factors and their effect on the pressure transient responses of a well, and possibly to take remedial action against unfavorable situations, the reservoir simulator described in this paper was developed. paper was developed.This simulator offers many new features as compared with the one used by Perrine and the one used by Earlougher et al. For instance, this simulator has an added vertical dimension, z; therefore, reservoir layering and gravity segregation and gas coning can be studied. Also, this simulator can cross the bubble point; it calculates the new bubble points at each node during a buildup test as the node pressures near the wellbore increase. A most important feature of this simulator is that it includes wellbore storage effect in two-phase flow as a correct boundary condition. This feature is not included in more than one phase in any of the published simulators. There also are other features in the simulator that have been included specifically for vanslent testing purposes.
Studies on supersaturation have been reported in several articles. Based on the experimental work of Refs. 2 and 4 on small core samples, it appears that, for prevailing pressure decline rates occurring in uniform prevailing pressure decline rates occurring in uniform porosity petroleum reservoirs, the supersaturation is porosity petroleum reservoirs, the supersaturation is between 0 and 50 psia. Furthermore it has been concluded that the solution gas drive oil recovery in these reservoirs is not affected by such supersaturations. Nonetheless, it was thought that it might be beneficial to include supersaturation phenomena in a reservoir-size simulator where the flow conditions are more complex.
Residual solubility hysteresis was studied experimentally by Motyakoa et al. They concluded that in the presence of a porous medium, there is a residual solubility hysteresis because of capillary phenomena; this means that some gas will never dissolve during reservoir repressurization.
JPT
P. 1401