Application of New Pseudo-Pressure for Deliverability Test Analysis in Stress-Sensitive Gas Reservoir
Authors: Fang Yang , Yang Bin 
Published: June 2014

Abstract
Changes in reservoir fluids during production have long been recognized, but the reservoir strata themselves typically have been considered to be static systems, the deliverability within many, if not most, reservoirs has been found to vary to some degrees as a function of a stress-sensitive conductivity that changes with changing stresses. In order to estimate the productivity of stress-sensitive gas reservoir accurately and incorporate the variable properties in these estimates, a new pseudo-pressure is defined to evaluate the combined effects of stress, fluid flow and reservoir property changes on well performance, in particular, we pay more attention to the interpretation of deliverability test data and to changes in the production characteristics of wells. Based on this new defined pseudo-pressure, a new deliverability model which takes into account variable rock properties in gas reservoir is proposed. This model is different from the conventional deliverability model as the coefficients are the function of pressure and change with the producing time. A brief discussion is followed on how to calculate the parameters including the coefficients and new pseudo-pressure utilized in the equation. The results reveal that if the stress-sensitive coefficients increase by 1%, then the AOF will decrease 12%.This model permits us to address the issues we have raised in a comprehensive manner and thus presents a basis for the study of deliverability test analysis in stress-sensitive gas reservoir.

Introduction
Because of the effect of mass depleting and stress unloading, the pressure of fluid in the porous media starts to decline, and the effective stress on the matrix increases during the development of oil and gas field, which leads to the deformation of rock skeleton and property changes of reservoir rock[1–4], especially the permeability and porosity. The above phenomenon which is caused by the change of formation stress field is called as the stress sensitivity. References [5–9] think that the relatively great deviation will be caused if using the conventional evaluating method to estimate the productivity of stress-sensitive gas reservoir. This is because of the ?stress pollution? phenomenon[10–13]during the development of this kind of gas reservoir. In this case, the permeability distribution in the pressure cone of depression near the wellbore is also formed to be the shape of cone; thus, a great extra pressure drop will be created. The pressure decrease or the change of inflow system in the gas reservoir with stress sensitivity will make the stress field redistributed, and thus the spatial distribution of permeability will be changed correspondingly. Therefore, it can be seen that the outflow parameters will change continuously during the whole development process, so the productivity of gas reservoir with stress sensitivity needs evaluating dynamically. With the consideration of the continuous change of reservoir outflow parameters, this paper defines a new pseudo-pressure, which involves stress field change, to evaluate the productivity of gas reservoir, and presents the changing principle of productivity in the stress-sensitive gas reservoir after pressure declines or outflow system is changed. Hence, the methods in this paper not only can be used to interpret the obtained data of deliverability test, but also can provide valuable reference for optimizing production system of gas reservoir which has stress sensitivity.