Analytical solutions and type curves for the constant rare radial flow of fluid in both conventional and naturally fractured reservoirs including the effect of wellbore phase redistribution are presented. All automated procedure for non-linear least square minimization using the analytical solution and their derivatives with respect to the unknown parameters has been developed to analyze the pressure build up data affected by phase redistribution. Field examples and analysis are also presented.
Theoretically the Horner plot of a pressure build-up test in a radial infinite porous media should be a straight line. Some of the variations from this behavior, such as the curved portion immediately after shut-in which results from after production and skin effects, and the flattened portion due to boundary effects are known. The bottom hole pressure (BHP) response in a pressure build up test is controlled by many factors in both the reservoir (i.e heterogeneities and boundaries) and the wellbore conditions such as limited entry, skin and wellbore contents effect.
The effect of the wellbore contents on a pressure build up test has been described by two phenomena: wellbore storage and phase redistribution. Wellbore storage, noted by Van Everdingen and Hurst 1, has been described in detail by Ramey 2 and Agarwal et al3. When a producing oil well is shut-in at the surface, due to compressible nature of the content of the well, fluids continue to flow from the reservoir into the wellbore (after flow) for a time. If after shut-in gas and liquid are simultaneously flowing into the wellbore, gravity effects will cause segregation of phases. Since the gas cannot expand on its way to the top of the well and because of the difference between gas and oil compressibilities, it causes a net increase in the wellbore pressure.
General analysis of wellbore phase redistribution was first presented by Stegmeier and Matthews4 and Pitzer et al5. Fair 6 later showed the effect of wellbore phase redistribution to be a storage effect and presented analytical solutions for the radial infinite reservoir. Winterfeld 7 examined the effect of wellbore on pressure buildup tests by solving the flow equations in the wellbore/reservoir system with finite difference approximation and found that after a sufficiently long time, gas and liquid phases were completely segregated.
In this work we propose, new type curves for analyzing pressure transient data effected by phase redistribution in naturally fracture reservoirs. We have also treated Fair's conventional model differently and have obtained type curves in terms of PD vs t0/C0 similar to those presented by Grngarten et al 8 but including the effect of phase redistribution. We have considered the Laplace space solutions and their derivatives with respect to the unknown reservoir parameters with an automated procedure and have been successful in analyzing a pressure build-up test conducted on a well located in Southwest of Iran.