Determination of Absolute and Relative Permeability Using Well Test Analysis

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Author:	Abdul Jaleel Abdullah Al-Khalifah
Year:	1988
Degree:	PhD
Advisers:	Horne, Aziz

Abstract:

Multiphase flow is modeled with a diffusivity equation using p2 as the dependent variable. Such a model applies to systems in which a gas phase is present (i.e. gas-oil and gas-oil-water reservoirs) where it represents the physics of multiphase flow better than existing models and with fewer restrictive assumptions. This new approach allows reasonable estimates of reservoir and wellbore parameters such as effective oil permeability and wellbore skin.

This dissertation also presents a new method to estimate two- and three-phase relative permeabilities in-situ, using pressure transient analysis. The technique requires a short draw- down test, consisting of a number of steps of increasing flow rate. The resulting estimates of relative permeabilities reflect the properties of the entire drainage area, rather than those of a small laboratory core. The method estimates the relative permeabilities at sandface saturations. which cover a range of reservoir conditions that will take place in the future.

The proposed relative permeability method applies solutions of a multiphase diffusivity equation in terms of the pseudopressure function, m(p). These solutions had already been reported for constant rate tests in solution gas-drive reservoirs by Raghavan (1976). This work extends the pseudopressure solutions to three-phase systems. Two- and three-phase solutions were then superposed to obtain multiple-rate solutions. The saturation equation developed by B$e et al. (1981) for solution gas-drive reservoirs, is extended to three-phase reservoirs. These solutions are then used to estimate relative permeability-saturation values during the test. When reservoir absolute permeability is not known, the proposed relative permeability technique results in estimates of the effective permeability as a function of the saturation. These results can then be fitted with a simple relation to infer the absolute permeability. A rate-normalization method applicable to multiphase well tests is formulated and applied to simulated tests with varying flow rates. Such a normalization results in reasonable estimates of individual phase permeabilities and thereby an accurate value of total system mobility.

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