The theories and models of well testing analysis of dual porosity reservoirs with uniform thickness have been discussed in detail in the literature. In order to completely describe the situations of real reservoirs, this paper first studies the pressure behavior of dual-porosity composite reservoirs with non-uniform thickness and lateral heterogeneity. In this paper, the dual-porosity composite reservoir with non-uniform thickness and lateral heterogeneity is defined as the dual-porosity reservoir that consists of many zones with non-uniform thickness, different fluid and formation properties. A new effective radius mathematical model of this composite reservoir in the presence. of skin, wellbore storage and phase redistribution is presented. Laplace-space solutions for this mathematical model with outer constant pressure boundary or outer impermeable boundary are obtained by Laplace transformation and the typical curves for the modern welltesting analysis are given by numerically inverting method. The mathematical model has improved the welltesting analysis theories and the pressure behavior of this reservoir is discussed. The model and solution can be used in the fractured reservoir with variable formation properties or containing water injection wells, gas injection wells, polymer injection wells or finite damaged zone.

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