In this paper, we present a model of the complete characteristic transient response from a composite reservoir including the effects of skin, wellbore storage and phase redistribution at the well. We present six flow regimes and the combined effects of wellbore storage and phase redistribution on pressure behavior in composite reservoirs.Using an automatic history matching approach, we analyzed three buildup tests and a pressure falloff test.This method eliminated the serious uniqueness problem associated with type curve analysis. We demonstrate that incorrect reservoir parameter estimates and incorrect production performance predictions would result from the use of any model that lacks the capabilities of the model we present in this paper.We also demonstrate possible misinterpretations of pressure data ~at may result from not recognizing the presence of phase redistribution in the buildup test data or not recognizing the composite reservoir behavior.