Pressure transient behaviours of vertical wells in low permeability reservoirs with threshold pressure gradient

Many studies show that the threshold pressure gradient (TPG) is physics behind the upwarp of pressure derivative curves in intermediate and later time by using superposition principle to solve mathematics model with TPG, which misleads us to a dilemma: although TPG can match the measured build-up data, the interpreted TPG does not accord with reservoir development. Our research shows that this dilemma is caused by wrongly applying superposition principle to non-homogeneous equation. In this paper, a fully implicit numerical scheme is developed to solve the flow model incorporating TPG and is used to study the error caused by wrongly using the superposition principle. The error is so big that the results based on superposition principle are totally wrong and lead to dilemma. Therefore, the main contribution of this paper is that the physics behind upwarp of derivative curves is not TPG, and we should go further to find out the true flow mechanism in the low permeability reservoirs.