Analytical Model for Vertical Interference Tests Across Low-Permeability Zones

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Abstract
A mathematical model is developed that describes fluid flow and pressure behavior in a reservoir consisting of two permeable zones separated by a zone of low permeability, or a "tight zone." This model can be used to design and to interpret buildup, vertical, interference, and pulse tests conducted in a single well or multiple wells across lithological strata. Dimensionless pressure functions and corresponding parametric type curves are derived to interpret vertical interference test data for tight-zone vertical permeability. Application of these type curves is illustrated using field data from two vertical interference tests. Test results obtained with the tight-zone model are shown to compare favorably with results obtained by using (1) computer simulations and (2) Burns' method based on the uniform anisotropy assumption. Computer simulation using a numerical model also shows that high near-wellbore conductivity from a packer leak or poor cement job could not have adversely affected test results. The model presented and the type-curve interpretation method outlined are accurate for designing and interpreting single-well vertical interference tests across low-permeability zones.