This paper presents a linear flow water influx analysis method where the aquifer is separated from the reservoir by a partially communicating fault. Transient pressure distributions are considered both in the reservoir and in the aquifer. Cases where the leaky fault is located within the aquifer can be analyzed with this model given a superposition of constant rate flow periods at the oil-water interface. Constant production rate is specified at the inner boundary, without inner boundary storage and skin. The partially communicating fault is modeled as a boundary skin of infinitesimal thickness having no storage. The aquifer considered in this paper is infinite in the lateral extent. The problem is posed and solved using the Laplace transformation, yielding Laplace solutions of the exponential form. The solutions presented in this paper, along with a set of type curves extend the transient linear flow work presented by Hurst (1958) and by Nabor and Barham (1964). When the inner region, the reservoir, has an infinite permeability and a finite storage, it acts like a tank, where the boundary pressure is equal to average pressure in the inner region. This case is identical to the linear water influx model presented by Hurst (1958). When the inner region has no storage associated with it, the constant inner boundary rate is transmitted to the second infinite region, hence yielding the simple linear flow case presented by Nabor and Barham (1964). This paper extends the current solutions by allowing pressure variations in the reservoir or the inner region as well as in the infinite aquifer. Also, the model presented in this paper considers the effects of skin located at the boundary between the two regions of the system that may be caused by a partially communicating fault separating these two regions.

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