Abstract

This paper reviews some concepts related to the evaluation of the wellbore pressure behavior in a fractal reservoir. The purpose of this work is to show the impact of the mechanical skin on the pressure drop and its derivative behavior, and therefore on the interpretation of the well test data to determine parameters of a reservoir with fractal geometry.

We use the solution for an infinite fractal reservoir without and with matrix participation, with a well producing at constant rate, including wellbore storage and skin effects. This solution is in the Laplace domain; applying numerical inversion with the Stehfest algorithm we obtain the pressure solution in time.

It is shown that the characteristic power law behavior of both pressure drop and semilogarithmic derivative not only depends on the parameters of fractal dimension (dmf) and connectivity index of fractures (θ), but also on the skin factor. The parallel straight lines behavior may be valid at long times during the transient period, but at early times, the skin and wellbore storage effects may inhibit this behavior. This effect, at early times, is greater for fractal dimension values close to the Euclidian dimension (i.e. dmf~2).

Thus, if the fractal dimension (dmf) and/or the connectivity of fractures decrease (θvalue increases), the pressure drop in the reservoir may be larger than the pressure drop due to the skin effect, consequently the parallel behavior of pressure and its derivative would be even valid at early times. But if the skin is big enough, the parallel behavior would only be valid at long times during the transient period.

The direct determination of the skin is not possible for these systems because the skin and fractal parameters are affecting the pressure response at the same time. A new definition of dimensionless time, which includes a new equivalent wellbore radius concept to take into account the skin effect in a general way, is proposed. With this definition of dimensioless time, it is possible to get the parallel straight lines behavior even at early times.

It is presented a sensibility analysis to fractal dimension, connectivity of the fracture network, skin factor and wellbore storage constant, for a well on a radial fractal reservoir.

The proposed methodology is important because the direct determination of the skin is not possible for fractal systems as it can be done for classical Euclidean reservoirs, with a logarithmic behavior, mainly because the skin and fractal parameters are affecting the pressure response at the same time.

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