Abstract

ABSTRACT The effect of the partial penetration of an infinite conductivity fracture on the transient pressure behavior of a vertically fractured well is investigated. Analysis of results shows that the pressure behavior of a well intersected by a partially-penetrating infinite conductivity vertical fracture can be divided into three flow periods: 1) the early time flow period which is characterized by a formation linear flow as in the case of a fully-penetrating infinite-conductivity vertical fracture, 2) the infinite-acting flow period and 3) the pseudoradial flow period which develops after the effects of the vertical boundaries of the reservoir are felt in the pressure behavior of the well. A log-log graph of log(hf/h)pwD versus log tDxf shows a slope of one half during tine early time How period of a well with an infinite-conductivity partially penetrating fracture. The time for the end of the early time flow period is directly related to the square of the dimensionless height of the fracture, hfD, which is defined as the ratio between the height of the fracture and its half length. This time becomes so small for small values of hfD that the linear formation flow period will not show up for practical purposes. The solutions during the infinite-acting flow period are, for the different values of penetration ratio and a given value of hfD, characterized by a single envelope curve in the log-log graph previously mentioned. The time for the start of the pseudoradial flow period shows no dependence on the penetration ratio and on the dimensionless fracture height except for fractures with dimensionless heights larger than about 1 and penetration ratios smaller tha 1/5. Even though solutions were mainly obtained for the case of a fracture located at the middle of the formation, the effect of offsetting the fracture was investigated for some particular cases. As expected, the solutions are the same up to the end of the infinite acting flow period which slightly varies as a function of the fracture location. The solutions are presented in the form of type curves suitable for transient pressure analysis procedures.

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