In using hydraulically fractured wells for aggressive reservoir exploitation, the spacing of vertical wells and/or transverse fractures in long horizontal wells becomes quite an important consideration. The geometry and conductivity of single fractures in infinite-acting reservoirs have been related to productivity by the well known Cinco-Ley and Samaniego work. Later work by Valkó and Economides provided physical optimization under pseudosteady-state conditions in regularly shaped (circular or square reservoirs) using the novel concept of the Proppant Number as a normalizing and descriptive parameter.

However, the shape of the drainage is rarely square and, especially it is not so when a given drainage area is split by the drilling of in-field vertical wells or, in the case of a horizontal well, multiple transverse fractures are executed. The shape of the drainage, encompassing parallel, tightly spaced fractures, becomes a controlling variable for the calculation of the individual and total productivity indices. This is particularly important in our quest to maximize well performance, not just to fracture wells. Until now, such work was the realm of numerical simulation with all the associated benefits and problems.

In this work, the pseudosteady-state productivity index of a fractured well in reservoirs with different aspect ratios (ye/xe) was calculated using the Direct Boundary Method. For relatively small Proppant Numbers, there is a simple relationship that allows for the use of already developed correlations by Valkó and Economides for maximum productivity index and optimum fracture conductivity (and the indicated fracture geometry). For larger Proppant Numbers, this work provides factors labeled Fopt that account for the departure from the square optimum. These factors facilitate the calculation of the maximum JD in different reservoirs for any Proppant Number. The work allows for drainages of a large range of aspect ratios and any fracture penetration.

You can access this article if you purchase or spend a download.