Production from many naturally fractured reservoirs is only marginally profitable. Thus, determining the drilling direction for maximum production in such reservoirs is very important. A simple analysis is presented for determining the optimum drilling direction in a naturally fractured reservoir. Two-dimensional scanline analysis is used to find the maximum fracture interception rate, then is generalized to find the maximum fracture-flow interception rate. Finally, the analysis is further generalized to the three-dimensional case.

In this analysis, fractures are presumed to occur in sets. In fracture sets, fractures are assumed to have a common orientation, uniform closest spacing (S^*), and a representative flow aperture (e), which govern the capacity of each set to contribute to flow into the well bore. The optimum drilling direction is controlled by the aperture, spacing, and orientation of fracture sets with respect to the well bore. The optimum direction favors the direction of closest spacing for the fracture set having the largest ratio of flow aperture to spacing (e³/S^*), i.e., the fracture set that has the greatest capacity for conducting fluid to the well bore.

To introduce the method of analysis, focus is given to finding the optimum direction to drill a horizontal well through two intersecting sets of vertical fractures. A nomograph for this solution is provided. The analysis is extended to a general case, where any number of fracture sets may exist, each with its own representative flow aperture and orientation.

A degenerate form of the general case pertains to sets of vertical fractures penetrated by an inclined hole. This degenerate case can be reduced to a two-dimensional form by projecting the well bore onto the horizontal plane. The optimum drilling direction can then be found by the two-dimensional solution outlined in this paper, but the resulting fracture interception rate is reduced as a function of the well bore inclination.