Industry Applications of a New Analytical Method of Solving Complex Three-Dimensional Geologic Problems: Forward Modeling, Measuring While Drilling, and Other Analyses

James J. Willis

A new analytical method has been developed for solving complex three-dimensional geologic problems, many of which have important relevance towards the oil and gas and coal industries. Previous methods are, in addition to being of limited applicability, somewhat time consuming and difficult, involving numerous equations, complicated graphical constructions, and/or other factors. This new analytical method, however, is based on a single "master" formula, which despite its relative simplicity is capable of solving numerous types of complex three-dimensional problems with minimal time and effort. The method is also easily incorporated into computer programs.

Some of the more straight-forward problems that can be easily solved utilizing this new method include depth determinations, apparent and true dip calculations, and thickness corrections. As these aspects play a role in every well drilled, the method can likewise be utilized during planning (or forward modeling) of well-bore trajectories, especially in situations involving substantial well-bore deviation. The method can also be used in fractured reservoirs for planning optimal trajectories for maximum penetration of fracture sets. Although these forward-modeling approaches are certainly beneficial, the method truly exhibits its applicability during actual drilling, especially for horizontal wells. For example, information, such as down-hole location and well-bore deviation, gained fro measurement-while-drilling techniques can be continuously inputted into the methodology to help determine stratigraphic position and therefore compare to actual MWD log information. Furthermore, the calculations actually determine whether the bit is drilling upsection or downsection, thus the method can be used to determine exact location within the target horizon and to predict when (or if) the bit will leave the horizon, and therefore allow for adjustment of the well-bore trajectory to remain in that horizon and to maximize intersection of fracture sets.

The method is also particularly useful for working in faulted terranes, both in well bore and in outcrop, allowing for rapid determination of various fault parameters, including throw, heave, vertical separation, and other separation parameters, and with certain information slip parameters as well. Other applications, including stereonet analysis, also exist not only in the hydrocarbon industry, but also in structural geology, field methods, stratigraphy, hydrogeology, education, and other fields of study. The versatility of this new method is unsurpassed by any other previous method, including other single-formula type methods, and its applicability towards industry-type problems make it particularly beneficial.

AAPG Search and Discovery Article #91020©1995 AAPG Annual Convention, Houston, Texas, May 5-8, 1995