ABSTRACT
A unique feature of the production of fluids from geologic media is that for a variety of reasons, the surfaces through which fluid has to be extracted have complicated geometrical features. The conventional wellbore (the simplest case) is assumed to be a cylindrical surface that extends over the entire thickness of the porous medium (in all of the following we assume that the porous medium is horizontal). Such a wellbore is usually approximated by a line source. When extracting fluids from geologic media, it is not unusual for wellbores to be in contact with only a part of the porous medium; that is, fluid is not extracted over the entire thickness of the porous medium, and in this case, we need to examine flow in three dimensions. Similarly, wellbores are not always vertical; in many oil fields, wells are frequently “inclined” and, in some cases, even horizontal. In such situations, we must, again, contend with flow in three dimensions. In geologic media that are not very permeable, it is not unusual to extend the surface area available for withdrawal by creating cracks known as hydraulic fractures. Such cracks are usually filled with sand and can be treated as a porous medium with properties distinct from those of the reservoir rock. Because of the prevailing stresses in the reservoir rock, such cracks are usually vertical, although horizontal cracks may develop at shallow depths. Hydraulic fractures or cracks are usually considered to be rectangular or circular sources.
