Abstract
The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is generally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so serious as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same.
Introduction
This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen, consider these same effects. In addition to providing more general results for vertical fractures than are available from the literature, the present paper gives the equivalent well radius of fractures having different lengths and Capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here.
Extreme cavity expansion in soft solids: Damage without fracture