A three-dimensional reservoir simulation study indicates that propped fracture height in excess of the productive thickness of the reservoir can add to well productivity. The effect of excess propped fracture height is more evident when fracture conductivity is relatively low compared to formation conductivity. The simulations indicated that in cases where dimensionless fracture conductivity (cd, as defined by Cinco et al,' is less than ten, any excess fracture height will increase well productivity. The magnitude of the productivity increase is a function of the dimensionless fracture conductivity and excess height.
A series of type curves is presented that compares the transient pressure behavior of hydraulically fractured wells where the propped fracture extends uniformly above and below the reservoir to the same wells where there is no excess fracture height. In addition, a comparison of the pseudo steady-state productivity increase that would be expected for a hydraulically fractured well is presented for wells with and without excess propped fracture height.
Selected cases are presented to illustrate the economic impact of excess propped fracture height and how it may affect proppant selection.
The ability to achieve adequate fracture conductivity is an essential part of fracture design. Many authors 2 have investigated the effect of fracture length and conductivity on post-fracture well productivity for vertically fracture reservoirs. The initial studies assumed pseudo steady-state or steady-state flow in the reservoir and fracture height equal to the reservoir thickness. Later, work by Tinsley et a investigated the relationship between fracture height and well productivity for cases where the fracture height was equal to or less than the reservoir thickness. All of these early works employed the use of two-dimensional mathematical or physical analog models to predict post-fracture well productivity.
The transient pressure behavior of vertically fractured wells was investigated by Cinco et al 1 using a mathematical model and by Agarwal et al using a two-dimensional reservoir simulator. As with earlier investigations, Cinco et all and Agarwal et al assumed that fracture height was equal to reservoir thickness. These authors presented type curves based on dimensionless variables to aid in evaluating well test data and production histories from hydraulically fractured reservoirs.
The earlier works of McGuire and Sikora and Tinsley et ap and the more recent publications of Cinco et all and Agarwal et al present relationships between fracture conductivity, reservoir permeability-thickness product, fracture length and post-fracture well productivity. Generally, the literature indicates that for a given reservoir and fracture length, there is an optimum fracture conductivity. Exceeding this optimum fracture conductivity will provide a negligible increase in production. However, if the optimum fracture conductivity is not attainable due to physical limitations of fracturing fluids, equipment, proppants, etc., any increase in fracture conductivity will increase well productivity.
The assumption that propped fracture height is equal to or less than the reservoir thickness predominates the literature available that evaluates post-fracture well performance. Currently, the majority of fracture modeling is based on constant height formulations. More recent developments in three-dimensional fracture modeling indicate that hydraulic fractures, in many cases, are not limited to the reservoir thickness. A number of research projects are currently aimed at quantifying fracture geometry and post-fracture well performance, which includes the Department of Energy's (DOE) Multiwell Experiment (MWX).