Production of either wells completed in low permeability reservoirs or damaged wells has been possible because of hydraulic fracturing. The estimation of both the geometric and flow characteristics of a fracture represent a useful information for the calibration of fracture design methods and permits forecasting well flow behavior.
Transient pressure well test analysis has been used with success to estimate well conditions and reservoirs parameters. Conventional methods of interpretation are based on radial flow theory. This is a limitation when applied to fractured wells because they exhibit other type of flow at different times in a test.
Several authors have presented different techniques to calculate both reservoir and fracture parameters. These methods include the linear flow graph (delta p vs root of t), the bilinear flow graph (delta p vs root of t), the semilog graph (delta p vs log t) and type curve matching. Among these techniques, the type curve method deserves special attention because it allows both the analysis of pressure data and the detection of different flow regimes.
Transient pressure analysis techniques have been proved to be an excellent formation evaluation tool. Interpretation of wellbore pressure data yields average values of pressure data yields average values of formation characteristics and allows to detect some heterogeneities in the reservoir. These techniques were developed initially, for radial flow conditions and later modified to take into consideration different types of flow geometry.
At the same time, stimulation techniques were developed to increase the productivity of both damaged wells or wells producing from low permeability reservoirs. Hydraulic fracturing stands as on of the most effective stimulation methods because its application generally allows production of wells to be economical.
It was recognized early that wells intercepted by a fracture have different flow behavior than unfractured wells, consequently, application of pressure analysis methods based on radial flow theory to these cases can yield erroneous results.
Many studies have been published to examine different flow situations for fractured wells. Table 1 presents a summary of these publications. Initially, most works dealt with steady state flow toward fractured wells; both horizontal and vertical fractures were considered and the main objective was to determine the effect of a fracture on well productivity.
The first study on the unsteady-state flow behavior for fractured wells was presented by Dyes et al. They investigated the effect of a vertical fracture on the semilog straight line and concluded that the slope of the straight line is affected when a fracture extends over fifteen percent of the drainage radius.
Later, Prats showed that a well intersected by an infinite conductivity vertical fracture exhibits an effective wellbore radius equal to one half of the fracture length; this conclusion was reached before by Muskat.
Russell and Truitt studied the transient pressure behavior of an infinite conductivity vertical fracture in a closed square reservoir. They calculated the well bore pressure as a function of time for several fracture penetration ratios. It was demonstrated that the semilog analysis applies to these cases if the reservoir radius is much greater than the fracture length.