New Mathematical Technique for Step Rate Test Analysis Aids Determination of Fracture Pressure and Overcomes the...

Experience in the oil industry has shown that it is challenging to sustain successful long-term matrix injection, as injection water quality cannot be maintained rigorously due to facility hiccups and membrane clogging. Most oil field operators have resolved this problem of injectivity decline by increasing the surface injection pressure to part the formation and inject just above the fracture gradient with strict offtake management for zonal conformance. This is not an easy task as injection much above fracture opening pressure can lead to water fingering and poor sweep that results in uneconomical waterflood recovery. The operators, thus, strive to inject at a pressure just above the fracture opening pressure so that the fracture opens near the wellbore but does not extend and then maintain the pressure just above the fracture closing pressure. Therefore, determination of the fracture opening pressure and fracture closing pressure has remained critical data for the success of waterflood projects. The most reliable industry approach to estimating fracture opening and fracture closing pressures comes from the step rate test (SRT). This traditional approach of Cartesian analysis of pressure-rate plot fits straight lines through the data in a plot of injection pressure against injection rate and then estimates the fracture pressure from the intersection of these lines having different slopes. The data received often do not exhibit one clear change in slope, thus resulting in multiple possible solutions, making it difficult for the operator to use the data for high CAPEX facilities design. Most past studies indicate the subjectivity of this Cartesian slope fitting technique. Alternative solutions through multirate superposition analysis found limited application in the analysis of SRT data due to considerable sensitivity to the value of initial pressure used for superposition and lack of stability of rate and pressure data. In this article, a new technique of SRT analysis is presented, which provides a unique solution for fracture opening and fracture closing pressures. It helps to overcome the limitations of the traditional technique of arbitrary fitting of straight lines. It uses the mathematical understanding of cumulative derivatives to recognize that the matrix opens when the cumulative growth of the rate of injectivity shows a change. It estimates the derivative of the injection rate with respect to injection pressure at each step. Then, it estimates the fracture pressure from the plot of the cumulative of this derivative against pressure at each step. It helps to overcome the challenge SRT solutions posed by the nonlinear trend of pressure data at each injection step both before fracture and after fracture is initiated. It also overcomes the limitations of the multirate superposition technique, as it is not sensitive to the value of initial pressure used for superposition.