Improving Well-Performance-Data Analysis in Laplace Space by Using Cubic Splines and Boundary Mirroring

Abstract

Abstract Despite unequivocal advantages of using sampled well-performance data in the Laplace transform domain, time-domain analysis of pressure and production data have been more popular lately. This is because of the unresolved problems in the transformation of sampled data to Laplace domain as opposed to the demonstrated success of the recent real-time deconvolution algorithms. However, the transformation of sampled data to Laplace domain has a broader range of applications than deconvolution and the limited success of the past approaches to transform tabulated data to Laplace domain, such as piece-wise linear approximations, is an algorithmic issue; not a fundamental defect. Specifically, an adequate algorithm to transform the piecewise-continuous sampled data into the Laplace space and an appropriate numerical Laplace inversion algorithm capable of processing the exponential contributions caused by the tabulated data are essential to exploit the potential of Laplace domain operations. In this paper, we introduce a new algorithm which uses inverse mirroring at the points of discontinuity and adaptive cubic splines to approximate rate or pressure versus time data. This algorithm accurately transforms sampled data into Laplace space and eliminates the Numerical inversion instabilities at discontinuities or boundary points commonly encountered with the piece-wise linear approximations of the data. The approach does not require modifications of scattered and noisy data or extrapolations of the tabulated data beyond the end values. Practical use of the algorithm presented in this paper has applications in a variety of Pressure Transient Analysis (PTA) and Rate Transient Analysis (RTA) problems. Our renewed interest in this procedure has arisen from the need to evaluate production performances of wells in unconventional reservoirs. With this approach, we could significantly reduce the complicating effects of rate variations or shut-ins encountered in well-performance data. Moreover, the approach has proven to be successful in dealing with the deconvolution of highly scattered and noisy data. To illustrate the applications, typical field examples, including shale-gas wells, are presented in the paper.