Journal of Petroleum Science and Technology

Journal of Petroleum Science and Technology

An Improved Semi-Analytical Framework Based on Similarity Transformation with Time-Dependent Correction Factors for Transient Flow in Infinite-Acting Reservoirs

Articles in Press

Document Type : Research Paper

Authors
Pouya Hosseinifar 1
Rohallah Hashemi 2
1 Department of Gas Engineering, Ahvaz Faculty of Petroleum, Petroleum University of Technology, Ahvaz
2 Department of Chemical Engineering, Isfahan University of Technology, Isfahan, Iran
10.22078/jpst.2026.5806.1988
Abstract
Several mathematical approaches have been developed for solving the pressure-diffusivity equation governing unsteady-state flow in petroleum reservoirs. However, conventional similarity formulations may exhibit significant deviations at early dimensionless times because of the line-source approximation. In this study, an improved semi-analytical similarity framework is developed by introducing two time-dependent correction factors to enhance the accuracy of the finite-wellbore pressure response in an infinite-acting reservoir. The correction functions are formulated as data-informed functions of dimensionless time and calibrated against Chatas’ numerical reference solution. Their robustness was assessed using five-fold cross-validation and an independent hold-out test. Model 1 provided the best predictive performance, with a test MAPE of 0.938%, RMSE of 1.554%, maximum absolute error of 4.660%, and R^2=0.999. A controlled synthetic reservoir-parameter recovery analysis further demonstrated the practical significance of the improved pressure representation: permeability and skin-factor errors were reduced to 0.008% and 0.014%, respectively, for Model 1. The proposed formulation therefore for transient simple and accurate semi-analytical alternative for transient pressure calculation and can improve the interpretation of pressure-transient responses, particularly in the formation-dominated early-time regime.
Keywords
Petroleum reservoir
Infinite-acting reservoir
Pressure-transient analysis
Diffusivity equation
Similarity solution
Journal of Petroleum Science and Technology

Articles in Press, Accepted Manuscript
Available Online from 30 September 2026