Geomechanical Laplace-Fourier Transform Model Applied to Log-Log Well-Test Diagnostics of Compaction Damage and Underground Geological CO2/H2 Storage Near Partially Communicating Faults with Non-Uniform Reservoir Thickness

Abstract Some of the potential risks associated with underground geological CO2/H2 storage include leakage, induced seismicity, groundwater contamination, cap-rock integrity, and operational challenges regarding the capture, storage, utilization, and injection. This paper presents a transient 2-D analytical model for well-test diagnostics with unequal formation thickness effect during oil production near partially communicating faults. Moreover, the response of the compaction caused by depletion in production is also simulated. The modeling combines the Laplace and Fourier transforms to compute the solution of 2 hydraulic diffusivity equations. The results show that the total pressure drop, Δp is modeled by 2 Ei(U) and erfc(U) functions. The first function is coupled with the source raised from the real well (production well), and the second is related to the image well (no source effect). The depletion and effective stress derivatives for the observation region (∂ΔpD1/∂tDL and ∂σ′DL/∂tDL) and for the active one (∂ΔpD2/∂tDA and ∂σ′DA/∂tDA) are used to identify potential leakage and sealing zones for underground geological CO2/H2 storage. A computational code was developed in Python® software, and the results were highly convergent. The main advantages of the proposed model are its ease of implementation and the quick run of the code. Furthermore, the model presented can be used for potential sites identification for underground geological CO2/H2 storage.