Numerical RTA Extended to Complex Fracture Systems: Part 2

Abstract

Abstract This paper is a continuation of the work presented in URTeC 3718584 (Carlsen & Whitson, 2022), and focuses on practical usage of ‘fractional RTA’ theory when applied to both simulated data and field data from the SPE data repository. Most of the theory presented in Part 1 is kept for completeness. An inherent assumption in most industry RTA is equally spaced fractures. However, as shown in several field studies (Raterman 2017, Gale 2018), the distance between individual fractures tends to be unevenly spaced along the wellbore (e.g., "fracture swarms"). In this paper, we extend the original numerical RTA workflow proposed by Bowie and Ewert (2020) to account for uneven fracture spacing. Acuna's (2016, 2020) heterogeneity parameter, delta (δ), is introduced to generalize the linear flow parameter (LFP) to account for complex fracture systems (LFP’ = Akδϕ1-δ = 4nfhxfkδϕ1-δ). For evenly spaced fractures, δ = 0.5, simplifying LFP’ to the familiar LFP = A√k = 4nfhxf√k. For uneven fracture systems, 0 ≤ δ ≤ 0.5. With known (a) well geometry, (b) fluid initialization (PVT and water saturation), (c) relative permeability relations, and (d) bottomhole pressure (BHP) time variation (above and below saturation pressure), three fundamental relationships exist in terms of LFP' and OOIP. Numerical reservoir simulation is used to define these relationships, providing the foundation for numerical RTA, also wells with complex fracture systems. Namely, that wells: (1) with the same value of LFP', the gas, oil and water surface rates will be identical during infinite-acting (IA) behavior; (2) with the same ratio LFP'/OOIP, producing GOR and water cut behavior will be identical for all times, IA and boundary dominated (BD); and (3) with the same values of LFP' and OOIP, rate performance of gas, oil, and water will be identical for all times, IA and BD. These observations lead to an efficient, semi-automated process to perform rigorous RTA, assisted by a symmetry element numerical model. The numerical RTA workflow proposed by Bowie and Ewert solves the inherent problems associated with complex superposition and multiphase flow effects involving time and spatial changes in pressure, compositions and PVT properties, saturations, and complex phase mobilities. This paper extends the approach to complex fracture systems that can be described by the Acuna parameter δ. Numerical RTA workflow decouples multiphase flow data (PVT, initial saturations and relative permeabilities) from well geometry and petrophysical properties (L, xf, h, nf, φ, k, δ), providing a rigorous yet efficient and semi-automated approach to define production performance for many wells. Contributions include a technical framework to perform numerical RTA for unconventional wells, irrespective of fracture spacing. Semi-analytical models, time, and spatial superposition (convolution), pseudopressure and pseudotime transforms are not required.