An analytical plane-strain solution for surface uplift due to pressurized reservoirs. (March 2018)

• Record Type: Journal Article
• Authors: Wangen, Magnus; Halvorsen, Gotskalk; Gasda, Sarah E.; Bjørnarå, Tore
• Is Part Of: Geomechanics for energy and the environment. Volume 13(2018)
• Page Start: 25
• Page End: 34
• Publication Date: 2018-03
• Subjects: Reservoir injection -- Geomechanics -- Surface uplift -- Poroelasticity; Engineering geology -- Periodicals; Power resources -- Periodicals; Energy development -- Technological innovations -- Periodicals; Engineering geology -- Environmental aspects -- Periodicals; Energy development -- Technological innovations; Engineering geology; Engineering geology -- Environmental aspects; Power resources; Geology -- Periodicals; Energy-Generating Resources -- Periodicals; Periodicals; Electronic journals; 621.042
• DOI: 10.1016/j.gete.2018.03.002
• Languages: English
• ISSNs: 2352-3808

Abstract

Abstract: In this paper, we present an analytical plane strain solution for surface uplift above pressurized reservoirs. The solution is based on a Fourier representation of the reservoir pressure. The plane strain model is developed in two stages: First, an exact solution is derived for the displacement field for the reservoir alone subjected to a periodic overpressure distribution of one wavelength. This one-layer model forms the basis for the analytical plane strain solution for a two-layer model — a pressurized reservoir with an overburden. We give an example where numerically computed uplift is quite accurately estimated by a simple 1D estimate, except for in the near well area. The plane-strain solution is well suited to study conditions for when the simple 1D approximation of the uplift is accurate. A condition for the accuracy of the simple 1D approximation is first derived for just the reservoir expanded by a periodic overpressure distribution of one wavelength, which corresponds to one term in a Fourier series. The 1D estimate is accurate for wavelengths larger than 2 π times the reservoir thickness. Then, a condition is derived for when the 1D estimate is accurate for the two-layer model. We show that the wavelength of the overpressure distribution must be larger than 2 π times the maximum of the reservoir thickness and the overburden thickness for the 1D approximation to be accurate. We demonstrate how uplift is computed from a Fourier decomposition of the reservoir overpressure. The resulting uplift is analysed in terms of Fourier coefficients, using the knowledge of how a single wavelength behaves. The analytical results for the displacement field and the uplift are tested by comparison with finite element simulations, and the match is excellent. Highlights: Exact poroelastic solutions for reservoir expansion and surface uplift. Conditions for when the 1D vertical solution is a good approximation. Verification of the exact solutions with numerical solutions. The usefulness of the 1D vertical approximation is demonstrated on a field case.