Improved solution of displacements due to a compacting reservoir over a rigid basement

Tempone, Pamela; Fjær, Erling; Landrø, Martin

doi:10.1016/j.apm.2010.02.025

Cited by 29 publications

(20 citation statements)

References 13 publications

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“…(16) is in effect an expansion in eigenfunctions of the differential operator defined by Eq. ( 12 ), with eigenvalues chosen to satisfy the initial and boundary conditions stated in (14) . Using the same eigenfunctions to expand the solution of ( 22 ) yields the analytical solution:…”

Section: Pressure Head Perturbationmentioning

confidence: 99%

“…However, pore pressure perturbations in response to the geologic loading changes can be significant in some situations, such as earth and oceanic tides [1,2] , wave propagation [3][4][5][6] , erosion [7][8][9] , sedimentation [10][11][12] , subsidence [13,14] , pumping [15][16][17][18] and even changes in atmospheric pressure [19,2] . Therefore, it is of great importance to understand the fluid-to-solid mechanical coupling for the prediction of groundwater movement.…”

Section: Introductionmentioning

confidence: 99%

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Variability quantification of excess pressure head in heterogeneous deformable aquifers

Chang

Yeh

2016

Applied Mathematical Modelling

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a b s t r a c tThe direct effect of changes in applied total stresses on fluid-saturated geologic materials is reflected in fluctuations in pore pressure. The quantification of these pressure changes has traditionally been based on the classical poroelasticity theory, developed ignoring the natural variability in aquifer properties (parameters). Uncertainty of excess pore pressure prediction is therefore expected to be large when applying the classical model to field aquifer systems which generally have high degree of heterogeneity. Very limited attention to this issue has been paid. The motivation for this work is to quantify the uncertainty associated with the classical model, the spatial variability of the predicted excess pressure head in the field, where the groundwater flow is produced by the changes in total stress. The stochastic methodology used to develop the results of this study is based on the nonstationary spectral approach. It is found that the heterogeneity and correlation length scale of the log hydraulic conductivity process, and the pore compressibility parameter play essential roles in enhancing the variability in excess pressure head. In addition, the pore pressure head distribution predicted using the classical poroelasticity theory is subject to large uncertainty at a large depth in heterogeneous aquifers.

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Section: Pressure Head Perturbationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variability quantification of excess pressure head in heterogeneous deformable aquifers

Chang

Yeh

2016

Applied Mathematical Modelling

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“…Early on, Van Opstal (1974) studied the vertical displacement at the free surface of a half-space by adding a rigid basement to Geertsma's model. More recently, Tempone et al (2010) addressed the same problem and elaborated the results for the components of strain and stress. A semi-analytical model of land displacement above elastic and visco-elastic layers of subsurface rock was developed using successive point source/sink images (Fokker and Orlic, 2006).…”

Section: Introductionmentioning

confidence: 96%

Geertsma’s subsidence solution extended to layered stratigraphy

Mehrabian

Abousleiman

2015

Journal of Petroleum Science and Engineering

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“…The classical model of Geertsma (1973) has recently been modified by Tempone et al (2010): the infinite half-space was replaced by a rigid basement underneath the reservoir. Tempone et al (2010) compare the displacement, stress and strain of their model with the classical Geertsma model (Geertsma 1973).…”

Section: Introductionmentioning

confidence: 99%

A Three-Dimensional Analytical Solution for Reservoir Expansion, Surface Uplift and Caprock Stress Due to Pressurized Reservoirs

Wangen

Halvorsen

2019

Math Geosci

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An analytical solution is presented for the displacement, strain and stress of a three-dimensional poro-elastic model with three layers, where the three layers are an underburden, a reservoir with a given fluid pressure, and an overburden. The fluid pressure in the reservoir is assumed symmetrical around the z-axis and represented by a Fourier cosine series. The poro-elastic solution is expressed as a superposition of the solutions for each term in the Fourier series. It is shown that the bulk strain in the reservoir layer is proportional to the fluid pressure and that the bulk strain in the underburden and overburden is zero. Using these properties of the bulk strain, a solution is derived for the three-layer model where the fluid flow and mechanics are fully coupled. A particular aim of the model is to study the surface uplift from a given reservoir pressure. The expansion of the reservoir and the uplift of the surface are studied in terms of the wavelengths in the Fourier representation of the pressure. It is shown that the surface uplift can be written in a similar form to the 1D vertical expansion of the reservoir layer, but where the fluid pressure is based on the Fourier series. It is shown that the amplitudes with average wavelengths longer than 2π times the thickness of the reservoir give expansion of the reservoir, but average wavelengths much shorter than this limit do not. Similarly, amplitudes with average wavelengths much longer than 2π times the thickness of the overburden produce surface uplift, but wavelengths much shorter do not. The stress in the overburden, which is generated by the reservoir fluid pressure, is also analysed in terms of the wavelengths. A case is given where the analytical uplift is compared with the results of a numerical simulation and the agreement is excellent.

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Improved solution of displacements due to a compacting reservoir over a rigid basement

Cited by 29 publications

References 13 publications

Variability quantification of excess pressure head in heterogeneous deformable aquifers

Variability quantification of excess pressure head in heterogeneous deformable aquifers

Geertsma’s subsidence solution extended to layered stratigraphy

A Three-Dimensional Analytical Solution for Reservoir Expansion, Surface Uplift and Caprock Stress Due to Pressurized Reservoirs

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