Theory Of Linear Poroelasticity Research Articles

Analysis on pore pressure in an anisotropic seabed in the vicinity of a caisson

This paper presents an analysis of pore pressure around a caisson-type breakwater subjected to dynamic wave loading. Unlike previous investigations for wave-seabed-caisson interaction, cross-anisotropic soil behaviour is considered in this paper. Based on a linear poro-elastic theory, a finite element model is developed. A parametric study related to the effects of wave parameters, soil characteristics and geometry of caisson and rubble mound base on the pore pressure around a caisson is performed. The numerical results indicate that the effects of anisotropic soil behaviour on the wave-induced pore pressure in a sandy bed beneath a caisson are not negligible.

Stress-strain analysis in productive gas/oil reservoirs

A numerical study of the stress–strain distribution in a thin disc-shaped reservoir embedded in a poro-elastic half-space and subject to a unit pore pressure decline is presented. The results are then compared with those of a geometrically equivalent porous cylindrical body which is either free to or prevented from expanding laterally (oedometric analogy). The analysis is based on the linear theory of poro-elasticity solved with the aid of the finite element method. The strength source is provided by the pressure gradient generated in a small region surrounding the gas/oil field where pore pressure dissipates. The influence of the burial depth c is also investigated. The results show that the reservoir rock undergoes a vertical compaction δ which is independent of c and very close to the compaction of the equivalent confined cylinder. The confinement factor is also similar. The horizontal displacement is, however, much larger. Its maximum value occurs at the boundary of the field and is of the same order of magnitude as δ. In addition, at the outer reservoir margin shear stresses develop which are totally missing in both the free and the constrained cylinders. It is shown that the vertical displacements of reservoir top and bottom, as well as the radial ones, are sensitive to c, especially in shallow formations. Finally, the largest shear stress is found to be related to the magnitude of the pressure gradient, i.e. to the radial size of the neighbouring volume where pore pressure vanishes. Copyright © 1999 John Wiley & Sons, Ltd.

Deformation and fluid flow due to a source in a poro-elastic layer

The flow of fluid from a point source or sink at some arbitrary height in a layer of deformable porous material is considered. This problem is applicable to filtration through beds of sand and flow in soils. The porous material is assumed to be an isotropic, homogeneous, linear elastic solid. The equations governing the behavior of the medium and fluid are derived for an axisymmetric geometry using linear poro-elasticity theory and are solved using the Hankel transform with the Hankel inversion integral evaluated numerically. The upper surface is stress free and permeable, with the lower surface impermeable to fluid flow. Two different boundary conditions are applied to the lower surface; stress free and tethered. Results are given for the pressure contours, surface fluid velocity, and the displacement of the solid matrix for a variety of source heights and boundary conditions. These results provide an indication of the amount of swelling of the medium and subsequent deformation of the free surface as a function of the location of the point source and boundary conditions.

Swelling of shale around a cylindrical wellbore

A modified form of Biot’s linear theory of poroelasticity is applied to shale swelling in contact with an aqueous electrolyte. The shale is assumed to behave as an isotropic, perfect ion exclusion membrane, and in this limit swelling depends only upon the total stress and on the chemical potential of water within the pores of the rock. An axisymmetric, plane-strain analysis of swelling around a wellbore is first presented, and this is subsequently extended to include swelling of a cylindrical hole in a finite, cylindrical shale sample. It is predicted that swelling is prevented if the chemical potential of water within the shale equals that within the wellbore. The predictions of the analysis are compared with experimental results obtained when drained outcrop shale swelled in contact with aqueous solutions of KCl or NaCl. The experimental swelling did indeed vary with water chemical potential, and could be prevented if the salt concentration within the wellbore fluid was sufficiently high. However, post-mortem chemical analysis of the shale showed that ion-exchange had taken place, with consequent modification of the shale’s mechanical and chemical properties. Ion exclusion was therefore imperfect, and an analysis that incorporates the chemical potentials of components other than water is necessary.

Land subsidence due to gas/oil production in inhomogeneous transversally anisotropic half‐space by a boundary element method

AbstractIn a previous paper1 the authors have developed and implemented a new boundary element (BE) model to simulate and predict land subsidence occurring over three‐dimensional gas/oil fields in a homogeneous and isotropic half‐space. The approach relies on Betti's reciprocal theorem and makes use of the classical fundamental solution of Boussinesq in the framework of the theory of linear poroelasticity. The BE method is here extended to inhomogeneous, transversally anisotropic soils by the aid of a two‐dimensional finite element (FE) model which provides a fundamental numerical solution for the actual multi‐layer setting of the subsurface system. The new FE–BE approach is then used to simulate the subsidence caused by gas production over the deep reservoir of Campo Ravenna Terra, Ravenna (Italy) from 1950 to 1980. The results compare very favourably with the outcome from a full more expensive three‐dimensional FE model of the same occurrence.

Tensile test of fluid-filled poroelastic specimen. Theoretical consideration.

The literature shows that nonlinear stress-strain curves have been obtained in tensile tests of epoxy-coated hourglass-shaped rock specimen under confining pressures and concludes that this nonlinearity is caused in part by plasticity and mainly by nonlinear elastic behavior. However, in addition to these causes, some contribution of the pore-fluid diffusion in specimen is expected. The present theoretical analysis based on the linear theory of poroelasticity shows how much the pore-fluid diffusion contributes to the nonlinearity and concludes that this apparent non-linearity is small but not negligible. A formula is given to estimate how much a stress-strain curve bends due to the diffusion.

Permeability measurement by the pulse-decay method: Effects of poroelastic phenomena and non-linear pore pressure diffusion

Permeability values inferred from data obtained by the pulse-decay, or transient pulse method, might be affected by two phenomena not previously considered to be important: poroelastic coupling between sample cores and pore fluid, and non-linear pore pressure diffusion associated with large pore pressure gradients. The theoretical reasons for these complications are discussed, as well as the results of two simple experiments designed to test the theory. Poroelastic effects introduce an inherent sample-size dependence into the transient-pulse method: experiments suggest such a dependence, but possibly masked by material inhomogeneity. Non-linear pore pressure diffusion limits the size of the pore pressure pulse that may be used in the pulse-decay scheme; this is well-demonstrated by experimental results. Furthermore, direct measurements of poroelastic strains associated with pulse propagation show very good agreement with predictions of linear poroelasticity theory.

Consolidation under an isotropic total stress increase: part I, analysis for compressible constituents

The response of a fluid-saturated porous body to a rapid change in external pressure is analysed using the theory of linear poroelasticity, accounting for compressible constituents. Because water is more compressible than most mineral grains, the sample initially undergoes undrained deformation accompanied by a negative excess pore pressure (suction). Subsequently, external fluid diffuses into the body, the effective compressive stresses relax, and the soil matrix expands. The initial excess pressure, undrained displacement, relaxation rate and asymptotic drained displacement are direct indicators of a pore pressure coefficient, the undrained bulk modulus, the consolidation coefficient and the solid constituent bulk modulus. Thus, measurements of the surface displacement and the pore pressure at one internal point determine four of the eight material properties needed to characterize fully a linearly elastic porous body. L'article analyse la réponse d'un corps poreux saturé de fluide à un changement rapide de la pression externe à l'aide de la théorie de la poroélasticité linéaire, prenant en considération les constituants compressibles. Parce que l'eau est plus compressible que la plupart des grains minéraux, au commencement l'échantillon subit une déformation non-drainée, accompagnée d'une surpression interstitielle négative (succion). Par la suite le fluide externe se diffuse dans le corps, les contraintes de compression effectives se relâchent et la matrice du sol se dilate. La surpression initiale, le déplacement non-drainé, la vitesse de relâchement et le déplacement drainé asymptotique représentent des indicateurs d'un coefficient de pression interstitielle, du module de masse non-drainée, du coefficient de consolidation et du module de masse des constituants solides. Les mesures du déplacement superficiel et de la pression interstitielle à un point interne déterminent quatre des huit proprié tés matérielles nécessaires pour la caractérisation complète d'un corps poreux linéairement élastique.

Some Rock-Mechanical Aspects of Oil and Gas Well Completions

Abstract Elementary borehole- and perforation-stability problems in friable clastic formations for unrestricted fluid flow between reservoir rock and underground opening are treated on the basis of linear poroelastic theory. Thermal stress effects caused by a temperature difference between reservoir and borehole fluids can be predicted from the mathematical similarity of poro- and thermoelasticity. A tension-failure condition applies for the prediction of hydraulic fracture initiation in a formation around injection wells. The resulting equations are partially well-known. Similarly, a uniaxial compression-failure condition should predict perforation failure leading to sand influx in production wells. The major difference between these situations is that, at sufficient depth of burial, the tensile strength of a friable rock mass has only a minor effect on the fracturing pressure level, but the actual value of the compressive strength plays a crucial role in the prediction of sand-influx conditions. Practical suggestions for resolving the latter are given.