The fundamental poroelastic solutions provide the framework for modeling of flow-induced stresses and deformations in saturated porous rocks, which is of significant interest in petroleum and mining geomechanics.
We have developed an extended solution for the mechanical response of the poroelastic hollow cylinder under non-stationary stress and pressure boundary conditions. The solution was obtained in Laplace space and it was verified with published results for the special case of boundary conditions using numerical Laplace inversion.
The proposed solution was successfully used to model and interpret laboratory tests. It was found that the solutions with simplified assumption of instantaneously applied pressure might overestimate the flow induced tensile radial stresses and under some conditions the results differ even qualitatively. The change in average axial stresses versus hole pressure obtained from the laboratory test was in good agreement with the model prediction.
The developed solution can be used for laboratory test interpretation, optimization of the openhole completion and well control operations, prediction of wellbore collapse and bridging during oil or gas blowouts, and the subsequent estimation of probability of blowouts "self-killing".
1. INTRODUCTION
One of the dominating methods of oil and gas blowout control is bridging, or wellbore sealing with rock fragments from the collapsing formation [1, 2]. The majority of bridged blowouts have a short duration [3]. It is generally assumed that at early time intervals the formation stability is controlled by a tensile failure and fluid flow induced stresses [4, 5], therefore formation stability can be predicted using fundamental poroelastic solutions of problems involving axisymmetric deformation of a saturated poroelastic media [6-10].
However, the prediction of pore pressure, stresses and deformations is usually obtained assuming some highly idealized pressure histories, either constant or changes in pressure following a step function (see e.g. Wang [11]). The actual boundary pressures and stresses encountered in laboratory experiments and industrial processes exhibit more complex behavior with time [12-14].
In this paper we have developed an extended solution for the mechanical response of the poroelastic hollow cylinder under non-stationary stress and pressure boundary conditions. The solution was obtained in Laplace space and it was verified with published results for the special case of boundary conditions using numerical Laplace inversion.
The proposed solution was successfully used to model and interpret laboratory tests. The results of laboratory experiments on hollow cylinders of Berea sandstone indicate that the determination of realistic boundary conditions is crucial to the correct prediction of mechanical responses of the rock.
2. POROELASIC SOLUTION FOR THE AXISYMMETRIC PLANE STRAIN PROBLEM
2.1. Basic equations
The purpose of the analysis is to describe the transient pore pressure, stresses and deformations, occurring during and immediately after the change in pressure at the walls of a saturated permeable thick-walled hollow cylinder of inner radius, Ri, and outer radius, Ro. We use conventional cylindrical coordinates (r; ¿; z) with the origin in the center of the lateral cross-section of the cylinder and the z axis along the axis of symmetry. The principal stresses are denoted as follows: radial, srr; tangential, s¿¿; and axial, szz (Figure 1). The analysis is linear poroelastic with full coupling. Possible pressure and stress dependencies of mater
