Wellbore Stress Distribution Produced by Moisture Adsorption

Abstract

Summary. For this study, we evaluated the stress distribution produced by moisture adsorption around a wellbore by applying the mechanics of deformable solids. This paper shows that the moisture-adsorption process is governed by a diffusion equation and that the equations governing the moisture-induced stresses around the hole are similar to those equations used in thermoelasticity. A computational method is developed for calculating the stress distribution around the borehole, and the experimental procedure for obtaining the material constants needed in the computation is presented. This paper also studies the effect of borehole pressure on the stress distribution around the hole. Results show that the pressure on the stress distribution around the hole. Results show that the magnitude and distribution of stresses around the borehole are very sensitive to the adsorption characteristics and the moisture-induced modulus change of the material. Introduction Shale is an argillaceous rock that contains moisture-sensitive clay minerals. When moisture is adsorbed, the rock swells. The material properties of shale rock under the influence of moisture have properties of shale rock under the influence of moisture have been extensively studied by Chenevert, who demonstrated experimentally that the percentage of expansion (or strain) of the material is directly proportional to the weight percentage of water adsorbed by the material. Fig. 1 shows a typical experimental-strain/ water-adsorption curve for Mancos shale tested under atmospheric conditions. Note that the strain produced by moisture adsorption is proportional to the weight percentage of water being adsorbed. The last proportional to the weight percentage of water being adsorbed. The last data point (marked by an asterisk) was obtained by placing the rock in direct contact with the fluid. Furthermore, we observed that for this shale, the amount of expansion (or strain) perpendicular to the bedding planes was nearly 1.4 times larger than the strain parallel to the bedding planes was nearly 1.4 times larger than the strain parallel to the bedding planes. planes. An experiment was also conducted to study the process of moisture adsorption into the interior of the rock. Three strain gauges were attached on the surface of a rock sample (see Fig. 2). The sample was then coated with wax except for one end that was left open for exposure to a moist environment. Using this arrangement. Chenevert was able to observe the time history of water adsorption and advancing. Fig. 3 shows the typical moisture-adsorption/time curves. If the rock sample were rigidly confineand thus prevented from expanding freely, the adsorption of water would produce a stress state in the rock sample. Chenevert called this stress, which was induced by moisture adsorption, the "hydrational stress". Chenevert regarded moisture adsorption by shale rocks to be a chemical reaction caused by the difference in humidity between the material and its environment and postulated that the hydrational stress in the material was in the form of a hydrostatic pressure. The magnitude of the hydrational stress was calculated by pressure. The magnitude of the hydrational stress was calculated by p = (RT/V)ln(ps/pw)......................(1) Chenevert treated the hydrational stress as a pore pressure in the analysis of borehole instability. The objectives of this study are to evaluate the moisture-induced stresses on the basis of the mechanics of deformable solids and to calculate the stress distribution produced by moisture adsorption around the wellbore. The next section demonstrates that the stresses produced by moisture adsorption are similar to those stresses produced by temperature changes in an anisotropic elastic produced by temperature changes in an anisotropic elastic medium. The moisture-induced stresses around the wellbore are thus evaluated by applying the thermoelasticity theory. Problem Formulation Problem Formulation Equilibrium Equations. Consider the vertical well shown in Fig. 4. The well is assumed to be in a state of plane strain (i.e., z = 0). It is further assumed that the strain produced by moisture adsorption in the horizontal bedding planes, H, differs from the strain produced in the vertical direction, V, by an anisotropy ratio, F ani; i.e., H = F ani V.................................(2) F ani, which differs for different type of shales, is to be determined experimentally. The axisymmetric stress/strain relationships for the material under a plane strain condition can thus be written as .............(3a) .............(3b) .............(3c) Note that E and are not constants; their magnitudes are influenced by the moisture content in the material. According to Fig. 1, V can be related to the water content in the medium, w(r, t), by a quadrature function as follows: .............(4) where constants K1 and K2 are expansion coefficients to be determined from the moisture-adsorption test (Fig. 1). The equilibrium equation for the medium around the hole can be written as ..........(5) By substituting Fq. 4 into Fq. 5 and observing that rr = ds/dr.....................................(6) and = s/r..................................(7) we can write the equilibrium equation for the wellbore as ,.......(8) where the slope, m = dE/dw, is to be determined experimentally. In the derivation of Fq. 8, Poisson's ratio, was assumed to be constant. The justification of this assumption will be discussed later. The boundary conditions for Eq. 8 are = 0 at r = rw............................(9a) and = 0 at r = ........................(9b) If the distribution of the adsorbed water, w(r, t), around the wellbore is known, Eqs. 8 and 9 can be solved numerically by applying the finite-element method (FEM). Adsorption of Water Into the Rock Medium. If u is the mass flux of water adsorption and w(r, t) is the amount of the adsorbed water, the conservation of mass requires that .........................(10) SPEDE P. 311