The energy industry, including the new focus on geothermal and carbon sequestration processes, deals with porous and permeable formations. Under the influence of effective stress, these formations undergo elastic and inelastic deformation, fracturing, and failure, including porosity and permeability changes during production. Grain and Bulk moduli of elasticity are two key parameters that define net effective stress due to partitioning of stresses between the pore pressure and grain-to-grain contact stresses. Effective stress explains poroelastic behavior; however, tight rock behavior under in-situ conditions is still not predictable. This paper proposes a new method, which uses formation evaluation (FE) measurements, and an integration of rock physics and geomechanics concepts, to constrain effective stress in tight rocks. Examples are presented demonstrating the usefulness of the work.
Effective stress (σ′) is expressed as the difference between total applied stress (σ) and pore pressure multiplied by Biot's coefficient (α). The ‘α’ for highly porous rocks is unity where applied load is counteracted equally by grain-matrix and pore-pressure. However, for tight rocks, only a fraction of load is shared by pore fluid and the ‘α’ is much smaller than unity.
Biot's coefficient ‘α’ is expressed in terms of bulk modulus (Kb) and matrix modulus (Kma). Kb is estimated from acoustic logs as well as measured by hydrostatic compression tests in the laboratory. However, Kma is much more difficult to measure safely and economically, especially in tight or very low permeable formations, and as such, the common practice is to estimate it theoretically. A simple and clear methodology is proposed to estimate Kma from FE logs as well asX-RayDiffraction (XRD) mineralogy obtained from formation core and drill cuttings. Kma can be constrained by an upper-bound (Voigt, 1910), a lower-bound (Reuss, 1929), and an average of the two, (Hill, 1963) models. Kb, on the other hand, can be reliably estimated using dynamic acoustic wave velocity and the static equivalents calculated during calibrations from core tests under net effective in-situ stress conditions. The Kma and Kb, thus obtained, will give a good estimate of Biot's coefficient ‘α’ in tight rocks.
The work provides an improved estimate of net-effective-stress in tight rocks, which leads to safety and cost savings through better prediction of drilling rates, hydraulic fracture design and production decline. The work also examines a new method in which Kma could be estimated by weight fraction of minerals.
