Effective properties of a porous medium with aligned cracks containing compressible fluid

SUMMARY Understanding the wave propagation in fluid-saturated cracked rocks is important for detecting and characterizing cracked reservoirs and fault zones with applications in geomechanics, hydrogeology, exploration geophysics and reservoir engineering. In sedimentary rocks, microscopic-scale pores are usually filled with fluid. One logical means of modelling the essential features of such rocks is to use poroelasticity theory. But previous models of wave propagation in cracked porous medium are either restricted to low frequencies at which effects of the elastic scattering (scattering into fast-P and S waves via mode conversion at the crack faces) are negligible or to the case that the crack-filling fluid is assumed to be incompressible. To overcome these restrictions, we consider the effects of crack fluid compressibility by extending spring condition into poroelasticity and derive exact solutions of the scattering problem of an incident P wave by a circular crack containing compressible fluid in a porous medium. Based on the solutions, we develop two different effective medium models to estimate frequency-dependent effective velocity and attenuation in a fluid-saturated porous rock with a set of aligned cracks. The mixed-boundary value problem reveals that both the wave-induced fluid flow (WIFF) and elastic wave scattering can cause important velocity dispersion and attenuation. The diffusion-type WIFF dominates the velocity change and attenuation for the low frequency range, while the elastic scattering dominates them for the relatively higher frequency range. The dependences of the P-wave velocity on the crack fluid compressibility are different at different frequencies. For the WIFF-dominated frequency range and Rayleigh-scattering frequency range, the P-wave velocity decreases with the crack fluid compressibility. In contrast, for the Mie scattering frequency range, the opposite occurs (the P-wave velocity increases with the crack fluid compressibility).

On the use of Fredlund gas–fluid compressibility relationship to model medium-dense gassy sand behavior

This paper presents the influence of gas bubbles trapped in a soil mass on the stress–strain–strength response of medium-dense sands. A hypoplastic constitutive sand model enhanced with the intergranular strain concept was coupled with the Fredlund gas–fluid compressibility relationship to capture gassy soil behavior. Boundary value element representations in a finite element platform of oedometer and saturated drained and undrained triaxial compression tests are performed for the calibration of soil parameters. For the numerical simulation of gassy soil behavior, pore fluid compressibility is modified to account for the presence of free gas in the pore fluid. The gassy soil mechanical response is studied by using only one set of parameters determined from the saturated soil response. The testing bed for this evaluation is a laboratory experimental program conducted on sands retrieved from the Oakridge Landfill, a sanitary landfill located in South Carolina, USA. The hypoplasticity sand model specialized with the Fredlund relationship reproduces reasonably well the stress–strain–strength response of these sands for a wide range of loading conditions and at a reasonable level of testing for the calibration of constitutive parameters. It is found that a slight reduction in the degree of saturation significantly decreases the undrained shear strength of the soil and causes changes in volume (i.e., drained-like behavior).

Effect of Fluid Compressibility on Toughness-Dominated Hydraulic Fractures With Leakoff

Summary Hydraulic fracturing using supercritical carbon dioxide (CO2) has a recognized potential to grow in importance for unconventional oil and gas reservoirs. It is characterized by higher compressibility than traditional liquid-phase hydraulic-fracturing fluids. Motivated by the larger compressibility of supercritical CO2, this paper considers the problem of a hydraulic fracture in which a compressible fluid is injected at a constant rate to drive a hydraulic fracture in a permeable and brittle rock. The two cases of a plane-strain fracture and a penny-shaped fracture are considered. It is shown that for many practical cases, the formation has a large enough fracture toughness that the propagation is in a regime for which the pressure inside the hydraulic fracture can be treated as spatially uniform (“toughness dominated”). Both numerical simulations and analytical solutions for the relevant limiting regimes show that fluid compressibility affects fracture shape only at the very beginning period, which corresponds to the storage regime, and has little effect on fracture growth in the leakoff regime. Overall, because the transition from the storage regime to the leakoff regime is expected to often take place in a short time after the fracture starts propagating, the influence of compressibility in the storage regime is very brief and can be quickly ignored. Therefore, even relatively sizable fluid compressibility has almost no effect on fracture growth in the toughness-dominated regime when leakoff is taken into account.