Matrix Compressibility Research Articles

Use of Barometric Response to Obtain In-Situ Compressibility of a Coalbed Methane Reservoir

Summary A theory is presented for calculating the constrained (matrix) compressibility for aquifers from responses to tides and changes in surface pressure when both gas and water are present. With this theory, a new method to determine matrix compressibility without a pump test is developed. The method is then applied to a coalbed methane well in the Piceance basin.

The influence of formation material properties on the response of water levels in wells to Earth tides and atmospheric loading

The water level in an open well can change in response to deformation of the surrounding material, either because of applied strains (tidal or tectonic) or surface loading by atmospheric pressure changes. Under conditions of no vertical fluid flow and negligible well bore storage (static‐confined conditions), the sensitivities to these effects depend on the elastic properties and porosity which characterize the surrounding medium. For a poroelastic medium, high sensitivity to applied areal strains occurs for low porosity, while high sensitivity to atmospheric loading occurs for high porosity; both increase with decreasing compressibility of the solid matrix. These material properties also influence vertical fluid flow induced by areally extensive deformation and can be used to define two types of hydraulic diffusivity which govern pressure diffusion, one for applied strain and one for surface loading. The hydraulic diffusivity which governs pressure diffusion in response to surface loading is slightly smaller than that which governs fluid flow in response to applied strain. Given the static‐confined response of a water well to atmospheric loading and Earth tides, the in situ drained matrix compressibility and porosity (and hence the one‐dimensional specific storage) can be estimated. Analysis of the static‐confined response of five wells to atmospheric loading and Earth tides gives generally reasonable estimates for material properties.

Stoneley‐wave attenuation and dispersion in permeable formations

The tube wave, or low‐frequency manifestation of the Stoneley wave, has been modeled previously using the quasi‐static approximation; I extend this method to include the effect of the formation matrix compressibility, which tends to marginally increase the tube‐wave attenuation. Using the Biot theory of poroelasticity, I develop a fully dynamic description of the Stoneley wave. The dispersion relation derived from Biot’s equations reduces in the low‐frequency limit to the quasi‐static dispersion relation. Comparisons of the quasi‐static and dynamic theories for typical sandstones indicate the former to be a good approximation to at least 1 kHz for oil and water infiltration. At higher frequencies, usually between 5 and 20 kHz for the formations considered, a maximum in the Stoneley Q is predicted by the dynamic theory. This phenomenon cannot be explained by the quasi‐static approximation, which predicts a constantly increasing Q with frequency. Instead, the peak in Q may be understood as a transition from dispersion dominated by bore curvature to a higher frequency regime in which the Stoneley wave behaves like a wave on a flat fluid‐porous interface. This hypothesis is supported by analytical and numerical results.

Analysis of an anisotropic coastal aquifer system using variable-density flow and solute transport simulation

The groundwater system in southern Oahu, Hawaii consists of a thick, areally extensive freshwater lens overlying a zone of transition to a thick saltwater body. This system is analyzed in cross section with a variable-density groundwater flow and solute transport model on a regional scale. The simulation is difficult, because the coastal aquifer system has a saltwater transition zone that is broadly dispersed near the discharge area, but is very sharply defined inland. Steady-state simulation analysis of the transition zone in the layered basalt aquifer of southern Oahu indicates that a small transverse dispersivity is characteristic of horizontal regional flow. Further, in this system flow is generally parallel to isochlors and steady-state behavior is insensitive to the longitudinal dispersivity. Parameter analysis identifies that only six parameters control the complex hydraulics of the system: horizontal and vertical hydraulic conductivity of the basalt aquifer; hydraulic conductivity of the confining “caprock” layer; leakance below the caprock; specific yield; and aquifer matrix compressibility. The best-fitting models indicate the horizontal hydraulic conductivity is significantly greater than the vertical hydraulic conductivity. These models give values for specific yield and aquifer compressibility which imply a considerable degree of compressive storage in the water table aquifer.

The Relative Importance of Compressibility and Partial Saturation in Unconfined Groundwater Flow

The flow of water in an unconfined aquifer is viewed within the framework of the Biot theory as extended for two‐fluid flow and for conditions of a vertical displacement with constant load. Order of magnitude inspection and an objective criterion, obtained from similitude considerations, are dealt with to estimate the relative importance of the compressibility of aquifer matrix and water and that of partial saturation. Finally, these are used to reconcile some apparently contradictory findings of past studies.

Fluorescence Lifetimes of Aromatic Hydrocarbons under Pressure

The fluorescence lifetimes of 12 aromatic hydrocarbons embedded in polymethylmethyacrylate have been measured as a function of pressure to 30 kbar. The lifetime τf is shortened 15%–40% in the 0–30-kbar interval for this class of compounds. The observed magnitude and sign of the pressure dependence of τf are in agreement with rough estimates derived from the compressibility and refractive index of the polymer matrix. The conclusion is reached that radiative and nonradiative transition rates are similarly (within a factor of 2) affected by external pressures.

ULTRASONIC SHEAR‐WAVE VELOCITIES IN ROCKS SUBJECTED TO SIMULATED OVERBURDEN PRESSURE AND INTERNAL PORE PRESSURE

Change in shear‐wave velocity for four dry sedimentary rocks has been studied as a function of the variation of both external hydrostatic pressure and internal pore pressure in the range 0 to 2,500 psi. The experimental method employs a beam of ultrasonic energy passing through a liquid in which a copper‐jacketed parallel‐sided slab of rock is rotated. The shear‐wave velocity is calculated from the laws of refraction and reflection of waves at a liquid‐solid boundary applied to the angle at which minimum energy is transmitted. The variation of shear‐wave velocity with pressure has been found to be a function of net overburden pressure, [Formula: see text], where [Formula: see text] hydrostatic pressure on the jacketed sample, [Formula: see text] pore pressure and n = a pressure‐dependent factor less than unity. The values of n at several differential pressures were chosen to yield a smooth curve passing through the displaced data points when the shear‐wave velocities were plotted as a function of net overburden pressure. Using the n values so obtained, the matrix compressibility [Formula: see text] for two of the sandstones has been calculated from the relation [Formula: see text]. The bulk compressibility [Formula: see text] for these two rocks had previously been obtained experimentally as a function of differential pressure. The values obtained for the matrix compressibility are in the range expected from a knowledge of the grain and cementing materials for these sandstones.