Function Of Differential Pressure Research Articles

Stress and frequency dependence of wave velocities in saturated rocks based on acoustoelasticity with squirt-flow dissipation

SUMMARY We perform seismic and ultrasonic measurements in carbonate and shaley sandstone samples as a function of differential pressure. The velocities show a strong frequency and pressure dependence. The dispersion disappears with increasing pressure and the squirt flow in turn inhibits the pressure dependence. To model these effects, we combine the Gurevich's squirt-flow model with the Mori–Tanaka scheme and the David Zimmerman model, and extend it with third-order elastic constants, to obtain a frequency-dependent acoustoelasticity model. Comparisons between measurements from this study and literature and modelling results show that the P-wave velocity increases non-linearly first and then nearly linearly, dominated by crack closure and acoustoelasticity, respectively. The pressure dependence of wave velocities is reduced by liquid substitution and further by the squirt-flow mechanism. The effects of fluid properties and crack closure on P-wave velocity decrease with differential pressure. The results will feed a new model and help better understanding the wave propagation in pre-stressed rocks at different scales.

A rock-physics model to determine the pore microstructure of cracked porous rocks

SUMMARY Determining rock microstructure remains challenging, since a proper rock-physics model is needed to establish the relation between pore microstructure and elastic and transport properties. We present a model to estimate pore microstructure based on porosity, ultrasonic velocities and permeability, assuming that the microstructure consists on randomly oriented stiff equant pores and penny-shaped cracks. The stiff pore and crack porosity varying with differential pressure is estimated from the measured total porosity on the basis of a dual porosity model. The aspect ratio of pores and cracks and the crack density as a function of differential pressure are obtained from dry-rock P- and S-wave velocities, by using a differential effective medium model. These results are used to invert the pore radius from the matrix permeability by using a circular pore model. Above a crack density of 0.13, the crack radius can be estimated from permeability, and below that threshold, the radius is estimated from P-wave velocities, taking into account the wave dispersion induced by local fluid flow between pores and cracks. The approach is applied to experimental data for dry and saturated Fontainebleau sandstone and Chelmsford Granite.

Estimation of pore microstructure by using the static and dynamic moduli

The variations of the static and dynamic moduli of porous rocks as a function of differential pressure have been described in terms of pore microstructure, i.e., the effects of cracks (soft pores) and intergranular (stiff) pores. Specifically, the first play a major role on the elastic properties of rocks. By using the Mori-Tanaka theory, this work relates rock elastic properties to the pore microstructure. Then, we estimate the distribution of pore aspect ratios by using the static bulk modulus instead of the dynamic one. The approach is applied to data from the Navajo and Weber sandstones. The results show that the cumulative crack porosity and density obtained from the static bulk modulus are higher than those estimated from the dynamic moduli, while the dominant crack aspect ratio is lower. The total porosity estimated from the static modulus agrees better with the experimental data. Furthermore, the cumulative crack (soft or compliant) porosity are estimated by the method, which also agrees with results from stress-strain relation and from bulk compressibility curves.

Ultra-thin nanocrystalline diamond membranes as pressure sensors for harsh environments

Glass and diamond are suitable materials for harsh environments. Here, a procedure for fabricating ultra-thin nanocrystalline diamond membranes on glass, acting as an electrically insulating substrate, is presented. In order to investigate the pressure sensing properties of such membranes, a circular, highly conductive boron-doped nanocrystalline diamond membrane with a resistivity of 38 mΩ cm, a thickness of 150 nm, and a diameter of 555 μm is fabricated in the middle of a Hall bar structure. During the application of a positive differential pressure under the membrane (0–0.7 bar), four point piezoresistive effect measurements are performed. From these measurements, it can be concluded that the resistance response of the membrane, as a function of differential pressure, is highly linear and sensitive.

High precision stress measurement of ion projection lithography mask membranes

In this article, we describe an instrument for measuring the mean stress of large-area membranes for ion projection lithography (IPL) stencil masks. The apparatus incorporates two improvements over the conventional bulge technique, where the deflection at the center of a membrane is measured as a function of differential pressure across it, that provide a hundred-fold improvement in the precision of the measurement. The first is to simply place the membrane, without an o-ring or mechanical clamp, on an optically flat silicon ring separating the two pressure chambers. This eliminates the in-plane mounting forces that previously resulted in 1–2 MPa errors. The close contact between the integral ring supporting the mask and the silicon ring provides an adequate vacuum seal between the chambers. The second improvement is to provide an isothermal environment to reduce stress errors due to temperature variations in the membrane. As a result, the measured stress is independent of temperature and the standard deviation (1σ̣) of measured stress is 0.02 MPa.

Estimation of aspect-ratio changes with pressure from seismic velocities

Abstract Seismic velocities are modeled as a function of rock mineralogy, porosity, fracture density, aspect ratio and fluid saturation. We compare the model with seismic velocity measurements made by Nur and Simmons in 1969 and predict quantitative aspect ratio changes as a function of differential pressure. The velocity change with pressure is initially caused by the deformation and collapse of pre-existing cracks and pores followed by the initiation of new cracks. For low porosity Casco granite (0.25% pore and 0.45% crack), we estimate that crack aspect ratio increases from 5.9 e −3 to 0.01, then decreases to 5.0 e −5 for a pressure increase from 0 to 300 MPa. Most pre-existing cracks and pores close at differential pressures < 40MPa, a lower pressure than predicted with standard approximations. These model results can be used to determine in situ porosity, fluid content, and pore pressure from seismic data by inversion and for reservoir monitoring from drilling and core data.

PREDICTION OF MICROANNULUS BEHIND CASINGS DUE TO BALLOONING EFFECT—A KEY PROBLEM IN GAS WELLS

Casings are pressurised for various reasons during cementing. This pressure inflates casing just like a balloon. As the cement sets and the pressure is released, the elastically deformed casing tends to come back to its original shape leaving behind a microannulus at the cement casing bond. This annular space between cement and casing is too narrow to allow communication of liquids, nevertheless it is permeable enough for gas to flow through. An 8-node, quadrilateral, thin shell finite element model with plane stress and plate flexure capabilities has been used to study the formation of a microannulus during cementing of gas wells. The results of this study suggest that formation of a microannulus is a function of differential pressure across the wall of the casing, steel properties, casing dimensions and cementing temperature.

Pore-Compressibility Study of Arabian Carbonate Reservoir Rocks

Summary In the laboratory, we determined the pore-compressibility characteristics of some limestone samples obtained from a Saudi Arabian petroleum reservoir. The samples were saturated with water and subjected to confining pressure, pc, and pore pressure, pp, in a core holder, and the resulting reduction in PV was measured. We used differential pressure, pc–pp, ranging from 0 to 4,500 psi. Differential pressure was increased incrementally by reducing the internal (pore) pressure while maintaining a constant hydrostatic confining pressure on the rock samples. We present the experimental data here in the form of relative porosity and hydrostatic pore-compressibility values as functions of differential pressure. We analyzed the test results after grouping the rock samples on the basis of their lithological description. Four groups of limestone samples consisting of grainstones, packstones, wackestones, and mudstones were studied. Also, Berea sandstone was tested for comparison with limestone. The results show linear negative correlations on a log-log scale between pore compressibility and differential pressure for all the tested samples. Consequently, we computed the pore compressibility vs. differential-pressure power-fit parameters (referred to here as parameters Ac and Bc). We found that parameters Ac and Bc are correlated with initial porosity for the tested samples and inter-related within the same lithologic group. Mathematical expressions for predicting pore compressibility and porosity as functions of differential pressure are given for the tested samples.

An Experimental Study of Indexed Dull Bit-Tooth Penetration Into Dry Rock Under Confining Pressure

Abstract A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 psi and atmospheric pore pressure. Experimental results obtained with a 45 degrees wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variety of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increasing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required for chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopically of a pseudo plastic nature compare favorably with previous theoretical results for indexed dull bit-tooth penetration into an idealized, rigid, perfectly plastic rock. Introduction To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surface by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock interaction under simulated borehole environmental conditions has been extensively reviewed. Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigation of the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interaction or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four varieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrations by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant, confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration.

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.