Permeability Modulus Research Articles

Analysis of Transient Linear Flow in Stress-Sensitive Formations

Summary Rate- and pressure-transient analysis of unconventional gas and oil reservoirs is a challenge because of the complex reservoir characteristics that dictate flow. Transient linear flow is usually an important flow regime for these reservoirs and is often associated with linear flow to induced hydraulic fractures. One of the complications in the analysis of this flow regime is stress sensitivity of porosity and permeability. This work provides a new method for analysis of transient linear flow in stress-sensitive tight oil reservoirs. A correction factor is used to correct the results of the conventional method for analysis of transient linear flow in tight oil reservoirs. A new method is developed for calculating the correction factor by use of an analytical solution to the flow equation. The correction factor is used for production-data analysis of two examples for constant-pressure and constant-rate production. The results indicate that the correction factor becomes more important for higher values of permeability modulus and pressure drawdown. Further, we demonstrate that the correction factor can eliminate the considerable error of the conventional analysis method in estimating initial reservoir permeability or hydraulic fracture half-length.

The Northwest Geysers EGS Demonstration Project, California: Pre-stimulation Modeling and Interpretation of the Stimulation

The Northwest Geysers Enhanced Geothermal System (EGS) demonstration project aims to create an EGS by directly and systematically injecting cool water at relatively low pressure into a known High Temperature (280–400 °C) Zone (HTZ) located under the conventional (240 °C) geothermal steam reservoir at The Geysers geothermal field in California. In this paper, the results of coupled thermal, hydraulic, and mechanical (THM) analyses made using a model developed as part of the pre-stimulation phase of the EGS demonstration project is presented. The model simulations were conducted in order to investigate injection strategies and the resulting effects of cold-water injection upon the EGS system; in particular to predict the extent of the stimulation zone for a given injection schedule. The actual injection began on October 6, 2011, and in this paper a comparison of pre-stimulation model predictions with micro-earthquake (MEQ) monitoring data over the first few months of a one-year injection program is presented. The results show that, by using a calibrated THM model based on historic injection and MEQ data at a nearby well, the predicted extent of the stimulation zone (defined as a zone of high MEQ density around the injection well) compares well with observed seismicity. The modeling indicates that the MEQ events are related to shear reactivation of preexisting fractures, which is triggered by the combined effects of injection-induced cooling around the injection well and small changes in steam pressure as far as half a kilometer away from the injection well. Pressure-monitoring data at adjacent wells and satellite-based ground-surface deformation data were also used to validate and further calibrate reservoir-scale hydraulic and mechanical model properties. The pressure signature monitored from the start of the injection was particularly useful for a precise back-calculation of reservoir porosity. The first few months of reservoir pressure and surface deformation data were useful for estimating the reservoir-rock permeability and elastic modulus. Finally, although the extent of the calculated stimulation zone matches the field observations over the first few months of injection, the observed surface deformations and MEQ evolution showed more heterogeneous behavior as a result of more complex geology, including minor faults and fracture zones that are important for consideration in the analysis of energy production and the long-term evolution of the EGS system.

Microscale modeling of coupled water transport and mechanical deformation of fruit tissue during dehydration

Water loss of fruit typically results in fruit tissue deformation and consequent quality loss. To better understand the mechanism of water loss, a model of water transport between cells and intercellular spaces coupled with cell deformation was developed. Pear (Pyrus communis L. cv. Conference) was chosen as a model system as this fruit suffers from shriveling with excessive water loss. A 2D geometric model of cortex tissue was obtained by a virtual fruit tissue generator that is based on cell growth modeling. The transport of water in the intercellular space, the cell wall network and cytoplasm was predicted using transport laws using the chemical potential as the driving force for water exchange between different microstructural compartments. The different water transport properties of the microstructural components were obtained experimentally or from literature. An equivalent microscale model that incorporates the dynamics of mechanical deformation of the cellular structure was implemented. The model predicted the apparent tissue conductivity of pear cortex tissue to be 9.42±0.40×10−15kgm−1s−1Pa−1, in the same range as those measured experimentally. The largest gradients in water content were observed across the cell walls and cell membranes. A sensitivity analysis of membrane permeability and elastic modulus of the wall on the water transport properties and deformation showed that the membrane permeability has the largest influence. The model can be improved further by taking into account 3-D connectivity of cells and intercellular pore spaces. It will then become feasible to evaluate measures to reduce water loss of fruit during storage and distribution using the microscale model in a multiscale modeling framework.

Permeability and dynamic elastic moduli of controlled porosity ultra-precision aerostatic structures

Porous ceramic aerostatic bearings enable precise and smooth motion and improved stiffness compared with widely used orifice restrictor bearings. However, the processing techniques so far used are too complex or rely in lowering the sintering temperature to increase fluid flow.Preferred combinations of fine-grade alumina powders and starch granules were used to produce quality porous structures using fixed processing parameters. Component shrinkage, permeability, pore size and elastic properties were comprehensively characterised as a function of porosity.The new porous ceramic structures exhibited controllable and reproducible permeability and modulus, within the range required for ultra-precision porous aerostatic applications.

Decline Curves of a Vertical Well in Stress-Sensitive Reservoir

Stress-sensitivity effects have been recognized to have impact on the pressure/rate transient behavior of wells in several reservoirs. Although the effects of stress-sensitivity have been considered in well testing theory in the past thirty years, little has been done to determine their influence on rate decline behavior. This paper presents a single phase flow model considering stress-sensitive formation permeability to investigate the characteristic of production rate decline of a vertical well. The stress-sensitive permeability is considered as an exponential form. The permeability changes with pressure drop are described by a permeability modulus. By introducing two pseudo functions, the equations of the mathematical model are linearized and approximate semi-analytical solutions are obtained. The analytical solutions are carefully verified through numerical simulation. Two sets of new decline type curves are diagramed on a log-log plot for constant rate case and constant bottomhole pressure case respectively. The influence of stress-sensitive permeability on decline curves are analyzed and compared. From this work, we recognized that the rate decline characteristics of stress-sensitive reservoir under constant rate and constant bottomhole producing condition are different. New analysis method should be developed to analyze field variable rate/variable pressure drop data.

Evaluation of friction properties of hydrogels based on a biphasic cartilage model

Characterizing hydrogels using a biphasic cartilage model, which can predict their behavior based on structural properties, such as permeability and aggregate modulus, may be useful for comparing active lubrication modes of cartilage and hydrogels for the design of articular cartilage implants. The effects of interstitial fluid pressurization, inherent matrix viscoelasticity and tension–compression nonlinearity on mechanical properties of the biphasic material were evaluated by linear biphasic (KLM), biphasic poroviscoelastic (BPVE) and linear biphasic with anisotropy cartilage models, respectively. The BPVE model yielded the lowest root mean square error and highest coefficient of determination when predicting confined and unconfined compression stress–relaxation response of hydrogels (n=15): 0.220±0.316MPa and 0.93±0.08; and 0.017±0.008MPa and 0.98±0.01 respectively. Since the differences in error between models were not statistically significant, the simplest model we considered, KLM model, was sufficient to predict the mechanical response of this family of hydrogels. The coefficient of friction (COF) of a hydrogel–ceramic articulation was measured at varying loads and pressures to explore the full range of lubrication behavior of hydrogel. Material parameters obtained by biphasic models correlated with COF. Based on the linear biphasic model, COF correlated positively with aggregate modulus (spearman's rho=0.5; p<0.001) and velocity (rho=0.3; p<0.001), and negatively with permeability (rho=−0.3; p<0.001) and load (rho=−0.6; p<0.001). Negative correlation of COF with load and positive correlation with velocity indicated that hydrogel–ceramic articulation was separated by a fluid film. These results together suggested that interstitial fluid pressurization was dominant in the viscoelasticity and lubrication properties of this biphasic material.

Geostatistical relationships between mechanical and petrophysical properties of deformed sandstone

Petrophysical and mechanical properties of sandstone reservoirs are likely to change as a result of faulting. In this paper, we investigate the distribution of deformation features (structures) such as fractures and deformation bands in the Navajo and the Entrada sandstones in the fault core and damage zones of two faults in two localities in southeast (Cache Valley) and central (San Rafael Swell) Utah. These two localities had different degree of calcite cementation and hence are of interest to study the mechanical and petrophysical properties of these localities, in order to find out the impact of cementation on these properties and their possible relations. We have performed in-situ measurements by Tiny-Perm II and Schmidt hammer to examine the distribution of permeability and strength/elasticity of rock within the damage zone of these faults. We have studied the statistical relation between (i) Tiny-Perm II measurements and Schmidt hammer values, (ii) permeability and uniaxial compressive strength, and (iii) permeability and Young's modulus of deformed rocks. The statistical results demonstrate that there are correlations between the studied parameters, but the dependencies vary with the degree of calcite cementation in mineralogically similar sandstones (quartz sandstone). Statistical results demonstrate to first approximation that an exponential law is more suitable for description of the relations (i), (ii) and (iii) of non-cemented Navajo sandstone whereas for cemented Navajo sandstone these relations are better approximated by power law.

A new method for production data analysis of tight and shale gas reservoirs during transient linear flow period

Pseudo-pressure has historically been used in analytical solutions of the diffusivity equation for analysis of real gas flow in conventional gas reservoirs. The accuracy of analytical solutions during the transient flow period is contingent on the validity of the assumption of constant hydraulic diffusivity which is implicit in the background formulations. However, the assumption of pseudo-pressure-independent hydraulic diffusivity during transient flow is not valid for the cases of high pressure drawdown at the wellbore. For tight and shale gas reservoirs, this dependency is more pronounced due to the complexities associated with non-Darcy flow, adsorption/desorption phenomena, stress-sensitivity of permeability and porosity, and condensation in porous media.The current study focuses on rate transient analysis of tight and shale gas reservoirs during transient linear flow period for a single fractured well producing under constant well bottom-hole pressure. The results of the analytical solution of real gas flow in porous media are corrected for the effects of high pressure drawdown, non-static permeability, and condensate formation. The method proposed in this study includes three key elements: introducing a measure of nonlinearity (departure of dimensionless hydraulic diffusivity from linearity); differential and integral formulation of the correction factor (used to correct the slope of the square-root-of-time plot); implementing the iterative integral method for solution of flow equation; and evaluating the correction factor for constant-pressure production during transient linear flow period. The results show that the correction factor becomes more important for higher values of drawdown, permeability modulus, and condensate saturation.

Developing high-performance concrete incorporating highly-reactive rice husk ash

The aim of this study is to present results of an investigation about the developing of a high-performance concrete (HPC) using a highly reactive pozzolan made from chemically treated rice husk ash (ChRHA) prepared by a chemical-thermal attack to the rice husk. This particular rice husk ash (RHA) consists of 99% of silica, highly amorphous, white in color and of greater pozzolanic activity than the silica fume and another rice husk ash prepared with only by a thermal treatment. The results of the physical, chemical and mineralogical characteristics of ChRHA are analyzed. In this study, the compressive strength, flexural strength, water absorption, resistance to carbonation, total charge-passed derived from rapid chloride permeability test (RCPT) and modulus of elasticity of hardened concrete were determined in the laboratory. Test results indicate that it is possible to produce HPC with the incorporation the chemically treated RHA. The incorporation of the chemically treated rice husk ash into the concrete enhances the compressive strengthand the durability properties being comparable to the properties of high performance concretes with silica fume (SF) made with the same replacement levels.

Material Property Identification of Artificial Degenerated Intervertebral Disc Models — Comparison of Inverse Poroelastic Finite Element Analysis with Biphasic Closed Form Solution

ABSTRACTDisc rheological parameters regulate the mechanical and biological function of intervertebral disc. The knowledge of effects of degeneration on disc rheology can be beneficial for the design of new disc implants or therapy. We developed two material property identification protocols, i.e., inverse poroelas-tic finite element analysis, and biphasic closed form solution. These protocols were used to find the material properties of intact, moderate and severe degenerated porcine discs. Comparing these two computational protocols for intact and artificial degenerated discs showed they are valid in defining bi-phasic/poroelastic properties. We found that enzymatic agent disrupts the functional interactions of proteoglycans which decreased hydraulic permeability and aggregate modulus but increased the Poisson's ratio. The fatigue loading, which damages disc structure, and squeezes and occludes the matrix pores, further decreased the hydraulic permeability and the Poisson's ratio but increased the elastic modulus. The FE simulations showed the stress experienced during the creep test increases with severe degeneration but steady-state fluid loss decreases for the both moderate and severe degenerated discs. Discriminant analysis declared that the probability of correct classification using the FE analysis is higher than the results of the closed form solution. The specimen-specific models extracted from FE analysis can be additionally used for complimentary investigations on disc biomechanics.

Analysis of quantitative magnetic resonance imaging and biomechanical parameters on human discs with different grades of degeneration

To establish relationships between quantitative MRI (qMRI) and biomechanical parameters in order to help inform and interpret alterations of human intervertebral discs (IVD) with different grades of degeneration. The properties of the nucleus pulposus (NP) and annulus fibrosus (AF) of each IVD of 10 lumbar spines (range, 32-77 years) were analyzed by qMRI (relaxation times T1 and T2, magnetization transfer ratio [MTR], and apparent diffusion coefficient [ADC]), and tested in confined compression and dynamic shear. T1 and T2 significantly decreased in both the NP and AF with increasing degeneration grades while the MTR increased significantly with grade 4. In contrast to the other qMRI parameters, the ADC had a tendency to decrease with increasing grade. Disc degeneration caused a decrease in the aggregate modulus, hydraulic permeability and shear modulus magnitude along with an increase in phase angle in the AF. In contrast, disc degeneration of NPs demonstrated decreases in shear modulus and phase angle. Our studies indicate that qMRI can be used as a noninvasive diagnostic tool in the detection of IVD properties with the potential to help interpret and detect early, middle, and late stages of degeneration. QMRI of human IVD can therefore become a very important diagnostic assessment tool in determining the functional state of the disc.

The effects of break point location and nominal maximum aggregate size on porous asphalt properties

Porous Asphalt (PA) is typically used to mitigate traffic noise, reduce splash and spray behind vehicles and improve wet-weather skid resistance at high speeds. However, its widespread application is hampered by short service life due to raveling and clogging. Improvement in service life may be possible with improved aggregate gradation since the aggregate matrix provides the main load bearing skeleton of the mix. This paper evaluates the effects of break point (BP) locations and nominal maximum aggregate sizes (NMAS) on PA properties. Several gradations were proposed based on the Dutch PA gradation PAC 0/16 limits but varying the NMAS and BP. The Dutch PA gradation was referred to in view of its durability with service life up to 16years on the fast lane. Specimens are prepared using a conventional binder penetration grade 60/70 and subjected to permeability, resilient modulus, abrasion loss and indirect tensile strength tests. The results indicated that permeability and resilient modulus improved when larger NMAS and BP were used. For instance, the resilient modulus of mix with NMAS 25mm is 24.2% higher than the mix using NMAS 14mm. However, the tensile strength and resistance to abrasion loss of PA decrease when the NMAS and BP increase.

Thermal, oxygen barrier and mechanical properties of polylactide–organoclay nanocomposites

Abstract Polylactide (PLA) nanocomposites reinforced with commercially available organoclays, Nanomer I.28E and Nanomer I.34TCN, were prepared using a melt intercalation technique. In this work, two different clay concentrations (2 and 4 wt.%) were considered. The morphology of the resulting nanocomposites was observed by TEM micrographs while the interaction between polymer and clay was measured by FTIR analysis and contact angle measurements. Better dispersion quality and interaction with the polymer matrix was observed for I.34TCN organoclay. The effect of clay dispersion and its interaction with PLA was investigated by measuring the thermal, oxygen barrier and mechanical properties of the prepared nanocomposites; consequently, higher improvements were observed in the properties of nanocomposites containing I.34TCN compared to the I.28E counterpart. Besides, 2 wt.% clay content was found as an optimum concentration for enhancing the different properties of the resulting nanocomposites with respect to neat PLA. However, higher improvements in oxygen permeability and tensile modulus were achieved by embedding 4 wt.% organoclay into the PLA matrix.

Laboratory monitoring of &lt;italic&gt;P&lt;/italic&gt; waves in partially saturated sand

Energy dissipation is observed on seismic data when a wave propagates through a porous medium, involving different frequency regimes depending on the nature of rock and fluid types. We focus here on the role of partial fluid saturation in unconsolidated porous media, looking in particular at P-wave phase velocity and attenuation. The study consists in running an experiment in a sand-filled tank partially saturated with water. Seismic propagation in the tank is generated in the kHz range by hitting a steel ball on a granite plate. Seismic data are recorded by buried accelerometers and injecting or extracting water controls the partial saturation. Several imbibition/drainage cycles were performed between the water and gas residual saturations. A Continuous Wavelet Transform applied on seismic records allowed us to extract the direct P-wave at each receiver.We observe an hysteresis in phase velocities and inverse quality factors between imbibition and drainage. Phase velocities and inverse quality factors are then jointly inverted to get a final poro-visco-elastic model of the partially saturated sand that satisfactorily reproduces the data. The model formulation consists in generalizing the Biot theory to effective properties of the fluid and medium (permeability and bulk modulus) in order to properly explain the phase velocity variation as a function of the saturation. The strong level of attenuation measured experimentally is further explained by an anelastic effect due to grain to grain sliding, adding to Biot's losses. This study shows that fluid distribution at microscopic scale has strong influence on the attenuation of direct P-waves at macroscopic scale and confirms that seismic prospection may be a powerful tool for the characterization of transport phenomena in porous media.

Research on Coupling of Seepage and Stress Fields with Variable Modulus of Elasticity

According to the characteristics that permeability and elastic modulus vary with stress, the variation of elastic modulus of sandstone change with confining pressure was researched through the triaxial test. And combined with empirical formula proposed by Louis (1967), mathematical model of coupling of seepage and stress fields is established. This study shows that: the groundwater has a relatively great effect on rock stress and deformation and is adverse to the slope stability. The elastic modulus that chang with confining pressure influences a lot on rock deformation, meanwhile, the variation of rock stress changes permeability, therefore groundwater is the main influencing factors.

Digital rock physics benchmarks—Part I: Imaging and segmentation

The key paradigm of digital rock physics (DRP) “image and compute” implies imaging and digitizing the pore space and mineral matrix of natural rock and then numerically simulating various physical processes in this digital object to obtain such macroscopic rock properties as permeability, electrical conductivity, and elastic moduli. The steps of this process include image acquisition, image processing (noise reduction, smoothing, and segmentation); setting up the numerical experiment (object size and resolution as well as the boundary conditions); and numerically solving the field equations. Finally, we need to interpret the solution thus obtained in terms of the desired macroscopic properties. For each of these DRP steps, there is more than one method and implementation. Our goal is to explore and record the variability of the computed effective properties as a function of using different tools and workflows. Such benchmarking is the topic of the two present companion papers. Here, in the first part, we introduce four 3D microstructures, a segmented Fontainebleau sandstone sample (porosity 0.147), a gray-scale Berea sample; a gray-scale Grosmont carbonate sample; and a numerically constructed pack of solid spheres (porosity 0.343). Segmentation of the gray-scale images by three independent teams reveals the uncertainty of this process: the segmented porosity range is between 0.184 and 0.209 for Berea and between 0.195 and 0.271 for the carbonate. The implications of the uncertainty associated with image segmentation are explored in a second paper.

On the Influence of Permeability and Young's Modulus on the Dehydration of a Strongly Shrinkable Two-Phase Porous Medium: A Model Sensibility Analysis and the Development of a Contact Mechanics Measurement Setup

A model that describes the mass transfer in a two-phase shrinkable porous media by using a classic Darcy law for the fluid relative to solid transfer has been recently developed by Cáceres et al.[ 1-2 ] This model describes the coupling between the fluid pressure and the solid structure deformation tensor by using the Terzaghi stress tensor decomposition for the media and elastic constitutive law for the solid structure.[ 3 ] The aim of this article is to point out the sensitivity of this model relative to the two main physical parameters that govern the coupled mass transfer and stress level in a strongly shrinkable porous medium, namely, permeability and the Young's modulus. An experimental setup that makes possible the simultaneous measurement of those two parameters as well as the Poisson ratio is developed in agreement with the recent theoretical suggestions of Lin et al. The experimental evolution of these quantities versus the moisture content is discussed for an agar gel.

Radial detection depths of borehole Stoneley modes

Propagation features of Stoneley modes are widely used for measurements of reservoir permeability and rock anisotropy in acoustic logging. Through the finite difference algorithm, the radial detection depth of the Stoneley wave along a fluid-filled borehole is investigated. The radial variations of the displacement components Ur for Stoneley wavefronts are presented as the particle motions in that direction are controlled by the permeability and transverse shear modulus of the medium surrounding the wellbore. It is shown that the Stoneley-wave energy reaches a peak value at the borehole wall and attenuates exponentially with the increasing radial depth in the formation. By comparison of reflected Stoneley-wave amplitudes from reflectors with various distances to the borehole wall, the prospecting depths of Stoneley modes can be confirmed. It is generally no more than 0.2 meters with the frequency range of acoustic logging. This result reveals that only a very shallow region around the wellbore can be detected from the Stoneley-wave responses.

Evaluation of Compacted Cementitious Composites for Porous Bearings

The use of porous materials as a restrictor in aerostatic bearings provides many advantages over conventional restrictors, such as small variation of temperature, high damping, high operational speeds, limited wear, and capacity to support radial, axial, and combined loading. A design of experiment (DOE) was carried out to evaluate cold‐pressed cementitious composites as an air restrictor in thrust bearings. The physical and mechanical properties such as the apparent porosity, permeability, and elastic modulus were investigated in this work, thus verifying the structural and flow characteristics of the composites for such application. The composites fabricated with low compacting pressure and small silica particles provided the material requirements for porous bearings.

Permeability and elastic modulus of cement paste as a function of curing temperature

The permeability and elastic modulus of mature cement paste cured at temperatures between 8°C and 60°C were measured using a previously described beam bending method. The permeability increases by two orders of magnitude over this range, with most of the increase occurring when the curing temperature increases from 40°C to 60°C. The elastic modulus varies much less, decreasing by about 20% as the curing temperature increases from 20°C to 60°C. All specimens had very low permeability, k<0.1nm2, despite having relatively high porosity, ϕ ~40%. Concomitant investigations of the microstructure using small angle neutron scattering and thermoporometry indicate that the porosity is characterized by nanometric pores, and that the characteristic size of pores controlling transport increases with curing temperature. The variation of the microstructure with curing temperature is attributed to changes in the pore structure of the calcium–silicate–hydrate reaction product. Both the empirical Carmen–Kozeny, and modified Carmen–Kozeny permeability models suggest that the tortuosity is very high regardless of curing temperature, ξ ~1000.