Discrete Boltzmann trans-scale modeling of high-speed compressible flows
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We present a general framework for constructing trans-scale discrete Boltzmann models (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function that satisfies additional nonhydrodynamic kinetic moments. To characterize the thermodynamic nonequilibrium (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two measures are presented: (i) the relative TNE strength, describing the relative strength of the (N+1)th order TNE effects to the Nth order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted is best described by the relative TNE intensity and/or the discrepancy rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with 26 discrete velocities at Burnett level is formulated, verified, and validated.Keywords:
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Abstract The paper reports measurements of rock compressibility performed by means of an equipment capable to operate up to 150 MPa confining pressure. Measurements have been performed on 32 samples from 3 sandstone and 3 carbonatic reservoirs. The experimental apparatus was designed to perform both static investigations (deformation tests, to calculate bulk and pore compressibilities) and dynamic investigations (acoustic tests, for the evaluation of undrained compressibility). Results show that compressibility is not constant, but is a function of reservoir pressure. In particular, compressibility of sandstones follows an exponential trend, decreasing rapidly in the first part of the loading cycle, and remaining almost constant at high pressure. Compressibility of carbonatic samples shows the same behaviour, but increases for stresses close to the yield point. The attempt to correlate dynamic and static tests reveals the necessity of additional investigations; in fact, it has been noticed that undrained compressibility measured by dynamic tests yields inconsistent results for non-elastic rocks, and, generally, dynamic measurements do not correspond to the static ones.
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The compressibility of gas isn't related to the compressibility factor directly. It is determined by the partial derivative of its compressibility factor to the pressure at a certain temperature. The smaller the partial derivative is, the greater its compressibility.
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Abstract A variety of different compressibility terms, including cleat compressibility and bulk compressibility, are used when modelling coal seam gas (CSG) reservoirs. The relationship between different compressibility terms is often theoretically straightforward, but in practice may be much more complex, particularly when considering heterogeneous and/or fractured rocks. This paper outlines experimental work measuring different compressibility terms using printed rock samples, and analysis that demonstrates some of the challenges associated with relating these compressibilities. Three-dimensional printed rock samples with heterogeneity (layers of different stiffness), some of which included planar fractures, were created. The compressibility of these samples was measured based on changes in permeability (as might be used to estimate cleat/fracture compressibility) and also based on volumetric strain. Simple models were history matched to estimate the cleat compressibility, which is then used to calculate a bulk compressibility based on theoretical relationships. This is then compared to the bulk compressibility measurement based on volumetric strain. Initial results indicate that the relationship between the different compressibility terms is much more complex than theory suggests. The theoretical relationship of bulk compressibility with pore compressibility yields values up to one order of magnitude different from that of laboratory measurements. Our study highlights the importance of cleat compressibility in modelling CSG reservoirs and the significance of bulk compressibility in estimating deformation associated with CSG production. We believe our findings will contribute to a better understanding of compressibility terms in CSG reservoir modelling and encourage further research in this area.
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Abstract The effect of density compressibility of granular polymeric solids on the pressure development inside the feed zone of a single screw extruder was calculated. Results indicate that, for a given flow rate, density compressibility enhances pressure rise inside the extruder, remedying the under estimation of previous theory. A substantial rise in pressure buildup may result for compressibility above a certain level. This may explain observed surging during the processing of low bulk density materials.
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Abstract We propose novel two‐ and three‐dimensional truss structures made from rods of different materials connected together through pin‐joints to form triangular units which can exhibit anomalous compressibility properties. In particular, we show that these systems may be made to exhibit negative linear compressibility along certain directions or compressibilities that are even more positive than any of the component materials, i.e. the end product is a system with tunable compressibility properties that can be tailor made for particular practical applications. We also show that in specific cases, these systems can exhibit an overall negative area compressibility and sometimes even negative volumetric compressibility (i.e. negative bulk modulus) thus confirming that this property can indeed exist. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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There are three volumes and three stresses used to describe rock,nine compressibilities are determined accordingly,of which only four are independent.The rock compressibility used in reservoir engineering is actually the one of pore volume of rock.Rock compressibility plus the compressibility of reservoir liquids is called the total compressibility,which can be converted to the effective compressibility by oil saturation.The comprehensive compressibility used conventionally is obscure conceptually,which is not suggested to be used any more.Formation compressibility is easily confused,which can neither be measured nor be used in engineering,so is not suggested to be lectured in school for students any more,and had better be immediately eliminated from textbooks.
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Abstract Compressibility of deep fluids-filled cavern is discussed. Compressibility is measured both through statical and dynamical tests. Statical compressibility is influenced by cavern shape and cavern fluids nature. This parameter plays an important role for such applications as the determination of stored hydrocarbons volume, of volume lost during a blow-out, and of pressure build-up rate in a closed cavern. Dynamical compressibility is measured through the periods of waves triggered by pressure changes. Both tube waves and longer period waves associated to the existence of an interface between a liquid and a gas can be observed. They can provide additional information, for instance the existence of trapped gas in the well-head. P. 105
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Abstract Pore volume compressibility is one of the physical properties of a reservoir that must be specified in many reservoir engineering calculations. In this research, the effect of compacting pressure, temperature and porosity on compressibility was investigated. A total of nine different cores were tested, eight were sandstone and one was limestone. Core samples were placed in copper jackets and subjected to compacting pressure up to 15,000 PSI. Runs were made pressure up to 15,000 PSI. Runs were made at room temperature and at 400 degrees F. Very late has been published concerning the effect of temperature on the pore volume compressibility of reservoir rock. This work shows that the pore volume compressibility increases with increasing temperature for the same pressure. In most cases, about a twenty percent increase in compressibility was noted at 400 degrees F. as compared to room temperature. The compressibility was found to be a continuous function of compacting pressure. The compressibility at 14,000 PSI compacting pressure was only about one-third of the pressure was only about one-third of the compressibility at 1,000 PSI. From the research that has been performed, no method has been found for performed, no method has been found for accurately predicting pore volume compressibility. Therefore, when accurate compressibility data for a reservoir are needed, laboratory measurements should be made on core samples from the specific formation simulating reservoir temperature and compacting pressure. Introduction In the past few years, much emphasis has been placed on sophisticated reservoir engineering such as mathematical reservoir models and transient reservoir flow tests. One of the physical properties that must be specified in this type of work is the pore volume compressibility of the reservoir rock.
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Pore volume compressibility is one of the physical properties of a reservoir that must be specified in many reservoir engineering calculations. In this research, the effect of compacting pressure, temperature and porosity on compressibility was investigated.A total of nine different cores were tested, eight were sandstone and one was limestone. Core samples were placed in copper jackets and subjected to compacting pressure up to 15,000 PSI. Runs were made pressure up to 15,000 PSI. Runs were made at room temperature and at 400 degrees F.Very late has been published concerning the effect of temperature on the pore volume compressibility of reservoir rock. This work shows that the pore volume compressibility increases with increasing temperature for the same pressure. In most cases, about a twenty percent increase in compressibility was noted at 400 degrees F. as compared to room temperature.The compressibility was found to be a continuous function of compacting pressure. The compressibility at 14,000 PSI compacting pressure was only about one-third of the pressure was only about one-third of the compressibility at 1,000 PSI.From the research that has been performed, no method has been found for performed, no method has been found for accurately predicting pore volume compressibility. Therefore, when accurate compressibility data for a reservoir are needed, laboratory measurements should be made on core samples from the specific formation simulating reservoir temperature and compacting pressure.Introduction. In the past few years, much emphasis has been placed on sophisticated reservoir engineering such as mathematical reservoir models and transient reservoir flow tests. One of the physical properties that must be specified in this type of work is the pore volume compressibility of the reservoir rock.
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