Variation Of Pressure Gradient Research Articles

RETRACTED: Flow and thermal analysis of Jeffrey nanofluid in a microchannel: Buongiorno's Model

The present consideration explores the thermal energy and mass transfer process in conducting Jeffrey nanofluid flows through a microchannel. The slip boundary conditions, Brownian motion and temperature-dependent thermal conductivity were considered. The dimensionless governing models have been solved to the best possible investigative solutions using the Runge-Kutta-Fehlberg 4 −5th order numerical procedure. The impact of physical parameters on the momentum, energy, concentration, irreversibility and irreversibility ratio was revealed graphically in detail. It is concluded that the resultant momentum profile is augmented with the relaxation and retardation times parameter all over the flow region. The temperature-dependent thermal conductivity contributes to the resulting thermal energy of the flow system ever-growing to high. The concentration profile was diminutions through growing in the Brownian motion parameter. The irreversibility and irreversibility ratio were obtained mathematically and explained concerning the notable parameters. The magnetic parameter was to diminish the irreversibility rate, but it was augmented by increasing the parameter for the relaxation and retardation times ratio. Effect of thermal radiation, variable thermal conductivity, pressure gradient, buoyancy force and thermophoresis on the Jeffery nanofluid in a microchannel by the Buongiorno model have been inspected for the first time. The effects of this works are innovative and original.

Numerical study of single bubble mobility in triangular and deltoid microchannels using the boundary element method

The study of bubbly liquid dynamics in microchannels of unconventional shapes is of great importance for different fields of science and industry. This work investigates the dynamics of the incompressible single bubbles in the slow periodic flow of viscous liquid in a triangular channel with a variable pressure gradient. The numerical approach used in this research is based on the boundary element method (BEM). This method is widely used for solving three-dimensional problems and problems in areas with complex geometry. The influence of the bubble’s initial position relative to the channel centerline on the bubble deformation, the relative velocity of the bubble, and its center of mass displacement in the channel are considered.

Statistical characterization of free-stream turbulence induced transition under variable Reynolds number, free-stream turbulence, and pressure gradient

In this work, the free-stream turbulence (FST) induced transition of a flat plate boundary layer is studied using particle image velocimetry (PIV) under variable Reynolds number (Re), FST intensity, and adverse pressure gradient (APG). Overall, 10 different flow conditions were tested concerning the variation of these parameters. The streak spacing and the probability density function (PDF) of turbulent spot nucleation are computed for all cases. The streak spacing is shown to be constant in the transition region once scaled with the turbulent displacement and momentum thickness, with resulting values of around 3 and 5, respectively. Nucleation events are shown to occur near the position where the dimensionless streak spacing reaches such constant values. The streamwise position where most turbulent spots are formed is strongly influenced by the FST intensity level. Additionally, the PDF of spot nucleation becomes narrower with increase in the APG, while FST has the opposite effect. A common distribution of all the PDFs is provided as a function of a similarity variable accounting for the streak spacing, the shape factor of the boundary layer, and the FST intensity.

Small-Scale Atmospheric Turbulence and Its Impact on Laminar-to-Turbulent Transition

Using flight measurements conducted between altitudes of 700 and 3000 m, this work characterizes atmospheric turbulence and investigates the effects of an increase in turbulence level on the laminar–turbulent transition taking place on the pressure side of a laminar airfoil. Flight conditions ranging from calm to moderately turbulent and natural transition driven by Tollmien–Schlichting waves are considered. The inflow conditions are first characterized and reported using single and two-point statistics. Moreover, it is shown how characteristic parameters can be estimated from the turbulence intensity. Then, the sensitivity of the transition location to an increase of turbulence level is investigated. Flight results show a low sensitivity of the transition location to an increase of turbulence level, when the latter is not associated with significant variations of pressure gradient. Similar investigations are also conducted in a wind tunnel where the turbulence level is increased using an active grid and a significant change of the transition location is observed with increasing turbulence level. The differences in the response of the transition to freestream turbulence level in flight and in the wind tunnel are postulated to be attributable to differences in the probability density distributions of the inflow velocity fluctuations.

Numerical Simulation Study on Waterflooding Heavy Oil Based on Variable Threshold Pressure Gradient

The heavy-oil flow in porous media is characterized by non-Darcy law with variable threshold pressure gradient (TPG) due to the large fluid viscosity. However, available analytical and numerical models hardly consider this effect, which can lead to erroneous results. This paper is aimed at presenting an innovative approach and establishing a numerical simulator to analyze the heavy-oil flow behavior with waterflooding. The apparent viscosity of the oil phase and flow correction coefficient characterized by the TPG were applied to describe the viscosity anomaly of heavy oil. Considering the formation heterogeneity, the TPG was processed into a variable related to mobility and the directionality. The discretization and linearization of the mathematical model were conducted to establish a fully implicit numerical model; the TPG value on each grid node was obtained through oil phase mobility interpolation, and then, the Jacobi matrix was reassembled and calculated to solve pressure and saturation equations. The corresponding simulator was thus developed. The pre-/postprocessing module of the simulator is connected to ECLIPSE; then, an efficient algorithm is introduced to realize a fast solution. Results show that considering the TPG will not only reduce the waterflooding area but also reduce the oil displacement efficiency because of aggravating the nonpiston phenomenon and interlayer conflict. The numerical simulation study on the TPG of heavy oil provides theoretical and technical support for the rational development and adjustment of water-driven heavy oil.

Small-Scale Atmospheric Turbulence and Its Impact on Laminar-to-Turbulent Transition

Using flight measurements conducted between altitudes of 700 and 3000 m, this work characterizes atmospheric turbulence and investigates the effects of an increase in turbulence level on the laminar–turbulent transition taking place on the pressure side of a laminar airfoil. Flight conditions ranging from calm to moderately turbulent and natural transition driven by Tollmien–Schlichting waves are considered. The inflow conditions are first characterized and reported using single and two-point statistics. Moreover, it is shown how characteristic parameters can be estimated from the turbulence intensity. Then, the sensitivity of the transition location to an increase of turbulence level is investigated. Flight results show a low sensitivity of the transition location to an increase of turbulence level, when the latter is not associated with significant variations of pressure gradient. Similar investigations are also conducted in a wind tunnel where the turbulence level is increased using an active grid and a significant change of the transition location is observed with increasing turbulence level. The differences in the response of the transition to freestream turbulence level in flight and in the wind tunnel are postulated to be attributable to differences in the probability density distributions of the inflow velocity fluctuations.

Not All Piggybacks Are Equal: A Retrospective Cohort Analysis of Variation in Anhepatic Transcaval Pressure Gradient and Acute Kidney Injury During Liver Transplant.

Complete inferior vena cava clamping in cavalreplacement during livertransplantis associated with substantial physiological derangement and postoperative morbidity. Partial clamping in the piggyback technique may be relatively protective, but evidence is lacking. Having observed substantial variation in transhepatic inferior vena cava pressure gradient with piggyback, we hypothesized that the causative mechanism is the extent of caval clamping rather than the surgical approach. We used internal jugular and femoral catheters to estimate suprahepatic and infrahepatic inferior vena cava pressures during clamping. Pressure gradients were calculated, and distributions were compared by surgical technique. We estimated adjusted odds ratios for pressure gradient on acute kidney injury at 72 hours. In 115 case records, we observed substantial variation in maximum pressure gradient; median values were 18.0 mm Hg(interquartile range, 8.0-25.0 mm Hg) with the piggyback technique and 24.0 mm Hg (interquartile range, 19.5-27.0 mm Hg) with caval replacement. Incidence of acute kidney injury was 25% (29 patients). Pressure gradient was linearly associated with probability of acute kidney injury (odds ratio, 1.06; 95% CI, 1.01-1.13). We report 2 novel findings. (1) Anhepatic inferior vena cavapressuregradient variedsubstantially in individuals undergoing piggyback, and (2) gradient was positively associatedwith early acute kidney injury. We hypothesize that this (unmeasured) variation explains the conflictingfindings ofprevious studies that compared surgical techniques. Also, we propose that caval pressure gradient could be routinely assessed to optimize real-time piggyback clamp position during livertransplant surgery.

Increase of Portal Vein Pressure Gradient After Hepatectomy Predicts Post-operative Liver Dysfunction.

Background. Post-hepatectomy liver failure (PHLF) is an important cause of mortality and morbidity. Whether Child-Pugh A patients with varying degrees of cirrhosis are good candidates for hepatectomy is disputed. The purpose of this study was to analyze the impact of portal venous pressure gradient (PVPG) variation during surgery on PHLF. Methods. PVPG, the pressure gradient between the portal vein and central vein, was measured in consecutive patients before and after liver resection. The optimal cutoff of PVPG to predict PHLF was determined by receiver operating characteristic curve analysis. Risk factors for PHLF were subjected to univariate and multivariable analysis. Results. Sixty Child-Pugh A patients were recruited. The mean PVPG was increased from 5.17 ± 4.78mm of mercury (mmHg) to 6.37 ± 4.44mmHg after liver resection. The optimal cutoff value of PVPG increments to predict PHLF was 1.5mmHg. Multivariable analysis showed prothrombin time (PT), post-hepatectomy PVPG increments of 1.5mmHg or greater, and resected liver segments of 3 or more to be independent predictors of PHLF. Conclusions. Acute PVPG increase after hepatectomy is associated with a higher risk of PHLF in Child-Pugh A patients.

Heat transfer and entropy generation in a MHD Couette–Poiseuille flow through a microchannel with slip, suction–injection and radiation

Flow, heat transfer and entropy generation in a vertical microchannel made of two parallel porous plates (the injection plate kept at rest while the suction plate is moving in upward/downward direction) under the combined action of buoyancy force and transverse magnetic field are studied. Variable pressure gradient (favorable/adverse) due to Couette–Poiseuille (C–P) flow is considered here. This is one of the fundamental problems of applied science and engineering. Slip conditions for the velocity at plates are implemented for both moving-plate directions and pressure gradients with the help of classical C–P flow. The basic equations are solved numerically by using Runge–Kutta–Fehlberg method along with shooting technique. Numerical results are in concordance with previously published results for specific cases. The present results are frequently compared with those of the classical C–P flow. Influence of operational parameters (plate movement, pressure gradient, injection–suction rate, slip length, Grashof Number, temperature ratio (between hotter to colder side) and viscous dissipation effect) on the flow and heat transfer characteristics (velocity, temperature, Nusselt number (Nu) distribution, entropy generation and Bejan Number) are investigated here. An effort is made to search singularity in the variation of Nu with some parameters, and find the parameters’ values at which the global entropy is minimally generated in the channel. Finally, a critical analysis is conducted on the individual contribution of irreversibilities due to heat flow, fluid friction and Joule heating to the total entropy generation.

Heat stream in electroosmotic bio-fluid flow in straight microchannel via peristalsis

Current study investigates the heat characteristics of electroosmotic phenomenon in bio fluid through a peristaltic wavy microchannel. To analyze the heat transfer, viscous dissipation is well-thought-out. The transport model includes of continuity, momentum, heat and electric potential equations with suitable boundary conditions. Debye Hückel linearization approximation is considered. Analytical solution of subsequent non-linear problem is presented to evaluate the variation in velocity, pressure gradient, pressure rise and temperature through the perturbation technique. We validate the approximate analytical solutions by comparing those with results from numerical analysis. Shear stresses and Nusselt number are calculated indeed. Presented graphical results explore the impact of the factors affecting the physical problem. Eyring fluid parameter expressively affects all the transport characteristics.Pressure gradient is more for Eyring fluid parameter and Helmholtz-Smoluchowski velocity and declines for averaged time flow rate and electroosmotic parameter. Shear stress strongly depends on Eyring-Powell fluid parameter A, electroosmotic parameter and Helmholtz-Smoluchowski velocity. The results reported provides a good insight into biological systems in biomedical engineering.

Simplified Transition and Turbulence Modeling for Oscillatory Pipe Flows

One-dimensional unsteady Reynolds-averaged Navier–Stokes computations were performed for oscillatory transitional and turbulent pipe flows and the results were validated against existing experimental data for a wide variety of oscillatory Reynolds and Womersley numbers. An unsteady version of the Johnson–King model was implemented with optional near-wall modification to account for temporal pressure gradient variations, and the predictions were compared with those of the Spalart–Allmaras and k–ε turbulence models. Transition and relaminarization were based on empirical Womersley number correlations and assumed to occur instantaneously: in the former case, this assumption was valid, but in the latter case, deviations between data and predictions were observed. In flows where the oscillatory Reynolds numbers are substantially higher than the commonly accepted steady critical value (~2000), fully or continuously turbulent models produced the best correspondence with experimental data. Critically and conditionally turbulent models produced slightly inferior correspondence, and no significant benefit was observed when near-wall pressure gradient effects were implemented or when common one- and two-equation turbulence models were employed. The turbulent velocity profiles were mainly unaffected by the oscillations and this was explained by noting that the turbulent viscosity is significantly higher than its laminar counterpart. Thus, a turbulent Womersley number was proposed for the analysis and categorization of oscillatory pipe flows.

Influence of the interval length of hydraulic packer systems on thermally-induced pore pressure measurements in rock

During the past several decades, hydraulic packer systems have generally been used to measure the thermally-induced pore pressures in many in-situ experiments in nuclear waste management programs. The measured value using hydraulic packer system is a combined value of the pore pressures in the rock along the packer interval, and not the pore pressure at the middle point. The suitability of using the packer system measured value to represent the thermally-induced pore pressure at the middle point of the packer interval needs to be assessed. The accuracy of using hydraulic packer systems is examined in this paper using a coupled thermal-hydraulic-mechanical (THM) model for fully saturated conditions developed using the finite element program COMSOL. The results indicate that there could be large errors in the measured values, with the size of the error dependent on the size of the packer interval, the variation of pore pressure gradient along that interval and the orientation of the packer measurement borehole. To improve the accuracy of the measurement using packer systems, the variation in pore pressure gradient along the packer interval should be small; or if a substantial gradient variation is expected, the length of the packer interval should be made as small as possible. A packer interval with a length less than 0.5 m is suggested. If a packer system has been installed with a large interval length in a location where a large pore gradient variation may exist, calibration of any associated numerical model using this measurement should incorporate the packer measurement system. The numerical results of this coupled THM model are in good agreement with the integration of a point heat source theoretical solution throughout the heater line.

ИССЛЕДОВАНИЕ СТРУКТУРЫ ТУРБУЛЕНТНОГО ПОТОКА ПРИРОДНОГО СЫРЬЯ В ТРУБОПРОВОДАХ С СЕКЦИЕЙ ПЕРЕМЕННОГО ПО ДЛИНЕ ПОПЕРЕЧНОГО СЕЧЕНИЯ КОНФУЗОРНО-ДИФФУЗОРНОГО ТИПА

Актуальность работы вызвана необходимостью: понимания механизмов перестройки гидро-динамических, тепловых и диффузионных процессов, сопровождающих течение углеводородных вязких сред; уяснения характера их взаимодействия в ограниченных внутренних областях под действием комплексных эффектов, сопровождающих течение в сложных трубопроводах; выработки эффективных решений по оптимальному управлению транспорта природного сырья и повышения надежности функционирования энерго-напряженных узлов трубопроводов. Объектом исследования являются пристеночные потоки капельных и газообразных углеводородных сред в конструктивных элементах внутренних систем, часто встречаемых в инженерных приложениях, в частности, нефтегазовой, химико-технологической и тепло-энергетической отраслях промышленности. Такие элементы представляют собой участки коротких или протяженных трубопроводов с криволинейной поверхностью стенки в форме, подобной соединительным узлам или секциям переменного по длине поперечного сечения конфузорно-диффузорного типа. Причем течения в них осложнены эффектами влияния кривизны линий тока, пространственной деформацией, изменениями динамической структуры и давления. Цель: уяснение неопределенностей, особенностей и закономерностей течений, а также возможности применения современных моделей турбулентности к прогнозу процессов в трубопроводах с секциями конфузорно-диффузорного типа; детальное исследование изменений «тонкой» структуры сложного сдвигового течения; выдача рекомендаций в практику расчета пристеночных потоков в указанных гидро-динамической конфигурации и интенсивных режимах работы оборудования. Методы: теоретические и практические методы математического моделирования и численного исследования пространственных турбулентных течений, особенностей изменений их пульсационной структуры по схемам (моделям) с большим числом уравнений – RANS-модели турбулентности, включающие опорную динамическую двух-параметрическую базу. Выбор последней зависит от представлений: с какой степенью она способна воспроизвести статистические корреляции либо параметры сложного движения, локальные свойства (интегральный масштаб, кинетическую энергию, скорость ее диссипации и т. д.) вихря; учитывает ли неоднородный и анизотропный характер изменений структуры потока из-за деформационных эффектов, возбуждаемых переменным давлением и градиентами рейнольдсовых напряжений. Результаты. Проанализированы особенности турбулентных течений углеводородов вязких сред в трубопроводах, включающих соединительные элементы конфузорно-диффузорного типа. Изучены возможности популярных в расчетах сложных сдвиговых течений вязких сред в трубопроводах с криволинейной границей стенки многопараметрические статистические модели турбулентности второго порядка, реализуемые в высоко- и низко-рейнольсовых версиях. Обнаружено, что лучшее описание интенсивности и размеров рециркуляционных зон в трубопроводах дают k-klω/kL- и RSM-kL-модели, как более консервативные и устойчивые к возмущениям, идущим со стенок трубопровода. Поэтому включение их в опорную базу для RSM-модели вполне целесообразно. Расчетами выявлено существование второй зоны отрывного течения. Показано, что наибольшие изменения турбулентной кинетической энергии турбулентности, нормальных компонент тензора напряжений Рейнольдса локализованы в зоне взаимодействия сдвигового слоя с возвратным и прямоточным оторвавшимся течением, а генерация – вблизи точки отрыва. Соответствие расчетов структуры подобных течений данным других авторов позволяет утверждать, что понимание процессов, прогноз интенсивности динамических нагрузок в локальных зонах присоединения потока к стенкам по представленным моделям не приведет к аварийности функционирования оборудования и обеспечит оптимальное управление транспортировкой сырья по трубопроводам.

Tridimensional upper airway assessment in male patients with OSA using oral advancement devices modifying their vertical dimension.

Mandibular advancement devices (MADs) constitute an alternative treatment in selected patients with OSA. A mandibular advanced position has been suggested to be beneficial, whereas its combination with an increased bite-raise may increase its adverse effects. The objective of this study was to assess upper airway (UA) volume and inspiratory pressure gradient variations in a group of 17 patients with OSA. The study was performed under 3 mandibular positions: intercuspal position (P1), MAD position in closed mouth (P2), and MAD position with an increased bite-raise (P3). We conducted a 3-dimensional reconstruction of the pharynx using the finite element method via a computed tomography scan and the subsequent calculation using fluid-dynamic analysis. One hundred percent of the patients showed an increase in UA volume in both P2 and the MAD position with an increased bite-raise, P2 being the position where 76.47% of the patients showed the largest UA volume. P2/velopharynx was the position/region where the largest UA volume increase was achieved (4.73 mm³). A better gradient in P2 (mean = 0.62) in 58.82% of the patients and a better gradient in P3 (mean = 0.74) in 41.18% of patients respect P1 was observed. In 82.35% of patients, a better volume-pressure gradient match was also found. The best efficiency scores for both volume increase and better inspiratory pressure gradient were obtained in P2. This study findings suggest that in a MAD, the minimal bite opening position necessary for mandibular protrusion is more effective in increasing airway volume and inspiratory gradient compared to a larger bite-raising (15 mm).

Numerical Study of Three-dimensional Boundary-layer Flow over a Wedge: Magnetic Field Analysis

The magnetohydrodynamic flow of a viscous fluid over a constant wedge in three- dimensional boundary-layer has been analyzed both numerically and asymptotically. The magnetic field is applied normal to the flow. The mainstream flows aligned with wedge surface are assumed to be proportional to the power of the coordinate distances. The system is described using three-dimensional MHD boundary-layer equations which are converted to couple nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using the Keller-box method which is second-order accurate and asymptotically for far-field behavior. Both numerical and asymptotic solutions give good agreement in predicting the velocity behaviors and wall shear stresses. The effects of Hartmann number, pressure gradient and shear-to- strain-rate on the velocity fields are studied. Particularly, it is shown that the solutions of three-dimensional boundary-layer for variable pressure gradient exist, its effects are important on the boundary-layer flow. Results show that there are new families of solutions for some range of shear-to-strain-rate and there exists a threshold value of it beyond which no solutions exist. For some range of parameters, there is a reverse flow at which our boundary-layer assumptions are no longer valid. Various results for the velocity profiles, wall-shear stresses and displacement thicknesses are also obtained. The physical mechanisms behind these results are discussed.

Flow enhancer influence on non-isothermal systems for heavy crude oil production

Production of heavy and extra-heavy crude oils generally entails high costs, especially in the winter season, due to heat losses. This work studies the effect of a flow enhancer (a chemical formulation based on biodiesel and oxidized biodiesel of soy oil) on the viscosity of heavy crude oil from different wells in Northern Mexico. The observed results indicate a non-linear decreasing behavior of viscosity concerning temperature and volume fraction of the viscosity reducer. It is also presented a theoretical model that predicts the flow increase that can be achieved using the enhancer in systems in which crude oil temperature is higher than the temperature of the environment. Results showed adequate correspondence between experimental and predicted data. It was found that the enhancer increases the volume of crude oil that can be processed without varying pressure gradient.

Response of a flat plate laminar separation bubble to Reynolds number, free-stream turbulence and adverse pressure gradient variation

An extensive data set describing separated flows with different Reynolds numbers (Re), free-stream turbulence intensities (Tu) and adverse pressure gradients (APG) is used for the statistical characterization of laminar separation bubbles (LSBs). Measurements were performed by means of time-resolved particle image velocimetry along a flat plate installed between two adjustable endwalls, providing a test matrix of 3 Re, 4 Tu levels and 4 APGs. In this paper, 22 flow conditions are considered, which are related to the occurrence of boundary layer separation for each combination of the flow parameters. Boundary layer integral parameters, the root mean square of velocity fluctuations and the intermittency function distributions were computed for each condition. The connections between the main quantities that are commonly adopted for the statistical characterization of separated flows are clearly highlighted, thus providing the description of a LSB by means of a reduced set of these parameters. Empirical correlations predicting the transition onset location as well as the main dimensions (i.e., length and height) describing the geometry of a LSB are included in this work. Proper orthogonal decomposition is also adopted for the statistical characterization of the shedding process developing as a consequence of the Kelvin–Helmholtz instability. The frequency, wavelength and propagation velocity of the large-scale structures shed near the bubble maximum displacement are computed for each condition, showing the relation between the dominant shedding frequency and the average flow field at the separation position, and how these quantities are affected by Re, Tu and APG.

Numerical-analytical method for determining the barodiffusion coefficient of technological process of ion-exchange suspension filtration

A method for determining an experimental parameter of the barodiffusion coefficient for conducting computational experiments in technological process of filtering liquid ionized solutions is given in the paper. The developed mathematical model allows obtaining calculated data for the study of other parameters of the unit, taking into account the physicomechanical properties of fluid when cleaning solutions in an ion-exchange column. An analytical solution to the systems of linear equations of diffusion and mass transfer with a constant flow velocity and a variable pressure gradient is obtained. Using these data we can verify the adequacy of the developed mathematical models of the mass transfer process in porous media.

Compressible plane turbulent wakes under pressure gradients evolving in a constant area section

Development of statistically two-dimensional (2-D) turbulent wakes under pressure gradients is a common feature of many industrial and aerodynamic flows. The usual set-up is to generate a wake, and study its development through a passage with a variable area; if the downstream area decreases (increases) a favourable pressure gradient or FPG (adverse pressure gradient or APG) is imposed. In applications such as in turbomachinery, however, the wakes develop in a periodic constant area passage in the stator–rotor gap and with an imposed pressure gradient. To study these flows, here, we develop a canonical set-up for this new kind of wake evolution in FPG and APG of different strengths by placing a 2-D flat plate normal to the flow in a periodic constant area passage and a fixed inflow mass flux. Employing compressible direct numerical simulations, we impose pressure gradients through a ramped body force term to the momentum and total energy equations while the wake is allowed to develop spatially in a region of fixed width. The resultant mean velocity statistics, wake width, energy budgets and entropy generation rates are scrutinised to assess the effect of the pressure gradients, and where possible, the similarities and differences to the conventional case of variable area pressure gradients are discussed. The results show that the effect of a constant area pressure gradient on flow statistics is non-trivial, resulting from significant density changes. The pressure gradients also have an effect on the different energy budgets, which produces a gain for FPG and loss for APG in the mean kinetic energy. Consequently, the entropy generation rate diminishes and augments for the FPG and APG, respectively, compared to the zero pressure gradient. Finally, the effect of different passage heights ( ) relative to the wake half-width ( ) is studied using large eddy simulations. We find that wake width and hence the spreading, depends primarily on the wake–wake interaction for small and pressure gradients for larger , and this has implications for the design of turbomachinery.

Radial Permeability Measurements for Shale Using Variable Pressure Gradients

AbstractShale gas is becoming an important component of the global energy supply, with permeability a critical controlling factor for long‐term gas production. Obvious deviation may exist between helium permeability determined using small pressure gradient (SPG) methods and methane permeability obtained under actual field production with variable pressure gradients (VPG). In order to more accurately evaluate the matrix permeability of shale, a VPG method using real gas (rather than He) is established to render permeability measurements that are more representative of reservoir conditions and hence response. Dynamic methane production experiments were performed to measure permeability using the annular space in the shale cores. For each production stage, boundary pressure is maintained at a constant and the gas production with time is measured on the basis of volume change history in the measuring pump. A mathematical model explicitly accommodating gas desorption uses pseudo‐pressure and pseudo‐time to accommodate the effects of variations in pressure‐dependent PVT parameters. Analytical and semi‐analytical solutions to the model are obtained and discussed. These provide a convenient approach to estimate radial permeability in the core by nonlinear fitting to match the semi‐analytical solution with the recorded gas production data. Results indicate that the radial permeability of the shale determined using methane is in the range of 1×10−6 – 1×10−5 mD and decreases with a decrease in average pore pressure. This is contrary to the observed change in permeability estimated using helium. Bedding geometry has a significant influence on shale permeability with permeability in parallel bedding orientation larger than that in perpendicular bedding orientation. The superiority of the VPG method is confirmed by comparing permeability test results obtained from both VPG and SPG methods. Although several assumptions are used, the results obtained from the VPG method with reservoir gas are much closer to reality and may be directly used for actual gas production evaluation and prediction, through accommodating realistic pressure dependent impacts.