Analytical Flow Model Research Articles

Effects of the capillary-entrapped phase on fines migration in porous media

A residual gas or oil present during fines migration in porous media can highly affect particle detachment, migration, and straining and thereby decrease rock permeability. Those effects are due to capillary forces and partial accessibility of the attached fines to the injected water under the presence of capillary-entrapped gaseous or oleic phase. We performed systematic study of fines migration in engineered sand-packs that contain different percentage of kaolinite and residual oil. Each coreflood consists of seven injections, the first with seawater ionic strength and the last with fresh water, and with piecewise-constant salinity decrease from step to step. Higher decline of permeability is found to occur during fresh water injection and to be accompanied by intensive fines production. Compared with fines migration under single-phase flow, having a residual phase significantly decreases the formation damage and the amount of produced kaolinite. For the first time, we determined dependencies of end-point saturations and end-point relative permeabilities versus kaolinite content. We established the phase permeability decrease with decrease in salinity for different kaolinite contents. The coreflood data are found to be in close agreement with the analytical model of 1D linear flow under the presence of residual phase. The laboratory-tuned model coefficients are used for well behaviour prediction using numerical 1D axisymmetric injection model.

An analytical model of subcritical and critical vapor-liquid flow through a granular bed

This paper presents a computational and experimental justification of a theoretical model for the two-phase vapor-liquid flow through a fixed bed of solid particles. The theoretical description is based on the equations of gas dynamics of the granular bed and the homogeneous model of a single-component two-phase flow, given the difference between the velocities of liquid and vapor phases. Relationships between the phase slip ratio and polytropic coefficient of isenthalpic expansion of vapor-liquid flow were obtained using the multi-parameter nonlinear regression. We used the experimental data on the vapor-liquid flow with an inlet pressure, P1, of 0.6-1.2 MPa and an inlet flow quality, x1, of 0.016-0.178 through a H=50-355 mm bed consisting of steel spheres, 2 and 4 mm in diameter, d. An expression for the critical pressure ratio in the granular bed is proposed. The developed model makes it possible to predict the values of mass velocity of the mixture over the entire range of experimental data with an average error of 3%. Based on the model equations, we obtained expressions for dimensionless mass velocity depending on the pressure ratio that can be applied to two-phase flows through both granular beds and other porous media.

An empirically-based model of the upstream heliopause and outer heliosheath - Current status

We describe a simplified model of the outer heliosheath upstream of the heliopause in an attempt to extract the heliosheath properties from the IBEX-Lo neutral He observations. The distribution of incident He on the sky shows a primary beam surrounded by an irregular cloud of secondary particles. These secondaries are generated by charge-exchange interactions between the neutral primary beam, carrying the properties of the distant interstellar medium, and the nearby interstellar plasma that is deflected around the obstacle posed by the heliosphere. We construct an analytical model for the plasma flow around an arbitrarily-shaped obstacle and compute the resulting distribution of neutral He at IBEX, to compare with the observed He fluxes. Here, we report on the current status of this modelling effort.

АНАЛІЗ ІСНУЮЧИХ ПРОГРАМНИХ КОМПЛЕКСІВ ДЛЯ РОЗРАХУНКУ ЧАСУ ЕВАКУАЦІЇ ЛЮДЕЙ ПІД ЧАС ПОЖЕЖІ

В статті розглядаються існуючі програми для розрахунку часу евакуації людей під час пожежі. Розглянуто наукові роботи з вивчення моделей руху людей під час евакуації з приміщень з використанням різних методів математичного розрахунку. Проведений порівняльний аналіз існуючих програмних комплексів в області розрахунків. Наведено порівняльний аналіз математичних методів закономірностей руху людей під час пожежі у програмних продуктах. Дано висновок щодо функціональності досліджуваних програмних комплексів.

Measurements of Blowdown Thrust Loading in Natural Gas Facilities

Abstract The thrust loading on a vertical blowdown stack during a natural gas blowdown was investigated using a combined experimental and modeling approach. A gravimetric vessel initially at 4000 kPa-g was blown down through two geometrically different stack assemblies. Thrust loads were measured using a dynamic weigh scale typically used for gravimetric calibration of gas flow meters. A one-dimensional (1D) compressible flow model, calibrated using the experimental data, revealed stagnation pressure losses at the entrance to the riser, resulting in lower thrust loads. A comparison between thrust loading obtained from the measurements and the 1D compressible flow model is presented. This work shows that the analytical flow model predicts the blowdown thrust loads within ±30%.

Surface Tension Measurement of Water Surface Under IPA Vapor and the Impact of Its Concentration Dependence on the Marangoni Convection in Wafer Drying Process

As higher integration of semiconductor devices has progressed recently, mechano-chemical polishing process is playing a very important role. At the same time, cleaning and drying technologies after the polishing process have been more and more important in order to ensure the surface cleanliness of the wafer products. As a drying process after the cleaning, there is a method of supplying pure water and IPA (Iso-Propyl Alcohol) vapor simultaneously to the surface of the water meniscus region on a rotating wafer (which is called Rotagoni drying method). This technique causes a surface tension difference on the liquid surface and then gives rise to the convection by the Marangoni effect, which is thought to efficiently remove impure particles on the wafer surface. In this method, IPA vapor impinges on the vicinity of the liquid meniscus on the wafer. It is very difficult to measure the surface tension of the liquid surface in that part in situ, and the details about the convection are not well understood. As this technique further advances in near future in order to remove ultra-fine foreign particles on the wafer surface more efficiently, observation and understanding of the Marangoni convection in the meniscus region are necessary for the future progress of the technique. In this study, in order to consider the actual situation of the drying process, not only the measurement of the surface tension of the droplet of the IPA aqueous solution, but also the measurement by exposing pure water droplet to various concentrations of the IPA vapor were performed, and the relationship between the concentration of IPA vapor and the surface tension of the droplet was investigated. The latter situation is much closer to actual drying situation. Specifically, in measurements, a small pure water droplet was placed in a glass container, and the container was filled with a constant concentration of IPA vapor. At the time when it was judged that the IPA adsorption to the liquid surface had reached equilibrium by confirming that the shape of the droplet became unchanged, the image of the droplet shape was taken from the side of the container with digital camera. It is known that the static shape of a droplet which is flattened under the influence of gravity can be analytically expressed by a mathematical equation in consideration of surface tension and mechanical equilibrium. In this study, the surface tension was deduced by assuming that a uniform concentration of IPA and a uniform surface tension over the whole droplet surface. In another project of the authors’ group, physical simulation using a two-dimensional PDMS flow channel was performed to reproduce a situation of impinging IPA vapor to the meniscus region, and PIV (Particle Image Velocimetry) method was applied to obtain the flow velocity of the Marangoni convection. The measurement of IPA concentration on water surface during the actual drying process is very difficult, and moreover, the in-situ measurement of surface tension is almost impossible. From the data of surface tension as a function of IPA concentration and the measured velocity data with a simple analytical flow model, the estimation of surface tension and IPA concentration on the droplet surface will be discussed. END Figure 1

A review of analytical and semi-analytical fluid flow models for ultra-tight hydrocarbon reservoirs

In the last decade, numerous approaches, e.g., analytical and semi-analytical pressure solutions, production decline curve, reservoir-scale numerical models, have been used to increase our understanding of fluid transport in hydraulically fractured ultra-tight reservoirs and to improve predictions of well production. Among these approaches, analytical and semi-analytical methods have proved useful to petroleum engineers, because of the balance between the reliability of theoretical model outputs and the computational cost. Analytical or semi-analytical solutions can be used to analyze pressure-transient responses, to estimate hydraulic and induced fracture properties, to forecast production, and to optimize well spacing and multi-stage hydraulic fracking.This work reviews the development of analytical/semi-analytical multi-linear and radial flow models for hydraulically-fractured horizontal wells over the past decade. In particular, the review summarizes and compares the fundamental physics and mathematics of the gas transport mechanisms that are important in unconventional reservoirs. We highlight the analytical approaches that have successfully coupled 1) reservoir spatial heterogeneity, e.g., subdivision of the stimulated reservoir volume (SRV) and fractal SRV, 2) non-continuum flow mechanisms, e.g., Knudsen diffusion, surface diffusion, and gas slip, into diffusivity equations, and 3) the impact of pressure depletion on gas desorption, and pore size change in propped and unpropped fractures. We also discuss the gas permeability models that have been proposed in the past decade and the challenges that remain to the development of oil flow models. Our knowledge of fluid transport, especially for confined fluid at multiple reservoir scales, remains incomplete, and our understanding of flow contributions from different flow regions, and mass transfer between them remains limited.

Generalized analytical model of Transient linear flow in heterogeneous fractured liquid-rich tight reservoirs with non-static properties

• New analytical transient linear flow is rigorously modeled in heterogeneous fractured liquid-rich tight reservoirs with non-static properties . • Improved rate-transient analysis workflow is proposed to estimate reservoir/fracture properties. • Three liquid-rich shale field examples in North America are analyzed to demonstrate the practical applicability of new model. The industry is increasingly reliant on rate-transient analysis (RTA) to extract valuable information about the reservoir and hydraulic fractures. However, the application of current, commercially-available RTA models can lead to incorrect estimates of reservoir/fracture properties, potentially causing costly mistakes to be made in capital planning and reserve estimation. The root cause of these errors is that currently-available analytical solutions used in RTA models largely ignore reservoir heterogeneities, and assume static reservoir properties. In this work, a new transient linear flow is rigorously modeled in unconventional reservoirs with (1) pressure-dependent rock and fluid properties and (2) both continuous and discontinuous (heterogeneous) porosity and permeability. To achieve this, new transformations of pseudo-pressure, pseudo-time and pseudo-distance are first introduced to reduce the temporal and spatial non-linear diffusivity equation to that with approximately constant coefficients. Both a Laplace-domain solution and approximate analytical solution to the diffusivity equation are verified against a series of fine-grid numerical simulations for the assumption of fractal-based reservoir heterogeneity (over a wide range of stress-dependent rock and fluid properties). The results indicate that reservoir heterogeneity can result in nonlinear square-root-of-time plots. Further, rock and fluid pressure-dependencies act to decrease the slope of the square-root-of-time plot and affect reservoir/fracture property evaluations. Three liquid-rich shale (LRS) field examples in North America are analyzed to demonstrate the practical applicability of the new RTA models. Additional value of new RTA models over the sophisticated numerical simulation is to provide us an improved backforward-analysis workflow that can be used to quantify both effective fracture half-length and non-uniform permeability distribution around the fractures. The major contribution of this work is the introduction of a new analytical model for evaluating the transient linear flow period for the cases of arbitrary reservoir heterogeneity and non-static reservoir properties. This new approach is particularly useful for evaluating the effectiveness of hydraulic fracturing operations by extracting the spatial variability of reservoir quality within the stimulated reservoir volume (SRV).

Bilayer Predictive Power Flow Controller for Bidirectional Operation of Wirelessly Connected Electric Vehicles

This paper presents a comprehensive solution that allows a wirelessly connected electric vehicle (EV) to be autonomously charged and discharged, during long-term parking and/or transient stops. A bilayer power flow controller for bidirectional wireless power transfer system (BWPTS) in EVs applications is proposed. The proposed controller can manage the power flow between the EV and surrounding infrastructures, such as utility grid, home micro-grid, building micro-grid, road, or another vehicle. It consists of two control layers; the first is responsible for communicating with the surrounding infrastructures and gathering information from the vehicle operator, charging station, utility grid, and battery management system. These data are analyzed to generate the reference power signal with information about the mode of operation (charge, discharge, or abstain) and rate. The second layer receives the reference signal and predicts the control parameters for the resonant converters (on both the vehicle and grid sides) to track the desired power. The proposed algorithm is adaptively estimating the mutual inductance to consider the misalignments in the system, based on a new simple real-time mutual estimation algorithm using a single voltage measurement from the vehicle side. The second control layer is designed based on an accurate analytical model for the BWPTS's power flow. For verification purposes, a prototype for BWPTS was built and driven by the proposed controller, which was implemented using a field-programmable gate array integrated circuit. Also, a vehicle-level simulation was performed to validate the operation of the proposed controller in quasi-dynamic wireless charging at traffic signals. The proposed controller shows fast and stable response during both the transient and steady-state operation in comparison with the conventional proportional-integral controller.

Modeling Carbon Emission Flow in Multiple Energy Systems

Multiple energy systems (MESs) bring different types of energy together and are able to improve energy utilization efficiency and promote the integration of renewable energy. The embedded carbon emission in MES is coupled among the energy flow across different energy systems. The understanding of how the embedded carbon emission should be allocated along with the energy delivery and conversion is significant in the policy making and market design to facilitate carbon emission reduction. A novel analytical model for carbon emission flow (CEF) in MES is proposed in this paper to quantify the carbon emission associated with the energy delivery and conversion process. First, key indicators and basic principles of CEF are defined. Then, the explicit CEF models for different energy networks, including the power network, gas network and heating network, are established. On the basis of the CEF models of energy converters, the CEF model for an energy hub is further formulated to analyze the flow of carbon emission across different energy systems during the conversion process. Finally, the procedure of CEF calculation in MES is provided. The case study results based on two systems are presented to verify the effectiveness of the proposed method.

An exact analytical model for fluid flow through finite rock matrix block with special saturation function

An exact analytical solution for one-dimensional fluid flow through rock matrix block is presented. The nonlinearity induced from flow functions makes the governing equations describing this mechanism difficult to be analytically solved. In this paper, an analytical solution to the infiltration problems considering non-linear relative permeability functions is presented for finite depth, despite its profound and fundamental importance. Elimination of the nonlinear terms in the equation, as a complex and tedious task, is done by applying several successive mathematical manipulations including: Hopf-Cole transformation to obtain a diffusive type PDE; an exponential type transformation to get a convective-diffusive type PDE with suitable boundary conditions; Laplace transformation; Integral transformation to homogenize the boundary condition in the Laplace domain; and finally Laplace inversion method to find the time domain solution. The obtained solution is used for developing a new matrix-fracture transfer function. The developed analytical equations are used for prediction of drying front in the case of evaporation from deep water table. The model results are in close agreement with the experimental data and numerical simulation of the process. Results of sensitivity analysis of different parameters on recovery rate and ultimate production based on design of experiment method are also discussed.

A new analytical model for flow in acidized fractured-vuggy porous media

Acidizing is one of the widely used technologies that makes the development of naturally fractured-vuggy reservoirs effective. During the process of acidizing, carbonate minerals are dissolved by hydrochloric acid, which can create high conductivity channels and wormholes to connect fractures and pores. In this work, a new analytical model, incorporating the heterogeneity of the pore networks into acidizing region, is proposed to study the flow characteristics in acidized fractured-vuggy reservoirs. The model is coupled by an acidized inner region and a conceptualized outer region of common triple medium. The porosity and permeability of inner region, which are rather heterogeneous and disordered when observed at different length scales, can be well addressed by fractal theory. The properties of the outer region can be described with three basic parameters: the matrix block size LM, the space interval of fracture LF and the radius of the vug Lv. Results show that the flow characteristic curves can be characterized by six flow stages (i.e. wellbore storage stage, radial flow stage in the interior region, fracture-vug inter-porosity flow stage, transition flow stage, fracture-matrix inter-porosity flow stage and external boundary response stage). It can be applied to estimate reservoir parameters for uncertainty reduction using inverse modeling.

Investigation of material flow behaviour and chip formation mechanism during grinding of glass-ceramics by nanoscratch

Abstract Material flow analysis is important for revealing the mechanisms of chip formation and material removal in ductile regime machining of glass-ceramics. However, the analysis is limited by a lack of elastic–plastic stress field modelling of the scratch process. Therefore, this paper proposes an analytical stress field model of material flow for glass-ceramics to reveal the material removal mechanism at a microscale. This model includes the grit tip radius and nominal rake angle, which have a significant effect on material flow. Theoretical analysis results show that the material flow direction and chip formation depend on the relative grit sharpness. With greater relative grit sharpness, more material flows upwards and a chip is easily formed owing to the smaller effective rake angle, whereas less relative grit sharpness results in a larger effective rake angle such that all the material flows downwards and no chip is formed. To validate the proposed model, a taper nanoscratch experiment was conducted. The experimental and theoretical results are in good agreement. These findings of material flow behaviour can help predict chip formation and achieve the ductile regime grinding of glass-ceramics.

Distributed Flow Estimation for Autonomous Underwater Robots Using Proper Orthogonal Decomposition-Based Model Reduction

Flow estimation plays an important role in the control and navigation of autonomous underwater robots. This paper presents a novel flow estimation approach that assimilates distributed pressure measurements through coalescing recursive Bayesian estimation and flow model reduction using proper orthogonal decomposition (POD). The proposed flow estimation approach does not rely on any analytical flow model and is thus applicable to many and various complicated flow fields for arbitrarily shaped underwater robots, while most of the existing flow estimation methods apply only to those well-structured flow fields with simple robot geometry. This paper also analyzes and discusses the flow estimation design in terms of reduced-order model accuracy, relationship with conventional flow parameters, and distributed senor placement. To demonstrate the effectiveness of the proposed distributed flow estimation approach, two simulation studies, one with a circular-shaped robot and one with a Joukowski-foil-shaped robot, are presented. The application of flow estimation in closed-loop angle-of-attack regulation is also investigated through simulation.

An Experimental Test for Application of Analytical Model of Surge Flow under Drought and Wet Conditions in a Semi-Arid Region

In this paper, an analytical solution is investigated in the zero-inertia problem for surge flow phenomena in non-prismatic channels considering the impact of infiltration (introduced by Technische Univ. Dresden) in dry-channels under drought and wet conditions in a semi-arid climate in Iran. The hydrodynamic analytical model introduced by Dresden University is free of numerical troubles, easy to run, computationally efficient, and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model can be compared favorably with a full hydrodynamic numerical model (HEC-RAS) in a permeable non-prismatic channel. In the next step, a sensitivity and error analysis was conducted and found that the Manning-Strickler coefficient, hydraulic radius, and inflow hydrograph have important effects on the velocity of the surge, suggesting the importance of an adequate description of the topography. The new approach is finally applied to simulate and compare 10 scenarios to manage artificial groundwater recharge in three channels in the downstream of Garin Dam under wet (more than 25%) and drought (less than 5%) conditions in the west of Iran. Based on tested scenarios, infiltration rate of bad and suitable scenarios varies from 3 to 85% and 1 to 76% of the total volume of released water in Garin in wet and drought phases, respectively.

Study of gas-liquid upward annular flow through a contraction

Transient response of two-phase flow is important in many analyses of nuclear reactor accident scenarios. In the present work, we study the response of vertical annular flow to a sudden or gradual pipe contraction. The three component fields of gas-liquid annular flow, namely, the liquid film, the entrained liquid droplets and the gas core, show different behaviour as they pass through an area change section because of their very different inertias. Pressure variation through the contraction is a result of the integrated effect of these responses. In order to throw light on these, pressure profiles along the upstream and downstream sections of the contraction have been measured in air-water flow through a vertical converging pipe section for diameter ratios of 1.5 and 2.0 and for half-cone angles of 8°, 15° and 90°. The gas-droplet field interaction has been studied using computational fluid dynamics simulations while the gas-film flow interaction has been studied using an analytical model for film flow. These studies highlight the role of droplet inertia as the principal contributor to the pressure change in the contraction. A semi-empirical model has been developed for the pressure loss coefficient in the contraction.

Analytical multiphase fluid flow model for reservoirs producing under bottom water drive mechanism

The existing of transition zone in oil reservoirs causes alteration in pressure response of the producing wells and distorts the accuracy of the models which analyse the reservoir behaviour. An analytical multiphase flow model for oil reservoirs producing under bottom aquifer drive mechanism has been developed to predict the accurate reservoir pressure drop during the transient flow period, as well as the capillary-saturation relationship under reservoir conditions. The contacted fluids are linked across free water level which reflects the interaction degree between reservoir-aquifer rocks and their own fluid properties. The results show that the conventional flow models which assume single phase fluid flow in porous media or weighted rock and fluid properties mislead the accuracy in predicting reservoir pressure. The error of these models increases with increasing the interaction degree between the reservoir and the aquifer, which depends on both of reservoir-aquifer rocks and their own fluid properties.

Analytical multiphase fluid flow model for reservoirs producing under bottom water drive mechanism

Analytical multiphase fluid flow model for reservoirs producing under bottom water drive mechanism

A Transient Flow Model for Multilateral Horizontal Wells in Bottom Water Drive Reservoirs

The aim of this paper is to describe the pressure dynamic behaviour around a multilateral horizontal well in bottom water reservoir and get the productivity by establishing an analytical transient flow model. An exact solution of the model is derived by means of orthogonal transformation, method of mirror images and the theory of potential superimposition. For bottom water reservoirs, there is a supplementary boundary for the water aquifer. Given enough time, the transient flow will change to steady flow gradually. Correspondingly, the productivity index for wells in bottom water drive reservoirs can be calculated. We conclude that the analytical solution to the model can provide a valuable tool to compute the productivity and pressure dynamic behaviour of the multilateral horizontal wells in the bottom water reservoirs. Moreover, the case study shows that the calculated results agree with the practical situation. [Received: August 12, 2017; Accepted: March 16,2018]

Experimental, numerical and theoretical investigations of Tesla turbines

We use analytical, numerical and experimental methods to characterize the laminar flow inside a Tesla turbine rotor gap. A comparison based on one particular set of operating conditions mutually validates the three approaches. The simplicity of the analytical flow model allows for a cost efficient optimization of the underlying turbine parameters. Performance charts exhibit general trends and serve as a guide for preliminary turbine design and optimization. In terms of the ratio of half the gap width to inlet radius and the ratio of outletto inlet radius, the designer of a tesla turbine has to find a compromise between optimal efficiency and optimal power output.