Analysis of Factors Influencing Mobility and Adsorption in the Flow of Polymer Solution Through Porous Media

1974 ◽  
Vol 14 (04) ◽  
pp. 337-346 ◽  
Author(s):  
G.J. Hirasaki ◽  
G.A. Pope
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Polymer Solution ◽  
Polymer Adsorption ◽  
Rock Properties ◽  
Dimensionless Number ◽  
Permeability Reduction ◽  
Flow Rates ◽  
System Properties ◽  
Effective Pore Radius

Abstract Displacement of oil by polymer solution has several unique characteristics that are not present in normal waterflooding. These include non-Newtonian effects, permeability reduction, and polymer adsorption. polymer adsorption. The rheological behavior of the flow of polymer solution through porous media could be Newtonian at low flow rates, pseudoplastic at intermediate flow rates, and dilatant at high flow rates. The pseudoplastic behavior is modeled with the pseudoplastic behavior is modeled with the Blake-Kozeny model for power-law model fluids. The dilatant behavior is modeled with the viscoelastic properties of the polymer solution. properties of the polymer solution. The reduction in permeability is postulated to be due to an adsorbed layer of polymer molecular coils that reduces the effective size of the pores. A dimensionless number has been formulated to correlate the permeability reduction factor with the polymer, brine, and rock properties. This polymer, brine, and rock properties. This dimensionless number represents the ratio of the size of the polymer molecular coil to an effective pore radius polymer molecular coil to an effective pore radius of the porous medium.A model has been developed to represent adsorption as a function of polymer, brine, and rock properties. The model assumes that the polymer is properties. The model assumes that the polymer is adsorbed on the surface of the porous medium as a monolayer of molecular coils that have a segment density greater than the molecular coil in dilute solution. Introduction Displacement of oil by polymer solutions has several unique characteristics that are not present in normal waterflooding. These include non-Newtonian effects, permeability reduction, and polymer adsorption. In principle, the effects could polymer adsorption. In principle, the effects could be measured experimentally for each fluid-rock system of interest over the entire range of flow conditions existing in the reservoir. However, there are seldom complete data on all systems of interest. A correlation that represents these effects as a function of the polymer, brine, rock properties, and flow conditions would result in a more accurate evaluation of systems that may not have been measured in the laboratory at the desired conditions. Moreover, if the dependence of these effects on the system properties were known, it would aid the search for an optimal system. A model is proposed for representing the effects as a function of the system properties. The model is consistent with a number of experimental observations but enough data have not yet been acquired to determine the extent of applicability of a correlation. It is hoped that the presentation of these models will encourage further research to verify or improve the models. MODEL FOR PSEUDOPLASTIC FLOW THROUGH POROUS MEDIA The Blake-Kozeny model represents the porous medium as a bundle of capillary tubes with a length that is greater than the length of the porous medium by a tortuosity factor, tau. The equivalent radius of the capillary tubes can be related to the particle diameter of a packed bed from the hydraulic radius concept or to the permeability and porosity by comparison with Darcy's law for Newtonian fluids.The modified Blake-Kozeny models represents the flow of a power-law fluid in the capillaries. The relationship between the pressure drop and flow rate can be expressed as a product of the friction factor and Reynolds number.(1) This expression can be related to the apparent viscosity and the rock permeability and porosity through the following relationships:(2) where(3) SPEJ P. 337

Shear Viscosities of Ionic Polyacrylamide Solutions

1972 ◽  
Vol 12 (06) ◽  
pp. 469-473 ◽  
Author(s):  
Necmettin Mungan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Shear Rate ◽  
Polymer Solution ◽  
Polymer Solutions ◽  
Mobility Control ◽  
Permeability Reduction ◽  
Experimental Conditions ◽  
Molecular Weights ◽  
Stock Solutions

Abstract Solutions of ionic polyacrylamide polymers behave pseudoplastic in purely viscometric flow. Flow rate, polymer molecular weight and electrolytes affect solution viscosities to a large extent. Equations are given for the viscosity-shear rate relations in a form that can be used conveniently to account for the effect of viscosity on mobility. Introduction Polymers are being used increasingly in oil recovery operations, and therefore, an understanding of their flow behavior is gaining pragmatic importance. Past studies have shown that in the flow of polymeric fluids through porous media, the increase in solution viscosity, decrease in permeability, and viscoelastic deformations cause permeability, and viscoelastic deformations cause the fluid mobility to be greatly reduced. In general, viscoelasticity, i.e., extensional flow, is not so important because, for the largest part of a reservoir, polymer solution moves at very low and fairly steady polymer solution moves at very low and fairly steady velocities. Jennings et al. have concluded this for the specific polymers that they studied. Permeability reduction plays an important role in Permeability reduction plays an important role in the mobility control, particularly in porous media having low permeabilities initially. Reductions ranging from 25 to 70 times have been reported. However, the alterations that take place in a porous medium during polymer flow, the coupling between the geometry of the porous medium and the properties of the flowing fluid, and the influence of the flow regime on permeability have not been looked into in sufficient detail. A separate study, directed to the understanding of these important phenomena is required. In the present work, the purely viscous behavior of solutions of three partially hydrolized polyacrylamide polymers was obtained under experimental conditions far polymers was obtained under experimental conditions far more extensive than any reported in the literature. Some data have been available in the past for two of the polymers, but the third is a new polymer for which no data have been reported before. Using a Weissenberg rheogoniometer, Cannon-Fenske viscometers, and various capillary cubes, viscosities were measured over 8 decades of shear rate, ranging from 10 to to 10 (5) sec-1. These are the limits of measurable rates of shear and cover those that may apply to flow in reservoirs. Distilled water and various NaCl solutions were used as solvents to afford comparison of the rheological properties between fresh and saline solutions. Measurements were also made with solutions containing calcium' and magnesium to study the effect of divalent cations. EXPERIMENTAL The three polymers, Nos. 500, 700 and NC 1870, are partially hydrolized polyacrylamides manufactured by The Dow Chemical Co., and were from lots 8085, 52 and 87-8100E, respectively. Polymer NC 1870 is currently at a developmental stage and can be obtained in limited quantities; the other two have been available commercially for some time, have been used in the laboratory and in the field. All three are hydrolized to the same extent, containing approximately 25 percent polyacrylate, with the remainder being polyacrylamide. The molecular weights of Nos. 500 and 700 are 2 to 3 and 3 to 7 million, respectively. That of the NC 1870 is higher, but has not been measured due to the usual difficulties in measuring such high molecular weights. Polymer and salt concentrations are given on a weight-parts per million basis. Reagent grade chemicals and double-distilled deaerated water, having a pH of 6.5, were used in all solutions. Formaldehyde was added as a bactericide. To the extent possible, air was kept out of the solutions to avoid oxidation-type degradation of the polymers. Polymer solutions were mixed using magnetic Polymer solutions were mixed using magnetic stirrers and carefully avoiding any mechanical degradation. Solutions of desired concentrations were prepared from stock solutions by dilution. The latter had been passed through 1-micron millipore filters, were optically clear, containing no fish-eyes. The polymer concentration of stock solutions was determined by turbidimetry and nitrogen analysis, the two methods usually agreeing within a few percent. percent. SPEJ P. 469

Unsteady Radial Flow of Gas Through Porous Media

1953 ◽  
Vol 20 (2) ◽  
pp. 210-214
Author(s):  
R. Jenkins ◽  
J. S. Aronofsky
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Radial Flow ◽  
Transient Flow ◽  
Gas Reservoirs ◽  
Punch Card ◽  
Flow Rates ◽  
Pressure Distributions ◽  
History Of ◽  
Natural Gas Reservoirs

Abstract This paper presents a numerical method for describing the transient flow of gases radially inward or outward through a porous medium in which the initial and terminal pressures and/or rates are specified. Specific examples are worked out which have application in the study of natural-gas reservoirs. The computations were carried out by means of punch-card machines. The pressure distribution as a function of time has been calculated for various ratios of reservoir diameter to well diameter and for various dimensionless flow rates for a well penetrating the center of a homogeneous disk-shaped reservoir. A simple means of predicting the well pressure at any time in the history of such an idealized field has been developed. Flow rates and pressure distributions within the radial reservoir also have been calculated for the case in which the well pressure is suddenly lowered from its initial static value, and then held constant.

Effect of Concentration on HPAM Retention in Porous Media

SPE Journal ◽  
2014 ◽  
Vol 19 (03) ◽  
pp. 373-380 ◽  
Author(s):  
Guoyin Zhang ◽  
R.S.. S. Seright
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Polymer Solution ◽  
Polymer Concentration ◽  
Retention Mechanism ◽  
Dynamic Measurements ◽  
Polymer Molecules ◽  
Adsorbed Polymer ◽  
Hydrolyzed Polyacrylamide ◽  
Polymer Retention

Summary This paper investigates the effect of hydrolyzed polyacrylamide (HPAM) polymer concentration on retention in porous media by use of both static and dynamic measurements. Consistent results by use of these two methods show that different polymer-retention behaviors exist in dilute, semidilute, and concentrated regions. In both the dilute and concentrated regions, polymer retention has little dependence on concentration. In contrast, in the semidilute region, polymer retention is concentration dependent. If a porous medium is first contacted sufficiently with dilute polymer solution to satisfy the retention, no significant additional retention occurs during exposure to higher HPAM concentrations. On the basis of the experimental results, a concentration-related retention mechanism is proposed that considers the orientation of the adsorbed polymer molecules and the interaction between molecular coils in solution. By use of this model, we explain why polymer retention does not show much dependence on concentration in the dilute and concentrated regimes. Further, in the semidilute region, we explain how moderate coil interactions lead to mixed adsorbed-polymer orientation and magnitude on rock surfaces, and retention becomes concentration dependent. In field applications of polymer and chemical floods, reduced polymer retention may be achieved by first injecting a low-concentration polymer bank.

scholarly journals Dispersion Coefficients for Gases Flowing in Consolidated Porous Media

1967 ◽  
Vol 7 (01) ◽  
pp. 43-53 ◽  
Author(s):  
Max W. Legatski ◽  
Donald L. Katz
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Electrical Resistivity ◽  
Natural Gas ◽  
Dispersion Coefficient ◽  
Longitudinal Dispersion ◽  
Rock Properties ◽  
Dispersion Coefficients ◽  
On Line ◽  
Mixing Problem

Abstract The best currently available description of the longitudinal mixing properties of a porous medium is an equation of the formEquation 1 which relates the effective longitudinal dispersion coefficient Dl to the molecular diffusion coefficient D0, the electrical resistivity factor F, the porosity f and a Peclet number. If the parameters dps and m are determined for a porous medium of known porosity and electrical resistivity factor, then a dispersion coefficient may be estimated for a given flow rate and a given gas pair. A new method, featuring on-line gas analysis by thermal conductivity and on-line data reduction by analog computation, was developed and used to determine these mixing parameters for eight naturally occurring sandstones and two dolomite samples. The exponent m of the above equation was found to vary between 1.0 and 1.5. The characteristic length dp s in the above equation was found to vary between 0.25 and 1.9 cm, with an average value of 0.4 cm for sandstones. Measurements were made on two cores in which paraffin wax had been deposited by evaporation from a pentane solution. They indicated that the presence of an immobile phase such as connate water could increase the dispersion coefficients significantly. INTRODUCTION While the petroleum and chemical industries have studied the mixing of miscible liquids flowing in consolidated porous media and of miscible gases flowing in unconsolidated porous media, relatively little data have been presented to describe the mixing of gases flowing through consolidated porous media. Such data are of particular interest to the gas storage industry. For instance, the U.S. Bureau of Mines is storing large quantities of a rich helium-nitrogen gas in contact with a natural gas in a dolomite reservoir. Since the rich gas occupies only 15 percent of the total reservoir volume, it is essential that the extent of rich gas-natural gas mixing be predicted and understood as a function of rock properties, pressure and rate of movement. This investigation was concerned only with the determination of longitudinal dispersion coefficients. It is understood that a transverse dispersion coefficient, which characterizes mixing perpendicular to the direction of flow, may be an order of magnitude less than the coefficient characterizing mixing in the direction of bulk flow.5,19 It should also be recognized that the use of any dispersion coefficient is in itself a simplification. It is necessary to assume that mixing in a porous medium may be characterized by the equationEquation 2 for flow in a single direction. A number of authors1 have pursued the mixing problem, not in terms of the so-called "dispersion model" described by Eq. 1, but in terms of a "mixing cell model". This model supposes that a porous medium is constructed of a large number of small mixing chambers and that the concentration of the diffusing component within each mixing chamber is uniform. Fick's law (Eq. 1) assumes that there is no gross by-passing of one fluid by another, and that there are not stagnant pockets of gas in the system under consideration as discussed by Coats and Smith.8 These assumptions are not always valid for flow through porous media and it is important to recognize the limitations upon Eq. 1.

scholarly journals Colloid clogging of saturated porous media under varying ionic strength and roughness during managed aquifer recharge

2019 ◽  
Vol 9 (3) ◽  
pp. 225-231 ◽  
Author(s):  
Du Xinqiang ◽  
Song Yalin ◽  
Ye Xueyan ◽  
Luo Ran
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Ionic Strength ◽  
Smooth Surface ◽  
Saturated Porous Medium ◽  
Managed Aquifer Recharge ◽  
Permeability Reduction ◽  
Saturated Porous Media ◽  
Aquifer Recharge ◽  
Pore Throat

Abstract Column experiments were conducted to examine the clogging effects of colloids under controlled conditions of solution ionic strength (IS) and porous media roughness. The results showed that colloids in recharge water play an important role in the clogging process of saturated porous media, such that even a small amount of colloid may cause a large reduction in the permeability of the porous medium. Clogging at the pore throat was inferred to be the main reason for the severe permeability reduction of porous media. The characteristics of colloid clogging were clearly influenced by both IS and medium roughness. Recharge water with a higher IS facilitated greater attachment of colloids to the surface of the saturated porous medium, which lead to superficial clogging, while collectors with a rough surface resulted in greater clogging than collectors with a smooth surface.

Correlations of Physical Properties of Porous Media

1967 ◽  
Vol 7 (03) ◽  
pp. 266-272 ◽  
Author(s):  
W. Douglas Von Gonten ◽  
R.L. Whiting
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Regression Analysis ◽  
Physical Properties ◽  
Physical Property ◽  
Rock Properties ◽  
Petroleum Reservoir ◽  
Formation Factor ◽  
Naturally Occurring ◽  
Formation Resistivity

Abstract Regression analysis was used to correlate the physical properties of 478 sandstone and 90 carbonate core samples. Porosity, permeability, electrical formation resistivity factor, capillary pressure and the sonic velocity of the shear and compressional waves were measured. Prediction equations for porosity, permeability and electrical formation resistivity factor were found which should be useful in understanding the relationships between the physical properties of porous media in formation evaluation. Introduction The physical properties of porous media are important to the petroleum engineer and geologist. To evaluate fully the potential and behavior of a subsurface formation such as a petroleum reservoir, certain physical properties of the porous medium must be known. The problem of accurately determining physical properties of subsurface formations has not been solved because many determinations must be made by indirect measurements and because of the difficulties caused by complex pore structure and presence of clays in most naturally occurring porous media. Due to the difficulty in measuring some of the physical properties of porous media, it would be advantageous to be able to predict a certain physical property of a rock from other physical properties of the rock which could be measured more easily and more accurately. Since most potential reservoir rocks are heterogeneous, relationships between the physical properties are very complex and thus far no satisfactory correlations based on theory or laboratory models have been developed. It appears that empirical relationships obtained by measuring the physical properties of a large number of samples of naturally occurring porous media and applying regression analysis to develop for one physical property in terms of other rock properties is the best approach. REVIEW LITERATURE The three physical properties used as dependent variables for correlating purposes were porosity, permeability and formation factor. Since formation factor is more difficult to determine, a brief review of the literature is provided on this property. The first work on determining formation factors was published by Archie in 1942. He defined this property of a porous medium as Ro ...............................(1) F =RW where Ro is the resistivity of the porous medium when completely saturated with a brine of resistivity Rw. Archie found the best correlation between formation factor and porosity was the following equation, F = - m..................................... (2) where is the porosity fraction and m is the constant characteristic of the rock. The value of m was 1.3 for unconsolidated sand packs, and ranged from 1.8 to 2.0 for consolidated sandstones. In 1950 Patnode and Wyllie and De Witte observed that the formation factor as determined by Eq. 1 was valid only when the porous medium contained no conductive solids such as clay or shale. When conductive solids are -present the formation factor is also dependent on the resistivity of the saturating fluid. Therefore, in samples containing conductive solids the formation factor decreased as resistivity of the saturating fluid increased. Because of this, the measured formation factor was called the apparent formation factor and was designated Fa. Patnode and Wyllie proposed the following equation. SPEJ P. 266ˆ

Flow Characteristics of Surfactant Solutions in Porous Media and Their Role in Permeability Modification

1981 ◽  
Vol 21 (06) ◽  
pp. 709-720 ◽  
Author(s):  
B. Kalpakci ◽  
E.E. Klaus ◽  
J.L. Duda ◽  
R. Nagarajan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Bulk Viscosity ◽  
Effective Viscosity ◽  
Flow Characteristics ◽  
Surfactant Solution ◽  
Surface Characteristics ◽  
Initial Permeability ◽  
Permeability Reduction ◽  
Surfactant Solutions

Kalpakci, B., SPE, Standard Oil Co. (Ohio) Klaus, E.E., Pennsylvania State U. Pennsylvania State U. Duda, J.L., SPE, Pennsylvania State U. Pennsylvania State U. Nagarajan, R., Pennsylvania State U. Pennsylvania State U. DECEMBER 1981 Abstract This paper presents results of a study on flow properties of surfactant solutions in porous media, properties of surfactant solutions in porous media, using the Penn State porous media viscometer. The effects of permeability, shear rate, and surface characteristics of porous media on the flow of oil- and water-external microemulsions, as well as surfactant solutions with lamellar structures, are examined. Untreated Bradford and Berea sand- stones, oil- and water-wet treated sandstones, and filter papers are used as porous media. The study shows that the effective viscosity of the surfactant solution (as measured in porous media), on the basis of initial permeabilities, is greater than the bulk viscosity (as measured by conventional viscometers). This increase is small for Newtonian surfactant solutions but is quite substantial for non- Newtonian surfactant solutions. The difference between bulk and effective viscosities of Newtonian surfactant solutions is eliminated when the effective viscosity is determined on the basis of the final permeability of the porous medium to calibration permeability of the porous medium to calibration solution. This indicates that the permeability of the porous medium during now of these Newtonian porous medium during now of these Newtonian surfactant solutions is equal to that during flow of postcalibration solutions. In contrast, in the case of postcalibration solutions. In contrast, in the case of the non-Newtonian surfactant solution with lamellar structures, the effective viscosity based on the final permeability remains higher than the bulk viscosity permeability remains higher than the bulk viscosity of the solution. Plausible explanations for the lower permeability during surfactant flow compared with permeability during surfactant flow compared with the final permeability, in this case, are discussed. It is found that the flow of surfactant solutions causes a permanent decrease in the permeability of the porous. medium. Initial permeability is not restored even by thorough flushing of the porous medium with surfactant-free brine solution. Residual permeability reductions of 2 to 51% are observed. permeability reductions of 2 to 51% are observed. The residual permeability reduction increases with decreasing initial permeability. The residual permeability reduction is relatively insensitive to the type permeability reduction is relatively insensitive to the type of surfactant solution. However, it depends on surface characteristics of the porous medium and decreases in this order: untreatedfired is greater th an oil-wet treated. Introduction According to Gogarty, about 60% of the potential oil reserves are estimated to be amenable to chemical flooding with surfactant and polymers. In surfactant/polymer flooding, the interaction of various chemicals with each other and with reservoir fluids and rocks, the permeability, the porosity, and the operating conditions are critical factors in determining the effectiveness of the process. Many studies of surfactant systems have been carried out relating to phase behavior, interfacial tension, and retention or adsorption characteristics. But only a few studies have been conducted on flow characteristics in porous media of surfactant fluids prepared with petroleum sulfonates, hydrocarbons, prepared with petroleum sulfonates, hydrocarbons, water, and electrolytes. These latter studies have not examined fully the flow characteristics over a wide range of permeabilities and shear rates, the influence of the permeability of porous media on the residual permeability reduction, and the influence of surface permeability reduction, and the influence of surface characteristics of porous media. Considering that sufficient viscosity level is an essential factor in mobility control during surfactant flooding, the importance of the rheology of surfactant solution in porous media is quite obvious. Information on porous media is quite obvious. Information on injectivity, effective viscosity, and permeability modification during the flow of surfactant solutions is also essential. SPEJ P. 709

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Capillary Imbibition Dynamics in Porous Media

2014 ◽  
Author(s):  
Swayamdipta Bhaduri ◽  
Pankaj Sahu ◽  
Siddhartha Das ◽  
Aloke Kumar ◽  
Sushanta K. Mitra
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Paper Strip ◽  
Capillary Imbibition ◽  
Flow Physics ◽  
Fundamental Understanding ◽  
Paper Based Microfluidics ◽  
To Come

The phenomenon of capillary imbibition through porous media is important both due to its applications in several disciplines as well as the involved fundamental flow physics in micro-nanoscales. In the present study, where a simple paper strip plays the role of a porous medium, we observe an extremely interesting and non-intuitive wicking or imbibition dynamics, through which we can separate water and dye particles by allowing the paper strip to come in contact with a dye solution. This result is extremely significant in the context of understanding paper-based microfluidics, and the manner in which the fundamental understanding of the capillary imbibition phenomenon in a porous medium can be used to devise a paper-based microfluidic separator.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Sign in / Sign up

Export Citation Format

Share Document