In the very low reynolds number regime fully developed laminar flow is assumed and in the higher laminar reynolds number regime the forchheimer nondarcy effect is modelled through reference to form drag induced by the solid constituents. Derivation of the phase distribution model for packed beds based. Modelling heat transfer during flow through a random packed bed of. Modified ergun equation for airflow through packed bed of. One is the kozenycarman equation, used for flow under very viscous conditions. Application of the erguns equation in porous ceramic based. For nonspherical particles, replace the diameter dby. The density and viscosity values of air and producer gas are similar to air, since most of what is in producer gas is pretty similar to air co, n2, and to a lesser extent co2.
The technique has been validated against experimental measurements of pressure drop and velocity distribution in a model of a filter system for a range of filter parameters and inlet velocities. The ergun equation is applicable to both laminar and turbulent flows, which are covered by the two terms in the equation see the subramanian paper. Jan 08, 2018 a sample question for ergun equation and darcys law. Study on ergun equation at vacuum pressures for sodium fluoride adsorbents.
Satisfactory results are obtained for both gas and liquid systems. Experimental flow in various porous media and reconciliation. Erguns equation flow through packed beds and fluidized. We adapt ergun equation for our packed bed reactor. Oct 03, 20 the ergun equation provides a good description for the relationship of the pressure drop with the flow rate and the gas properties. Dupuit4related u c and u 1 by the following argument. The boundary condition near the filter underdrain also violates the assumption of an infinitely extended packed bed made by the ergun equation. It is known that pressure drop is caused by simultaneous viscous and inertia kinetic energy losses.
The pressure loss through the bed was calculated from the ergun equation, using the local voidage. Erguns equation to the polydisperse particles systems taking into account the particle size distribution 2,3. General m,odel for prediction of pressure drop and. Algorithm for isothermal reactor design mole balance and design equation rate law stoichiometry combine evaluate algorithm algorithm algorithm algorithm algorithm pressure drop in packed bed reactors pressure drop in packed bed reactors ergun equation. I made an equation in a separate document not using mail merge, just the equation editor and it prints fine. Hence, we need an additional relationship between pressure and conversion. Analytical quantification of coefficients in the ergun. Oct 31, 2011 pressure gradient problems with the ergun equation posted in student. Hi, im currently designing a plant to convert syngas to liquid fuels through fischertropsch synthesis. Calculation of pressure drop across a porous media debris. The ergun equation for calculating clean bed headloss table 82 has been proposed for use in cases where larger media and higher filtration rates are used such as deep bed monomedium filters. The ergun equation is commonly expressed as follows in different references. Ergun s equation to the polydisperse particles systems taking into account the particle size distribution 2,3.
This was calculated from the ergun equation 1, which gives the pressure drop per unit length through a packed bed as. Fluidization refinery application fluidization drug application fluidization at fluidization, the gravity force on the particles in the bed must be balanced fk 0 by the drag, buoyancy, and pressure forces. Pressure drop along a packed bed reactor the above always applies, especially for multiple reactions. On the continuum level, the second order velocity term demonstrates that the ergun equation also includes the pressure drop due to inertia, as described by the darcyforchheimer equation. This is the ergun equation see bird 1960 where redp. The ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. In this equation, conversion is a function of pressure. Lundstrom ts, marjavaara d 2012 piv analysis of merging flow in a simplified model. Example oxidation of oxylene to phthalic anhydride1 the gas phase oxidation is highly exothermic. Estimation prediction of permeability using the erguna. Porescale derivation of the ergun equation to enhance its. University of groningen particle transport in fluidized beds.
As the superficial gas veloc ity increases, the pressure drop across the bed increases in accordance with the ergun equation 2. Two simpler results, each obtained by ignoring one or the other term in the ergun equation also are in use. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity. To increase the knowledge about higher re flow through porous media we will here. The ergun equation, derived by the turkish chemical engineer sabri ergun in 1952, expresses the friction factor in a packed column as a function of the modified reynolds number. In a cube of side x, the volume of free space is ex3 so that the mean crosssectional area for. Describes how to use the ergun equation to calculate the pressure drop in a packed bed. Blake 1922 suggested that modified friction factor should be plotted against modified reynolds number.
The ergun equation gives satisfactory predictions for the particle reynolds numbers, re p, in the range from 0. Eliminate unknown surface occupancies catalysis engineering kinetics site balance. This equation is known to be reasonably accurate for densities up to about 0. The results show that the drag coefficient predicted by ergun equation should be modified. The predicted permeability constant was obtained using erguns law from equation 1. Modeling of porosity equation for water flow through packed bed of monosize spherical packing.
Pressure drop depends on a series of factors such as void fraction, media particles diameter, reynolds number, fluid density and velocity. The ergun equation, contd usually, the ergun equation is rewritten in a simplified form simplified only with regard to writing. The ergun equation, commonly used to calculate pressure drop through catalyst packed beds, can be used to calculate pressure drop through bed sections packed with proxsvers inert catalyst support balls. The ergun equation for calculating clean bed headloss. The ergun equation gives the pressure drop for unit length of a fluid flowing through granular media. Assumes e equation intermediate flow ergun equation note. Pressure gradient problems with the ergun equation student. For nonspherical quartz filtration sand particles the best fit was obtained using ergun s equation, with a mean absolute deviation of 10. We can solve them simultaneously using an ode solver such as polymath. Chapter 4 flow of fluids through granular beds and packed. The experimental system contains two identical columns with diameter 1. Implementation of a demoisturization and devolatilization model in multiphase simulation of a hybrid. Water flow semiempirical equations semiempirical formulas for modeling water flow through packed bed were modiefied for the parameters affecting the pressure drop using buckingham.
They proposed that the constants in the dimensionless form of the ergun equation, developed by niven 14. Modified equations for water flow through packed bed for. For a packed bed, the ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed. This equation is known as the burkeplummer equation. It tells us the pressure drop along the length of the packed bed given some fluid velocity.
Single phase incompressible fluid flow pressure drop updated compressible fluid flow through a pipe updated nonnewtonian power law fluid flow through a pipe updated nonnewtonian bingham plastic fluid. Flow through a packed bed can be described by the ergun equation. Applying the ergun equation to the degradation of a reactor. Kozeny modelled the layer as many small capillary tubes of diameter d making up a layer of cross sectional area a. Calculation for pressure losses in pipes and fittings for a variety of fluid flows that include single and twophase flows.
The details of the minimum velocity depend upon a number of factors, including the shape, size, density, and. If the fluid were a liquid i think ergun equation would be the right way to go. Feb 06, 2015 pressure drops in fluidized beds, packed beds and pipes. The law was formulated by henry darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. Flow through porous media at moderate reynolds number. Wen and yu 1966 developed an expression for the minimum fluidization velocity for a range of particle types and sizes by assuming the following approximations to hold based on experimental data.
The ergun equation does not have a micromechanical basis and the geometrical parameters shaping the form of the equation are therefore unknown. For the transition region, the ergun equation is to be used. Study of pressure drop in fixed bed reactor using a computational. This may be done by usage of the empirical ergun equation 12. Effect of material type and particle size distribution on. The first term in the ergun equation accounts for viscous forces.
Pdf modeling of porosity equation for water flow through. The new correlation had a mean absolute deviation between experimental and calculated values of pressure drop of 9. General m,odel for prediction of pressure drop and capacity. The above always applies, especially for multiple reactions. Flow of fluids through granular beds and packed columns 195 assumption that l is directly proportional to l. Nemec and levec 12 demonstrated that the original ergun equation systematically under predicts the pressure drop in flow over nonspherical particles. The extension of the ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by akgiray and saatc. In laminar flow conditions the first component of the equation dominates with the ergun equation essentially reducing to the carmankoreny equation presented in section 3, although with a slight variation in the constants used due to variations in the experimental data with which the. Made by faculty at the university of colorado boulder, department of. Mail merge in equation hi, i have a document with mail merged variables inside of various equations. Physical insight into the ergun and wen and yu equations for fluid flow in packed and fluidized beds article pdf available in chemical engineering science 573. The original ergun equation of the total energy loss can be rearranged as follows. Hydrodynamics of trickle bed reactors washington university.
The two bestknown theoretical relations are the forchheimer equation 7,8 and ergun or ergun type equations 9,10. Non dimensionalisation of basic equation you have seen the buckingham method to nondimensionalise the relations or form nondimensional relation for various experimental data. Fluidization emf depends on the shape of the particles. You also developed or came up with nondimensional numbers or parameters. Derivation of the stream function from a minimization of the vorticity. Substituting the ergun equation for the pressure drop. The prediction of pressure drop and flow distribution in. These are devices in which a large surface area for contact between a liquid and a gas absorption, distillation or a solid and a gas or liquid adsorption, catalysis is obtained for achieving rapid mass and heat transfer, and particularly. Profile of pressure is calculated using ergun equation. Mole balance and design equation choose reactor type 2. Ergun, fluid flow through packed columns, journal of. Shankar subramanian chemical engineering operations commonly involve the use of packed and fluidized beds.
The ergun equation 1 is quite effective for estimating the pressure. Request pdf porescale derivation of the ergun equation to enhance its adaptability and generalization the empirical nature of the wellknown ergun. Ergun, fluid flow through packed columns, journal of chemical engineering progress, vol. Aaa fullpaper an experimental and analytical study to. Select multiple pdf files and merge them in seconds. A semiempirical equation based on leva equation had been modeled to evaluate the minimum fluidization velocity. Figure 1 shows the general behavior of the ergun equation on a loglog plot with the blakekozeny and burkeplummer equations for reference.
The equation published by ergun about sixty years ago remains the most popular and the most widelyquoted pressure dropflow rate relation for fluid flow. Click on the curve to see the effects of increased gas velocity on particle movement. Darcys law is an equation that describes the flow of a fluid through a porous medium. Jul 23, 20 the ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed.
Pdf study on ergun equation at vacuum pressures for. In figure i, the dashed line represents values of n obtained from equation 2 when reverted to the form of equation 1. When the gas velocity is increased to a certain value however, the total drag on the particles will equal the weight of the bed, and the particles will begin to. Previous works also indicate that the parameters of the ergun equation may be improved 2, 3. Minimum fluidization velocity this equation can be used to calculate the minimum fluidization velocity umf if the void fraction emf at incipient fluidization is known. Modification of ergun equation for application in trickle bed. University of groningen particle transport in fluidized. The other is the burkeplummer equation, used when viscous effects are not as important as inertia. The ergun equation calculates the particlegas drag force per unit volume of bed void space as follows.
Fixed and fluidized beds university of california, berkeley. Activated sludge design equations iowa state university. Its basic form includes a viscous resistivity and an inertial resistivity parameter that are respectively used for a linear and quadratic relationship of the flow rate to the pressure drop. Pdf physical insight into the ergun and wen and yu. Pressure drops and ergun equation for pbr reactor engineering class 77 duration. Chapter 4 fluid flow through packed bed of particles. Chemical reaction engineering asynchronous video series chapter 4, part 3.
For pbr, we often write the design equations in terms of catalyst weight rather than reactor length. The actual cross sectional area for the flow path is a. Real gases are nonhypothetical gases whose molecules occupy space and have interactions. The ergun equation, derived by the turkish chemical engineer sabri ergun in 1952, expresses the friction factor in a packed column as a function of the modified. Modeling of proppant permeability and inertial factor for.
It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. The drag coefficient for single gas phase flow in a porous media has been calculated by cfd simulation and the results compared to the ergun equation. Both are widely used 8, and there is no specific reason for choosing one. When applying the ergun equation, one has to know the minimum fluidization voidage. When the gas veloc ity is high enough that the drag force on the particles equals the weight of the particles i. Modeling and simulation of single phase fluid flow and heat. May 16, 2011 based on a slit model, a pellet scale model has been developed for calculation of drag force imposed on trilobe catalyst particles in a packed bed reactor. Erguns equation with the forchheimer equation results in a deterministic set of equations that describe the fracture permeability and inertial factor as functions of the proppant diameter, pack porosity, sphericity, and fracture width. Equation 2 describes the influence of void fractions on friction factor and provides the basis for the derivation of the pressure drop model. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. P is equal to the bed weight per unit crosssectional area, and the particle sphericity. For each ceramic, a comparative study between the predicted and the measured permeability value is present. The plot below represents the ergun equation the first equation shown above, where the left hand side of the equation is the pressure drop. The two expressions are coupled ordinary differential equations.
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