As for the ergun equation issue, you have to apply different coefficients for different adsorbents size and see if the criteria for minimum pressure drop of 0. Because the crosssectional area of the reactor is small near the inlet and outlet, the presence of catalyst there would cause substantial pressure drop. 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. 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. 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. Fluidization chemical engineering at the university of floridahome. Feb 06, 2015 pressure drops in fluidized beds, packed beds and pipes. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. General m,odel for prediction of pressure drop and capacity.
The ergun equation gives satisfactory predictions for the particle reynolds numbers, re p, in the range from 0. Fluidization emf depends on the shape of the particles. 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. The experimental results for pressure drop were compared with values predicted by a proposed modifiedergun equation.
Hagenpoiseille equation substituting suitable relations. For pbr, we often write the design equations in terms of catalyst weight rather than reactor length. Effect of material type and particle size distribution on. In recent years, the combination of realistic representations of the pore space and accurate models of porelevel physics has allowed. Water flow semiempirical equations semiempirical formulas for modeling water flow through packed bed were modiefied for the parameters affecting the pressure drop using buckingham. 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. Calculation of bubbles size variation along the bed, as well as the mean and maxi bubble diameters. This module provides a number of information on the bubbling aspects of the fluidized bed. Modelling of flow through porous packing elements of a co2. Best of all, pdf creator is absolutely free for anyone to use.
Graduate thesis or dissertation dynamics behavior of a. Pressure drops in fluidized beds, packed beds and pipes. Nov, 2012 describes how to use the ergun equation to calculate the pressure drop in a packed bed. From the ergun equation equation 422, 422 we know that by decreasing g, the pressure drop will be reduced signi. Jul 23, 20 the ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. A reconciliation of packed column permeability data. Substituting the ergun equation for the pressure drop.
We can solve them simultaneously using an ode solver such as polymath. Sabri ergun 1 march 1918 18 february 2006 was a turkish chemical engineer. Pdf on feb 1, 2002, robert k niven and others published physical insight into the ergun and wen and yu equations for fluid flow in. Erguns equation to calculate the pressure drop of a fluid through. Modification of ergun equation for application in trickle bed. Please, do not simply list the procedures in your report. The results of a comprehensive computational evaluation of the ergun and forchheimer equations for the permeability of fibrous porous media are reported in this study.
Dear all, i am looking for the constants used in ergun s equation to estimate the pressure drop through a packed bed. Sometimes, an empirical coefficient of 180 instead of 150 is recommended, and equation 10 is then usually referred to as the carmankozeny equation. Sep 14, 2001 the results of a comprehensive computational evaluation of the ergun and forchheimer equations for the permeability of fibrous porous media are reported in this study. Estimation prediction of permeability using the erguna. Presentation of fluidization state on the rehs modified diagram. Based on equation 14 we can rewrite the relationship between velocity and pressure drop as. The boundary condition near the filter underdrain also violates the assumption of an infinitely extended packed. Flow through a packed bed can be described by the ergun equation. We adapt ergun equation for our packed bed reactor. The ergun equation can be regarded as direct method of pressure drop calculation. He is known for the ergun equation, which expresses the pressure drop across a packed bed biography. Application of the erguns equation in porous ceramic based. To increase the knowledge about higher re flow through porous media we will here. Click on the curve to see the effects of increased gas velocity on particle movement.
Assumes e equation intermediate flow ergun equation note. The ergun equation calculates the particlegas drag force per unit volume of bed void space as follows. Then, once the flow behavior in a single pore or throat is known, the overall flow in the network can be computed. Analytical quantification of coefficients in the ergun. The objective is to derive design equations to calculate the pressure drop as a function of. Qualitative observations indicate that vigorous bubbling in the liquid. The ergun equation does not have a micromechanical basis and the geometrical parameters shaping the form of the equation are therefore unknown. 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. The results show that the drag coefficient predicted by ergun equation should be modified. The extension of the ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by akgiray and saatc. They compared their results with ergun equation, and it fits well to ergun equation. Modeling of proppant permeability and inertial factor for. 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. The regimes of fluidization as a function of the fluid velocity.
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. This great pdf converter and pdf creator is quick and. Made by faculty at the university of colorado boulder. 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. Flow through porous media at moderate reynolds number.
It is known that pressure drop is caused by simultaneous viscous and inertia kinetic energy losses. 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. Pdfcreator download for free, download pdf printer, pdf. 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. Made by faculty at the university of colorado boulder, department of. The ergun equation was verified using the pressure drop over a packed bed. In figure i, the dashed line represents values of n obtained from equation 2 when reverted to the form of equation 1. For each ceramic, a comparative study between the predicted and the measured permeability value is present. Ergun later suggested a better value was 150 when the particles are greater than about 150 m in diameter. The ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. Download the free pdf converter and create pdf files from any application with pdf creator.
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. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. Pdf physical insight into the ergun and wen and yu equations for. The predicted permeability constant was obtained using erguns law from equation 1. Describes how to use the ergun equation to calculate the pressure drop in a packed bed. To calculate the pressure drop in a given reactor, the following equation may be deduced. Erguns equation to calculate the pressure drop of a fluid. Aaa fullpaper an experimental and analytical study to. The experimental pressure drop values were generally higher than the predicted values. Hostmath online latex formula editor and browserbased. 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 reynolds number where and are defined as.
Pressure drop along a packed bed reactor the above always applies, especially for multiple reactions. Chapter 4 fluid flow through packed bed of particles. Two simpler results, each obtained by ignoring one or the other term in the ergun equation also are in use. Aspen plus pfr reactors tutorial using styrene with. A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. The two expressions are coupled ordinary differential equations. Pdf physical insight into the ergun and wen and yu. Blake 1922 suggested that modified friction factor should be plotted against modified reynolds number. Modified equations for water flow through packed bed for. Fixed and fluidized beds university of california, berkeley.
Pdf experimental investigation of pressure drop in packed beds of. One is the kozenycarman equation, used for flow under very viscous conditions. 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. Superficial velocity through the bed will always be the same for a constant diameter vessel regardless of size of the mol sieve adsorbent. Previous works also indicate that the parameters of the ergun equation may be improved 2, 3. Satisfactory results are obtained for both gas and liquid systems.
Erguns equation to the polydisperse particles systems taking into account the particle size distribution 2,3. The friction factor based on ergun s equation is defined as. Square and hexagonal arrays of uniform fibers have been considered, as well as arrays in which the fiber size is allowed to change in a regular manner, expressed by a size variation parameter. Made by faculty at the university of colorado boulder, department of chemical and biological engineering.
The best pdf creator helps you convert any printable files to pdf, supports doc, xls, ppt, html, jpg, epub etc, nohard to create pdf, its funny. 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. Shankar subramanian chemical engineering operations commonly involve the use of packed and fluidized beds. Assumes e, experimental results may instead be correlated in terms of the blakeplummer equation.
Erguns equation flow through packed beds and fluidized. This is an applet to make a linear equation from two points. A semiempirical equation based on leva equation had been modeled to evaluate the minimum fluidization velocity. For a packed bed, the ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed. Next, specify the reactions to complete the specification for the pfr. Add pressure drop calculation for both reactors using the ergun equation as done in lab 3 with particle diameter of 4. You can convert word, excel, images, html, text, epub and other formats to pdf. In this simulation the pressure drop will be calculated by using the ergun equation given in the steadystate simulation manual section 9. The ergun equation, contd usually, the ergun equation is rewritten in a simplified form simplified only with regard to writing. For highly turbulent flow where inertial forces predominate, n re,p, experimental results may instead be correlated in terms of the blakeplummer equation.
A computational evaluation of the ergun and forchheimer. Ergun equation is based on the length of the reactor we want an equation based on the mass of the. He is known for the ergun equation, which expresses the pressure drop across a packed bed. Chung and long in 2007 chung and long 2007 studied how the pressure drop of a packed bed is related to the flow rate of the fluid coming into the column, they compared their results to the pressure drop predicted by the ergun equation. The plot below represents the ergun equation the first equation shown above, where the left hand side of the equation is the pressure drop. Erguns equation to calculate the pressure drop of a fluid through packed bed. How to calculate superficial velocity in mol sieve bed. I am looking for the constants used in erguns equation to estimate the pressure drop through a packed bed. 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. The boundary condition near the filter underdrain also violates the assumption of an infinitely extended packed bed made by the ergun equation. 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. It tells us the pressure drop along the length of the packed bed given some fluid velocity.
Type in two points to get an equation of a linear line that goes through the two points. Ergun s equation to calculate the pressure drop of a fluid through packed bed. Applying the ergun equation to the degradation of a reactor. The ergun equation provides a good description for the relationship of the pressure drop with the flow rate and the gas properties. Sabri ergun was born on 1 march 1918 in gerede in the ottoman empire now turkey. 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. Validate the ergun equation 14 for the friction coefficient fp in the bed of particles.
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