It tells us the pressure drop along the length of the packed bed given some fluid velocity. Flow through a packed bed can be described by the ergun equation. 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 ergun equation is applicable to both laminar and turbulent flows, which are covered by the two terms in the equation see the subramanian paper.
The ergun equation gives the pressure drop for unit length of a fluid flowing through granular media. In this study an analytical ergun type equation is proposed for porous foams. Sabri ergun 1 march 1918 18 february 2006 was a turkish chemical engineer. Pressure drop along a packed bed reactor the above always applies, especially for multiple reactions. Prediction of cleanbed head loss in crumb rubber filters. We adapt ergun equation for our packed bed reactor. Extension of ergun equation for the calculation of the. Feb 06, 2015 pressure drops in fluidized beds, packed beds and pipes. Describes how to use the ergun equation to calculate the pressure drop in a packed bed.
Pressure drop depends on a series of factors such as void fraction, media particles diameter, reynolds number, fluid density and velocity. The extension of the ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by akgiray and saatc. Mar 29, 2019 since porosity is often expressed as a percent, once you have found the decimal value, it is common to multiply this value by 100%. 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. Download limit exceeded you have exceeded your daily download allowance. Made by faculty at the university of colorado boulder, department of. Two simpler results, each obtained by ignoring one or the other term in the ergun equation also are in use.
I would appreciate if anyone could help me with this spherical 18 activated alumina based adsorbent. There are many alternative expressions for permeability, but the kozeny approach is. There is a critical need for precise prediction of cleanbed head loss for engineering design purposes. A reconciliation of packed column permeability data. Pdf application of erguns equation in food unit operations. The prediction of pressure drop and flow distribution in.
Macdonald addressed the problem of multisized particles present in a porous media. Prediction of ceramic foams permeability using erguns. General m,odel for prediction of pressure drop and capacity. Symbols are data from experiments, the dashed line is the carmankozney equation, and ergun s correlation is represented by the solid line. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. Erguns equation to the polydisperse particles systems taking into account the particle size distribution 2,3. Since porosity is often expressed as a percent, once you have found the decimal value, it is common to multiply this value by 100%. It is known that pressure drop is caused by simultaneous viscous and inertia kinetic energy losses. Erguns equation flow through packed beds and fluidized. The porous media model can be used for a wide variety of single phase and multiphase problems, including flow through packed beds, filter papers, perforated plates, flow distributors, and tube banks. Determination of pressure drop for air flow through. Pressure drop estimation for adsorbents posted in industrial professionals. Request pdf determination of pressure drop for air flow through sintered metal porous media using a modified ergun equation sintered metal porous media currently play a significant role in a. Calculation of pressure drop across a porous media debris.
The plot below represents the ergun equation the first equation shown above, where the left hand side of the equation is the pressure drop. Must use the differential form of the mole balance to separate variables. Shankar subramanian chemical engineering operations commonly involve the use of packed and fluidized beds. Friction factor as a function of reynolds number for a packed bed of particles. Nekarvis part v fluid flow data are presented for beds of uniformly sized spheres consolidated with resin over a porosity range from 36. Using the same values from the above examples, your equation will look similar to this. Comparisons between achieved equation, ergun equation and. Modification of ergun equation for application in trickle bed. Modification of ergun equation for application in trickle.
Blake 1922 suggested that modified friction factor should be plotted against modified reynolds number. Pressure drop through porous media university of michigan. Water flow semiempirical equations semiempirical formulas for modeling water flow through packed bed were modiefied for the parameters affecting the pressure drop using buckingham. Aiming to propose a correction of ergun equation to expand its applicability into the flow resistance calculation of porous media with higher porosity and opencelled structure, this work numerically studied the flow field inside the rectangular channel partially filled with porous media and the average velocity in the zone adjacent to porous media against relative height, porosity and. Fixed and fluidized beds university of california, berkeley. Analyze the following second order gas phase reaction that occurs isothermally in a pbr. Assumes e ergun assumed that the particle diameter is at least a fifth of the size of the column diameter. The ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. 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. Click on the curve to see the effects of increased gas velocity on particle movement. University of groningen particle transport in fluidized.
Estimated equations for water flow through packed bed of mono. A semiempirical equation based on leva equation had been modeled to evaluate the minimum fluidization velocity. Analytical quantification of coefficients in the ergun. For a packed bed, the ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed. Pressure drop through particle bedsporous media uniud.
In deriving the ergun equation ergun assumed that the. To calculate the pressure drop in a given reactor, the following equation may be deduced. The results show that the drag coefficient predicted by ergun equation should be modified. Sometimes, an empirical coefficient of 180 instead of 150 is recommended, and equation 10 is then usually referred to as the carmankozeny equation. The ergun equation calculates the particlegas drag force per unit volume of bed void space as follows. Made by faculty at the university of colorado boulder, department of chemical and biological engineering. Satisfactory results are obtained for both gas and liquid systems. The results from ergun equation using similar conditions have been represented. The ergun equation, contd usually, the ergun equation is rewritten in a simplified form simplified only with regard to writing. There are many alternative expressions for permeability, but the kozeny approach is the most frequently encountered. Adding the carmankozeny and burkeplummer equations, erguns equation is obtained.
As a second example, consider the modeling of a packed bed. Liquid packedbed reactors with momentum equations and local interaction closures. Kozenycarman equation revisited jack dvorkin 2009 abstract the kozenycarman equation is often presented as permeability versus porosity, grain size, and tortuosity. Pressure drops in fluidized beds, packed beds and pipes. Chapter 4 fluid flow through packed bed of particles. Calculation of pressure drop across a porous media debris bed. Nov, 2012 describes how to use the ergun equation to calculate the pressure drop in a packed bed. For a particle larger than this recommended size, the wall affects the void fraction of the particle. The results show that the drag coefficient predicted by ergun equation should be. The objective is to derive design equations to calculate the pressure drop as a function of. 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. When applying the ergun equation, one has to know the minimum fluidization voidage. The actual cross sectional area for the flow path is a. Previous works also indicate that the parameters of the ergun equation may be improved 2, 3.
It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity. 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. Prediction of cleanbed head loss in crumb rubber filters hao l. Modified equations for water flow through packed bed for. In turbulent flows, packed beds are modeled using both a permeability and an inertial loss coefficient. Sabri ergun was born on 1 march 1918 in gerede in the ottoman empire now turkey. For highly turbulent flow where inertial forces predominate, n re,p, experimental results may instead be correlated in terms of the blakeplummer equation.
A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. If the fluid were a liquid i think ergun equation would be the right way to go. Pressure drop estimation for adsorbents industrial. Hello all, i am trying to estimate pressure drop across fixed bed adsorber liquid phase upflow direction but i cannot find ergun. In chapter 3, relations are given that permit the calculation of re 0 u 0 d.
The ergun equation does not have a micromechanical basis and the geometrical parameters shaping the form of the equation are therefore unknown. Using the ergun equation to derive porous media inputs for a packed bed. The original ergun equation of the total energy loss can be rearranged as. From the ergun equation equation 422, 422 we know that by decreasing g, the pressure drop will be reduced signi. 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. One is the kozenycarman equation, used for flow under very viscous conditions. To increase the knowledge about higher re flow through porous media we will here. He is known for the ergun equation, which expresses the pressure drop across a packed bed biography. 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. When it is used to estimate permeability evolution versus porosity, some of these arguments e. When you use this model, you define a cell zone in which the porous media model is applied and the pressure loss in the flow is determined via your inputs as. Calculation based on classical form of porous medium flow ergun equation viscous term kinetic term.
Pdf on jan 1, 20, alessandro schiavi and others published ergunwu equation. We can solve them simultaneously using an ode solver such as polymath. Kozeny modelled the layer as many small capillary tubes of diameter d making up a layer of cross sectional area a. 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. Kozenycarman equation revisited jack dvorkin 2009 abstract. Equation 2 describes the influence of void fractions on friction factor and provides the basis for the derivation of the pressure drop model. Jul 23, 20 the ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. Ergun later suggested a better value was 150 when the particles are greater than about 150 m in diameter. Application of the erguns equation in porous ceramic based. Should i take into account any special consideration. Ergun and orning were the first to piece together an equation for flow in porous media which contained a viscous term and a kinetic term and in.
Assumes e equation intermediate flow ergun equation note. Equation 10 is known as the blakekozeny equation, and reproduces experimental data for porous media of uniform spheres rather well up to reynolds numbers of about 10. Flow through porous media at moderate reynolds number. Introduction permeability is an important parameter for the characterization of ceramic foams employed in filtration applications. 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. If you would like to express that value as a percent, you would. A modified ergun equation taking into account air compressibility is developed. 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. 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. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Pdf physical insight into the ergun and wen and yu. Request pdf an analytical ergun type equation for porous foams the empirical coefficients of the ergun equation for granular packed beds have often been adjusted in the literature towards. Determination of pressure drop for air flow through sintered.