The ergun equation, while reliable for systems on the surface of the earth, is unreliable for predicting the behavior of systems in microgravity. The ergun equation can be used to predict the pressure drop along the length of a packed bed given the fluid velocity, the packing size, and the viscosity and density of the fluid. Pdf physical insight into the ergun and wen and yu. 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. General m,odel for prediction of pressure drop and. Ergun equation validation free download as pdf file.
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. Because the crosssectional area of the reactor is small near the inlet and outlet, the presence of catalyst there would cause substantial pressure drop. To increase the knowledge about higher re flow through porous media we will here. It can thus be considered that the original form of ergun s correlation should be modified for nonspherical particles. Review article a reconciliation of packed column permeability. A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. Ergun s equation to the polydisperse particles systems taking into account the particle size distribution 2,3.
The ergun equation, contd usually, the ergun equation is rewritten in a simplified form simplified only with regard to writing. Erguns equation to calculate the pressure drop of a fluid. Since then, many talented artists created very interesting sculptures topmod. Modified equations for water flow through packed bed for. Equation 2 describes the influence of void fractions on friction factor and provides the basis for the derivation of the pressure drop model. 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 ratio of pressure gradient to superficial fluid velocity in packed columns is shown to be a linear function of fluid mass flow rate. Water flow semiempirical equations semiempirical formulas for modeling water flow through packed bed were modiefied for the parameters affecting the pressure drop using buckingham. When it is used to estimate permeability evolution versus porosity, some of these arguments e. Pdf the ergun equation, an extension of darcy law, is the most popular equation used up to now to represent the relationship. The initial version of the software, topmod has been available as free software since 2007. 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. The two expressions are coupled ordinary differential equations.
The reduced forms of ergun and kta equations are similar to each other in many ways, 1 d. Kozenycarman equation revisited jack dvorkin 2009 abstract. Satisfactory results are obtained for both gas and liquid systems. A modification on erguns correlation for use in cylindrical. Flow through packed beds and fluidized beds citeseerx. Assumes e equation intermediate flow ergun equation note. 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. Pdf knowledge of the minimum fluidizing velocity of solid particles is essential for the effective. An experimental study is conducted to determine the characteristics of frictional pressure drops of fluid flow in porous beds packed with nonspherical particles. Where there are particles, the bed void fraction is approximately at the value that prevails at the point of incipient fluidization. The plot below represents the ergun equation the first equation shown above, where the left hand side of the equation is the pressure drop.
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. The ergun equation is based upon a basic principle annunciated by ergun and orning in their 1949 publication which they expressed as follows. 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. An equation is said to be linear if the unknown function and its derivatives are linear in f. Fixed and fluidized beds university of california, berkeley. The ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. 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. Previous works also indicate that the parameters of the ergun equation may be improved 2, 3. 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 above always applies, especially for multiple reactions. Flow through porous media at moderate reynolds number. For pbr, we often write the design equations in terms of catalyst weight rather than reactor length. Symbols are data from experiments, the dashed line is the carmankozney equation, and erguns correlation is represented by the solid line. Click on the curve to see the effects of increased gas velocity on particle movement. How to calculate superficial velocity in mol sieve bed.
The prediction of pressure drop and flow distribution in. Estimated equations for water flow through packed bed of mono. We adapt ergun equation for our packed bed reactor. Pdf application of erguns equation in food unit operations. Describes how to use the ergun equation to calculate the pressure drop in a packed bed. Pressure drops in fluidized beds, packed beds and pipes. The ergun equation gives the pressure drop for unit length of a fluid flowing through granular media. A reconciliation of packed column permeability data. The minimum fluidising velocity, umf, may be expressed in terms of the free falling velocity u0 of the particles in the fluid. Erguns equation flow through packed beds and fluidized.
It tells us the pressure drop along the length of the packed bed given some fluid velocity. Jul 23, 20 the ergun equation combines both the laminar and turbulent components of the pressure loss across a packed bed. 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. Experimental study on the effective particle diameter of a. It can thus be considered that the original form of erguns correlation should be modified for nonspherical particles. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity. The ergun equation provides a good description for the relationship of the pressure drop with the flow rate and the gas properties. If you want to learn differential equations, have a look at differential equations for engineers if your interests are matrices and elementary linear algebra, try matrix algebra for engineers if you want to learn vector calculus also known as multivariable calculus, or calculus three, you can sign up for vector calculus for engineers. We can solve them simultaneously using an ode solver such as polymath. In recent years, the combination of realistic representations of the pore space and accurate models of porelevel physics has allowed. In fact, i would like to find the adapted constants for different shapes and sizes of. University of groningen particle transport in fluidized. In deriving the ergun equation, ergun assumed that the particle diameter is at least a fifth of the size of the column diameter.
Applying the ergun equation to the degradation of a. Shankar subramanian chemical engineering operations commonly involve the use of packed and fluidized beds. 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. 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. Differential equations department of mathematics, hkust. The extension of the ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by akgiray and saatc. Made by faculty at the university of colorado boulder, department of chemical and biological engineering.
Nov, 2012 describes how to use the ergun equation to calculate the pressure drop in a packed bed. I am looking for the constants used in ergun s equation to estimate the pressure drop through a packed bed. Fluid flow through packed columns, ergun 34wm1vk71jl7. The minimum fluidising velocity, u mf, may be expressed in terms of the free falling velocity u 0 of the particles in the fluid. Erguns equation to the polydisperse particles systems taking into account the particle size distribution 2,3. The ergun equation that is commonly employed is given below. Ergun equation validation fluid dynamics viscosity.
Calculation for pressure losses in pipes and fittings for a variety of fluid flows that include single and twophase flows. The ergun equation does not have a micromechanical basis and the geometrical parameters shaping the form of the equation are therefore unknown. Friction factor as a function of reynolds number for a packed bed of particles. Chapter 4 flow of fluids through granular beds and packed columns. Download limit exceeded you have exceeded your daily download allowance.
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. Pressure drop depends on a series of factors such as void fraction, media particles diameter, reynolds number, fluid density and velocity. Applying the ergun equation to the degradation of a reactor. A semiempirical equation based on leva equation had been modeled to evaluate the minimum fluidization velocity. From the ergun equation equation 422, 422 we know that by decreasing g, the pressure drop will be reduced signi. Dimensional analysiswikipedia, the free encyclopedia. For example, a timevarying current j on a linear antenna generates a circulating. Comparisons between achieved equation, ergun equation and experimental results. Flow through a packed bed can be described by the ergun equation. Superficial velocity through the bed will always be the same for a constant diameter vessel regardless of size of the mol sieve adsorbent.
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. Modified ergun equation for airflow through packed bed of. Chemical reaction engineering asynchronous video series chapter 4, part 3. This was calculated from the ergun equation 1, which gives the pressure drop per unit length through a packed bed as. Chemengineering free fulltext study of pressure drop in. Pdf foundation of the ergun equation for the calculation of. The ergun equation, an extension of darcy law, is the most popular equation used up to now to represent the relationship between pressure drop and fluid flow in fludized or packed beds. 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.
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 1949 paper we begin our discussion of the ergun papers by going back to ergun and orning s original paper, not only because. Symbols are data from experiments, the dashed line is the carmankozney equation, and ergun s correlation is represented by the solid line. When applying the ergun equation, one has to know the minimum fluidization voidage.
Fluid flow through packed columns semantic scholar. The objective is to examine the applicability of the ergun equation to flow resistance assessment for packed beds with nonspherical particles. General m,odel for prediction of pressure drop and capacity. Then, once the flow behavior in a single pore or throat is known, the overall flow in the network can be computed.
Kozeny modelled the layer as many small capillary tubes of diameter d making up a layer of cross sectional area a. The results from ergun equation using similar conditions have been represented in the. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. The pore space is represented by alattice ofpores connected by throats. Analytical quantification of coefficients in the ergun. In figure i, the dashed line represents values of n obtained from equation 2 when reverted to the form of equation 1. To calculate the pressure drop in a given reactor, the following equation may be deduced.
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. Kozenycarman equation revisited jack dvorkin 2009 abstract the kozenycarman equation is often presented as permeability versus porosity, grain size, and tortuosity. I also have a significant body of work in modeling nonorientable surfaces and cyclic woven structures. Blake 1922 suggested that modified friction factor should be plotted against modified reynolds number. The actual cross sectional area for the flow path is a. If the free space in the bed is assumed to consist of a series of tortuous channels, equation 4.
If the free space in the bed is assumed to consist of a series of tortuous channels. The experiments are carried out on the pomecofl facility at kth. The bubbles grow until they fill the crosssection, and then. 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. 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. This article illustrates the foundation of the ergun equation used to calculate the minimum fluidizing velocity. 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 along a packed bed reactor the above always applies, especially for multiple reactions. Also for the incompressible liquid, the momentum equation was. The ergun equation was verified using the pressure drop over a packed bed. Orning 7 have platted aplv ag inst numerous other data taken from the literature have been included in g and obtained straight lines as expected from equation 2. It is known that pressure drop is caused by simultaneous viscous and inertia kinetic energy losses. Feb 06, 2015 pressure drops in fluidized beds, packed beds and pipes.
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