Analyze the following second order gas phase reaction that occurs isothermally in a pbr. Please, do not simply list the procedures in your report. Mathmagic lite is yet another free math equation editor software for windows. Feb 06, 2015 pressure drops in fluidized beds, packed beds and pipes. 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. Pdf study on ergun equation at vacuum pressures for. Ergun s 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. Chapter 4 fluid flow through packed bed of particles. Flow through a packed bed can be described by the ergun 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. The results show that the drag coefficient predicted by ergun equation should be modified. Must use the differential form of the mole balance to separate variables. I did the procedure that is explaned in using the ergun equation to derive porous media inputs for a packed bed in fluent user guide.
The ergun equation, contd usually, the ergun equation is rewritten in a simplified form simplified only with regard to writing. The minimum soluble bod concentration that can be achieved as. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Lundstrom abstract in modelling of flow through porous media inertiaeffects must sometimes be considered. Like other free math equation editors in this list, this one also comes with a lot of templates. Shankar subramanian chemical engineering operations commonly involve the use of. The kozeny carman equation or carman kozeny equation or kozeny equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. Analytical quantification of coefficients in the ergun. Equation editor is a special version of the math type equation editor from design science that is customized for use with microsoft applications. 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. The main reason of this deviation was that ergun s. 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. The ergun equation provides a good description for the relationship of the pressure drop with the flow rate and the gas properties. By comparing the pressure drop given by the ergun equation to the pressure drop for minimum fluidization, you can calculate the superficial velocity necessary for fluidization.
Equations are developed to predict the entropy generation rates in terms of. Pressure drops in fluidized beds, packed beds and pipes. The ergun equation is based upon a basic principle annunciated by ergun and orning in their 1949 publication which they expressed as follows. You can undo and redo your equations at your convenience. Effect of material type and particle size distribution on. Blake 1922 suggested that modified friction factor should be plotted against modified reynolds number. Once the porosity e is quantified, ergun s relationships eqs. The kozenycarman equation or carmankozeny equation or kozeny equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. Porescale derivation of the ergun equation to enhance its. It tells us the pressure drop along the length of the packed bed given some fluid velocity. Fluidization chemical engineering at the university of floridahome. Click on the curve to see the effects of increased gas velocity on particle movement. Erguns equation flow through packed beds and fluidized.
But, it should be noted that there are a number of ad hoc assumptions in the derivation of. We adapt ergun equation for our packed bed reactor. Validate the ergun equation 14 for the friction coefficient fp in the bed of particles. Flow through porous media at moderate reynolds number. Presentation of fluidization state on the rehs modified diagram. Erguns equation to the polydisperse particles systems taking into account the particle size distribution 2,3. Fixed and fluidized beds university of california, berkeley. The ergun equation can also be expressed in terms of. Fluidization refinery application fluidization drug application fluidization. A semiempirical equation for water flow through packed bed has been. 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. Water flow semiempirical equations semiempirical formulas for modeling water flow through packed bed were modiefied for the parameters affecting the pressure drop using buckingham. Pressure drop along a packed bed reactor the above always applies, especially for multiple reactions. Click on the curve to see the effects of increased gas velocity on.
Oct 03, 20 the pressure drop across a vapor phase packed bed reactor can increase with the degradation of the catalyst in the reaction. View notes ergun s equation from ench 331 at university of calgary. Ergun 1952, using a extensive set of experimental data covering a wide range of particle size and shapes, presented a general equation. Assumes e equation intermediate flow ergun equation note. A set of experiments were conducted to determine if an equation used to predict the pressure drop in a packed nonmoving bed the ergun equation would match experimental results.
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. This module provides a number of information on the bubbling aspects of the fluidized bed. It tells us the pressure drop along the length of the packed bed given some fluid. 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. Calculation of bubbles size variation along the bed, as well as the mean and maxi bubble diameters. Satisfactory results are obtained for both gas and liquid systems.
In 1952, sabri ergun derived the following equation to predict the pressure drop in packed beds. Moreover, it is a straightforward software, by which you can create both complex and simple mathematical equations. The extension of the ergun equation to fluidized beds, where the solid particles flow with the fluid, is discussed by akgiray and saatc. Prediction of ceramic foams permeability using erguns equation. Study on ergun equation at vacuum pressures for sodium fluoride adsorbents. The plot below represents the ergun equation the first equation shown above, where the left hand side of the equation is the pressure drop. By comparing the pressure drop given by the ergun equation to the pressure drop for minimum. Pdf physical insight into the ergun and wen and yu. Complete fluid mechanics tutorials chapter1 part1introduction to fluid mechanics tutorial s. Previous works also indicate that the parameters of the ergun equation. Modeling of proppant permeability and inertial factor for. Applying the ergun equation to the degradation of a reactor. 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 results show that the drag coefficient predicted by ergun equation should be modified for various bed porosities, particle aspect ratio and gas densities.
Pdf application of erguns equation in food unit operations. Prediction of ceramic foams permeability using ergun s equation. Activated sludge design equations iowa state university. Flow through porous media at moderate reynolds number j. If the stokes equation was applied, a deviation of 0. Then, once the flow behavior in a single pore or throat is known, the overall flow in the network can be. Abstract in the article a sensitivity analysis of linear and nonlinear terms in the kozenycarman and ergun equations was.
Positron emission particle tracking observations of charge and slurry flow have shown that the pressure drop is effectively described by an euler equation modified by a darcylike term. It can thus be considered that the original form of ergun s correlation should be modified for. Pressure drop depends on a series of factors such as void fraction, media particles diameter, reynolds number, fluid density and velocity. This is often done by usage of the empirically derived ergun equation that can. It is known that pressure drop is caused by simultaneous viscous and inertia kinetic energy losses. The friction factor based on ergun s equation is defined as. The experimental system contains two identical columns with diameter 1. General equation for pressure drop through 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. Equation editor was a formula editor developed by design science that allowed users to construct math and science equations in a wysiwyg environment, and was included in microsoft office and several other commercial applications. Modified ergun equation for airflow through packed bed of. The analysis of singlephase flow through packed beds and the subsequent discussion put forward by this work suggests that the ergun equation is well suited for the description of flow through packed.
It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. Our intent here was to determine a reasonable char diameter to recommend for the gek filter canister. The objective is to derive design equations to calculate the pressure drop as a function of. A reconciliation of packed column permeability data.
Adding the carmankozeny and burkeplummer equations, erguns equation is. Using equation editor, you can build complex equations by picking symbols from a toolbar and typing variables and numbers. 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. 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. A new analytical derivation for momentum transport during laminar flow through granular porous media is discussed and some of its implied results described. The ergun equation does not have a micromechanical basis and the geometrical parameters shaping the form of the equation are therefore unknown. This author goes on to identify the value of 185 as the coefficient in his version of the equation. The ergun equation is unquestionably the most popular. Modified equations for water flow through packed bed for. Is there anyone out there who can help walk me through it. 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.
General m,odel for prediction of pressure drop and. Modification of ergun equation for application in trickle bed. Fluids free fulltext teach second law of thermodynamics via. According to this derivation, the constants a and b.
Now you can tell microsoft to go forth and multiply. Equation 7 allows to obtain an equivalent particle size for the cellular structure based on its mean pore size. This case is the fluid flow rates, while others are ap from equation 2 it is seen that as the one usually. A computational evaluation of the ergun and forchheimer. Equation editor is a strippeddown version of data sciences mathtype app that. Ui d2 e hagenpoiseille equation substituting suitable relations. For a packed bed, the ergun equation provides a re. If the fluid were a liquid i think ergun equation would be the right way to go. The ergun equation can also be expressed in terms of conversion then the differential form of ergun equation for the pressure drop in packed beds x f f f f t a t t 0 0 0 1 0 0 0 a t a y f f x f f t t 1 0 0 1 2 t t x y dw dy when is negative, the pressure drop p will be less than that for 0 for isothermal operation pressure drop when is. Modification of ergun equation for application in trickle. Review article a reconciliation of packed column permeability. Recently, du plessis and woudberg 35 proposed a new derivation of the ergun equation that is based on the porescale model for granular media. The pore space is represented by alattice ofpores connected by throats. For a packed bed, the ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed.
Predicting flows from the dynamic ergun equation sciencedirect. I have this modified ergun equation that i was asked to solve and i have no idea where to begin. Pdf prediction of ceramic foams permeability using ergun. The ergun equation can be regarded as direct method of pressure drop calculation. The ratio of pressure gradient to superficial fluid velocity in packed columns is shown to be a linear function of fluid mass flow rate. Ergun 1952, using a extensive set of experimental data covering a wide range of particle size and shapes, presented a general equation to calculate the pressure drop across a packed bed for all flow conditions laminar to turbulent. For pbr, we often write the design equations in terms of catalyst weight rather than reactor length. Therefore, a correction factor has been proposed to correct the ergun equation constants in various. The pressure drop also depends on the flow rate and properties of the gas. The ergun equation gives the pressure drop for unit length of a fluid flowing through granular media.
The region covered by the ergun equation is the rising portion of the plot section i. The ergun equation gives satisfactory predictions for the particle reynolds numbers, re p, in the range from 0. Jul 23, 20 general equation for pressure drop through a packed bed. They compared their results with ergun equation, and it fits well to ergun equation. 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.
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