Fixed bed and fluidized bed Ref BSL Mc

Fixed bed and fluidized bed Ref: BSL, Mc. Cabe & Smith n n Why fixed (or fluidized) bed? u Expensive Catalyst u enzyme (immobilized) u Large Surface area n n Used in reaction/adsorption/ elution (for example) Goal: Expression for pressure drop, try some examples IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n Filled with particles Usually not spherical u To increase surface area u To increase void fraction F To n decrease pressure drop For analytical calculation, assume all particles are identical u Usable, because final formula can be modified by a constant factor (determined by experiment) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n What are important parameters? (For example, for adsorption of a protein from a broth) u rate of adsorption (faster is better) u saturation concentration (more is better) n From the product requirement (eg X kg per day), density and product concentration in broth ==> volumetric flow rate IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n Assume quick adsorption (rate of adsorption is high) Calculate the surface area of particles needed for operation n Sphericity <=> specific surface area <=> average particle diameter n Sphericity u Volume A p, Vp of particle = Vp u Surface Area of particle = Ap u Surface Area of sphere of same volume (Vs =Vp) = As u Sphericity = As/Ap u May be around 0. 3 for particles used in packed beds u lower sphericity ==> larger surface area IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 A s, Vs

Fixed bed n Specific surface area u= Ap /Vp u Minimal value for sphere u Some books use S to denote area (instead of A) u Assume all the particles are identical F ==> all particles have exactly same specific surface area Rings (Raschig, etc) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 Tarus saddle Pall Ring

Fixed bed n What is the pressure drop we need, to force the fluid through the column? u n n (i. e. what should be the pump spec) We know the volumetric flow rate (from adsorption equations, productivity requirements etc) We know the area per particle (we assume all particles are identical). And the total area for adsorption (or reaction in case of catalytic reactor). Hence we can calculate how many particles are needed Given a particle type (eg Raschig ring) , the approximate void fraction is also known (based on experimental results) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n n What is void fraction? Volume of reactor = VR Number of particles = Np Volume of one particle = Vp Volume of all the particles = Vp * Np = VALL-PARTICLES Knowing void fraction, we can find the reactor volume needed u Alternatively, if we know the reactor volume and void fraction and the Vp, we can find the number of particles IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n n To find void fraction experimentally Prepare the adsorption column (or reactor. . ) and fill it with particles Fill it with water Drain and measure the quantity of water (= void volume) Calculate void fraction IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n Since we know Vp, Np, e, we can find VR Choose a diameter and calculate the length (i. e. Height) of the column (for now) u In normal usage, both the terms ‘height’ and ‘length’ may be used interchangeably (to mean the same thing) u Adsorption rate, equilibrium and other parameters will also influence the determination of height & diameter n To calculate the pressure drop u Note: columns with large dia and shorter length (height) will have lower pressure drop u What can be the disadvantage(s) of such design ? (tutorial) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed n n To calculate the pressure drop u You want to write it in terms of known quantities u Length of column, void fraction, diameter of particles, flow rate of fluid, viscosity and density Obtain equations for two regimes separately (turbulent and laminar) Consider laminar flow Pressure drop increases with u velocity u viscosity u inversely proportional to radius F Actually, not all the reactor area is available for flow. Particles block most of the area. Flow path is not really like a simple tube F Hence, use hydraulic radius IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar flow) n To calculate the pressure drop, use Force balance n Resistance : due to Shear u Find Contact Area u Find shear stress n Until now, we haven’t said anything about laminar flow. So the above equations are valid for both laminar and turbulent flows IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n n Find contact area n To calculate the shear stress, FOR LAMINAR FLOW n Here V refers to velocity for flow in a tube However, flow is through bed, NOT a simple tube IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n Find effective diameter (i. e. Use Hydraulic radius), to substitute in the formula Also relate the velocity between particles to some quantity we know To find hydraulic radius ( and hence effective dia) n Hydraulic diameter n n IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n n Vavg is average velocity of fluid “in the bed”, between particles Normally, volumetric flow rate is easier to find IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n n Can we relate volumetric flow rate to Vavg ? Use a new term “Superficial velocity” (V 0) I. e. Velocity in an ‘empty’ column, that will provide the same volumetric flow rate Can we relate average velocity and superficial velocity? IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n Force balance: Substitute for t etc. n Volume of reactor (say, height of bed = L) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n Pressure drop n Specific surface area vs “average diameter” n n Define “average Dia” of particle as Some books (BSL) use Dp IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar Flow) n n n Pressure drop However, using hydraulic radius etc are only approximations Experimental data shows, we need to multiply the pressure requirement by ~ 2 (exactly 100/48) In terms of average particle diameter IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 In terms of specific surface area

Fixed bed - pressure drop calculation (Turbulent Flow) n Pressure drop and shear stress equations n Only the expression for shear stress changes n For high turbulence (high Re), f Re n However IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Turbulent Flow) n n We have already developed an expression for contact area n Hence, force balance Volume of reactor (say, height of bed = L) IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Turbulent Flow) In terms of average particle diameter In terms of specific surface area n Value of K based on experiments ~ 7/24 n What if turbulence is not high? n Use the combination of laminar + turbulent pressure drops: valid for all regimes! Ergun Equation for packed bed IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar OR Turbulent Flow) Ergun Equation for packed bed n If velocity is very low, turbulent part of pressure drop is negligible If velocity is very high, laminar part is negligible n Some texts provide equation for friction factor n IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar OR Turbulent Flow) n n For pressure drop, we multiplied the laminar part by 2 (based on data). For the turbulent part, the constant was based on data anyway. Similarly. . . IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed bed - pressure drop calculation (Laminar OR Turbulent Flow) n n Multiply by 3 on both sides (why? ) Packed bed friction factor = 3 f Eqn in Mc. Cabe and Smith Reynolds number for packed bed IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Example n n n n Adsorption of Cephalosporin (antibiotic) Particles are made of anionic resin(perhaps resin coatings on ceramic particles) void fraction 0. 3, specific surface area = 50 m 2/m 3(assumed) column dia 4 cm, length 1 m feed concentration 2 mg/liter (not necessary to calculate pressure drop, but needed for finding out volume of reactor, which, in this case, is given). Superficial velocity about 2 m / hr Viscosity = 0. 002 Pa-s (assumed) What is the pressure drop needed to operate this column? IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fixed Bed n n n What is the criteria for Laminar flow? Modified Reynolds Number Turbulent flow: - Inertial loss vs turbulent loss u Loss due to expansion and contraction Packing uniformity u In theory, the bed has a uniform filling and a constant void fraction u Practically, near the walls, the void fraction is more Ergun Eqn commonly used, however, other empirical correlations are also used e. g. Chilton Colburn eqn 0. 8 e 0. 4 0. 2 IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 Edge Center Edge

Fixed Bed n Sphericity vs Void Fraction 1 f 0 IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 ~0. 4 e 1

Fixed Bed n n Alternate method to arrive at Ergun equation (or similar correlations) Use Dimensional analysis IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fluidized bed n n When the fluid (moving from bottom of the column to the top) velocity is increased, the particles begin to ‘move’ at (and above) a certain velocity. At fluidization, u Weight of the particles == pressure drop (area) u Remember to include buoyancy IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fluidized bed: Operation n n Empirical correlation for porosity Types of fluidization: Aggregate fluidization vs Particulate fluidization Larger particles, large density difference (r. SOLID - r. FLUID) ==> Aggregate fluidization (slugging, bubbles, etc) ==> Typically gas fluidization u Even with liquids, lead particles tend to undergo aggregate fluidization Archimedes number IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fluidized bed: Operation n n Porosity increases Bed height increases Fluidization can be sustained until terminal velocity is reached If the bed has a variety of particles (usually same material, but different sizes) u calculate the terminal velocity for the smallest particle Range of operability = R Minimum fluidization velocity = incipient velocity (min range) Maximum fluidization velocity = terminal velocity (max range) Other parameters may limit the actual range further u e. g. Column may not withstand the pressure, may not be tall enough etc R = Vt/VOM Theoretically R can range from 8. 4 to 74 IIT-Madras, Momentum Transfer: July 2005 -Dec 2005

Fluidized bed: Operation 80 n Range of operation depends on Ar R 40 0 104 Ar IIT-Madras, Momentum Transfer: July 2005 -Dec 2005 108

Fluidized bed: Operation n n Criteria for aggregate fluidization u Semi empirical Particulate fluidization u Typically for low Ar numbers u More homogenous mixture IIT-Madras, Momentum Transfer: July 2005 -Dec 2005