Mass transport - General Shell Balance.pptx

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1. MASS TRANSPORT

2. Shell Mass Transport & Boundary Conditions Steady state mass transfer problems for both non-reacting and reacting systems. A mass balance is made over a thin shell perpendicular to the direction of mass transport. This shell balance leads to a first-order differential equation , which is solved to get the mass flux distribution . Into this expression, relation between mass flux and concentration gradient is inserted ( Fick’s Law of molecular diffusion ). This results in a 2 nd order differential equation which is solved for the concentration profile . The integration constants are determined by the boundary conditions on the concentration and/or mass flux at the bounding surfaces.

3. Combined mass/ molarflux N A : The number of moles of ‘ A’ that go through a unit area in unit time, the unit area being fixed in space. Combined mass/molar flux of a particular species for multicomponent system = diffusive (molecular) molar or mass flux + convective (bulk contribution) molar or mass flux N A = ( j A )+( x A *N) --------- (1) j Az = -D AB ( C A / z) (Considering z-component) (For binary system) N = N A +N B Considering z-component: N = N Az +N Bz

4. Considering z-component, reexpressing eq (1): N A = ( j A )+( x A *N) N Az = ( j Az ) + ( x A *[ N Az + N Bz ]) N Az = -D AB ( C A / z) + ( x A *[ N Az + N Bz ]) N Az = - C*D AB (  x A / z) + ( x A *[ N Az + N Bz ]) Combined flux molecular/diffusive flux convective flux

5. Mass transfer in reacting systems Chemical reactions types : Homogeneous: chemical change occurs in the entire volume of the fluid Heterogeneous: chemical change takes place only in a restricted region , such as the catalyst surface Mathematically, both of these reactions are described differently : Homogeneous reaction : Rate of production of a chemical species appears as a source term in the differential equation obtained from the shell balance, just as the thermal source term appears in the shell energy balance ( ie heat production/volume appearing in differential equation from shell balance = S e = I 2 / k e ). ie Heterogeneous reaction : The rate of production of a species appears not in the differential equation, but rather in the boundary condition at the surface on which the reaction occurs.

6. Chemical Kinetics is used to express the rates at which the various chemical species appear or disappear by reaction. For homogeneous reactions , the molar rate of production of species A may be given by an expression of the form: R A = k n  C A n where: R A , moles/cm 3 -s (moles/(volume-time); C A, moles/cm 3 (moles/volume) ; n=order of reaction Triple Prime (‘’’) indicates volume source For heterogeneous reactions , the molar rate of production at the reaction surface may often be specified by a relation of the form:

7. where : N AZ , moles/cm 2 .s C A , moles/cm3 For 1 st order, k n ’’, cm/s Double prime (‘’) indicate surface source The law of conservation of mass of species ‘A’ in a binary system is written over the shell volume is of the form:

8. BOUNDARY CONDITIONS for Mass Transport Problems : The concentration at a surface can be specified; for example, x A = x A0 The mass flux at a surface can be specified; for example, N Az = N A0 . If the ratio N Bz / N Az is known, this is equivalent to giving the concentration gradient . If diffusion is occurring in a solid, at the solid surface substance ‘A’ is lost to a surrounding stream according to the relation: N A0 = k c (C A0 -C Ab ) [Interphase mass transfer] where : N A0 is the molar flux at the surface C A0 is the surface concentration, C Ab is bulk fluid stream concentration proportionality constant k c is a"mass transfer coefficient."

9. The rate of chemical reaction at the surface can be specified. i.e if substance ‘A’ disappears at a surface by a 1 st order chemical reaction, then N A0 = k 1 ’’C A0