Mass transfer continuity equational material balance

Material Balances Whenever mass-transfer applications involve equipment of specific dimensions, flux equations alone are inadequate to assess results. A material balance or continuity equation must also be used. When the geometiy is simple, macroscopic balances suffice. The following equation is an overall mass balance for such a unit having bulk-flow ports and ports or interfaces through which diffusive flux can occur ... 

If the process is continuous and under plug flow, for both the gas and slurry phases, the equations derived for trickle bed reactors are applicable (see Section 3.7.2) (Hopper el al., 2001) by using the appropriate mass transfer coefficients. Note that in trickle beds, the material balances are based on the reactor volume. 

The flow of materials is accounted for with two balances conservation of mass and conservation of momentum transfer. The most important is a momentum balance, which is also called the equation of motion. The mass balance (also called the continuity equation) makes sure that mass is conserved. 

Multiphase reactors can be batch, fed batch, or continuous. Most of the design equations derived in this chapter are general and apply to any of these operating modes. They will be derived for unsteady operation. The unsteady material balances include the inventories in both phases and mass transfer between the phases so that steady-state solutions fonnd by the method of false transients will be true transients if the initial conditions are correct. Compare Section 10.6. 

Let us investigate a continuous dryer calculation. In this case solid temperature will reach, depending on a number of transfer units in the dryer, a value between AST and WBT, which can easily be calculated from Equation 3.49 and Equation 3.50. Now mass and energy balances can be closed over the whole dryer and exit parameters of air and material obtained. Having... 

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