Component balances multiphase

The packed-bed reactors discussed in Chapters 9 and 10 are multiphase reactors, but the solid phase is stationary, and convective flow occurs only through the fluid phase. The reaction kinetics are pseudohomogeneous, and components balances are written only for the fluid phase. 

Remark Complications can arise when stream j is a multiphase mixture. The energy (enthalpy) balance in terms of the specific enthalpies will anyway hold true, as well as the individual component balances, where yi is the mass fraction of C ( in the whole mixture. The case will, however, require again a special consideration. Generally, new variables, say pj will occur, where p is mass fraction of phase fin stream j, obeying... 

Laboratory batch reactors can be single-phase (e.g., gas or liquid), multiphase (e.g., gas-liquid or gas-liquid-solid), and catalytic or non-catalytic. In this section we limit the discussion to operation at isothermal conditions. This eliminates the need to consider energy, and due to the uniform composition the component material balances are simple ordinary differential equations with time as the independent variable. 

The conservation of material can be written as in Eq. 1 except that the physical quantity ij/ could be p - partial pressure, c - concentration, x - mole firaction, or p - density. However, for the case of a mixture in a multiphase system, it is necessary to write material balances for each component in... 

Section 3.7 and Section 3.10.1 already represent the volume averaged stress components (Txx), ( yy) as long as the film is a single phase patterned material and the constraints of a thin film on a relatively thick substrate are satisfied. The case of a multiphase or composite film will be addressed subsequently. With reference to Figure 3.16, elementary force balances in the a —direction and y—direction lead to the relationships... 

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