Operating Parameters and Mathematical Formulation

The parameters required to define the operation of an absorber are discussed in relationship to a single stage. A single stage with a feed of fixed rate, composition, and thermal conditions has two degrees of freedom (Chapter 2). It is completely defined (zero degrees of freedom) if its pressure and heat duty are fixed. 

The operation of an absorber may be controlled to meet performance specifications by varying one of the feed rates or by applying variable heating or cooling duties at certain stages. Consider an absorber with fixed lean oil and gas feeds. The liquid and vapor product rates, compositions, temperatures, and other properties are determined. If it is desired to meet a specified purity of certain components in one of the products such as the vapor, the lean oil rate may be used as a control variable. Its rate must be determined in order to meet the vapor purity specification. 

Mathematical solution of absorbers, like other multistage separation processes, involves setting up material and energy balance equations and vapor-liquid equilibrium relations that describe the entire column. The resulting set of simultaneous equations is then solved by some suitable technique. 

An energy balance on stage j yields the following equation  

Phase equilibrium relationships are expressed in terms of Vj, Lj, and Lj. Since 

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