The Difference Point Equation for an MCS

By combining the overall and component material balances around the top of the MCS and any point down the membrane length (refer to figure 9.2), it can be shown that the change in retentate composition, x, along the MCS can be modeled using a slightly modified version of the DFE, as shown in Equation 9.1, and will be referred to as the membrane difference point equation (MDPE). The reader is referred to Peters et al. [1] for a detailed proof  

A is the net molar flow, as with distillative systems, and for an MCS is defined as 

As with distillative separations, is commonly referred to as the difference point, and is the vector of the net molar flowrates for all components divided by the total net molar flow. 

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