Much like in flash distillation, it is useful to recast our material balance expressions in the form y = F(x) (to facilitate future graphical solutions).

Assuming CMO in order to perform distillation calculations is
often called the **Lewis Method**.

In order to obtain these operating lines, we recall the generic balance equations for each section of the column. For the rectifying section, we have:

V_{j+1} = L_{j} + D

y_{j+1}V_{j+1} = x_{j}L_{j} +
x_{D}D

Applying the assumption of CMO, these become:

V = L + D

y_{j+1}V = x_{j}L + x_{D}D

Combining them, we get the rectifying section operating equation:

y_{j+1} = x_{j}(L/V) + x_{D}(1-L/V)

For the stripping section,

V' = L' - B

y_{f+1}V' = x_{f}L' - x_{B}B

which gives us the stripping section operating equation as:

y_{f+1} = x_{f}(L'/V') -
x_{B}(L'/V'-1)

L does **not** generally equal L'.

Determine the operating equations for CMO systems