For dilute solutions in which the mole fractions of x and y are small, the total molar flows GM and LM will be nearly constant, and the operating-curve equation is

This equation gives the relation between the bulk compositions of the gas and liquid streams at each height in the tower for conditions in which the operating curve can be approximated as a straight line.

Figure 14-6 shows the relationship between the operating curve and the equilibrium curve yt = F(x) for a typical example involving solvent recovery, where yt and xt are the interfacial compositions (assumed to be in equilibrium). Once y is known as a function of x along the operating curve, yt can be found at corresponding points on the equilibrium curve by

where LM = molar liquid mass velocity, GM = molar gas mass velocity, Hl = height of one transfer unit based upon liquid-phase resistance, and HG = height of one transfer unit based upon gas-phase resistance. Using this equation, the integral in Eq. (14-8) can be evaluated.

Calculation of Transfer Units In the general case, the equations described above must be employed in calculating the height of packing required for a given separation. However, if the local masstransfer coefficient kGayBM is approximately proportional to the first power of the local gas velocity GM, then the height of one gas-phase transfer unit, defined as HG = GM/kGayBM, will be constant in Eq. (14-9). Similar considerations lead to an assumption that the height of one overall gas-phase transfer unit HOG may be taken as constant. The height of packing required is then calculated according to the relation hT — HGNG — HQCNQ,

where NG = number of gas-phase transfer units and NOG = number of overall gas-phase transfer units. When HG and HOG are not constant, it may be valid to employ averaged values between the top and bottom of the tower and the relation hT — HgaNg — Hog*Nog

In these equations, the terms NG and NOG are defined by Eqs. (14-17) and (14-18).

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