A distillation column with a total condenser is shown in Fig. 3.3. The system to be studied in this problem has an average enthalpy of vaporization of 32 kJ/mol, an average C_P^L of 146 J/mol°-C, and an average C_P^V of 93 J/mol°-C. Variable names for the various stream flow rates and the heat flow rates are given in the diagram. The feed can be liquid, vapor, or a mixture represented using subscripts to indicate the vapor and liquid flows, F = F_V + F_L. The enthalpy flow due to feed can be represented as: for saturated liquid, F_LH^satL; for saturated vapor, F_VH^satV; for subcooled liquid, F_LH^satL + F_LC_P^L (T_F – T^satL); for superheated vapor, F_VH^satV + F_VC_P^V(T_F – T^satV); and for a mix of vapor and liquid, F_LH^satL + F_V H^satV.

(a) Use a mass balance to show F_V + V_S – V_R = L_S – L_R – F_L.

[For parts (b) - f), use the feed section mass and energy balances to show the desired result.]

(b) For saturated vapor feed, F_L = 0. Show V_R = V_S + F_V , L_S = L_R.

(c) For saturated liquid feed, F_V = 0. Show V_S = V_R, L_S = L_R + F_L.

(d) For subcooled liquid feed, FV = 0. Show V_R – V_S = F_LC_P(T_F – T^sat)/ΔH^vap.

(e) For superheated vapor feed, FL = 0, Show LS – L_R = –F_VC_P(T_F – T^sat)/ΔH^vap.

(f) For a feed mixture of saturated liquid and saturated vapor. Show V_R = V_S + F_V, L_S = L_R + F_L.

(g) Use the mass and energy balances around the total condenser to relate the condenser duty to the enthalpy of vaporization, for the case of streams L_R and D being saturated
liquid.

(h) Use the mass and energy balances around the reboiler to relate the reboiler duty to the enthalpy of vaporization.

(i) In the case of subcooled liquid streams L_R and D, the vapor flows out of the top of the column, and more variables are required. V′_R (into the condenser) will be smaller than the rectifying section flow rate V_R. Also, the liquid flow rate in the rectifying section, Also, the liquid flow rate in the rectifying section, L_R, will be larger than the reflux back to the column, L′_R. Using the variables V′_R, L′_R to represent the flow rate out of the top of the column and the reflux, respectively, relate V_R to V′_R L′_R and the degree of subcooling T_L – T^satL.

[For parts (j) - (o), find all other flow rates and heat exchanger duties ( values).]

(j) F = 100 mol/hr (saturated vapor), B = 43, L_R/D = 2.23.

(k) F = 100 mol/hr (saturated vapor), D = 48, L_S/V_S = 2.5.

(l) F = 100 mol/hr (saturated liquid), D = 53, L_R/D = 2.5.

(m) F = 100 mol/hr (half vapor, half liquid), B = 45, L_S/V_S = 1.5.

(n) F = 100 mol/hr (60°C subcooled liquid), D = 53, L_R/D = 2.5.

(o) F = 100 mol/hr (60°C superheated vapor), D = 48, L_S/V_S = 1.5.

Transcribed Image Text:

F, Z VR VR Ls LR D, XD Rectifying Section LR VsLs cond = VRAHap Total Condenser Feed Section Stripping Section Vs W Reboiler VR cond (1-9R)VRAHvap = ww 0 LR=(1-qR)VR greboiler=VAHvap B, XB Partial Condenser D=qRVR L11 L13 V11 V13 V12 V14 Tray 11 Tray 12 L12 Tray 13 (b) Figure 3.3 (a) Overall schematic of a distillation column with a total condenser showing five sections of a distillation column. and conventional labels; (b) a partial condenser; (c) schematic of liquid levels on bubble cap trays with the downcomers used to maintain the liquid levels.