Energy Balance on Distillation Column

Distillation Problem

Materials and Energy Balance on Distillation Column Print out a copy of this (by using the Print command of your browser) and keep this handy when you are watching the slide shows. You will also need Tables B1 and B2 from your textbook, copies of which are also available through the Tables link of distillation web page. Write down the calculations and the answers to each part of this problem in appropriate places while watching the slide show. Later, do the calculations by yourself to check whether you are getting the same answers or not; and then verify them with the results given in the Answers link

Problem Statement: A mixture that contains 65 mol% benzene and rest toluene is separated in a continuous distillation column at 1 atmospheric pressure. A flow chart of the operation is given below. The feed enters the distillation column at 25oC and at 1000 mol/h. The column overhead is a mixture of benzene at 1250 mol/h and toluene at 80 mol/h. Half of the condensate is withdrawn as the overhead product, and the remainder is refluxed back to the column. The liquid leaving the bottom of the column goes into a steam-heated reboiler, in which it is partially vaporized. The vapor is returned to the column at 100oC, and the residual liquid, also at 100oC, constitutes the bottoms product. All the physical properties of the components can be found in the Tables link, except for liquid toluene. The heat capacity of liquid toluene within the experimental temperature range should be calculated using the following equation: Cp (J/mol·oC) = 148.8 + 0.324 T( oC)

Page 1 of 4

Distillation Problem

Calculate the followings: (a) (b) (c) (d)

The flow rates and compositions of the product streams; The net heat requirement for the process (neglect heat of mixing) in kW; The heat removal from the condenser, Qc in kW; and The required heat input to the reboiler, Qr in kW

Solution Steps: 1. Do the material balance first, answer question (a) and complete the flow chart with the flow rates of the components for the product streams. 2. Gather all thermodynamic data from Tables B1 and B2 from your textbook or from the Tables link. 3. Construct an energy balance table with an appropriate reference temperature for parts (b) and (c). 4. Fill up all the unknowns in the above table. 5. Calculate parts (b), (c) and (d) Part (a): Material Balance The condensate stream flow rates for each of the components are: B = _______________ mol/h T = _______________ mol/h The inlet stream to the distillation column has a flow rate of 1000 mol/h with 65 mol% benzene, i.e., _______________ mol/h of benzene. Therefore, toluene flow rate in the inlet stream is ___________ mol/h. Now, when we do an overall material balance on the distillation column, we find the flow rate of the bottoms: B = ________ mol/h and T = ___________ mol/h The compositions of the product streams are as follows: Condensate or distillate: B =________________, i.e. ______ mol% benzene, and T = ____________, i.e., _____ mol% toluene. Bottoms: B = ______________ mol% benzene, and T = _____________________ mol% toluene. Answers to Part (a): Component

Feed Rate mol/h

Feed Comp. mol%

Condensate Rate Comp. mol/h mol%

Benzene Toluene Page 2 of 4

Bottoms Rate Comp. mol/h mol%

Distillation Problem Table 1: Thermodynamic Data required for Calculations Component Benzene

State of Boiling aggregation Point, Tb, oC Liquid

Heat capacities ∆Hv, kJ/mol [Units]

Vapor Toluene

Liquid Vapor

Part (b): Overall Heat Requirement Table 2: Energy Balance Table for Part (b) Reference: Benzene and Toluene liquids at 250C Hin, kJ/mol Component nin, mol/h Benzene (l, 25oC) Toluene (l, 25oC) Benzene (l, 75oC) Toluene (l, 75oC) Benzene (l, 100oC) Toluene (l, 100oC) -

Calculations for Hout (s): H B,l,25o C = = H T, l,25o C = = H B,l, 100o C = = = H T, l,100o C = Page 3 of 4

nout, mol/h

Hout, kJ/mol

310

12.7

Distillation Problem

= The open-system energy balance equation is given as follows: ∆H + ∆E k + ∆E p = Q + Ws Since kinetic energy, potential energy and the work done are negligible, Q = ∆H = ∑ ni H i − ∑ ni H i out

in

=

Part (c): Heat Removal for the Condenser Table 3: Energy Balance Table for Part (c) Reference: Benzene and Toluene liquids at 750C Component nin, mol/h Hin, kJ/mol Benzene (v, 85oC) Toluene (v, 85oC) Benzene (l, 75oC) Toluene (l, 75oC)

nout, mol/h

Hout, kJ/mol

H B,v,85o C = = In a similar way, calculate the enthalpy of toluene vapor at 85oC: 110.62

H T, v,85o C =

∫C

75

85 p ,l

dT + ∆H v +

∫C

p ,v

dT

110.62

= Both outlet enthalpies are zero because the output is in our reference phase and temperature, i.e. at liquid, 75oC. Once again, the open system energy balance equation reduces to: Qc = ∆H = ∑ n H − ∑ n H i i i i out in

Part (d): Heat Input to the Reboiler Q = Qc + Qr ; ⇒ Qr = Q – Qc = Page 4 of 4