# Determine the optimal reactor length to maximise P1.

1 Project Consider a system of 3 chemical reactions in liquid phase in a Plug Flow Reactor (PFR): � !! � � !! 2� 2� !! � The kinetic constants are listed in the appendix. The diameter, D, of the reactor is 2 cm and the length, L, can be varied between 2 to 30 cm. The process is isothermal. Molecular weights of A, B and C are 300, 300 and 150 gmol/mol. The velocity, �, is fixed at 1 mm/s. The changes of the reactants inside the reactor can be modelled below: ��! �� = 1 � (−�!�! + �!�! !) ��! �� = 1 � (�!�! − �!�!) ��! �� = 1 � (2�!�! − 2�!�! !) where CA, CB, CC are the concentrations of A, B and C respectively. B is the desired product. The process can be described in Fig. 1. Fig. 1. Initial process. Reactor Separator Evaporator Evaporator Feed U1 U2 U3 U4 W2 P1 W1 2 The fresh feed is 60 L/min, containing 1 mol/L of A. After the PFR reactor, the outflow (U1) goes through a separator, which separates the products into two streams, U2 and U3. – U2 contains B and water only (consists of 40% water and 60% B by weight). The amount of B in U2 equals to 50% B in U1. – U3 goes to an evaporator: W2 (which contains 70% of water from U3) and the remaining solution (U4) – Stream U2 is then completely dehydrated to produce powder product P1 (consists of B only). Question 1. a. Calculate and plot the chemical concentrations in the reactor as function of reactor length. b. What is the optimal length to maximise P1? At that point, what are the composition and flow rate of W2 and U4. Question 2. Stream U4 is recycled and mixed with the feed before entering the reactor. Fig. 2. Process with recycling. At steady state: a. Determine the optimal reactor length to maximise P1. b. What is the influence of the percentage of water removed through stream W2 on product P1. Reactor Separator Evaporator Evaporator Feed U1 U2 U3 U4 W2 P1 Water 3 Question 3. Another separator replaces the evaporator as seen in Fig. 3. Product P2 consists of 20% water, 40% B and 40% C, by weight. P2 contains 50% B from U3. Fig. 3. Alternative process. a. Determine the optimal reactor length to maximise P1. b. Determine the optimal reactor length to maximise the profit based on the prices and operation costs. c. If the new process is more profitable than the process in question 2? Question 4. There are several ways you could have solved this problem in Excel. Outline some of the possibilities you considered and briefly explain why you chose the approach you did. Notes: – The reactor length should be accurate to 5 mm – You need to state your model assumptions. – Answer all 4 questions (3 + 3 + 3 + 2 marks) – The presentation and formatting of the report worth 4 marks. Reactor Separator Evaporator Separator Feed U1 U2 U3 U4 P2 P1 Water 4 APPENDIX 1. Feed solution costs $250/L. 2. The costs of the vaporization and separation processes are assumed independent on the flow. 3. Other costs are listed in table. 1 Table 1. The reaction constants, prices and cost for your group are specified below: Reaction rates Market prices and cost ($) k1 (min-1) k2 (min-1) k3 (L/mol.min) Reactor (/L) P1 (/g) P2 (/g) 0.4 0.15 0.2 14 65 2

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