CHE555 2015

1 FACULTY OF CHEMICAL ENGINEERING

CHE 555 NUMERICAL METHODS & OPTIMIZATION

ASSIGNMENT 1

ANSWER ALL QUESTIONS

This is a group assignment (3 members) which has to be submitted within 1 week after receiving the

assignment. Standardize all the calculation up to 4 decimal points.

QUESTION 1

PO1, CO1, C3

An isothermic reaction is carried out adiabatically and the CSTR reactor design algorithm is shown as

below:

The reaction is second order in A. The feed which is equimolar in a solvent and A, and its enters the

reactor at a total volumetric flow rate, v0 of 10 dm3/min with the initial concentration of A being 4 M.

The rate constant, k given as 0.1 dm3/mol.min at 380 K. Determine the conversion can be achieved in

600 dm3 CSTR by using the following methods:

a) Graphically

b) False position method with initial guesses of Xl =0.6 and Xu =0.9

c) Secant method with initial estimates of X-1 = 0.6 and X0, =0.9

Iterate until the approximate error falls below 1 %. Find the absolute relative approximate error at the

end of each iteration.

(20 marks)

QUESTION 2

PO1, CO2, C4

A liquid-liquid extraction is used to extract nickel from the aqueous solution into an organic solution.

Table 1 shows the experimental data from the extraction process.

Table 1 Extraction of Nickel

Ni in aqueous phase, a (g/l) 4 8 12 16 20

Ni in organic phase, g (g/l) 6.3 12 15.5 18.3 21.5

Where g is the amount of nickel in the organic solution and a is the amounts of nickel in the aqueous

solution. Identify the best type of polynomial that fit to these data and determine its polynomial

CHE555 2015

2 FACULTY OF CHEMICAL ENGINEERING

equation. Then estimate the amount of nickel in the organic solution when 25 g/l of nickel is in the

aqueous solution.

(20 marks)

QUESTION 3

PO4, C03, C4

Compare answer from Question 2 with the answer from Excel and Matlab. Write the details command

(Excel and Matlab) and result of this problem.