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16 Nov 2019

The continuous flow stirred-tank reactor (CSTR), also known as water backmix reactor, is a common ideal reactor type in chemical engineering. A CSTR often refers to a model used to estimate the key unit operation variables when using a continuous agitated- tank reactor to reach a specified output.

It is amused perfect or ideal mixing in CSTR and we are checking the concentrations and temperature along time in CSTR.

Following equations can be obtained to describe the CSTR.

Problem:

1) Show the equations you need to solve C and T from current step to next step using Eulerâs method.

2) Using time step of 1 second to show calculate the values of C and T from 0 second to 21 seconds using Eulerâs method. Plot the changes of C and T over time.

Using following given initial values and parameters.

For mass: do 772 A0 dt For temperature: dT -E/RT CA) koCAe T) V VpCp E/RT Mixed prod UA(T

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Learning objectives To gain an understanding of how to derive mathematical models to describe the operation of batch, semi-batch and continuous flow reactors. To gain an understanding of how to use mathematical models, by employing a numerical method, to find the performance characteristics of chemical reactors such as the product distribution. Skills outcomes Ability to analyse modes of process operation of chemical reactors. Ability to solve problems related to reactor design and employ appropriate numerical techniques to perform quantitative analysis of reactor performance. Assignment Description Consider the batch process shown in Figure 1: a stirred tank (CSTR-100) is connected in series with a reactor (CRV 100) containing a mass per unit volume, W, of solid catalyst. The reactants and products of the reaction process are all liquids which are circulated via a pump (P-100), There is no feed to this closed-loop system and no product is withdrawn. No chemical reaction process occurs in the absence of catalyst hence none occurs in the stirred tank. Assume that initially the tank and reactor contain only reagent A You may also assume: the tank and the reactor are instantaneously well mixed, there is no change in fluid density accompanying the reaction process. the volume of the liquid in the connecting pipe work may be neglected, there is no resistance to mass transfer in the reactor (at the interface between the solid-catalyst particles and the liquid), Figure 1 schematic diagram of units in the batch process The reaction scheme is A notequalto B rightarrow C The first reaction is first order with respect to A in the forward direction, with rate constant, k_u and first order with respect to B in the reverse direction with rate constant, k_lb The second reaction is irreversible and first order with respect to B with rate constant k_a For a solid-catalysed process an appropriate batch-reactor performance equation for reagent A is I/C_A0 = V/W integral_0^XA dX_A/-r_A^r Here, t is elapsed time, C_sa is the initial concentration of reagent A V is the volume of liquid in the reactor, X_a is the fractional conversion of reagent A and r_A^r is the rate of appearance by chemical reaction of reagent A in moles per unit mass of solid-catalyst per unit time. What are the units of the rate constants The volume of the stirred tank is V_1 and the volume of the void-space in the reactor is V_2. By performing a material balance derive performance equations describing the time dependence of the concentration of reagent A and products Band C in the stirred tank. Explain the meaning of any terms you introduce Similarly derive performance equations describing the time dependence of the concentration of reagent A and products Band C in the reactor. Explain the meaning of any terms you introduce Using the performance equations you have derived in parts and investigate how the distribution of products the tank and in the reactor varies with time depending on la the ratio where q is the volumetric flow rate, the ratio the ratio and the ratio Assume that is constant, 1 mole/litre, and that v_2 and w are constant. In your assignment report you must provide the evidence on which you have based your investigation and hence your conclusions. This includes output from any numerical approach you use to solve the performance equations such as the Euler method implemented in an Excel spreadsheet, You must decide on an appropriate range of ratio values to use for (d and then justify the values you have selected in your write-up. You should mot write more than 2500 words for part excluding table captions and figure captions. Provide a brief summary to your report

You are part of a team working on the development of a process in which a mineral species (labeled A for proprietary reasons) undergoes a reaction to form a new pigment to be used in house paints. In a series of experiments in a large well-mixed stirred tank reactor, you fill a tank with a known quantity of an inert liquid, bring the liquid up to a specified temperature, add a known quantity of A, and measure the concentration of A in the tank as a function of time. The reaction gives off heat as it progresses, but cooling water circulating in a jacket around the reactor keeps the temperature of the reacting mixture constant. The following data are recorded.

	Concentration of A, C_A(mol A/L)
t(min)	T = 94Â°C	T = 110Â°C	T = 127Â°C	T = 142Â°C
10	9.30Ã10^â2	5.19Ã10^â2	2.10Ã10^â2	9.87Ã10^â3
20	6.17Ã10^â2	2.35Ã10^â2	1.33Ã10^â2	5.55Ã10^â3
30	4.41Ã10^â2	1.91Ã10^â2	8.15Ã10^â3	3.97Ã10^â3
40	3.12Ã10^â2	1.45Ã10^â2	5.92Ã10^â3	2.45Ã10^â3
50	2.58Ã10^â2	1.01Ã10^â2	4.48Ã10^â3	2.27Ã10^â3
60	9.30Ã10^â2	9.50Ã10^â3	4.36Ã10^â3	1.83Ã10^â3

A research article indicates that concentration of A should vary with time according to the following expression:

CA(t)=11CA0+kt

(1)

where CA0 (mol/L) is the initial concentration of A in the reactor [CA(t=0)] and k is called the reaction rate constant. Despite being called a constant, k is a strong function of the absolute temperature in the reactor:

k(T)=k0 expâEaRT(K)

(2)

In this equation (known as the Arrhenius equation after the Swedish chemist who proposed it), k0 is a constant, Ea(J/mol) is the reaction activation energy, and R=8.314 J/(molÂ·K) is the universal gas constant. Your task will be to verify that the expressions for CA(t) and k(T) fit the data, and if they do, to determine the parameters CA0 and k at each temperature and then the constants k0 and Ea.

(a)

What are the units of k, k0, and Ea if CA is in mol/L and t is in min?

(b)

Transform Equation 1 into an equation of the form y=at+b, so that if Equation 1 is valid, a plot of yvs. t would be a straight line. How would you determine CA0 and k from the slope and intercept of the line?

(c)

Create an Excel spreadsheet with the structure shown as Rows 1-10 in the figure at the end of this problem statement, and fill in the data table in Columns A-I. Then create the four scatterplots shown in Rows 15-21. In the âTrendlineâ options of each plot, check the boxes for âDisplay equation on chartâ and âDisplay R-squared value on chartâ but not the one for âSet intercept.â R2 is the coefficient of determination (it has several other names as well), and provides a measure of how well a straight line fits a set of data: the closer it is to 1, the better the fit. What can you conclude about Equation 1 from the four plots?

(d)

From the four trendline equations, calculate the values of k and CA0 for each of the four experimental temperatures and fill in Columns B-I in Rows 12 and 13 of the spreadsheet.

(e)

Enough A was initially added to the tank to make the initial concentration CA0=0.25 mol/L, yet you calculated four different values of CA0 in Part d. How do you explain this result?

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