Chemical Reaction Engineering (Homogeneous Reactions in Ideal Reactors) - Chapter 2: Interpretation of Batch Reactor Data - Mai Thanh Phong, Ph.D

Nội dung text: Chemical Reaction Engineering (Homogeneous Reactions in Ideal Reactors) - Chapter 2: Interpretation of Batch Reactor Data - Mai Thanh Phong, Ph.D

1. Chapter 2. Interpretation of Batch Reactor Data 1. Rates of reaction 1.1. Description of reaction rates Reaction rates depend usually in a complex manner on the concentrations, the temperature and often on the effect introduced by catalysts: r = f ( ci ,T, catalyst) The order of a reaction is related to the concentration dependence. Typical examples are: Irreversible Reactions: • First order: -1 A → Products: r = k(T)CA k in [s ] • Second order: 3 -1 -1 A + B → Products: r = k(T)CACB k in [m mol s ] 2 3 -1 -1 2A → Products: r = k(T)CA k in [m mol s ] Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 2
2. Chapter 2. Interpretation of Batch Reactor Data 1.2. Rate laws of simple reactions In this section, rate equations of simple reactions and the corresponding temporal change of concentration are analyzed. A closed system (isothermic, batch reactor) and aconstant volume are assumed. 1.2.1. Irreversible first-order reactions (Decomposition reactions) A → Products 1 dCi The rate equation is: r = = kCi (2.1)  i dt dC With i is A and v = -1, then: r = − A = kC (2.2) i dt A CA dC t C The integration form: − A = k dt or − ln A = kt (2.3) C CA0 CAo A 0 Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 4
3. Chapter 2. Interpretation of Batch Reactor Data Noting that the amounts of A and B that have reacted at any time t are equal and given by CA0XA, eq. (2.7) can be written in terms of XA as r = (2.8) (2.9) (2.10) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 6
4. Chapter 2. Interpretation of Batch Reactor Data 1.2.3. Empirical rate equations of nth order When the mechanism of reaction is not known, we often attempt to fit the data with an nth-order rate equation of the form (2.14) which on separation and integration yields (2.15) 1.2.4. Zero-order reactions Integrating and noting that CA can never become negative, (2.16) we obtain directly: Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 8
5. Chapter 2. Interpretation of Batch Reactor Data The k values are found using all three differential rate equations. First of all, eq. (2.17), which is of simple first order, is integrated to give (2.20) Then dividing eq. (2.18) by eq. (2.19) we obtain the following (2.21) which integrated gives simply (2.22) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 10
6. Chapter 2. Interpretation of Batch Reactor Data Assuming that at t = 0, concentration of A is CA0, and no R or S present, integration of eq. (2.23) gives (2.26) To find the changing concentration of R, substitute the concentration of A from eq. (2.26) into the differential equation governing the rate of change of R, eq. (2.24); thus (2.27) Solving the above differential equation gives (2.28) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 12
7. Chapter 2. Interpretation of Batch Reactor Data By differentiating Eq. (2.28) and setting dCRldt = 0, the maximum concentration of R and the time at which it occours can be found: (2.32) (2.33) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 14
8. Chapter 2. Interpretation of Batch Reactor Data 1.2.7. First-Order Reversible Reactions The simplest case is the opposed unimolecular-type reaction (2.34a) Starting with a concentration ratio M = CR0/CA0 th e rate equation is (2.34b) At equilibrium dCA/dt = 0. Hence from Eq. (2.34) we find the fractional conversion of A at equilibrium conditions to be (2.35) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 16
9. Chapter 2. Interpretation of Batch Reactor Data 1.2.8. Second-Order Reversible Reactions For the bimolecular-type second-order reactions (2.39a) (2.39b) (2.39c) (2.39d) with the restrictions that CA0 = CB0, and CR0 = CS0 = 0, the integrated rate equations for A and B are all identical, as follows (2.40) Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 18
10. Chapter 2. Interpretation of Batch Reactor Data The measured data can be inllustrated in a ln(CA/CA0) vs. T diagram. The slope of the straight line leads to the reaction rate constant (Figure 2.3). 2.6 of 2.3 Figure 2.3. Determination of the reaction rate constant k using the integrated method in a linearised formulation Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 20
11. Chapter 2. Interpretation of Batch Reactor Data ) A r log( Figure 2.4. Test for the particular rate Figure 2.5. Test for an nth-order rate form rA = kf(CA) by the differential method by the differential method. form. Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 22
12. Chapter 2. Interpretation of Batch Reactor Data 3. In the presence of a homogeneous catalyst of given concentration, aqueous reactant A is converted to product at the following rates, and CA alone determines this rate: We plan to run this reaction in a batch reactor at the same catalyst concentration as used in getting the above data. Find the time needed to lower the concentration of A from CA0 = 10 mollliter to CAf = 2 mol/liter. Mai Thanh Phong - HCMUT Chemical Reaction Engineering 30-Dec-22 24