Space time and Space velocity, CSTR

Chemical Reaction Engineering. Mehran University of Engineering & Technology Jamshoro, PK. Department of Chemical Engineering.

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2. Ideal Reactors for Single Reaction Under the Supervision of: Dr. Imran Nazir Unar Mujeeb UR Rahman 17CH106 Chemical Engineering Department Chemical Reaction Engineering (CH314) Mehran University of Engineering & Technology Jamshoro, Pakistan

3. Lecture Objectives Discussion on: Space-time and space-velocity terms Performance Equation of Steady-state Mixed Flow Reactor (CSTR) Problem

4. IDEAL REACTORS FOR A SINGLE REACTION Space-Time and Space-Velocity Just as the reaction time t is the natural performance measure for a batch reactor, so are the space-time and space-velocity the proper performance measures of flow reactors. These terms are defined as follows: (6) (7)

5. IDEAL REACTORS FOR A SINGLE REACTION Space-Time and Space-Velocity Thus, a space-velocity of 5 hr -1 means that five reactor volumes of feed at specified conditions are being fed into the reactor per hour. A space-time of 2 min means that every 2 min one reactor volume of feed at specified conditions is being treated by the reactor. Now we may arbitrarily select the temperature, pressure, and state (gas, liquid, or solid) at which we choose to measure the volume of material being fed to the reactor. Certainly, then, the value for space-velocity or space-time depends on the conditions selected. If they are of the stream entering the reactor, the relation between s and τ and the other pertinent variables is (8)

6. IDEAL REACTORS FOR A SINGLE REACTION Space-Time and Space-Velocity It may be more convenient to measure the volumetric feed rate at some standard state, especially when the reactor is to operate at a number of temperatures. If, for example, the material is gaseous when fed to the reactor at high temperature but is liquid at the standard state, care must be taken to specify precisely what state has been chosen. The relation between the space-velocity and space-time for actual feed conditions (unprimed symbols) and at standard conditions (designated by primes) is given by In most of what follows, we deal with the space-velocity and space-time based on feed at actual entering conditions; however, the change to any other basis is easily made. (9)

7. INTRODUCTION TO REACTOR DESIGN Performance Equation for STEADY-STATE MIXED FLOW REACTOR The performance equation for the mixed flow reactor is obtained from Balance equation (in previous presentation) which makes an accounting of a given component within an element of volume of the system. But since the composition is uniform throughout, the accounting may be made about the reactor as a whole. By selecting reactant A for consideration, Eq. becomes (10) Fig. 1: Notation for a mixed reactor.

8. INTRODUCTION TO REACTOR DESIGN Performance Equation for STEADY-STATE MIXED FLOW REACTOR As shown in Fig. 1, if F A0 = ν C A0 is the molar feed rate of component A to the reactor, then considering the reactor as a whole we have Introducing these three terms into Eq. 10, we obtain which on rearrangement becomes OR (11)

9. INTRODUCTION TO REACTOR DESIGN Performance Equation for STEADY-STATE MIXED FLOW REACTOR where X A and r A are measured at exit stream conditions, which are the same as the conditions within the reactor. More generally, if the feed on which conversion is based, subscript 0, enters the reactor partially converted, subscript i , and leaves at conditions given by subscript f , we have or For the special case of constant-density systems X A = 1 – C A /C A0 in, which case the performance equation for mixed reactors can also be written in terms of concentrations or (12) (13)

10. INTRODUCTION TO REACTOR DESIGN Performance Equation for STEADY-STATE MIXED FLOW REACTOR These expressions relate in a simple way the four terms X A , –r A , V, F A0 ; thus, knowing any three allows the fourth to be found directly. In design, then, the size of reactor needed for a given duty or the extent of conversion in a reactor of given size is found directly. In kinetic studies each steady-state run gives, without integration, the reaction rate for the conditions within the reactor. The ease of interpretation of data from a mixed flow reactor makes its use very attractive in kinetic studies, in particular with messy reactions (e.g., multiple reactions and solid catalyzed reactions).

11. INTRODUCTION TO REACTOR DESIGN Performance Equation for Ideal Batch Reactor Fig. 2: Graphical representation of the design equations for mixed flow reactor.

12. INTRODUCTION TO REACTOR DESIGN Problem: REACTION RATE IN A MIXED FLOW REACTOR Fig. 2: Graphical representation of the design equations for mixed flow reactor. One liter per minute of liquid containing A and B (C A0 = 0.10 mol/liter, C B0 =0.01 mol/liter) flow into a mixed reactor of volume V = 1 liter. The materials react in a complex manner for which the stoichiometry is unknown. The outlet stream from the reactor contains A, B, and C ( C Af = 0.02 mol/liter, C Bf = 0.03 mol/liter, C cf = 0.04 mol/liter. Find the rate of reaction of A, B, and C for the conditions within the reactor.

13. INTRODUCTION TO REACTOR DESIGN For a liquid in a mixed flow reactor ε A = 0 and Eq. 13 applies to each of the reacting components, giving for the rate of disappearance: Problem: REACTION RATE IN A MIXED FLOW REACTOR Fig. 3: Mixed Flow Reactor Conditions Solution: Thus A is disappearing while B and C are being formed.