ChE 402: Chemical Reaction Engineering Steady State Nonisothermal Reactor (Chapter 8) The energy balance Adiabatic operations Non-isothermal flow reactors with heat exchange Equilibrium conversion and adiabatic temperature Optimum feed temperature

The Energy Balance Because most reactions we not carried out isothermally, we now focus our attention on heat effect in chemical reactors. The basic design equations, rate laws, and stoichiomctrjc relationships derived and used in Chapter 4 for isothermal reactor design are still valid for the design of nonisothermal reactors. The major difference lies in the method of evaluating the design equation when temperature varies along the length of a PFR or when heat is removed from a CSTR.

The Energy Balance Rationale: To identify the additional information necessary to design nonisothermal Reactors: Example: Calculate the reactor volume necessary for 70% conversion: The reaction is exothermic and the reactor is operated adiabatically. As a result temperature will increase with conversion down the length of the reactor.

The Energy Balance

The Energy Balance First Law of Thermodynamics For a closed system the energy balance is

The Energy Balance open systems

The Energy Balance Evaluating the Work Term It is customary to separate the work term, into flow work and other work,

The Energy Balance Evaluating the Energy Term In almost all chemical reactor situations, the kinetic, potential, and "other" energy terms are negligible jn comparison with the enthalpy, heat transfer, and work terms, and hence will be omitted: that is.

The Energy Balance For steady state operation:

The Energy Balance

The Energy Balance

The Energy Balance

The Energy Balance

The Energy Balance

The Energy Balance We can use this sequence lo prepare a table of as a function of X. We can then proceed to size PFR and CSTRs. If there is cooling along the Length of a PFR. we could then apply Equation (T8-I .E) to this reaction to arrive at two coupled differential equations.

The Energy Balance Similarly, for the case of the reaction carried out in a CSTR. we could use Polymath or MATLAB to solve two nonlinear equations in X and T. These two equations are combined mole balance

The Energy Balance Heat of Reaction In general, For the generalized reaction: In general,

The Energy Balance Energy Balance Equation becomes:

The Energy Balance Enthalpies:

The Energy Balance A large number of reaction carried out in the industries without changing the phase To calculate the change in enthalpy (Hi - Hio) when the reacting fluid is heated without phase change from its entrance temperature, TR, to a temperature T Energy Balance Equation becomes:

The Energy Balance The heat of reaction at temperature T is given in terms of the enthalpy of each species at temperature T, that is, where the enthalpy of each species is given by

The Energy Balance

The Energy Balance

The Energy Balance The minus sign indicates the reaction is exothermic. If the heat capacities are constant or if the mean heat capacities over the range 25 to 3500C are readily available

The Energy Balance

ChE 402: Chemical Reaction Engineering Steady State Nonisothermal Reactor (Chapter 8) The energy balance Adiabatic operations Non-isothermal flow reactors with heat exchange Equilibrium conversion and adiabatic temperature Optimum feed temperature

The Energy Balance Heat of Reaction In general, For the generalized reaction: In general,

The Energy Balance Energy Balance Equation becomes:

The Energy Balance Enthalpies:

The Energy Balance A large number of reaction carried out in the industries without changing the phase To calculate the change in enthalpy (Hi - Hio) when the reacting fluid is heated without phase change from its entrance temperature, TR, to a temperature T Energy Balance Equation becomes:

The Energy Balance The heat of reaction at temperature T is given in terms of the enthalpy of each species at temperature T, that is, where the enthalpy of each species is given by

The Energy Balance

The Energy Balance

The Energy Balance The minus sign indicates the reaction is exothermic. If the heat capacities are constant or if the mean heat capacities over the range 25 to 3500C are readily available

The Energy Balance

The Energy Balance Heat of Reaction & Enthalpies In general, For the generalized reaction: In general,

The Energy Balance Energy Balance Equation becomes:

The Energy Balance Enthalpies:

The Energy Balance A large number of reaction carried out in the industries without changing the phase To calculate the change in enthalpy (Hi - Hio) when the reacting fluid is heated without phase change from its entrance temperature, TR, to a temperature T Energy Balance Equation becomes:

The Energy Balance The heat of reaction at temperature T is given in terms of the enthalpy of each species at temperature T, that is, where the enthalpy of each species is given by

The Energy Balance

The Energy Balance

The Energy Balance The minus sign indicates the reaction is exothermic. If the heat capacities are constant or if the mean heat capacities over the range 25 to 3500C are readily available

The Energy Balance

Adiabatic Operation Reactions in industry are frequently carried out adiabaticaIly with heating or cooling provided either upstream or downstream. Adiabatic Energy Balance

Adiabatic Operation In most systems, the work term, can be neglected In almost all of the systems we will study, the reactants will be entering the system at the same temperature; therefore, Adiabatic operation In many instances, the term in the denominator is negligible with respect to the term,

Adiabatic Operation

Adiabatic Operation Adiabatic Tubular Reactor

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation Recalling the rate law gives us

Adiabatic Operation Solution by Hand Calculalion

Adiabatic Operation

Adiabatic Operation

Adiabatic Operation

ChE 402: Chemical Reaction Engineering Steady State Nonisothermal Reactor (Chapter 8) The energy balance Adiabatic operations Non-isothermal flow reactors with heat exchange Equilibrium conversion and adiabatic temperature Optimum feed temperature

Non-isothermal flow reactors with heat exchange Steady-State Tubular Reactor we consider a tubular reactor in which heat is either added or removed through the cylindrical walls of the reactor In modeling, the reactor, we shall assume that there are no radial gradients in the reactor and that the heat flux through the wall per unit volume of reactor

Non-isothermal flow reactors with heat exchange Deriving the Energy Balance The heat flow to the reactor, ∆Q. is given in terms of the overall heat transfer coefficient, U, the heat exchange area, ∆A. and the difference between ambient temperature Ta;, and the reactor temperature T. where a is the heat exchange area per unit volume of reactor. taking the limit as Energy balance Equation becomes.

Non-isothermal flow reactors with heat exchange From a mote balance on species i. we have the enthalpy Equation Differentiating the enthalpy Equation

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

Non-isothermal flow reactors with heat exchange

ChE 402: Chemical Reaction Engineering Steady State Nonisothermal Reactor (Chapter 8) The energy balance Adiabatic operations Non-isothermal flow reactors with heat exchange Equilibrium conversion and adiabatic temperature Optimum feed temperature

Equilibrium Conversion The highest conversion that can be achieved in reversible reactions is the equilibrium conversion. For endothermic reactions, the equilibrium conversion is increases with increasing temperature up to a maximum of 1.0. For exothermic usually the equilibrium conversion decreases with increasing temperature.

Equilibrium Conversion Exothermic Reactions: To determine the maximum conversion that can be achieved in an exothermic reaction carried out adiabatically, we find the intersection of the equilibrium conversion as a function of temperature from Figure 8.4(b) with temperature conversion relationships from the energy balance

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion Endothermic Reactions: Because the reaction is endothermic, equilibrium conversion increases with increasing temperature. A typical equilibrium curve and temperature conversion trajectory for the reactor sequence are shown in Figure 8-8.

Equilibrium Conversion

Equilibrium Conversion that for an entering temperature of 300 K the adiabatic equilibrium conversion was 0.42. For 95% of equilibrium conversion (X, = 0,42), the conversion exiting the first reactor is 0.4. The exit temperature is found from a rearrangement of Equation 2. Calculate the Heat Load There is no work done on the reaction gas mixture in the exchanger, and the ,th e energy balance given

Equilibrium Conversion

Equilibrium Conversion We see that 220 kcal/s is removed from the reaction system mixture. The rate at which energy must be absorbed by the coolant stream in the exchanger is We consider the case where the coolant is available at 270 K but cannot be heated above 400 K and calculate the coolant flow rate necessary to remove 220 kcal/s from the reaction mixture. Rearranging Equation

Equilibrium Conversion let's next determine the counter current heat exchanger area

Equilibrium Conversion

Equilibrium Conversion The conditions entering the second reactor are T = 350 K and X = 0.4. The energy balance starting from this point is shown in Figure the equilibrium conversion is 60% and the corresponding exit temperature is T = 350 + (0.6 - 0.4)400 = 430 K The heat-exchange duty to cool the reacting mixture fmm 430 K back to 350 K can again be calculated from

Equilibrium Conversion

Equilibrium Conversion an entering temperature of 300 K the adiabatic equilibrium conversion was 0.42. For 95% of equilibrium conversion (X, = 0,421, the conversion exiting the first reactor is 0.4. The exit temperature is found from a rearrangement of Equation

Equilibrium Conversion

Equilibrium Conversion

Equilibrium Conversion We consider the case where the coolant is available at 270 K but cannot be heated above 400 K and calculate the coolant flow rate necessary to remove220 kcal\s from the reaction mixture.

Equilibrium Conversion

Equilibrium Conversion The conditions entering the second reactor are T = 350 K and X = 0.4. The energy balance starting from this point is shown The corresponding adiabatic equilibrium conversion is 0.63. Ninety-five percent of the equilibrium conversion is 60% and the corresponding exit temperature is T = 350 + (0.6 - 0.4)400 = 430 K. The heat-exchange duty to cool the reacting mixture from 430 K back to 350 K can again be calculated from Equation

Equilibrium Conversion Optimum Feed Temperature Adiabatic reactor of fixed size or catalyst weight. The reaction is reverse and exothermic.

Equilibrium Conversion

Equilibrium Conversion

ChE 402: Chemical Reaction Engineering Steady State Nonisothermal Reactor (Chapter 8) The energy balance Adiabatic operations Non-isothermal flow reactors with heat exchange Equilibrium conversion and adiabatic temperature Optimum feed temperature

CSTR with Heat Effects General Steady State Energy Balance Equation: CSTR Mole balance: Rearranging the above equation:

CSTR with Heat Effects Energy Balance for the Coolant

CSTR with Heat Effects Solving this equation to find the exit temperature: From the above equation we can get,

CSTR with Heat Effects General Energy Balance in term of Conversion

CSTR with Heat Effects Volume of CSTR Again, For pure component

CSTR with Heat Effects

CSTR with Heat Effects CSTR

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

CSTR with Heat Effects

ChE 402: Chemical Reaction Engineering Catalyis and Catalytic Reactors (Chapter 10) Definition of catalysis and catalytic processes Catalysts properties and classification Steps in a catalytic reaction and adsorption isotherms

Catalyst A catalyst is a substance that affects the rate of a reaction but emerges from the process unchanged. A catalyst usually changes a reaction rate by promoting a different molecular path ("mechanism") for the reaction. For example, gaseous hydrogen and oxygen are virtually inert at room temperature, bur react rapidly when exposed to platinum.

Homogeneous catalysis Homogeneous catalysis concerns processes in which a catalyst is in solution with at least one of the reactants. An example of homogeneous catalysis is the industrial 0x0 process for manufacturing normal isobutylaldehyde. It has propylene, carbon monoxide, and hydrogen as the reactants and a liquid-phase cobalt complex as the catalyst.

Heterogeneous catalysis A heterogeneous catalytic process involves more than one phase: usually the catalyst is a solid and the reactants and products are in liquid or gaseous form. Much of the benzene produced in this country today is manufactured from the dehydrogenation of cyclohexane (obtained from the distillation of crude petroleum) using platinum-on-alumina as the catalyst: A heterogeneous catalytic reaction occurs at or very near the fluid-solid interface. The principles that govern heterogeneous catalytic reactions can be applied for both catalytic and noncatalytic fluid-solid reactions. The two other types of heterogeneous reactions invoIve gas-Iiquid and gas-liquid-solid systems. Reactions between gases and liquids are usually mass-transfer limited.

Because a catalytic reaction occurs at the fluid-solid interface, a large inter cia1 area is almost always essential in attaining a significant reaction rate. many catalysts, this area is provided by an inner porous structure {i.e., solid contains many tine pores, and the surface of these pores supplies the a needed for the high rate of reaction),