Mixer, Splitter, and Reactor

Mixer, Splitter, and Reactor – p.1/11

Process Model: Mixer

Consider a mixer that is mixing n streams, each of which has k components.

Stream j_{1} is coming from unit i_{1} Stream j_{2} is coming from unit i_{2} . . Stream j_{n} is coming from unit i_{n}

Then, the mixer balance for component k is given by:

μ_{m}^{k} = μ_{i_{1},j_{1}}^{k} + μ_{i_{2},j_{2}}^{k} + ... + μ_{i_{n},j_{n}}^{k}

Consider a mixer that is mixing n streams, each of which has k components.

Stream j_{1} is coming from unit i_{1} Stream j_{2} is coming from unit i_{2} . . Stream j_{n} is coming from unit i_{n}

Then, the mixer balance for component k is given by:

μ_{m}^{k} = μ_{i_{1},j_{1}}^{k} + μ_{i_{2},j_{2}}^{k} + ... + μ_{i_{n},j_{n}}^{k}

Consider a mixer that is mixing n streams, each of which has k components.

Stream j_{1} is coming from unit i_{1} Stream j_{2} is coming from unit i_{2} . . Stream j_{n} is coming from unit i_{n}

Then, the mixer balance for component k is given by:

μ_{m}^{k} = μ_{i_{1},j_{1}}^{k} + μ_{i_{2},j_{2}}^{k} + ... + μ_{i_{n},j_{n}}^{k}

Process Model: Splitter

μ_{S_{1}}^{k} = ξ_{1}μ_{in}^{k}
μ_{S_{2}}^{k} = ξ_{2}μ_{in}^{k}
.
.
μ_{S_{n−1}}^{k} = ξ_{n−1}μ_{in}^{k}
μ_{S_{n}}^{k} = [1 − (ξ_{1} + ξ_{2} + ... + ξ_{n−1})] μ_{in}^{k}

μ_{S_{1}}^{k} = ξ_{1}μ_{in}^{k}
μ_{S_{2}}^{k} = ξ_{2}μ_{in}^{k}
.
.
μ_{S_{n−1}}^{k} = ξ_{n−1}μ_{in}^{k}
μ_{S_{n}}^{k} = [1 − (ξ_{1} + ξ_{2} + ... + ξ_{n−1})] μ_{in}^{k}

μ_{S_{1}}^{k} = ξ_{1}μ_{in}^{k}
μ_{S_{2}}^{k} = ξ_{2}μ_{in}^{k}
.
.
μ_{S_{n−1}}^{k} = ξ_{n−1}μ_{in}^{k}
μ_{S_{n}}^{k} = [1 − (ξ_{1} + ξ_{2} + ... + ξ_{n−1})] μ_{in}^{k}

Reactor

A reactor is a unit operation in which new chemical species are formed via chemical transformation.

There are three different types of reactor models Specific Kinetic Model Equilibrium-based Reactor Model Stoichiometric Reactor Model A reactor is a unit operation in which new chemical species are formed via chemical transformation.

There are three different types of reactor models Specific Kinetic Model Equilibrium-based Reactor Model Stoichiometric Reactor Model A reactor is a unit operation in which new chemical species are formed via chemical transformation.

There are three different types of reactor models Specific Kinetic Model Equilibrium-based Reactor Model Stoichiometric Reactor Model A reactor is a unit operation in which new chemical species are formed via chemical transformation.

There are three different types of reactor models Specific Kinetic Model Equilibrium-based Reactor Model Stoichiometric Reactor Model A reactor is a unit operation in which new chemical species are formed via chemical transformation.

Specific Kinetic Reactor Model

There are three different types of reactor models Specific Kinetic Model Equilibrium-based Reactor Model Stoichiometric Reactor Model This model relates concentrations of species via specific reaction kinetics.

The reaction kinetics are typically determined via laboratory experiments.

The type of reactor is taken into consideration in the model. For instance, in a CSTR, the reactor model may be written as:

F.C − F.C_{0} = V.r(C, T)

where r is the reaction rate This model relates concentrations of species via specific reaction kinetics.

The reaction kinetics are typically determined via laboratory experiments.

The type of reactor is taken into consideration in the model. For instance, in a CSTR, the reactor model may be written as:

F.C − F.C_{0} = V.r(C, T)

where r is the reaction rate This model relates concentrations of species via specific reaction kinetics.

The reaction kinetics are typically determined via laboratory experiments.

The type of reactor is taken into consideration in the model. For instance, in a CSTR, the reactor model may be written as:

F.C − F.C_{0} = V.r(C, T)

where r is the reaction rate This model relates concentrations of species via specific reaction kinetics.

The reaction kinetics are typically determined via laboratory experiments.

The type of reactor is taken into consideration in the model. For instance, in a CSTR, the reactor model may be written as:

F.C − F.C_{0} = V.r(C, T)

where r is the reaction rate

Equilibrium-based Reactor Model

Definition ?? The equilibrium constant K is related to the free energy ΔG and temperature T as follows:

K = exp (−\frac{ΔG}{RT})

Equilibrium-based Reactor Model

Definition ?? The equilibrium constant K is related to the free energy ΔG and temperature T as follows:

K = exp (−\frac{ΔG}{RT})

Equilibrium-based Reactor Model

Definition ?? The equilibrium constant K is related to the free energy ΔG and temperature T as follows:

K = exp (−\frac{ΔG}{RT})

Stoichiometric Reactor Model

The extent of reaction, η, for each reaction is specified by the user.

The reaction stoichiometry is used to determine the molar flowrate of each species at steady state.

The molar flow rates can be used to determine reactor size.

The extent of reaction, η, for each reaction is specified by the user.

The reaction stoichiometry is used to determine the molar flowrate of each species at steady state.

The molar flow rates can be used to determine reactor size.

The extent of reaction, η, for each reaction is specified by the user.

The reaction stoichiometry is used to determine the molar flowrate of each species at steady state.

The molar flow rates can be used to determine reactor size.

Stoichiometric Reactor Calculations

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \end{matrix}

It is given that A is the limiting reactant for the first reaction (with 60% conversion) and E is the limiting reactant for the second reaction (with 80% conversion).

If the molar flowrate of each species coming into the reactor

is known, compute the molar flowrate of each species going

out of the reactor.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \end{matrix}

It is given that A is the limiting reactant for the first reaction (with 60% conversion) and E is the limiting reactant for the second reaction (with 80% conversion).

If the molar flowrate of each species coming into the reactor

is known, compute the molar flowrate of each species going

out of the reactor.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \end{matrix}

It is given that A is the limiting reactant for the first reaction (with 60% conversion) and E is the limiting reactant for the second reaction (with 80% conversion).

If the molar flowrate of each species coming into the reactor

is known, compute the molar flowrate of each species going

out of the reactor.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \end{matrix}

It is given that A is the limiting reactant for the first reaction (with 60% conversion) and E is the limiting reactant for the second reaction (with 80% conversion).

If the molar flowrate of each species coming into the reactor

is known, compute the molar flowrate of each species going

out of the reactor.

\underline{Step 1}: Normalize all reactions w.r.t. limiting reactants.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ E + \frac{7}{2}B & ⟶ & 2C + 3D & η_{2} = 0.8 \end{matrix}

\underline{Step 2}: Generate stoichiomentric table using the convention: Reactants have negative sign, inerts are zero and products have positive sign.

r A B E C D
1 -1 -2 0 1 2
2 0 -7/2 -1 2 3

\underline{Step 1}: Normalize all reactions w.r.t. limiting reactants.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ E + \frac{7}{2}B & ⟶ & 2C + 3D & η_{2} = 0.8 \end{matrix}

\underline{Step 2}: Generate stoichiomentric table using the convention: Reactants have negative sign, inerts are zero and products have positive sign.

r A B E C D
1 -1 -2 0 1 2
2 0 -7/2 -1 2 3

\underline{Step 1}: Normalize all reactions w.r.t. limiting reactants.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ E + \frac{7}{2}B & ⟶ & 2C + 3D & η_{2} = 0.8 \end{matrix}

\underline{Step 2}: Generate stoichiomentric table using the convention: Reactants have negative sign, inerts are zero and products have positive sign.

r A B E C D
1 -1 -2 0 1 2
2 0 -7/2 -1 2 3

\underline{Step 1}: Normalize all reactions w.r.t. limiting reactants.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ E + \frac{7}{2}B & ⟶ & 2C + 3D & η_{2} = 0.8 \end{matrix}

\underline{Step 2}: Generate stoichiomentric table using the convention: Reactants have negative sign, inerts are zero and products have positive sign.

r A B E C D
1 -1 -2 0 1 2
2 0 -7/2 -1 2 3

\underline{Step 1}: Normalize all reactions w.r.t. limiting reactants.

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ E + \frac{7}{2}B & ⟶ & 2C + 3D & η_{2} = 0.8 \end{matrix}

\underline{Step 2}: Generate stoichiomentric table using the convention: Reactants have negative sign, inerts are zero and products have positive sign.

r A B E C D
1 -1 -2 0 1 2
2 0 -7/2 -1 2 3

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Stoichiometric Reactor Calculations

\underline{Step 3}: Write down the mass balance for the limiting reactants.

\begin{aligned}μ_{R}^{A} & = & μ_{in}^{A} − 0.6μ_{in}^{A} & = 0.4μ_{in}^{A} \\ μ_{R}^{E} & = & μ_{in}^{E} − 0.8μ_{in}^{E} & = 0.2μ_{in}^{E} \end{aligned}

\underline{Step 4}: Write down the mass balances for the remaining components based on stoichiometry.

\begin{aligned}μ_{R}^{B} & = & μ_{in}^{B} − 2 (0.6μ_{in}^{A}) − \frac{7}{2} (0.8μ_{in}^{E}) \\ μ_{R}^{C} & = & μ_{in}^{C} + 0.6μ_{in}^{A} + 2 (0.8μ_{in}^{E}) \\ μ_{R}^{D} & = & μ_{in}^{D} + 2 (0.6μ_{in}^{A}) + 3 (0.8μ_{in}^{E}) \end{aligned}

Note that in Steps 3 and 4, all equations are linear.

Mixer, Splitter, and Reactor – p.10/11

Series reactions

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}

\begin{matrix}A + 2B & ⟶ & C + 2D & η_{1} = 0.6 \\ 2E + 7B & ⟶ & 4C + 6D & η_{2} = 0.8 \\ D & ⟶ & F & η_{3} = 0.7 \end{matrix}

Balances for first reactor: Same as before Balances for second reactor:

\begin{aligned}μ_{R2}^{D} & = & μ_{R}^{D} − 0.7μ_{R}^{D} & = 0.3μ_{R}^{D} \\ μ_{R2}^{F} & = & μ_{R}^{F} + 0.7μ_{R}^{D} \end{aligned}