Design of Flash Unit

Design of Flash Unit – p.1/18

Any impatient student who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.

Flash Unit

Eric Temple Bell A flash is a single equilibrium-state distillation.

The feed is partially vaporized to give a vapor richer in the more volatile components than the remaining liquid.

The vapor and liquid leaving the unit are in equilibrium.

Unless the relative volatility is large, the degree of separation achievable in a two components in a single unit is poor.

Flashing is usually an auxiliary operation used to prepare the stream for further processing (vapor recovery system, liquid recovery system).

A flash is a single equilibrium-state distillation.

The feed is partially vaporized to give a vapor richer in the more volatile components than the remaining liquid.

The vapor and liquid leaving the unit are in equilibrium.

Unless the relative volatility is large, the degree of separation achievable in a two components in a single unit is poor.

Flashing is usually an auxiliary operation used to prepare the stream for further processing (vapor recovery system, liquid recovery system).

A flash is a single equilibrium-state distillation.

The feed is partially vaporized to give a vapor richer in the more volatile components than the remaining liquid.

The vapor and liquid leaving the unit are in equilibrium.

Unless the relative volatility is large, the degree of separation achievable in a two components in a single unit is poor.

Flashing is usually an auxiliary operation used to prepare the stream for further processing (vapor recovery system, liquid recovery system).

A flash is a single equilibrium-state distillation.

The feed is partially vaporized to give a vapor richer in the more volatile components than the remaining liquid.

The vapor and liquid leaving the unit are in equilibrium.

Unless the relative volatility is large, the degree of separation achievable in a two components in a single unit is poor.

Flashing is usually an auxiliary operation used to prepare the stream for further processing (vapor recovery system, liquid recovery system).

A flash is a single equilibrium-state distillation.

The feed is partially vaporized to give a vapor richer in the more volatile components than the remaining liquid.

The vapor and liquid leaving the unit are in equilibrium.

Unless the relative volatility is large, the degree of separation achievable in a two components in a single unit is poor.

Flashing is usually an auxiliary operation used to prepare the stream for further processing (vapor recovery system, liquid recovery system).

Flash Unit

Consider a Flash Unit with C components.

Variables: F, V, L, z_{i}, y_{i}, x_{i},

T_{F} , T_{V} , T_{L}, P_{F} , P_{V} , P_{L}, Q

Total:  3C + 10

Typically, the feed is specified (F, z_{i}, T_{F} , P_{F}). Thus, C + 3 variables are known.

Variables: F, V, L, z_{i}, y_{i}, x_{i},

T_{F} , T_{V} , T_{L}, P_{F} , P_{V} , P_{L}, Q

Total:  3C + 10

Typically, the feed is specified (F, z_{i}, T_{F} , P_{F}). Thus, C + 3 variables are known.

Variables: F, V, L, z_{i}, y_{i}, x_{i},

T_{F} , T_{V} , T_{L}, P_{F} , P_{V} , P_{L}, Q

Total:  3C + 10

Typically, the feed is specified (F, z_{i}, T_{F} , P_{F}). Thus, C + 3 variables are known.

Modeling Multicomponent Flash Unit

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Equation  Type  Number
P_{V} = P_{L}  mechanical equil.  1
T_{V} = T_{L}  thermal equil.  1
y_{i} = K_{i}x_{i}  phase equil.  C
F z_{i} = V y_{i} + Lx_{i}  mass balance  C
h_{F} F + Q = h_{V} V + h_{L}L energy balance  1
∑_{i}y_{i} − ∑_{i}x_{i} = 0  summation  1

Total = 2C+5

K_{i} is a function of T_{V} , P_{V} , y, x h_{F} is a function of T_{F} , P_{F} , z and h_{L} is a function of T_{L}, P_{L}, x

\begin{aligned}Degrees of freedom & = & \underbrace{(3C + 10)}_{(V ariables)} − \underbrace{(C + 3)}_{(F eed Specs.)} − \underbrace{(2C + 5)}_{(Equations)} \\ & = & 2 \end{aligned}

Designing Flash Unit

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Since there are two degrees of freedom, two of the variables need to be specified. The remaining variables can be computed from the mathematical modeled for the flash unit. The most common set of specifications are as follows:

T_{V} , P_{V}  Isothermal flash
V/F = 0, P_{L} Bubble point temperature
V/F = 1, P_{V} Dew point temperature
T_{L}, V/F = 0 Bubble point pressure
T_{V} , V/F = 0 Dew point pressure
Q = 0, P_{V}  Adiabatic flash
Q, P_{V}  Nonadiabatic flash
V/F, P_{V}  Percent vaporization flash

Solving Flash Unit Equations

In principle, if two of the variables are specified, one can solve for the remaining 2C + 5 variables by solving simultaneously the 2C + 5 equations that were shown previously.

However, this computation is not straightforward because T and P appear implicitly in the phase equilibrium equations:

y_{i} = K_{i}x_{i}

and the equation:

F z_{i} = V y_{i} + Lx_{i}

is nonlinear.

In principle, if two of the variables are specified, one can solve for the remaining 2C + 5 variables by solving simultaneously the 2C + 5 equations that were shown previously.

However, this computation is not straightforward because T and P appear implicitly in the phase equilibrium equations:

y_{i} = K_{i}x_{i}

and the equation:

F z_{i} = V y_{i} + Lx_{i}

is nonlinear.

In principle, if two of the variables are specified, one can solve for the remaining 2C + 5 variables by solving simultaneously the 2C + 5 equations that were shown previously.

However, this computation is not straightforward because T and P appear implicitly in the phase equilibrium equations:

y_{i} = K_{i}x_{i}

and the equation:

F z_{i} = V y_{i} + Lx_{i}

is nonlinear.

In principle, if two of the variables are specified, one can solve for the remaining 2C + 5 variables by solving simultaneously the 2C + 5 equations that were shown previously.

However, this computation is not straightforward because T and P appear implicitly in the phase equilibrium equations:

y_{i} = K_{i}x_{i}

and the equation:

F z_{i} = V y_{i} + Lx_{i}

is nonlinear.

Short-cut Method

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Assume that the vapor is an ideal gas and the solution is an ideal solution. Raoult’s law can be used.

Redefine equations in terms of split fractions and relative volatility with respect to key component. Relative volatility is not very sensitive to temperature and pressure.

Analyze relationship between pressure, temperature, and composition. These relationships are nonlinear.

Solve model equations sequentially.

Consider a mixture with n components.

Assume vapor is ideal gas and liquid is ideal solution.

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

y_{k} = \frac{P_{k}^{0}x_{k}}{P} k = 1, 2, ..., n

Define split fractions

\begin{matrix}ξ_{k} = \frac{v_{k}}{f_{k}} k = 1, 2, ..., n \\ 1 − ξ_{k} = 1 − \frac{v_{k}}{f_{k}} = \frac{l_{k}}{f_{k}} \end{matrix}

Define a key component, n

The key component is usually the most abundant in the mixture. If all components are nearly equal in moles, choose the one with intermediate volatility.

Design of Flash Unit – p.9/18

Define relative volatility w.r.t. key component.

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} k = 1, 2, ..., n − 1

Recall that

y_{k} = K_{k}x_{k} = \frac{P_{k}^{0}}{P_{n}^{0}}

This implies that

K_{k} = \frac{P_{k}^{0}}{P}

Thus:

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} = \frac{K_{k}}{K_{n}} k = 1, 2, ..., n − 1

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} k = 1, 2, ..., n − 1

Recall that

y_{k} = K_{k}x_{k} = \frac{P_{k}^{0}}{P_{n}^{0}}

This implies that

K_{k} = \frac{P_{k}^{0}}{P}

Thus:

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} = \frac{K_{k}}{K_{n}} k = 1, 2, ..., n − 1

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} k = 1, 2, ..., n − 1

Recall that

y_{k} = K_{k}x_{k} = \frac{P_{k}^{0}}{P_{n}^{0}}

This implies that

K_{k} = \frac{P_{k}^{0}}{P}

Thus:

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} = \frac{K_{k}}{K_{n}} k = 1, 2, ..., n − 1

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} k = 1, 2, ..., n − 1

Recall that

y_{k} = K_{k}x_{k} = \frac{P_{k}^{0}}{P_{n}^{0}}

This implies that

K_{k} = \frac{P_{k}^{0}}{P}

Thus:

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} = \frac{K_{k}}{K_{n}} k = 1, 2, ..., n − 1

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} k = 1, 2, ..., n − 1

Recall that

y_{k} = K_{k}x_{k} = \frac{P_{k}^{0}}{P_{n}^{0}}

This implies that

K_{k} = \frac{P_{k}^{0}}{P}

Thus:

α_{k/n} = \frac{P_{k}^{0}}{P_{n}^{0}} = \frac{K_{k}}{K_{n}} k = 1, 2, ..., n − 1

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

Rederive flash equations

K_{k} = \frac{y_{k}}{x_{k}} = \frac{v_{k}/V}{l_{k}/L} = \frac{ξ_{k}f_{k}/V}{(1 − ξ_{k})f_{k}/L} = \frac{ξ_{k}L}{(1 − ξ_{k})V}

Similarly:

K_{n} = \frac{ξ_{n}L}{(1 − ξ_{n})V}

Thus:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{ξ_{k}L/(1 − ξ_{k})V}{ξ_{n}L/(1 − ξ_{n})V} = \frac{ξ_{k}(1 − ξ_{n})}{ξ_{n}(1 − ξ_{k})}

Rearranging: ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Design of Flash Unit – p.11/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

P, T and composition at Equilibrium

Suppose there is a saturated liquid stream. The objective is to find a relation between pressure P and temperature T. We will use the bubble point equation for this calculation. At the bubble point, we have:

∑_{i=1}^{n} y_{i} = ∑_{i=1}^{n} K_{i}x_{i} = 1

Dividing the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = \frac{1}{K_{n}}

Note that the ratio K_{i}/K_{n} is the relative volatility α_{i}. Thus, we can define an average relative volatility as follows:

∑_{i=1}^{n} \frac{K_{i}}{K_{n}} x_{i} = ∑_{i=1}^{n} α_{i}x_{i} ≡ ᾱ

Design of Flash Unit – p.12/18

Recall that:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{P_{k}^{0}}{P_{n}^{0}} K_{k} = \frac{P_{k}^{0}}{P}

This implies:

\frac{P_{k}^{0}}{P} = K_{k} = α_{k/n}K_{n}

Recall from the previous slide:

\frac{1}{K_{n}} = ᾱ

Substituting, K_{n} in terms of ᾱ, we have:

\frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

which is a simplified bubble point equation.

Design of Flash Unit – p.13/18

Recall that:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{P_{k}^{0}}{P_{n}^{0}} K_{k} = \frac{P_{k}^{0}}{P}

This implies:

\frac{P_{k}^{0}}{P} = K_{k} = α_{k/n}K_{n}

Recall from the previous slide:

\frac{1}{K_{n}} = ᾱ

Substituting, K_{n} in terms of ᾱ, we have:

\frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

which is a simplified bubble point equation.

Design of Flash Unit – p.13/18

Recall that:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{P_{k}^{0}}{P_{n}^{0}} K_{k} = \frac{P_{k}^{0}}{P}

This implies:

\frac{P_{k}^{0}}{P} = K_{k} = α_{k/n}K_{n}

Recall from the previous slide:

\frac{1}{K_{n}} = ᾱ

Substituting, K_{n} in terms of ᾱ, we have:

\frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

which is a simplified bubble point equation.

Design of Flash Unit – p.13/18

Recall that:

α_{k/n} = \frac{K_{k}}{K_{n}} = \frac{P_{k}^{0}}{P_{n}^{0}} K_{k} = \frac{P_{k}^{0}}{P}

This implies:

\frac{P_{k}^{0}}{P} = K_{k} = α_{k/n}K_{n}

Recall from the previous slide:

\frac{1}{K_{n}} = ᾱ

Substituting, K_{n} in terms of ᾱ, we have:

\frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

which is a simplified bubble point equation.

Design of Flash Unit – p.13/18

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

P, T and composition at Equilibrium

Suppose there is a saturated vapor stream. The objective is to find a relation between pressure P and temperature T. We will use the dew point equation for this calculation. At the dew point, we have:

∑_{i=1}^{n} x_{i} = ∑_{i=1}^{n} \frac{y_{i}}{K_{i}} = 1

Multiplying the equation by K_{n}, we have

∑_{i=1}^{n} \frac{K_{n}}{K_{i}} y_{i} = K_{n}

Recall that K_{n} = \frac{P_{n}^{0}}{P} and \frac{K_{i}}{K_{n}} = α_{i/n} Thus, we have:

∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

T or P Specified at Bubble Point

At the bubble point, all the feed comes out as liquid.

ξ_{k} = 0 ; l_{k} = f_{k} ; x_{k} = z_{k}

Bubble Point Equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ} Choose k to be the most abundant component in the liquid phase. The bubble point equation simplifies to \frac{P_{n}^{0}}{P} = \frac{1}{ᾱ}. If P is fixed, calculate T from

P_{n}^{0}(T) = \frac{P}{ᾱ}

If T is fixed, calculate P from P = ᾱP_{n}^{0}(T)

Design of Flash Unit – p.15/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

Relation between ξ_{n} and ϕ

The split fraction of the key component ξ_{n} = \frac{v_{n}}{f_{n}} and the vapor fraction ϕ = \frac{V}{F} are related as follows:

y_{n} = K_{n}x_{n}

⇒ \frac{v_{n}}{V} = K_{n} \frac{l_{n}}{L}

⇒ \frac{v_{n}}{l_{n}} = K_{n} \frac{V}{L}

⇒ \frac{l_{n}}{v_{n}} = \frac{L}{K_{n}V}

Since l_{n} = f_{n} − v_{n} andL = F − V, we have :

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

Design of Flash Unit – p.16/18

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

\frac{f_{n} − v_{n}}{v_{n}} = \frac{F − V}{K_{n}V}

⇒ \frac{f_{n}}{v_{n}} − 1 = \frac{1}{K_{n}} \frac{F}{V} − \frac{1}{K_{n}}

Since ξ_{n} ≡ \frac{v_{n}}{f_{n}} and ϕ ≡ \frac{V}{F} :

\frac{1}{ξ_{n}} − 1 = \frac{1}{K_{n}ϕ} − \frac{1}{K_{n}}

Rearranging :

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

Recap

We derived the following equations: Split fractions:

ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Simplified bubble-point equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

Simplified dew-point equation: ∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

Vapor Fraction and Split Fraction:

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

Recap

We derived the following equations: Split fractions:

ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Simplified bubble-point equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

Simplified dew-point equation: ∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

Vapor Fraction and Split Fraction:

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

Recap

We derived the following equations: Split fractions:

ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Simplified bubble-point equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

Simplified dew-point equation: ∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

Vapor Fraction and Split Fraction:

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

Recap

We derived the following equations: Split fractions:

ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Simplified bubble-point equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

Simplified dew-point equation: ∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

Vapor Fraction and Split Fraction:

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}

Recap

We derived the following equations: Split fractions:

ξ_{k} = \frac{α_{k/n}ξ_{n}}{1 + (α_{k/n} − 1)ξ_{n}}

Simplified bubble-point equation: \frac{P_{k}^{0}}{P} = \frac{α_{k/n}}{ᾱ}

Simplified dew-point equation: ∑_{i=1}^{n} \frac{y_{i}}{α_{i/n}} = \frac{P_{n}^{0}}{P}

Vapor Fraction and Split Fraction:

ξ_{n} = \frac{1}{\frac{1}{K_{n}ϕ} − \frac{1}{K_{n}} + 1}