Performance Measurement and Analysis

Distillation is a complex and interacting process in which the column performance is dictated not only by column design, but also by process operation variables such as feed, reflux ratio, boil-up ratio, etc. In general, the performance of a distillation column can be assessed through performance metrics such as material and energy balances, efficiency performance, and hydraulic performance. All these performance metrics are interrelated through the process operation variables (e.g., reboiler duty and energy balance are related to vapour flow operation steam flow rate.). Knowledge of distillation performance is essential when designing a distillation column. For an existing column, performance measurement is an important tool for identifying capacity bottlenecks; troubleshooting performance problems; developing design correlations; determining the operating range and optimum operating conditions; and calibrating/validating computer simulations. Performance measurement can be achieved by:

1. experimental measurement of process streams such as temperature, concentration, and flow rates under various operation conditions.
2. experimental measurement of process variables such as temperature, concentration, and clear liquid height and froth height on individual trays under various operation conditions.
3. performance prediction through simulation. This predicted performance results are important for scaling up, optimizing, debottlenecking, and design studies.

Distillation is a process involving material exchange through different process streams such as feed, distillate, bottom product. Distillation is also an energy intensive process that involves energy supplied to the system through reboiler and removed through condenser. One of the important conditions for distillation operation and performance measurement is the conservations of materials and energy. The overall mass balance and component mass balance are:

$$ F=B+D $$

$$ Fx_F=Bx_B+Dx_D $$

where $F$, $B$, and $D$ are measured mole flow rate of feed, bottom product, and distillate, and $x_F$, $x_B$ and $x_D$ are mole fraction of more volatile component in feed, bottom product, and distillate.

Process side energy balance consists of heat required to boil up liquid mixture in the reboiler and heat required to condensate vapour coming into the condenser. Take ethanol-water system as an example, the process side reboiler duty, $Q_r$, is

$$Q_r=V(x_e\lambda_e+x_w\lambda_w)$$

where

$V$: Molar flow rate of vapour.

$x_e$, $x_w$: Mole fraction of ethanol and water in the reboiler, respectively.

$\lambda_e$, $\lambda_w$: Molar heat of vapourization for ethanol and water, respectively.

Similarly, the process side condenser Duty, $Q_c$, is

$$Q_c=V(x_e\lambda_e+x_w\lambda_w)+V(x_e\int_{T_v}^{T_c}C_{p,e}dT+x_w\int_{T_v}^{T_c}C_{p,w}dT)$$

where

$C_{p,e}$, $C_{p,w}$: Molar heat capacity of ethanol and water, respectively.

$T_v$, $T_c$: Vapour and condensate temperatures, respectively.

When a column operation reaches steady state, all the mass balances and process side energy balances above need to be satisfied within the measurement errors. This is not only necessary for the determination of the operation steady state but also for the validation of the experimental data for performance measurement.

Distillation efficiency performance is based on the separation efficiency of the distillation column. Overall column efficiency, $E_o$, is defined as the number of equilibrium stages, $N_{equil}$, required for a specified separation over the actual number of stages, $N_{actual}$.

$$E_o=\dfrac{N_{equil}}{N_{actual}} $$

The number of equilibrium stages, $N_{equil}$, can be measured through the McCabe-Thiele method summarized on the Distillation Column component page or by running the Python Simulation.

Distillation efficiency can also be evaluated based on point efficiency and Murphree tray efficiency. Point efficiency, $ E_{OG} $, is defined based on the concentration difference across any point on a tray,

$$E_{OG}=\left(\dfrac{y_n-y_{n+1}}{y_n^*-y_{n+1}}\right)_{point}$$

where

$y_n$: Composition of vapour leaving a specific point on tray $n$.

$y_{n+1}$: Composition of vapour coming to the specific point from tray $n+1$.

$y_n^*$: Equilibrium composition of vapour with liquid leaving the specific point on tray $n$.

Similarly, Murphree vapour tray efficiency, $E_{MV}$, is defined based on the concentration difference across a tray,

$$E_{MV}=\left(\dfrac{y_n-y_{n+1}}{y_n^*-y_{n+1}}\right)_{tray}$$

where $y_n$ is vapour composition leaving tray $n$, $y_{n+1}$ is vapour composition leaving tray $n+1$ and $y_n^*$ is the composition of vapour in equilibrium with liquid leaving tray $n$.

Point efficiency and Murphree efficiency for liquid side can also be evaluated in the same way as above. The distillation efficiency is related to the mass transfer and mass transfer in vapour phase is normally the rate-limiting step, that is part of the reason why the vapour efficiency often needs to be measured or evaluated. Based on the two resistance theories, the molar mass transfer rate at any point on a distillation tray is,

$$N=k_Ga_i(y_i-y)=k_La_i(x-x_i)=K_{OG}a_i(y^*-y)$$

where $k_Ga_i$, $k_La_i$ are volumetric mass transfer coefficient of vapour phase and liquid phase, respectively, and $K_{OG}a_i$ is the overall volumetric mass transfer coefficient of vapour phase.

As indicated above, the mass transfer at the specific point on a distillation tray is through vapour flowing across the froth of the tray, so the number of mass transfer units is related to the mass transfer coefficient by (Manivannan, et. al.),

$$N_G=k_Ga_it_G=\dfrac{k_Ga_ih_F}{u_G}$$

$$N_L=k_La_it_L=\dfrac{k_La_ih_F}{u_L}$$

where

$h_F$: Froth height on tray.

$u_G$: Vapor velocity based on the bubbling area on tray.

$u_L$: Liquid velocity based on the bubbling area on tray.

$N_G$: Number of mass transfer units of vapour phase.

$N_L$: Number of mass transfer units of liquid phase.

With the linear operating lines for both rectifying and stripping sections, as illustrated in Distillation Column component page, the number of overall mass transfer units for vapour phase, $N_{OG}$, becomes,

$$\dfrac{1}{N_{OG}}=\dfrac{1}{N_G}+\dfrac{\lambda}{N_L}$$

where $\lambda=\dfrac{m}{L/V}$, and $m$ is the slope of equilibrium line, $ L/V $ is the slope of the operating line. The number of overall mass transfer units is related to the overall vapour point efficiency by (Duss and Taylor, Manivannan, et. al.),

$$E_{OG}=1-exp(-N_{OG})$$

There are at least two cases where point efficiency can be easily correlated with Murphree tray efficiency, $E_{MV}$. If the liquid on the tray is well mixed, then the Murphree tray efficiency and point efficiency are equal, which is the case for most of the experimental measurement of tray efficiency. The other case is that the liquid flow on the tray is plug flow and the vapour is completely mixed between the trays (Manivannan, et. al.),

$$E_{MV}=\dfrac{exp(\lambda N_{OG})-1}{\lambda}$$

The Murphree vapour efficiency is more relevant in distillation than Murphree liquid tray efficiency as it is related to the overall column efficiency by,

$$E_o=\dfrac{ln[E_{MV}(\lambda-1)+1]}{ln\lambda}$$

There are various empirical correlations such as O’Conners correlation (Duss and Taylor) that can be used to estimate point efficiency. Fundamentally, the point efficiency as clearly delineated above, is closely related to tray design and hydraulic characteristic such as clear liquid height and froth height since the depth of the liquid and froth determine the contact time for mass transfer between vapour and liquid across the tray (Bennett et. al.). It is the mass transfer that connects the point efficiency with Murphree vapour tray efficiency and overall column efficacy, both of which can be more readily measured experimentally and more useful for distillation design. From the McCabe-Thiele method, it is clear that the overall column efficiency decreases when increasing reflux ratio, in other words, the overall column efficiency is bounded between two extreme operation reflux ratios: minimum reflux ratio and total reflux ratio for any distillation systems. Similar analysis can be applied to the effects of other operation variables such as boil-up rate and feed condition. Understanding these effects of distillation operations on column efficiency performance is critical for purported experimental design as well as distillation column design.

Hydraulic performance generally refers to column pressure drop, clear liquid height, froth height, and flooding, all of these operation characteristics can be directly measured through a well-designed pilot scale column such as the VR distillation column. As indicated on the Distillation Column component page, the tray type and design of a distillation column can affect the hydraulic performance along with the operation conditions such as boil-up rate and reflux ratio. Since the clear liquid height and froth height are closely related to the mass transfer efficiency on the tray, the evaluation and validation of hydraulic correlations is important for the accuracy of a distillation design.

There are multiple hydraulic correlations for different tray types, and the correlations summarized on the Distillation Column component page are based on sieve tray but can be used for other tray types as well. The correlations allow for the estimations of clear liquid height and froth height, which can be easily validated using the measured values from the pilot scale experiment. Ultimately, the validated correlation can be used to predict the distillation efficiency for more accurate distillation simulation and design.