2. Distillation Column

2.1. Distillation Column and Column Internals

A distillation column or tower is a vertical cylindrical shell that houses layers of column internals. (Click on the Piping and Instrumentation Diagram (P & ID) on the right in order to see the location of this component within the distillation column.) Depending on the design and mechanical nature of column internals, distillation columns are generally classified into two types: tray column with mechanical trays arranged in cascade, and packed column with randomly dumped or structured packings as column internals, as shown in Figures 2.1 and 2.2. Both tray columns and packed columns are widely used in various industries to facilitate gas-liquid contacts and separation of liquid and gas mixtures. From operation and design viewpoint, tray column is a stage-wise process in which mass transfer or separation only takes place on individual trays, whereas packed column is a differential mass transfer process in which mass transfer occurs continuously from the bottom to top of the column between liquid and vapour streams flowing countercurrently.

Figure 2.1. Schematic representation of a packed distillation column with random packings. | Description

Site Author(s) and University of Waterloo

Figure 2.2. Schematic representation of a tray distillation column with multiple trays in cascade and cross-flow pattern. | Description

Site Author(s) and University of Waterloo

Figure 2.3. Bubble cap tray: design, vapour and liquid flow path, and performance. | Description

Site Author(s) and University of Waterloo

Table 2.1. Comparison of performance characteristics of common tray types relative to random and structured packings.

	Bubble cap tray	Sieve tray	Valve tray	Random/structured packings
Capacity	3	3	2	3/5
Efficiency	3	3	3	4/5
Pressure drop	3	3	3	4/5
Turndown ratio	4	3	5	4/4
Operation flexibility	3	3	2	4/4
Corrosion sensitivity	3	2	3	1/1
Experience/know-how	5	5	4	5/5
Cost	5	3	2	3/2

Note: 1=Poor, 2=Fair, 3=Good, 4=Very Good, and 5=Excellent
Note: Turndown ratio is defined as the ratio of maximum and minimum vapour load a tray can handle.

(Gorak & Olujic, 2014), (Coker, 2010), (Green & Southard, 2019)

Apart from different column internals, tray column and packed column have similar layout for external flow arrangement. As shown in Figure 2.1 with a tray column, the feedstock mixture is typically introduced near the middle of distillation column, to a tray known as feed tray. The feed tray divides the column into the enriching or rectifying section with all the trays above the feed tray, and the stripping section with all the trays below the feed tray. Depending on the feed condition, the feed enters the feed tray and splits into a vapour stream and a liquid stream, adding to incoming vapour flow and liquid flow on the tray. The vapour generated in the reboiler flows up into the bottom tray, and eventually exits the top of the column. It is then cooled by the condenser to liquid again, and the overhead liquid is held in a holding vessel known as overhead drum. The overhead liquid is split into two streams, one recycled back to the top of the column as reflux, and the other removed from the column known as the distillate or top product. The reflux stream is necessary not only to reduce the number of trays required for a specified separation, but also be the source of liquid flow required for the enriching section. The liquid removed from the reboiler is known as bottom product. The number of trays required with a distillation column or column height for a specified separation depends on both the thermodynamic vapour-liquid equilibrium of the system and tray hydraulics. Despite many different tray designs available commercially, distillation column generally needs more plates than the number of equilibrium stages, as mass transfer limitations and poor contact efficiency prevent equilibrium being achieved on a plate. As a result, evaluating column performance and hydraulic characteristics is of great significance for both distillation column operation and design.

UWaterloo Chemical Engineering Virtual Learning. (2022, Feb 7). 2 Column With Bubble Cap Trays [Video]. YouTube. https://www.youtube.com/watch?v=tDC5vCNvb0c | Transcript

2.2. Tray Column Performance and Design

The underlying theories for distillation column operation performance and design are mass balance and energy balances around individual trays and the overall column. Performance characteristics such as tray temperature, vapour and liquid compositions, and flow rates can be obtained by solving mass balances, equilibrium relationship, composition summations, and heat balance equations (MESH equations) known as the rigorous method. Alternatively, with some justifiable assumptions such as constant molal overflow (CMO), the operation and design problem can be reduced to simply solving mass balance equations along with vapour-liquid equilibrium. This method is known as the McCabe-Thiele shortcut method.

The CMO assumption in the McCabe-Thiele method implies that the molar flows of vapour and liquid in each section is constant. The assumption can be justified by simply checking the heat of vapourization of all the components. For a binary system, this means that an intuitive graphic method known as the McCabe-Thiele diagram can be used to determine the operation performance or the number of equilibrium stages for a specified separation.

Figure 2.4 shows a schematic representation of liquid and vapour flows and compositions on any tray in the column denoted as Tray n. Because of the CMO assumption, both liquid and vapour flow rates remain constant across the tray. As well, the vapour leaving the tray with composition $ y_n $ is considered to be in equilibrium with liquid leaving the tray with composition $ x_n $.

Figure 2.4. Schematic representation of McCabe-Thiele shortcut method. | Description

Site Author(s) and University of Waterloo

The mass balance for Tray n in the enriching section leads to the following equation known as the enriching operating line equation,

$$ y_{n+1} = \dfrac{L}{V}x_n + \left(1-\dfrac{L}{V}\right)x_D $$

where $ y_{n+1} $ is composition of vapour coming into Tray n from Tray n+1, $ x_n $ is composition of liquid leaving Tray n, and $ x_D $ is the distillate composition. $ L $ and $ V $ are molar flow rate of liquid and vapour, respectively. As indicated above, the source of L is the reflux stream, so the operating line equation can also be written in terms of reflux ratio, $ R $,

$$ y_{n+1} = \dfrac{R}{R+1}x_n + \dfrac{x_D}{R+1} $$

Similarly, the operating line equation for stripping section is

$$ y_{n+1} = \dfrac{\overline{L}}{\overline{V}}x_n + \left(1-\dfrac{\overline{L}}{\overline{V}}\right)x_B $$

where $ x_B $ is the composition of bottom product, and $ \overline{L} $ and $ \overline{V} $ are molar flow rate of liquid and vapour in the stripping section, respectively.

The liquid and vapour flow rates in the enriching and stripping sections are related through feed flow rate and feed quality, $ q $ , which is defined as the fraction of feed into the liquid stream,

$$ \overline{L} = L + qF $$

and

$$ V = \overline{V} + (1-q)F $$

Once the feed condition is specified, the feed quality can be determined through the enthalpy balance on the feed tray as

$$ q = \dfrac{H_V-H_F}{H_V-H_L} = \dfrac{(H_V-H_L)+(H_L-H_F)}{H_V-H_L} = \dfrac{\lambda_F + \int_{T_F}^{T_b}C_{p,F}dT}{\lambda_F} $$

where:

$ \lambda_F $ = Average heat of vapourization of feed

$ T_F $ = Feed temperature

$ T_b $ = Feed boiling point which can be determined from vapour-liquid equilibrium

$ C_{p,F} $ = Average molar heat capacity of feed

Hence, the feed line equation can also be obtained through mass balance of the feed tray as

$$ y = \dfrac{q}{q-1}x-\dfrac{x_F}{q-1} $$

With the operating lines for enriching section, stripping section, and feed in place, a distillation design or the number of equilibrium stages required for a specified separation, $ N_{equil} $, can be determined graphically by stepping down against the equilibrium line as demonstrated for ethanol water system in Figure 2.5. A tray-by-tray calculation based on the above principles is also common with the aid of computers. Once $ N_{equil} $ is determined, the performance of an existing column can be evaluated against the actual number of trays or in terms of overall column efficiency as

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

As well, the above process is often used to troubleshoot operation problems in practical distillation operations. For a distillation column design, if the overall column efficiency, $ E_o $, is known, then the actual number of trays required or column height for a specified separation can also be determined.

Figure 2.5. Schematic representation of McCabe-Thiele shortcut method for ethanol-water separation. | Description

Site Author(s) and University of Waterloo

2.3. Tray Column Hydraulics and Design

As indicated above, the number of equilibrium stages required for a specified separation depends on the vapour-liquid equilibrium of the system as well as operation conditions (vapour and liquid flow rate, reflux ratio, feed flow rate, and among other conditions). The actual number of stages required for the separation further depends on the overall column efficiency or stage efficiency, which in turn depends on operation conditions along with the mechanical design of the column internals. In general, high stage efficiency requires high liquid flow rate on the tray to maintain a deep pool of liquid for long contact time. High vapour velocity is also necessary to generate sufficient bubbling and high interfacial area for vapour-liquid contact, and so high stage efficiency as shown in the performance diagram in Figure 2.6. In contrast, low vapour and liquid flow rates generally lead to low efficiency due to short contact time and weeping in cases such as sieve tray. However, at high vapour velocity, small droplets of liquid can be carried up by vapour to the top tray, causing sufficient entrainment or even flooding, and much reduced stage efficiency. As well, high vapour flow rate and deep liquid level on the tray both result in high pressure drop for the vapour to flow through the tray. The effects of the operation conditions, typically characterized by hydrodynamic terms such as froth height, flooding, and pressure drop, are important features for distillation column design, operation performance, and column efficiency.

Figure 2.6. Variations of distillation column performance and hydraulic characteristics with operation conditions. | Description

Site Author(s) and University of Waterloo

The total pressure drop across a tray in liquid height, $ h_T $, can be generally modelled as (Bennett, Agrawal & Cook, 1983, Bennett, Watson & Wiescinski, 1997)

$$ h_T = h_D + h_L + h_\sigma $$

where:

$ h_D $ = dry pressure drop (m)

$ h_L $ = pressure drop due to liquid on the tray (m)

$ h_{\sigma} $ = pressure due to surface tension (m)

The pressure drop across a dry tray can be modelled by the well-known orifice flow equation

$$ h_D = \dfrac{\rho _V V_h^2}{2g\rho _L C_v^2} $$

where:

$ V_h $ = vapour velocity based on hole area (m/s)

$ \rho_V $ = density of vapour (kg/m³)

$ \rho_L $ = density of liquid (kg/m³)

$ g $ = gravitational (m/s²)

$ C_v $ = orifice coefficient

The orifice coefficient, $ C_v $, is given by (Garcia & Fair, 2002)

$$ {C_v} = 0.74\left(\dfrac{A_h}{A_a}\right) + exp\left[ {0.29\dfrac{l_t}{D_h} - 0.56} \right] $$

where:

$ A_h $ = total hole or perforated area on the tray (m²)

$ A_a $ = total active or bubbling area on the tray (m²)

$ D_h $ = hole diameter (m)

$ l_t $ = thickness of the tray (m)

The pressure drop due to the surface tension of liquid is

$$ h_\sigma = \dfrac{4\sigma }{g\rho_L D_h} $$

where $\sigma$ is surface tension of liquid (N/m) and g is gravitational constant (m/s²).

The pressure drop due to vapour flow through a wetted tray can be expressed in terms of froth height of the liquid-continuous phase and overall froth height as illustrated in Figure 2.3 as (Bennett, Watson & Wiescinski, 1997)

$$ h_L = \varphi _e h_{Fe} = {\varphi_{oe}}{h_F} $$

$$ h_{Fe} = h_w + C \left( \dfrac{Q_L}{\varphi _e l_w} \right)^{2/3} $$

$$ C=0.501+0.439exp(-137.8h_w) $$

$$\varphi_e = exp(-12.55K_s^{0.91})$$

$$K_s = V_a \sqrt {\dfrac{\rho _V}{\rho_L - \rho_V}} $$

where:

$ h_L $ = liquid head or clear liquid height (m)

$ \varphi _e $ = effective froth density

$ h_{Fe} $ = effective froth height (m)

$ \varphi_{oe} $ = overall froth density

$ h_F $ = overall froth height (m)

$ h_w $ = weir height (m)

$ l_w $ = weir length (m)

$ Q_L $ = flow rate of liquid (m³/s)

$ K_s $ = density corrected vapour velocity over the active area (m/s)

$ V_a $ = vapour superficial velocity based on active area (m/s)

Once the effective froth height and clear liquid height are determined, the overall height of the froth on a tray, $h_F$, can be evaluated by (Bennett, Watson & Wiescinski, 1997),

$$ \dfrac{h_F}{h_{Fe}} = 1 + \left[ 1 + 6.9 \left( \dfrac{h_L}{D_h} \right)^{ - 1.85} \right] \dfrac{Fr_V}{2} $$

$$ Fr_V = \dfrac{V_{ej}^2}{gh_{Fe}} $$

$$ V_{ej} = 3K_s \sqrt {\dfrac{\sqrt 3}{(A_h/A_a)\varphi _e}} $$

Where $Fr_V$ is vapour Froude number and $V_{ej}$ is ejection velocity of the droplet from the top of the liquid-continuous region (m/s). Using Equation 9, 13~14, and 18, all the tray hydraulic characteristics including pressure drop, clear liquid height, and froth height can be evaluated for sieve tray. These equations may also be used to estimate the hydraulics for bubble cap tray and valve tray if equivalent tray dimensions are specified. Experimentally, all the hydraulic characteristics can easily be measured using a differential pressure transducer or visual observation.

The hydrodynamics of distillation column such as pressure drop and froth height have direct effects on the column efficiency and performance. As shown in Figure 2.6, high vapour and liquid flow velocities are generally favourable for high efficiency and capacity, but they can also cause excessive entrainment or flooding, depending on tray spacing. As a result, the design of a distillation column size usually relies on the determination of column flooding, or a fraction of flooding velocity is typically used as the basis for designing proper column diameter.

For tray column, the flooding velocity varies with tray spacing, and a generalized relationship between flow parameter, $ F_{LV} $, and capacity factor, $ C_{SB} $, is applicable for all tray types, as shown in Figure 2.7,

$$ F_{LV} = \dfrac{L_m}{V_m}\left(\dfrac{\rho_V}{\rho_L}\right)^{0.5} $$

$$ U_{NF} = C_{SB}\left(\dfrac{\sigma}{20}\right)^{0.2}\sqrt{\dfrac{\rho_L-\rho_V}{\rho_V}} $$

where:

$ F_{LV} $ = flow parameter

$ L_m $ = liquid mass flow rate in the column (kg/s)

$ V_m $ = vapour mass flow rate in the column (kg/s)

$ \rho_V $ = vapour density (kg/m³)

$ \rho_L $ = liquid density (kg/m³)

$ U_{NF} $ = vapour velocity through net area at flooding (m/s)

$ \sigma $ = surface tension of liquid (dyn/cm)

$ C_{SB} $ = flooding capacity factor (m/s)

For distillation column design, the vapour and liquid flow rates, along with the density of vapour and liquid, are known from the design specifications. Thus, the flow parameter can be calculated using Equation 22, and the capacity factor can be determined from Figure 2.7. Alternatively, a numerical correlation for $ C_{SB} $ is also available in terms of $ F_{LV} $ and tray spacing $ T_s $ in mm (Green & Southard, 2019) as below.

$$ C_{SB} = 0.0105 + 8.127\times10^{-4}T_s^{0.775}\text{exp}(-1.463F_{LV}^{0.842}) $$

Figure 2.7. Fair’s flooding correlation for distillation column with cross-flow trays: column capacity factor as a function of flow parameter for different tray spacing values. | Description

Site Author(s) and University of Waterloo

Knowing the capacity factor for the design, the flooding velocity, $ U_{NF} $, can be determined from Equation 22. Typically, the distillation column size design is based on the vapour flow in the column, and a fraction of vapour flooding velocity ranging from 0.65 to 0.9 (Wankat, 1988) is chosen as operation vapour velocity, i.e.,

$$ U_{OP} = f_1U_{NF} $$

With the specified vapour molar flow rates as above, the volumetric flow rate of vapour can be determined by

$$ Q_V = V\bar{M}_v /\rho_V $$

where $ \bar{M}_v $ is the average molar mass of the vapour. The volumetric vapour flow rate will be delivered by the net tray area and operation vapour velocity, hence, the column diameter can be determined by

$$ D_c = \sqrt{\dfrac{4 Q_V}{\pi f_1 f_2 U_{NF}}} $$

where $ f_2 $ is the fraction of the column cross-section area or net area that is available for vapour flow through the tray. The value of $ f_2 $ is typically 0.85~0.95, meaning that $ (1-f_2) $ is the fraction of the column area that is needed for downcomers. The diameter calculation can be done using vapour flow rate in the rectifying section, stripping section, or the average, and one of these values will yield the maximum diameter. The largest calculated diameter would be satisfactory for the design of most separation systems (Wankat, 1988).

It is important to note from Figure 2.7 that the capacity or flooding of a distillation column is highly dependent on the selected tray spacing for the design, higher tray spacing leads to higher vapour operation capacity, and smaller column diameter. The tradeoff of the design is sometimes an excessively tall column which could be undesirable from the viewpoint of both capital investment and operation. It is also clear from Equation 1 that the properties of a separation system such as surface tension and densities can be important factors for the selection of tray spacing. For foaming systems such as some organic systems, a large tray spacing is indeed necessary, but for non-foaming systems such as alcohol solutions, selecting a proper tray spacing for the design can lead to significant savings in both capital and operation costs. Obviously, tests with a pilot-scale distillation column such as the 360 VR column can provide the first-hand information and insights into the adequate tray spacing for the column design of the alcohol water systems.

---

References