Coursework 1: Computing Distillation

5CCE2HMT Heat and Mass Transfer

1    Overview—Ethanol Production using Distillation

Distillation is a process that separates substances from liquid mixtures using boiling and condensation heat transfer. Early evidence of distillation was found on Akkadian tablets dated circa 1200 BCE. Distillation was used in many parts of the world by early centuries of the Common Era [1]. For instance, the Chinese were distilling a beverage from rice beer by 800 BCE, and arrack was distilled in the East Indies. The Arabs produced a distilled beverage from wine, and the Romans started distilling spirits before 100 CE. Production of distilled spirits was reported in Britain before the Roman conquest (43–84 BCE). As of 2022, the UK accommodates 820 spirit distilleries (Figure 1), and the number continues to grow. Besides beverages, distillation is a common process widely found in the chemical industry.

Figure 1: Distillery.

Ethanol (common alcohol) is produced by fermenting sugars dissolved in water with yeast. Under appropriate conditions, yeast converts the sugars into ethanol and carbon dioxide and dies when the ethanol concentration reaches about 15% by weight (wt%). After filtration, a water-ethanol mixture is obtained. Distillation is then used to produce concentrated ethanol. In this process, the water-ethanol mixture is heated and boiled. As ethanol has a lower boiling point than water, ethanol evaporates more readily. The ethanol-rich vapour is then collected and condensed in a separate container, resulting in a concentrated ethanol solution (Figure 2 (a)). As shown in the phase diagram (Figure 2 (b)), a 15wt% mixture of ethanol and water undergoes boiling at approximately 88 °C, generating a 60wt% mixture of vapour. The liquified 60wt% mixture boils at ca. 81 °C, producing a more ethanol-rich vapour with a concentration of 80wt%. The vapour is condensed again, and the mixture then boils at ca. 79 °C, yielding a mixture with a concentration reaching 96.5wt%. At this point, the aqueous solution of 96.5wt% ethanol is an azeotrope and cannot be further purified by distillation.

Figure 2: (a) Schematic of distillation process of ethanol-water mixtures.  (b) Phase diagram repre- senting bubble point and dew point of ethanol-water mixtures [2].

In this coursework, you are asked to compute the distillation rate using a simplified heat transfer model.  To complete the task, you will need to be able to appropriately use heat transfer correlations and perform iterative calculations to reach a solution.

2 Problem Description

A mixture of water and ethanol is boiling on a horizontal 304 stainless-steel plate (thickness:  1 mm, thermal conductivity:  16.7 W/(m · K)) at 0.1 MPa. To improve the energy efficiency of the entire plant, saturated water steam at 150 °C exhausted from a separate process is used to heat the plate. The water steam is fed to the plate and condenses on its underside. Complete the following tasks:

1.  Obtain the following quantities for various ethanol concentrations i.e.,  15wt%, 60wt%, 80wt% and 95.6wt%:

(a)  Surface temperatures of each side  (hot and cold sides) of the plate in °C. (b)  Heat transfer coefficients of each side of the plate in kW/(m2·K).

(c) Heat flux in kW/m2 .

(d)  Hourly rate of steam generation of the mixture per unit area in kg/(m2·hr). (e)  Hourly rate of condensate of water per unit area in kg/(m2·hr)

2.  Repeat the above calculation for water steam temperatures of 180 。C and 200 °C + last 2 digits of your K-number e.g., if K21012345, then 200 + 45 = 245 °C.

Assume that the process is steady state, and the concentration of the mixture is unchanged during each distillation stage.  Concentration gradients within the boiling liquid are negligible.  Use Tables 1 and 2 for the thermophysical properties necessary for the analysis.

3 Report and Mark Scheme

Your report should be written on A4 paper with margins of at least 2 cm and a font size of 12pt in a suitable font.  It should be no longer than 8  pages in length, excluding the programme script.  Your report should contain at least the following information:

(A) detailed calculation procedures [20 marks];

(B) your programming script used for calculation [20 marks];

(C) tables to summarise the calculated values of (a)–(e) (see the previous section).  The table should look like [50 marks]:

The final [10 marks] are for the presentation of your report.

4 Correlations and Properties

4.1 Heat transfer correlation for condensation

Heat transfer coefficient h for condensation at a subcooling of ∆Tsub on a wall with a length of L, inclined at θ is given by Gerstmann and Griffith [3] as

where Nu and Ra are dimensionless Nusselt and Rayleigh numbers, respectively, and are given as

where g is the acceleration due to gravity, k is the thermal conductivity, ρ is the density, µ is the viscosity, σ is the surface tension of the fluid, and hf g is the latent heat of vaporisation. The subscripts l and v represent liquid and vapour phases, respectively. For the present problem, L = 1 m and θ = 0°as we are interested in the distillation performance per unit area i.e., 1 m × 1 m of a horizontal surface.

4.2 Heat transfer correlation for boiling

To calculate h for nucleate boiling at a system pressure of p, use Kutateladze’s correlation given below [4].

where is the Laplace constant, P r is the Prandtl number, q ′′ is the heat flux, and ν = µ/ρ is the kinematic viscosity.

Keep in mind that we are making big assumptions to simplify the analysis here. One of them is the use of Equation 3 for boiling of mixtures although it was originally derived for pure liquids. Mixtures make boiling phenomena even more complex! There are additional effects due to the presence of secondary component, which have not yet been understood completely. Many experimental results of boiling of binary mixtures show lower heat transfer coefficients than those in their corresponding pure fluids. Therefore, this simple analysis you are doing in the coursework should be considered a rough estimation for the design of distillation process. In practice, you would need to collect actual data from separate experiments to improve accuracy of your analysis. Nevertheless, boiling of mixtures found in common distillation process is still an active research topic. If you are interested in this topic, please refer to a review article by Xu et al. [5].

4.3 Fluid properties

Thermophysical properties of saturated water and ethanol-water mixture are summarised in Tables 1 and 2. If you cannot find exact values for a specific temperature of interest (e.g., 245 °C if your K-number ends with 45), estimate those by linear interpolation between the two closest values (e.g., those at 240 °C and 250 °C).

Table 1: Thermophysical properties of saturated water calculated using CoolProp [6].

Table 2: Thermophysical properties of saturated ethanol-water mixture at 0.1 MPa. The molar fraction of ethanol xethanol, bubble point temperature Tb, densities ρl and ρv, latent heat of vaporisation hlv, thermal conductivity kl , viscosity µl and Prandtl number P rl were calculated using CoolProp [6]. The surface tension σ was calculated using Phan’s model [7].