An overall material balance was performed on the proposed pressure swing distillation system for the separation of THF from water-THF-EtOH azetropic mixture ( Figure 4 ) using Equation (3) to obtain the streams’ compositions shown in Table 1 .

Input − Output + Generation − Dissipation = Accumulation (3)

where T1 and T2 represent the two distillation columns operated at 1.02 and 7.6 bar, and S represents the stream.

Streams S4 and S5 were obtained by performing an overall material balance for THF, EtOH, H₂O and BuOH.

The following assumptions were made:

An energy balance was carried out in order to determine the energy requirements for the condensers and reboilers of the separating system as shown in Figure 5 (Where V, L and D are the vapour flow rate, liquid flow rate and the Distillate). Prior to the energy balance analysis, a material balance was carried out using a reflux ratio of 3 to obtain the flow rate of the various streams and the utilities shown in Tables 2-4 . The heat duty of the condensers was calculated using Equations (4) and (5), while the heat duty of the reboilers was calculated using Equations (4) and (6). The results obtained are tabulated in Table 5 .

$\text{Duty}\left(\text{kJ}/\text{hr}\right)=\text{Latent heat}\left(\text{kJ}/\text{kmol}\right)\times \text{Flow rate}\left(\text{kmol}/\text{hr}\right)$(4)

$\text{Condenser}\text{Heat}\text{Duty}\left(Q_c\left(\text{kJ}/\text{hr}\right)\right)={\displaystyle \underset{i=1}{\overset{n}{\sum }}{Q}_c{}_i}={\displaystyle \underset{i=1}{\overset{n}{\sum }}{V}_i{h}_v{}_i}$(5)

$\text{Reboiler}\text{Heat}\text{Duty}\left(Q_R\left(\text{kJ}/\text{hr}\right)\right)={\displaystyle \underset{i=1}{\overset{n}{\sum }}{Q}_R{}_i}={\displaystyle \underset{i=1}{\overset{n}{\sum }}\left(D\left(R+1\right)\right)h_v{}_i}$(6)

where h is the enthalpy and R is the reflux ratio (which was set to a value of 3).

$V_n=L_n+D$ (7)

$L_n=RD$(8)

$V_n=D\left(R+1\right)$(9)

$L_b=V_b=V_m=V_n=D\left(R+1\right)$ (10)

The design of the pressure swing distillation system was carried out using Pro/II. Sieve trays, valve trays and packed distillation columns were investigated due to their merits [15] . For the trays columns (i.e. sieve and valve trays), tray’s efficiency, minimum reflux ratio, optimum number of trays, feed location, and optimum pressure for the second column were investigated as described by Towler and Sinnott [1] ; while for the packed columns, in addition to the minimum reflux ratio, and second column optimum pressure investigated, the optimum packing height and equivalent feed tray location were also investigated as described by Towler and Sinnott [1] .

Trays with an internal hole diameter of 0.381 m and a tray spacing of 0.609 m were chosen and used for the design of the sieve and valve tray columns.

The tray efficiency of the sieve and valve trays was calculated from the composition results generated by Pro/II, using the Mupheree tray efficiency equation below:

${\eta }_m=\frac{{y^{\prime }}_n-{y^{\prime }}_{n-1}}{y_n^{*}-{y^{\prime }}_{n-1}}$ (11)

where ${y^{\prime }}_n$ = actual vapour composition leaving plate n;

${y^{\prime }}_{n-1}$ = actual vapour composition entering plate n;

$y_n^{*}$ = Vapour composition in equilibrium with liquid leaving plate n.

The results obtained are tabulated and shown in Table 6 .

The minimum reflux ratio of both distillation columns was investigated columns as the simulation software cannot operate if either column is operated below this threshold. To achieve this, the number of trays in each column was incrementally increased until the reflux ratio stabilized. The results obtained from PRO/II for both columns, utilizing sieve and valve trays respectively, are depicted in Figure 6 and Figure 7 . As illustrated in Figure 6 , with an increase in the number of trays, the reflux ratio steadily decreases until it reaches its minimum value. Beyond this point, further additions of trays have no significant impact on the reflux ratio. This observation aligns with findings in the literature [16] [17] . Additionally, Figure 6 reveals that the minimum reflux ratio for column T1 is 46.50, whereas for column T2, it is 2.20. The higher reflux ratio in column T1 is attributed to the elevated ethanol content in the mixture. Figure 7 highlights that the minimum reflux ratio for column T1, using valve trays, is 50, while for column T2, it remains consistent with that obtained for the sieve trays. Discrepancies in the minimum reflux ratio for column T1 could stem from differences in tray geometry configurations.

For the sieve trays distillation columns, the first distillation column (T1) number of trays was optimized first by changing the number of trays while all other variables were kept constant, including the number of trays of the second column (T2). Each time the number of trays was changed, the software was run and the Net Present Value for a period of twenty years was calculated using the results generated by PRO/II. The capital cost of the heat exchangers, column shells and trays were calculated. After which, the total capital cost, operating cost, and the net present value (NPV) were calculated. The configuration that yielded the lowest NPV value was chosen as the optimum number of trays for the first column. The optimum number of trays for the first column was used to optimise the second tray, whereby only the second column number of trays was varied. The NPV of the second column was also calculated. The results obtained are shown in Figure 8 . The same method was used for valve trays distillation columns and the results obtained are shown in Figure 9 .

Figure 8 shows that the optimum number of sieve trays for column T1 and column T2 are 71 and 55 trays respectively as they incurred the lowest net present. The NPV decreases initially before increasing, as the number of trays increases. This is because initially, at low number of trays, the reflux ratio was high leading to high utilities and therefore high operating cost, which made the operating cost the controlling factor of the total cost. However, as the number of trays increases, the separation also increases which leads to the smaller amount of reflux and heat duties required by the reboilers and condensers. The decrease of NPV with an increasing number of plates continued until the minimum cost was achieved. The further increase in the number of trays will cause an increase in the NPV value due to capital cost, thus making the capital cost the controlling factor. It can be deduced from Figure 9 that the optimum number of valve trays for column T1 and column T2 are 74 and 39 trays respectively, as they yield the lowest net present value (NPV). This is however higher than the NPV obtained for the optimum sieve trays.

Research conducted by Iqbal and Ahmad [8] , Liang et al. [9] , and Wang et al. [10] , highlighted the optimal operating conditions for pressure swing distillation systems. According to the literature, the first column of the system should operate at atmospheric pressure, while the second column’s pressure is ideally maintained within the range of 5 - 10 bar. Consequently, our investigation focused solely on the pressure of the second distillation column, exploring values within the recommended range (5 - 10 bar). For each pressure value investigated, the Net Present Value (NPV) was calculated and plotted, as depicted in Figure 10 and Figure 11 for sieve and valve tray columns respectively. These figures provide insights into the economic implications of varying the pressure within the specified range, aiding in the selection of the most cost-effective operating conditions for the distillation system.

Figure 10 illustrates that the optimal operating pressure for the second distillation column equipped with sieve trays is 7.2 bar, while Figure 11 demonstrates that for the valve tray column, it is 7.4 bar. Both figures indicate that column T2 should be operated within the range of 6.5 - 7.6 bar to ensure feasible separation, as operating outside this range would result in impractical heat exchanger area requirements calculated by PRO/I.

The optimal feed tray location for both distillation columns was investigated using the optimizer in PRO/II. This investigation aimed to minimize the heat duties of the respective distillation column reboilers and condensers by adjusting the feed tray location for both columns.

The primary function of a packed column is to facilitate intimate contact between gaseous and liquid streams to enhance mass transfer efficiency. This is achieved by allowing the vapor to interact continuously with the downward-flowing liquid over the packing material’s length. For this study, a 0.254 m internal diameter of super Intalox saddles random packing, manufactured by Norton, with a packing factor of 196.85 m²·m⁻³, was employed.

This was carried out by increasing the packing height of each column continuously until the reflux ratio became constant. It can be seen from Figure 12 , that the minimum reflux ratio for column T1 and T2 are 44.50 and 2.15 respectively.

The optimum packing height was investigated by changing the packing height which in turn, changed the packing volume. The volume of packing material was calculated, and the cost analysis was performed. The results obtained are shown in Figure 13 .

The optimum reflux ratio is the reflux ratio calculated by PRO/II for the optimum packing height. From Figure 13 , the optimum packing height for column T1 and column T2 are both 21.95 m as they yield the lowest net present value.

Column T2 pressure was investigated using the same method as that of trays column. The results obtained are shown in Figure 14 .

Figure 14 shows that the pressure of column T2 for the packed column has little effect on the net present value. This might be a result of the range of pressure investigated. However, the stimulation software used shows that the separation will be infeasible outside this range. This leads to the conclusion that the optimum pressure for packed column T2 range from 7 bar to 7.8 bar.

The optimum equivalent feed tray location of both columns was investigated using the optimiser in PRO/II to minimise the heat duties of the columns’ reboilers and condensers by changing the location of the feed tray of both columns.

The total cost of investment includes both the capital and operating costs over a 20-year duration with a discount rate of 0.2. It was calculated using the Equation (12):

$\begin{array}{c}\text{Total Cost}=\text{Total Capital Cost}+\text{NPV}\left(\text{20 years}\right)\\ =\text{Total Capital Cost}+\left[C_1+\frac{C_2}{1+d}+\frac{C_3}{{\left(1+d\right)}^2}+\cdots +\frac{C_{20}}{{\left(1+d\right)}^{19}}\right]\end{array}$(12)

where C_n is the operating cost for year n, and d is the discount rate. The cost of feedstock was not incorporated into the equation as this will be constant.

The total capital cost (C_TC) was calculated by summing the cost of the heat exchangers, distillation column shells and packing material as shown in Equation (13).

$C_{TC}={\displaystyle \underset{i=1}{\overset{n}{\sum }}{C}_{H{E}_i}}+{\displaystyle \underset{i=1}{\overset{n}{\sum }}{C}_{C{S}_i}}+{\displaystyle \underset{i=1}{\overset{n}{\sum }}{C}_{C{M}_i}}$ (13)

The cost of a heat exchanger (C_HE) was calculated using the correlation:

$C_{HE}=450\left(\frac{C_1}{315}\right)A_{HX}^{0.7}\left(1.65+1.22F_M{\left(1+\left|P-1\right|\right)}^{0.09}\right)$ (14)

where A_HX is the heat exchanger area (between 100 m² and 1000 m²), P is the operating pressure (in barg), C₁ is the cost index and has a value of 500 (from the Chemical Engineering cost index, estimated for the year 2020) and F_M is the material factor. A F_M value of 4 was used as stainless steel was chosen to be used to minimise fouling and corrosion of the heat exchanger.

The cost of the distillation column shell was calculated using the expression:

$\begin{array}{c}{C}_{CS}=\frac{C_1}{315}\left(1780L^{0.87}{D}^{1.23}\right)(2.86+1.604F_M(1.09727+\left(0.05049\times \left|P-1\right|\right)\\ -\left(-6.82\times {10}^{-5}{\left(P-1\right)}^2\right)))\end{array}$(15)

For sieve and valve trays:

$L=0.6\times \left(N_{act}-1\right)+5$ (16)

For packed column:

$L=h+5$ (17)

where h is the height of the packing material and N_act is the actual number of trays required, and was calculated as shown below:

$N_{act}=\frac{N_{\text{theoretical}}}{E_0}$ (Rounded to the nearest integer) (18)

where D is the column diameter (m), E₀ is the tray efficiency, L is the column height (m), which was calculated using Equations (16) and (17).

For the tray distillation column, the cost of trays was calculated using Equation (19):

$C_{BM}=\frac{C_1}{315}\left(193.04+22.72D+60.38D^2\right)F_M{N}_{act}$ (19)

Stainless steel (F_M of 4) was used for the heat exchangers, while carbon steel (F_M of 1) was used for the column shells and trays. This is because steam and cooling water will be used in the heat exchangers, so therefore, the use of carbon steel will lead to high rate of corrosion, which will in turn contaminate the streams and, eventually reduce the efficiency of the reboilers and condensers.

For packed column, the costs of the various packing material sizes for the Norton Super Intalox saddles are shown in Table 7 .

The packing volume was calculated using Equation (20):

$V_{act}=\frac{V_{\text{calculated}}}{0.8}=\frac{\pi \frac{d^2}{4}h}{0.8}$ (20)

where V_act is the actual volume required, and V_calculated was calculated using the dimensions obtained from Pro/II. The column was designed to ensure that the height was not above 60 m.

The utility operating cost was deduced as the sum of all the costs of the utilities used (i.e. costs of steam and cooling water). This was calculated based on the utility specification as shown in Table 8 .