## Heat Balance Equations

HEAT REMOVAL CAPABILITY OF REFLUX = = ( htgo — ht'ODi), Btu/lb. REQUIRED PUMPBACK R E F L U X - ( Qr/q'R ), Ib./hr

Figure 3.10. Heat and material balance—overflash liquid condensing section.

2. Calculate the heat removal capability of the reflux available to the tray.

3. Calculate the pumpback reflux required to absorb the reflux heat.

4. Calculate and tabulate the external heat quantities as Q' values at the grid outlet.

5. Calculate and tabulate the vapor and liquids quantities leaving the grid.

First Sidestream Product (D1) Draw Tray

The heat and material balance relationships at this section of the tower are determined by making a balance around Envelope II as shown on Figure 3.9. Figure 3.II shows an expanded view of this section and gives the equations used in making the calculations. These equations are to be used in the following sequence.

### 1. Calculate the reflux heat at Tray D1.

2. It is assumed that the amount of hydrocarbon which is revaporized in the D1 product stripper falls to Tray D1 as part of the internal reflux from Tray (D1 + 1) and absorbs a small amount of the reflux heat in passing across the tray. Calculate the value of this heat removal.

3. Calculate the heat removal capability of the internal reflux to the tray.

4. Calculate the internal reflux required to absorb the excess heat at Tray D1.

5. Convert the internal reflux from pounds per hour to moles per hour. Calculate the mole fraction of hydrocarbon product vapor in the total vapor leaving the draw tray but neglect the presence of the product to be removed on the next draw tray up in the tower. From this, calculate the hydrocarbon partial pressure in this vapor and convert the atmospheric bubble point of the unstripped liquid product on the tray to this partial pressure. If this temperature does not check the value assumed earlier, repeat the procedure for a new assumed temperature.

6. Calculate and tabulate the external heat quantities to the base of Tray (D1 + 1). This will include the heat effects of product liquid Dl, the reflux cooler and the stripping steam to the product stripper.

7. Calculate and tabulate the vapor and liquid quantities at the base of Tray (Dl +1). HEAT BALANCE EQUATIONS Qi« ( AQ'go + Qi.di)-(Qvodi + Qd'i }.

HEAT ABSORBED BY Lvsi =Qlvsi = ( Lvsi) (c I <tdi-tdi +1). q'n ■ t H tdi - h Idi

HYDROCARBON PARTIAL PRESSURE ABOVE TRAY D1 P'hc=( PtdiJCLdi+i/ ( Vooi-D2 + Ldi >3

Figure 3.11. Heat and material balance—first sidestream product draw.

Second Sidestream Product (D2) Draw Tray

The heat and material balance relationships at this section of the tower are determined by making two balances. These balances are around Envelopes II! and IV as shown on Figure 3.9 and in detail on Figure 3.12. The calculations for this section are similar to those in the previous section, with the exception of handling the pumpback reflux. The sequence of calculations is as follows.

1. Calculate the pumpback reflux required to Tray (D2-1) by making a balance above this tray as shown by Envelope III.

2. Calculate the internal reflux to Tray D2 by making a balance above this tray as shown by Envelope IV.

3. Calculate the hydrocarbon partial pressure in the total vapor leaving the draw tray, neglecting the presence of product D3. Convert the atmospheric bubble point of the unstripped liquid product on the tray to this partial pressure and check the assumed temperature.

4. Calculate the reflux induced on Tray (D2 -I) by the use of subcooled reflux. This induced reflux is the amount of vapor from Tray (D2 - 2) which enters and is condensed on Tray (D2 - 1) for the purpose of converting the cooled pumpback reflux to bubble point liquid.

5. Calculate and tabulate the external heat quantities to the base of Tray (D2 + 1).

6. Calculate and tabulate the vapor and liquid quantities at the base of Tray (D2 + 1).

VOD2=VOD1 i QvOD2

AQ'Pl

ENV.iV ENV.

HEAT BALANCE EQUATIONS (1) ABOVE TRAY D2-1 -ENV. 3vo h fOD2 )

ABOVE TRAY D2-ENV. IV QH=[|AQ'dt •+ Qld2)-IQd'2 + QVOD2j

QlVS2 ={LvS2)(rl(t02 - tD2+ 1) q'*- H»D2-htD2-htD2+l L D 2 +1-IQRD2 - QlVS2 )/q'«

HYDROCARBON PARTIAL PRESSURE ABOVE TRAY 02 P'HC»= (PTD2l[(LD2 + i}/(Vooi-D3 + L 0 2 +1)]

INDUCED REFLUX ON TRAY D2-T R ¡D2 - 1 » Lb2[(hD2 -1 -htOD2) /(HtD2 -2 -hfD2 - lQ .

lvs 2

\QlD3