# Heat Balance Equations

Figure 3.8. Flash zone heat and material balance.

calculations in proceeding up the tower. The value of the tabulation will be seen in later sections.

Heat and Material Balance Calculations for Lube-Type Towers

This section outlines procedures for calculating product draw tray temperatures at all points in the tower and for making an overall heat balance around the system. The method is based on calculating the hydrocarbon product partial pressure in the vapor above each draw tray and converting the bubble point of the product liquid on the tray to this pressure. Prior to beginning these calculations, the overall system material balance and the properties of all product streams must have been defined.

### Steam to Product Strippers

These auxiliary towers will be used to strip only product and not the pumpback reflux, with the possible exception of the first product above the overflash liquid condensing section. For design* purposes, set a steam rate of 10 pounds per barrel of final product as measured at 60 degrees F. This will result in a stripout of approximately 5 weight percent and a temperature drop across the stripper of 15 to 20 degrees F. Locate and plot the EFV temperature for this degree of stripout on the product EFV curves which were drawn in the calculations following the previous section. Note that the bubble point to be used in the partial pressure calculations is that of the unstripped liquid on the tray.

Knowing the thermal condition of the steam, calculate the heat input to all the strippers.

### Tower Top Conditions

The temperature of the steam and noncondensible materials leaving the top of the tower is determined by setting a 50 to 75 degree F approach to the minimum practical cool oil temperature in the top pumparound system. This latter temperature is a function of the viscosity properties of the oil in question, and this data can usually be predicted from the crude assay. Normally, a cool oil temperature of 150 to 200 degrees F will not require excessive pump horsepower. This, in turn, allows an overhead temperature of 200 to 275 degrees F.

The amount of oil lost with the overhead stream is determined by making an oil vapor pressure calculation, assuming that the oil exerts its full vapor pressure at the temperature of the exit vapor. Maxwell's nomogram is useful in estimating this vapor pressure. The overall material balance should be adjusted to show the amount of oil lost with the overhead vapor. This oil loss is at the expense of the top sidestream product.

Calculate the amount of heat which leaves the system in the overhead vapor.

### Estimate of Tower Temperature Profile

Estimating draw tray temperatures for vacuum operations is much more difficult than in atmospheric towers because of the greater relative effect of calculated internal reflux on hydrocarbon partial pressure. As good a rule as any is to assume a hydrocarbon partial pressure equal to 30 to 50 percent of the total pressure at any tray. Plot the assumed profile for the trayed section of the tower.

The temperature of the cooled pumpback reflux is estimated at 100 to 150 degrees F lower than the draw tray temperatures except where, for specific reasons, a different value would be indicated. Upon completion of the total design, it is necessary to verify that the heat exchange system is capable of producing the assumed reflux temperatures. If this analysis uncovers significant differences, it will be necessary to recalculate the tower, based on a different set of cooled reflux temperatures.

Overflash Liquid (OL) Condensing Section

The overflash liquid condensing section is calculated as a single-stage flash condensation. The heat removal across this portion of the tower is accomplished internally by reva-porizing subcooled reflux which is pumped back from the next draw tray up in the tower.

Since this draw tray is a chimney tray and performs no fractionation, the temperature of the condensed liquid leaving the tray is estimated as being the dew point of the hydrocarbon vapor from the flash zone at the hydrocarbon partial pressure above the draw tray, the leakage air and the bottoms steam being defined as inerts. The temperature at this pressure is read from the vacuum region EFV curves. The vapor temperature leaving the grid is estimated in the same way but referred to the total pressure at that point.

The heat and material balance relationships around this section are determined by making a balance around Envelope I as shown on Figure 3.9. Figure 3.10 is 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 the exit of the grid. Reflux heat is defined as the difference between the heat input of the feed and at the product strippers and the heat outflow of liquid products, external cooling of tower streams (product coolers excluded) and the exit vapors of products plus steam at the point in question. Figure 3.9. Heat and material balance summary, lube type vacuum tower with pumpback reflux heat removal.

Vacuum Tower