# METHOD IMPROVES PYROLYSIS TLE OPERATION

Jan BartonChemopetrol

Labem, Czechoslovakia

An objective cost function was derived for optimizing the duration of an operating cycle of the transfer line heat exchanger, or waste-heat boiler, on ethylene furnaces for generation of high-pressure steam.

The objective function was developed to minimize both the cost of cleaning and the heat loss associated with the higher pyrolysis gas exit temperatures required by coke deposition on the heat transfer area of the transfer line heat exchanger.

The objective function is based on the amount of heat transfer surface area of the exchanger and the cost to clean the exchanger because these are the main parameters affecting the energy capacity and heat losses in transfer line heat exchangers (TLE's).

The TLE, using the heat of the pyrolysis gas leaving the pyrolysis tube reactor at roughly 800 C. for generating high-pressure steam at 12 MPa, represents an important part of an ethylene unit. TLE's are conventionally designed as tubular heat exchangers, where the pyrolysis gas from the pyrolysis tube reactor flows inside the tubes and the water boils in the shell side at 12 MPa.

Heat remaining in the pyrolysis gas, after the TLE, is quenched by oil.

The oil is used to generate low-pressure steam at 0.7 MPa that is mixed with the hydrocarbon feed entering the furnace.

The tube bundle of the TLE is usually situated vertically, closely connected to the pyrolysis reactor (Fig. 1).

### BASIS OF THEORY

Assume that for clean heat transfer areas of the TLE: K = K(i) and T2 = T2(i), initially. After a period of operation, T, the following relationships apply: TK = K(T) < K(i) and T2(T) > T2(i). See nomenclature box for definitions of variables and symbols. The heat loss is defined as the heat that cannot be used to generate steam, and is assumed to be associated with the heat lost through heat exchanger blowdown.

The heat transfer in the TLE is defined by:

[SEE FORMULA (1)]

It is assumed that a fraction of the heat, QL, which is not utilized for generating high-pressure steam in the exchanger due to the deposition of coke, is characterized by the parameter, PE(0,1), where 0 represents clean conditions and 1 represents coked conditions.

The cost per day, C1, resulting from the formation of coke and, hence, from the lower rate of high-pressure steam generation in the transfer line heat exchanger can be written as:

[SEE FORMULA (2)]

If the feed of a pyrolysis furnace that is out of service due to transfer line heat echanger cleaning is sent to another furnace, and thus no losses arise in the overall rate of the pyrolysis plant production, the cost per day of cleaning is determined by:

[SEE FORMULA (3)]

The form of the objective function is:

[SEE FORMULA (4)]

and it holds that the rate of change of the cost with respect to the operation is zero, or:

[SEE FORMULA (5)]

### BLOWDOWN RATE

The transfer line exchanger blowdown rate can be calculated from an enthalpy balance by the following equation:

[SEE FORMULA (6)]

where he is the exit steam enthalpy and hi is the entering water enthalpy.

The accuracy of the value of MB determined by Equation 6 can be assessed with the aid of the KOMAT program in which the error-spreading theory is used to calculate a nonmeasured quantity's error on the basis of errors recorded in measured quantities.1-3

The error of the calculation becomes tolerable if, in any case, the maximum relative error of the measured quantities did not exceed 0.5% relative.

This, however, is very difficult to achieve in terms of industrial practice.

Considerably more accurate results of the determination of the transfer line heat exchanger blowdown flow rate could be arrived at only by measuring the blowdown stream directly. In the case that the temperature, T4, Of the water fed into the transfer line heat exchanger approaches T3 in the exchanger, the heat losses are then concentrated in the preheating of the feed water to the transfer line heat exchanger.

### COKE FORMATION

Coke formation is an undesirable chemical reaction taking place in the course of the pyrolysis of all hydrocarbons. Due to the high value of the activation energy of coking during the pyrolysis of naphtha, coke formation is heaviest at the inlet of the transfer line heat exchanger tubes, on surfaces of highest temperature.

Line 2 of Fig. 2 shows the dependence of the overall heat transfer coefficient, K, on the overall operating time of the transfer line heat exchanger.

Considering fluctuations in the pyrolysis gas flow rate, the calculated value of the heat transfer coefficient was corrected according to:

[SEE FORMULA (7)]

where the quantities with the apostrophe correspond to mpG' = 40,250 kg/hr, chosen as the reference flow rate.

Line 1 in Fig. 2 shows the model dependence of K on T for MPG = 43,200 kg/hr (12 kg/sec).

It holds for the time dependence of K according to Line 1 that:

[SEE FORMULA (8)]

and it is assumed that K is independent of S, T1, and T3.

### OPTIMIZATION

The calculations of the optimum operating time, Topt, of the transfer line heat exchanger are based on the following assumptions:

- The flow rate of pyrolysis gas through the transfer line heat exchanger is constant (MPG = 12 kg/sec).
- The heat transfer area is within the range of 131-331 sq m.
- The pyrolysis temperature, T1, lies within the range 1,080-1,120 K. (301-341 C.).
- The parameter, P = 0.5, or 50% of the QL is used for generating process steam.
- The price ratio, W2/W1 0.3 to 1.0.
- The cost ratio, C2/W1, corresponds to 600-6,000 giga Joules.

### CALCULATION ALGORITHM

Multiple linear regression yielded the following dependencies:

[SEE FORMULA (9)]

[SEE FORMULA (10)]

[SEE FORMULA (11)]

where the temperatures, T1 and T3, are expressed in degrees K.

The values of parameters B, D, and E are given in Table 1.

The dependencies of these parameters on the terms, W2/W1 and C2/W1, were approximated by linear relations of the type:

[SEE FORMULA (12)]

[SEE FORMULA (13)]

The value of the parameters, b, d, and e, are presented in Table 2. They were also obtained by multiple linear regression of data from Table 1.

The effect of heat transfer area S is on the combined costs of exchanger cleaning and heat loss, QL.

The sum of the costs of cleaning the exchanger and heat losses over the whole service life, tL, of the exchanger may be written:

[SEE FORMULA (14)]

where the time required for cleaning the exchanger is excluded from the assumed yearly operating time.

The values of the Parameters B and D in Table 2 indicate that a change in S, T1, and T3, that brings about a decrease in Cmin results, at the same time, in an increase in Topt and a decrease in delta T.

Fig. 3 shows the dependence of the transfer line heat exchanger comparative cost value as a linear function of S on conditions that the relative cost of 1 sq m of the heat transfer area is W3/W1 = 100 giga Joules/sq m (Curve 2), and W3/W1 = 300 giga Joules/sq m (Curve 3).

The effect of S ON Cy/W1 at tL - 10 years, t = 7,500 hr, W2/W1 = 0.3, c2/W1 3,000 giga Joules, T1 = 830 C., and T3 = 320 C., is demonstrated by Curve 4.

Curve 5, also illustrating the dependence of Cy/W1 vs. S, was constructed with all conditions identical as for Curve 4, except for c2/W1 = 600 giga Joules. It is possible to estimate from Fig. 3, the recovery period for the investment cost of installing transfer line heat exchangers with a larger heat transfer area on assumption that W3/W1 = 100 giga Joules/sq m, i.e., approximately 2 to 5 years.

Fig. 4 shows the effect of S on the temperature of T2, at the constant number of tubes having a constant internal diameter, when K = 0.36 kw/sq m - K., T1 = 847 C. (1,120 K.), T3 = 301 C. (574 K.), and MPG 12 kg/sec.

### RECOMMENDATIONS

To reduce the undesirable losses of energy caused by excessive blowdown from the transfer line heat exchanger, which may be caused by leaks for instance, it is necessary to directly measure the blowndown flow rate.

When revamping a transfer line heat exchanger, it is advantageous to consider a larger heat transfer area (by as much as 50%) than is currently used in ethylene plants to obtain the temperature difference between the pyrolysis gas to the transfer line heat exchanger outlet and the point in the exchanger where steam is at roughly 25 C., taking the clean heat transfer area into account (if 12 MPa high-pressure steam is generated).

To reduce the costs of cleaning the heat transfer area in the transfer line heat exchanger, decoking of the pyrolysis tube reactor and transfer line heat exchanger should be done simultaneously. Reducing the cost of cleaning to one fifth of the original value enables the heat loss caused by coking in transfer line heat exchangers to be decreased by as much as 50%.

### REFERENCES

- Madron, F., Chem. Prum., Vol. 35, 1985, p. 337.
- Madron, F., Chem. Prum., Vol. 35, 1985, p. 517.
- Madron, F., Chemical Engineering Science, Vol. 40, 1985, p. 1955.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*