DESIGN OF HEAT EXCHANGERS FOR RECIRCULATION CRYSTALLIZERS GREGORY A.
R. T R O L L O P E ’
Department of Chemical Engineering, The Unicersity, Birmingham, England
Some of the facets of the design of the cooler for recirculation crystallizers are considered. The cooler should be operated concurrently and it is usually advantageous to recirculate the coolant.
THE progress of work (7) on a Krystal cooling crystallizer (2) was a t one stage hampered by the capacity of the cooler of the pilot plant equipment. After assessing the requirements, a new cooler was designed and built. Since its performance came close to expectation and several elements of the design were not readily apparent, the design procedure is presented below. Whether the hot feed should be introduced before or after the cooler depends upon whether, on mixing the feed with saturated solution a t the crystallization temperature in the proposed proportions, the resultant solution is undersaturated or supersaturated, respectively, a t the adiabatic mixing temperature. This may be deduced from solubility and enthalpy relationships. If the mixture is only slightly supersaturated, it may be better to gain the advantage of removing the heat a t a somewhat higher temperature by introducing the feed before the cooler. Regardless of the explanation of the physical processes involved or the experimental details of its measurement, there is a minimum temperature to which it is desirable to subject the process liquor in the cooler. This temperature may be a function of homogeneous and heterogeneous impurities, the degree of agitation, etc., and nucleation may in fact be occurring a t this temperature, but for any given set of circumstances, the minimum temperature is usually fairly sharply defined and may be considered unique. The “selection” of a suitable value for this temperature comes within the realms of pilot plant experiment, experience, and judgment. The lowest temperature of the process liquor occurs a t its interface with the scale on the process side of the cooling surface. For the maximum economy of heat transfer area, the entire outer surface of the scale should be operated a t the minimum temperature. T h e area requirement of the heat exchanger can be determined under these ideal conditions by applying the heat transfer equation
Q
=
h,AhrAT],,
to the process liquid heat transfer resistance alone. In practice this resistance will not be constant throughout the exchanger and the area should be based upon the highest local value of the resistance, rather than the mean value. T h i s clearly indicates the necessity for careful design of the exchanger. A constant scale surface temperature can be achieved only in an idealized concurrent heat exchanger and then only by carefully matching the temperature profiles of the process liquor and the coolant. T h e definition of ideality is that the scale on both process and coolant sides should be uniformly deposited, so that the heat transfer coefficient for the combination of the scale films and the wall, h,, is constant throughout Present address, Hooker Chemical Corp., Niagara, Falls, N. Y .
the exchanger, as are the individual coefficients for the process and coolant streams, h, and h,, respectively. All coefficients should be based on the process side surface area. Under these conditions it is shown in the Appendix that a constant scale surface temperature is achieved if the following criteria are met:
h,, h,, Gpup,T,, and TPi can be considered fixed by the process side design, so that the criteria establish the relationship between these quantities and h,, Gcuc, and Tci.If a value is assigned to any one of these latter variables, the other two become uniquely specified. If, for example, the coolant feed temperature were specified, both the feed rate of the coolant and its individual heat transfer coefficient in the exchanger would be given by the criteria. Evidently the geometry of the exchanger must be adjusted so that a t the given coolant feed rate, the requisite heat transfer coefficient would be obtained. This can lead to a heat exchanger with an unusual shape or with other impractical requirements. The exchanger would also be inflexible with respect to the feed temperature of the coolant if the crystallization temperature must be held constant. The design criteria are usually much easier to achieve if the coolant is recirculated by a suitable pump. The terms G, and Tci then refer to the combined coolant feeds. If, in addition, the facility is designed so that changes in the actual feed rate of the coolant cause negligible changes in G,, Tci can be maintained by a coolant feed rate controller. T h e third equality of the criteria may now be ignored for design purposes, since this merely specifies the operating point of the controller. With the freedom to select G,, it becomes much easier to adjust the design to a practical heat exchanger configuration. Whether the use of a recirculation pump to attain a constant scale temperature can be justified depends upon a classical balance of capital and operating costs. The capacity of the cooler could, in principle, be maintained during the uniform buildup of scale on the cooling surfaces, by increasing the recirculation rate of the coolant and lowering the set point of the temperature controller to maintain the design criteria. Also, a similar method of design may be applied to the oil-heated evaporator of a crystallizer crystallizing a solute with a negative temperature coefficient of solubility. The supersaturation of the liquor delivered to the crystallizer tank is the algebraic sum of the supersaturation due to mixing, the residual supersaturation in the mother liquor, and the supersaturation generated by the cooler. Ignoring for the present the contribution of the two former terms, the superVOL. 5
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saturation of the cooled liquor, in temperature units, is approximately (T,, - Tpo); the maximum possible supersaturation is ( T p i - T 8 ) . The surface area required in the cooler is critically dependent on the ratio of these supersaturations, so that the ratio may be considered a “coefficient of performance.” Prior to pilot plant experience, Ts will be unknown, so that a pilot plant cooler can be designed only for a given coefficient of performance. As a guide, maximum supersaturations are usually about 1’ to 2’ C. for inorganic salt solutions. Appendix
By simple proportion
and also
Thus the criteria may be written
Nomenclature
The criteria necessary to achieve a constant scale temperature in a concurrent exchanger may be derived as follows: Consider a differential element of area dA, located somewhere in the exchanger. T h e quantity of heat, dQ, transferred to this element from the bulk of the process liquor, temperature T p , a t this point, to the scale surface is given by
dQ
=
h, d A ( T ,
- Ts)
Likewise dQ is given from the rate of heat transfer from the scale surface to the bulk of the coolant, temperature T c ,by
dQ
= (hC-l
f hs-*)-l d A ( T s - T c )
Thus
Applying this equation to the terminal conditions
shc + h2hs
=
Ts - Tci Ts - Tco ____ - -~ Tpi
- Ts
Tpo
- Ts
process side heat transfer area, L2 mass feed rate, Me-’ heat transfer coefficient, based on A , QT-1L-28-1 cooler heat load, Qe-1 temperature, T g = specific heat, Q-1MT-l L = length M = mass e = time
A = G = h = Q = T =
SUBSCRIPTS = coolant i = inlet o = outlet p = process liquor s = process side of heat transfer surface G
Literature Cited (1) Bransom, S. H., Trollope, G. A. R., A.2.Ch.E. J. 10, 842 (1964). ( 2 j Periy, J. H., ed., “Chemical Engineer’s Handbook,” 4th ed., Chap. 17, McGraw-Hill, New York, 1963.
RECEIVED for review November 15, 1965 ACCEPTED March 21, 1966
CORRELATION FOR BOILING HEAT TRANSFER TO SATURATED FLUIDS IN CONVECTIVE FLOW JOHN C. CHEN Brookhaven National Laboratory, Upton, N . Y .
An additive mechanism of micro- and macroconvective heat transfer was formulated to represent boiling heat transfer with net vapor generation to saturated, nonmetallic fluids in convective flow. Interaction of the two mechanisms was taken into account by means of two dimensionless functions: an effective two-phase Reynolds number function, F, and a bubble-growth suppression function, S. F was obtained as a function of the Martinelli parameter by both empirical correlation of heat transfer data and a momentum-analogy analysis. S was obtained as an empirical function of the two-phase Reynolds number. The correlation was tested with available data for water and organic fluids. The average deviation between calculated and measured boiling coefficients for all (over 600)data points from ten experimental cases was 2 12%. HE complexity of the boiling heat transfer phenomenon is Twell known. I t is especially evident in the case of convective boiling with net generation of vapor. Under these conditions, the heat transfer is affected by the various flow parameters and the vapor quality, as well as by the parameters which are pertinent in pool boiling. A wide range of local conditions and different flow regimes can exist
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along the length of a boiler for such a case. In the subcooled region, both fluid and wall temperatures increase along the boiler as the liquid gains sensible heat. At the point where nucleate boiling starts, the wall temperature begins to decrease. The fluid temperature continues to increase until it reaches its saturation value, from which point on it decreases gradually, corresponding to the decreasing pressure. As the
