**UFBA**

# How to Calculate Tank Heat Losses

(Parte **1** de 2)

How to Calculate Tank Heat Losses

Tfl, METAL WALL TEMPERATURE

Tp =t+a(T-t) t ,AIR TEMPERATURE

T- t _ hi + ho hi + ho-h-o -

And assuming t = mean temperature of air, °F

To = temperature of (saturated) steam used for coil heating, °F

Tp = temperature of tank metal wall, °F c = speeifieheat of stored produet, Btu/Ib, °F p = density of stored produet, lh./ft. 3 f3 = eoeffieientof expansionof stored produet, 1/°F fl- = viseosity, lh./ft. hr. K = thermal eonduetivity of stored produet, Btu/ft. hr. °F

T-t ~==

T, STORED lIQUID TEMPERATURE

Fig. l-Shows temperature drop across storage tank wall.

The following relationship applies-:

-Ó.t Q='2:,R where '2.R indicates the sum of the resistances opposing I the heat fIow from inside to outside Btu/ft 2 hr,°F

T-t T-Tp and then the two relationships whence or

Franco Bisi and Sergio Menicatti, SNAM Progetti, San Donato Milano, Italy

THE PROBLEM OF EVALUATINGtho heat losses in storage and correctly sizing the elements for keeping the stored product at a convenient temperature, has often been dealt with. Since the problem is rather complex, attempts are generalIy made to arrive at approximate solutions, which are of great utility for the designer.

As a matter of fact, the degree of accuracy attainable is often sufficient for a satisfactory definition of the engineering problems.

This article gives an exact method for the calculation.

For clarity, the problem is divided as folIows: (1) general, (2) calculation of walI temperature, and (3) calculation of heat losses during heating and under normal operation.

.talculation of Wall Temperature. The basic relationips have been summarized.f 3 Heat is generalIy transrred from a heating source (such as a coil on the tank ottom) to the stored product. This can be put into the tank at soaking temperature or at a higher ternperature, or colder than required by viscosi ty requirements for

I?umping purposes. In such case it is clear that the prod-wilI be heated to the desired temperature.

In each case, the basic problem is the determination f the exact temperature of the metallic walI (supposed

.are) of the tank; such temperature wilI vary with time. he folIowing values are indicated below:

Q = amount of heat transfer in unit time, Btu/hr . .T = temperature of produet, °F fs.WeU within normalengineering .accuracy, this method resolves much empirical data into two working oharts with simple equations

"General. For this article, the study is limited to tanks without externaI thermal insulation. Moreover, we shalI not consider any formation of deposits by the stored product. These, as it is known,! sometimes form a layer of true insulation inside the tank. It is obvious that the infIuence of deposits can be taken into account by suitable values of a fouling factor which wiII add its own resistance to the heat fIow from the inside to the outside of the tank .

HOW TO CALCUlATE TANK HEAT LOSSES

Several surveys have been carried out by SNAM Progetti to evaluate the most convenient formulas to be used in the calculation of the coefficients hi and ho and to as- certain the effect of wind on ho. From the experimental results, the following relation- ships appear to hold:

In this article the first relationship will be used. For the values of ho, the effects of convection and radiation must be considered.

h.o = hconv + hrad hcon = 0.3(T - t)O.25

where E is the radiation factor of the outside surface of the tank. Several values of have been published." For a mean value we recommend E "" 0.8. We obtain:

To take into account the wind effect in a suitable way, we could introduce a multiplying factor of the convection coefficient hconv• Such factor À' would be a function of the wind velocity. In this article it is however considered more opportune to refer to a coefficient À which multi- plies both hcon and hrad. Such a factor has evidently no physical meaning, in contrast to the factor À'. Nonethe- less, it permits notable simplifications. Between the two coefficients there is the relationship

À = (À' • hconv + hrad)/(hconv + hrad)

Operating thus, we could obtain one family of curves of the type reported in Fig. 2. The difficulties now encountered in the evaluation of the wall temperature Tp, assigned T and t, are due to the very complex bond between a, T, t. This bond allows one to arrive at the value of Tp only by trial and error or by means of successive approximations.

To obviate this inconvenience, the temperature drop across the tank metal wall has been neglected, and the expression has been replaced by a simpler one without serious error, proceeding as follows:

The relationship (3), by replacement of h, and Iu, becomes:

where F = [(Tp + 460)/100]4 - [(t + 460)/100]4; with a fair approximation in the interval o<;Tp<;180°F 0<; t <; 180°F this gives: F = 6.95 (Tp - t) and then the preceding relationship can be written:

~ [P2 f3: K2 JO'3 a{ 0.3 [(T - t)] 0.25+ O.974}97(T-t)0.3(l-a)1.3

Equation (5) makes it possible to express in form the function

1 (p2 f3 CK2)0'3 J a = a T /l ' (T - t) reported in Fig. 2. As may easily be seen, given p, /3, c, p" K, À, (for a combination of determined physical characteristics and for a certain wind action) it is possible to represent ,a solely as function of the difference (T - t) of the temperatures, of the fluid and of the externaI air.

The calculation of the wall temperature is thus reduced to the evaluation of the coefficient a resulting from a simple reading of one graph only.

This was however not used in practice at SNAM Progetti, it being only an intermediate stage in the study for: a complete electronic calculation program of tank heat- ing system. By the use of the graph one could obtain the exact and direct evaluation of a.

Calculation of Heat Losses During Heating and Nor- mal Operation. The wall temperature, calculated as function of the difference between internaI and externaI temperature of the tank, as well as of the physical characteristics of the product, will then in general be variable in time with the variation of these parameters.

The calculation of the heat losses during normal operation presents itself as a particular case of the heating stage, namely for a time tending to infinity.

The amount of heat delivered by the heating sourc will in part contribute to an increase in the temperature of the stored product and in part will be transferred wards the outside.

Let A (ft. 2) be the surface of the heating coil. Supposes as occurs in the most cases, that saturated steam is use as hot fluido The heat delivered in unit time will be give by: Q=A·U·t1t where:

U= total coefIicient of exchange between cai! and oi1 (Btu/ft.ê hr.oF)

t1t= steam - oi1 temperature difIerence (OF)

301--+--------t------+---+----+----+---=~'"""'I::::-------+---- a=0.70

200 _----+------j A'300 v (h)

ligo 3 | Gives area of heating coil required for various temperatures. |

Fig. function for calculating wall temperature in a storage tank based on differences hetween temperatures of stored products and air, o I

\ hi FUNCTION FOR CALCULATlON OFWALLa=--hi-ho TEMPERATURE IN A STORAGE TANK. \ -. I'--...

(Parte **1** de 2)