3. Quantity of ice required

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It is possible to calculate the ice requirement if the operational conditions are known. These conditions are often variable and unrepetitive. Only a series of tests, under operational conditions, will establish the correct fish to ice ratio to be used to cool the fish and maintain chilled temperatures during the entire storage period.

Calculated values of ice usage can provide valuable information at the planning and design stages, and also promote a better understanding of the relative effect of the various elements which influence the rate of ice meltage. In addition, by considering all possibilities and calculating ice requirements, a more rational judgement can be made when selecting equipment and procedures to be used.

To determine the ice requirement, it is necessary to calculate the quantity of ice to cool the fish and also the quantity of ice required to maintain the fish at a chill temperature throughout the storage period. In addition, allowance has to be made to allow for losses and other contingencies in order to determine the ice manufacturing requirement.

Calculation of the ice requirement for cooling fish

The mass of ice needed to cool fish from the initial temperature to the final holding temperature can be calculated from an expression, which equates the heat taken up by the ice, on the left side of the equation, with the heat lost by the fish, on the right side of the equation.

(Mi) (Li) = (Mf) (Cpf) (ts-tc) (4)
Where
Mi= mass of ice which melts (kg)
Li= latent heat of fusion of ice (80 kcal/kg)
Mf= mass of fish (kg)
Cpf= specific heat of fish (kcal/kg°C)
ts= initial temperature of fish (°C)
tc= final temperature of fish (0°C)

From equation (4) the ice requirement will therefore be:

(5)

The specific heat of lean fish is approximately 0.8 kcal/kg C and this value should be used if there is a species mix or if there is a possibility that at times all the fish are of a lean species. The specific heat value, however, may be refined to take account of variations in the oil content of the fish and this refined value may be used if the fish composition is reasonably consistent.

Cpf = 0.5 XI + 0.3 Xs + 1.0 xw (6)

Where
Cpf = specific heat of fish (kcal/kg)
Xl = mass fraction of lipids (oil)
Xs = mass fraction of solids
Xw = mass fraction of water

To illustrate the effect of oil content on the quantity of ice required for chilling the following comparison is made between lean and fatty fish. Example (1) - 100 kg lean fish with 1% lipids, 19% solids and 80% water at an initial temperature of 20°C:

Cpf = (0.5 x 0.01) + (0.3 x 0.19) + (1.0x 0.8) = 0.862 kcal/kg°C

Example (2) - 100 kg of fatty fish with 21% lipids, 19% solids and 60% water at an initial temperature of 20°C.

Cpf= (0.5 x 0.21 ) + (0.3 x 0. 19) + ( 1.0 x 0.6)= 0.762 kcal/kg°C

The refined calculation for fatty fish shows only a small reduction in ice requirement and, since with most species the oil content is variable, it is advisable to treat all fish as if they were lean fish.

Calculation of the ice requirement for the storage of fish

Even if you are concerned with only one batch of fish held in identical containers, there are likely to be variations in ice meltage rates, which make it difficult to calculate the ice requirement accurately. If, for instance, the containers are stacked, then ice meltage may be different in containers located at the top, bottom, sides and within the stack.

In spite of the obvious difficulties and likely inaccuracies, a calculation of the ice meltage rate can still be useful at a planning stage to enable comparisons to be made between different options, and to allow preliminary estimates of quantities, costs and equipment to be made.

It would be difficult to identify containers which would eventually be located at more favourable locations within a stack. Therefore, all containers should be treated equally and the assumption made that each container is fully exposed to the surrounding air.

As a first step, heat transfer may be calculated using the following simple expression:

q = A.U. (t_o - t_c) kcal/day (7)

Where:
q = heat entering the container (kcal/day)
A = surface area of the container (m²)
U = overall heat transfer coefficient kcal/day m² °C)
t_o = temperature outside the container (°C)
t_c = temperature inside the container (0°C)

This overall calculation of heat transfer may require to be done in parts if, for instance, the lid or base of the container is made of a different material or has a different thickness. The heat transfer through the various areas are then added together to give the total heat transfer.

The heat entering melts the ice, therefore it follows that:

q = Li . mi kcal/day (8)
Where
q = heat required to melt ice (kcal/day)
Li = latent heat of fusion of ice (usually taken as 80 kcal/kg)
mi = mass of ice melted (kg/day)

In order to develop a mathematical expression for ice meltage rate during the storage period we suppose that ice meltage inside the containers is only due to heat transferred from the surrounding air. In this steady state approach, quantities (7) and (8) should be equal, therefore it follows that:

L₁ m_i = A.U. (t_o - t_c) (9)

Thus, the ice requirement will be:

(10)

If the fish containers are exposed to direct sunlight during the storage period, the above calculation, which is only based on the conductance of heat due to the difference between the internal and external temperatures, will result in a under-estimation of the ice requirement. To include the element of ice meltage due to radiated heat will make the calculation extremely difficult. Therefore, if the containers cannot be protected from direct sunlight or any other radiated heat source during the storage period, the calculated values for the ice requirement should be upgraded or used with caution.

Ice meltage tests

Calculation of ice meltage rates will seldom give an accurate indication of the ice requirement, since reliable data on both materials and conditions is often not readily available. Irregularities in the construction of containers, for instance, can greatly affect the containers "effective heat transfer coefficient". Variations in ambient conditions during the storage period make it difficult to calculate the ever changing ice meltage rates, even when the data are reasonably accurate.

More accurate calculations of the ice requirement can be made if meltage tests are used to determine the overall heat transfer coefficient of the container. This type of ice meltage test may be done using ice only, and the results will be equally valid for fish/ice mixtures.

Containers should be filled with ice and weighed accurately before commencing the test, which should be done with a constant surrounding air temperature. This may not be possible over the entire test period, but reasonably constant temperatures may be achieved for shorter periods between weight loss measurements and an average used in the calculations. Significant differences will be observed between containers completely within the stack and those on the periphery with exposed surfaces.

Some of the initial ice meltage will be the result of cooling the container and, depending on the container material, some melt-water may be absorbed so that it will not be a measurable weight loss. If the weight of the container and ice is frequently checked during the test period the weight loss pattern may be similar to that shown in Figure 6, which shows a fairly constant rate of weight loss after the initial cooling period.

To ensure that the ice meltage measurements relate to heat ingress, only the time interval between "X. and "Y" in Figure 6, during which the rate of weight loss is constant, should be considered for ice meltage calculations.

Fig. 6 Ice meltage during storage

The relationship between ice meltage and heat ingress was given above by equation (9):
Li . m_i = A.U. (t_o - t_c) (9)
This expression can be rearranged to give the overall heat transfer coefficient U as follows:
(11)

Where
U = overall heat transfer coefficient kcal/day m² °C)
L_i = latent heat of fusion of ice (80 kcal/kg)
m_i = ice meltage per day (between "X" and "Y", Figure 6) (kg/day)
A = surface area of the container (m²)
t_o = temperature outside the container (°C)
t_c = temperature inside the container (0°C)

Note: If m, is measured over a period other than one full day then the rate per day can be calculated as follows:

(12)

Where:
m_i = ice meltage rate (kg/day)
(M_x - M_y) = weight lost due to meltage between "X" and "Y" (kg)
(x - y) = time interval between "X" and "Y" (hours)

In such ice meltage tests, steps should be taken to ensure that all the melt-water is drained from the container before each weighing.

A final check on whether the correct quantity of ice is being used can be done at the end of each storage period, by noting the quantity of ice remaining in each container. It is important that not only should there be ice in every container, but that this ice should be uniformly distributed, so that all fish in each container are still being cooled. A more elaborate check is to monitor the temperature of the fish. It is often possible to identify the fish likely to be most vulnerable, such as those on the outside of containers which are located on the outside of a stack and thermometers can be located at these positions. However, during handling and transportation/he relative position of containers may change with respect to their vulnerability to heat ingress, and only random temperature checks and a series of tests will finally indicate the quality of the icing practice.

If there has to be any modification in the ice usage at this stage, it can only be achieved by changing the fish to ice ratio and consequently the number of containers necessary to hold the required quantity of fish.

Saving ice

The amount of ice needed to keep fish fresh is economically more important in tropical countries, since the warmer climate means that ice meltage rates are higher. The ice required for cooling the fish from the initial temperature is fixed and cannot be reduced, Fig 7, but the use of insulation and refrigeration can considerably reduce the ice requirement during the subsequent storage period.

Another advantage of using insulated storage, is that it helps to stabilise storage conditions. Thereby, it is easier to predict and maintain the correct ice requirement.

Insulation can be used in various ways and the choice between one system and another will depend mainly on local conditions. For instance, individual boxes may be insulated or boxes may be stored in larger insulated containers or chill stores.

A standard size of fish box used in temperate climates contains about 30 kg of fish and 15 kg of ice. If this size of container was insulated not only would this be costly, but there would be a significant loss in storage space. Individual insulated boxes therefore tend to be larger and, in most cases, there is a need for some form of mechanical handling.

The effect of unit size on the ice and storage space requirements is illustrated in the following comparison between two sizes of container:

Internal volume, box A
0.275 x 0.66 x 0.38 = 0.069 m³
Internal volume, box B
0.55 x 1.32 x 0.76 = 0.55 m³

Box B has a volume which is 8 times greater than that of Box A and will therefore contain 8 times the quantity of fish.

If each box is insulated to give a wall thickness of 0.035 m, the surface area of each box will be:

Box A 1.47 m²
Box B 5.06 m²

Box B has a surface area which is 3.44 times greater than Box A, therefore, the ice meltage rate will be 3.44 times greater.

Figure 7 Saving ice

Table 2 Comparison between Boxes A and B

The above comparison shows that although the ice meltage rate in Box B is 3.44 times greater than in Box A, the rate per unit weight of fish is greatly reduced due to the lower surface area to fish weight ratio.

Further comparisons could be made between the differences in storage space requirements and box costs. In the example given above, it would require 8 small boxes to hold the same quantity of fish as a single large box. Based on external box dimensions, the volume requirement for the smaller boxes would be about 25% greater. The surface area of the 8 smaller boxes is more than double the surface area of a single large box, therefore material costs will also be higher. Because the depth to which fish and ice is stowed is effectively doubled in the large box, consideration must be given to whether the fish is robust enough to withstand crushing. Further information on container storage is given in Chapter 9.

Total ice requirement

Factors other than higher ambient temperatures can result in an increase in the ice requirement in tropical countries.

The collection and marketing system may require that the fish and ice be separated for check weighing and sorting and, if correct procedure is followed, the old ice should be discarded and new ice used for re-icing. It is also advisable in tropical countries to precool water used during processing in order to avoid undesirable rises in fish temperature which would accelerate fish spoilage. Keeping the fish chilled at this stage also avoids the need to recool later. In more sophisticated systems, water precooling can be achieved using a mechanical refrigeration system and heat exchanger, but a more simple method is to merely add ice to the water in the supply tank.

The ice quantities given in Table 3 are typical figures for uninsulated containers which take into account losses during ice distribution. The quantities actually applied to the fish at each stage will therefore be less. More ice is generally used for prawns and other valuable shellfish species, in order to provide additional insurance against delays and other contingencies, even although the cooling requirement is much the same. The figures in Table 3 for ice requirements at different stages of handling and processing, are only a guide for the conditions prevailing in a tropical climate, and they may require modification either way as the result of experience.

Table 3 also shows that a collection, marketing and transport system which requires the fish to be periodically weighed and/or inspected will add considerably to the icing costs. Consideration should therefore be given to inspections being made by sample only or, preferably, to eliminating some of the stages where re-icing is required.

Table 3 Ice/fish ratios used to calculate ice requirements in tropical climates

Using the figures in Table 3 and a typical operation, the total ice requirement can be worked out as fallows:

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