Appendix - Ecoprofile methodology (cont'd)

A10.1. General principles

One of the first elements in any analysis of a system is to break down the overall system into a set of sub-systems, each of which corresponds to some unit operation for which data are available and each of which produces only a single usable or saleable output.

Unfortunately, few processing operations yield a single output and this is especially true in the chemical industries. For example, the electrolysis of brine produces chlorine, sodium hydroxide and hydrogen while the thermal cracking of naphtha produces ethylene, propylene, butenes and often a series of other products which may be used as materials or fuels in other processes. As a consequence, one of the first tasks in analyzing such systems is to break down the complex system into a series of separate sub-systems each of which produces a single product but which, when added together, exhibit the same total characteristics as the original single system. This is known as partitioning or co-product allocation.

To do this it is necessary to find a suitable quantity to act as an allocation parameter so that the inputs and outputs from the overall system can be assigned to the single product systems. The precise method of allocation will obviously vary from one example to another but the choice of parameter is not arbitrary. The aim is to find an allocation parameter that in some way reflects, as closely as possible, the physical behaviour of the system itself The other constraint of course is that the subsystems that are eventually produced must also obey the standard physical laws.

A10.2. Co-product allocation using mass

To illustrate the method of co-product allocation, consider system shown in Figure 6 where a production system takes in materials of mass M, energy E and produces three products 1, 2 and 3 of masses m₁, m₂ and m₃ respectively as well as a waste of mass W.

Figure 6.
Schematic diagram of a unit operation producing three main products.

The aim of co-product allocation is to break this system down into a set of three separate unit operations, shown in Figure 7 as sub-systems 1, 2 and 3. Note that the input materials and energy and the output waste has been partitioned between the different sub-systems.

Figure 7.
The single system, A, of Figure 6 analyzed into three separate sub-systems 1, 2 and 3. See text for a fuller explanation.

One way of doing this might be to use the mass of products as the allocation parameter. Thus the materials input to sub-system 1 will be

M₁ = M.m1/(m₁ + m₂ + m₃)

Similarly, the masses fed to sub-systems 2 and 3 will be

M₂ = M.m2/(m₁ + m₂ + m₃)

M₃ = M.m3/(m₁ + m₂ + m₃)

Exactly the same procedure can be used for allocating energy and waste. Hence the energy and waste to sub-system 1 will be:

E₁ = E.m1(m₁ + m₂ + m₃ )
W₁ = W.m1/(m₁ + m₂ + m₃ )

and so on for sub-systems 2 and 3.

Although mass is widely used as an allocation parameter, it is by no means the only parameter available. In energy systems, mass is irrelevant and co-product allocation is usually carried out on the basis of energy flows rather than mass flows. For other processes, different parameters may be more appropriate. For example, in coating applications, the area covered may be more relevant than the mass applied and in pasteurization the thermal capacity is more pertinent.

A10.3. Stoichiometric partitioning

Although simple and widely applied, co-product allocation using mass is not universally applicable and can, on occasions, lead to false results. This is especially true in the chemical industry. To illustrate the problem, consider the operation of a chlorine plant. Such a plant yields three main outputs; chlorine, sodium hydroxide and hydrogen. The overall reaction describing the process is of the form:

2NaCl(aq) + 2H₂O(l) = 2NaOH(aq) + Cl₂(g) + H₂(g)

Suppose that in a hypothetical plant, the inputs and outputs are as shown in Table A4.

The total output of usable products in Table A4 is 153 kg and therefore using a simple mass partition, the input sodium chloride is partitioned between chlorine, sodium hydroxide and hydrogen in the ratios 71:80:2. These ratios imply the following:

Table 4.
Materials inputs and outputs for a hypothetical operation producing chlorine, sodium hydroxide and hydrogen.

(117 x 0.464) = 54.3 kg of sodium chloride produce 71 kg of chlorine.
(117 x 0.523) = 61.2 kg of sodium chloride produce 80 kg of NaOH and
(117 x 0.013)= 1.5 kg of sodium chloride produce 2 kg of hydrogen.

Now, since the chlorine is derived totally from the sodium chloride, the mass of sodium chloride attributed to chlorine cannot be less than the mass of chlorine but the above procedure attributes only 54.3 kg of sodium chloride to the production of 71 kg of chlorine.

In contrast, no sodium chloride is needed in the production of hydrogen, which is derived solely from the water input, yet the above procedure attributes 1.5 kg to hydrogen.

Clearly, a different approach is needed which meets the stoichiometric demands of the process. The reaction leading to the production of chlorine from sodium chloride is strictly an ionic reaction and the ionic species attributable to the different products can be readily identified and related to the quantity of sodium chloride as shown in Table A5 and this method has been used in the analysis of the chlorine cell.

Table 5.
Partition of sodium chloride input from Table A3 using stoichiometric partitioning.

There are few practical processes in which the inputs exactly match the stoichiometric demand calculated from the outputs. Usually there is an excess of one or more reactant. In such cases, any excess input is allocated to the products on the basis of the relative demands determined by stoichiometry.

Unfortunately, not every input and output of a unit process follows stoichiometric rules - energy inputs are a good example. Therefore those inputs and outputs, which could not be subject to stoichiometric partitioning, have to be allocated using an alternative method - usually using mass.

A10.4. Hybrid allocation

Although stoichiometric co-product allocation is straightforward and has been used wherever possible, it relies on knowing the precise chemical composition of the usable output streams. Unfortunately this information is not always available. For example, in petrochemical reactions, there is usually one or more output products of well defined chemical composition but, in addition, there is commonly an output stream of undifferentiated hydrocarbons which is sent to some external process for further processing, separation and purification. In such circumstances, there would then be no simple way of allocating the hydrocarbon input even though the stoichiometric demand by the identified products could be determined. These uncertainties, therefore, lead to the third approach, which has been applied whenever strict stoichiometric allocation was not possible.

This method is essentially a mixture of the previous two approaches; that is, inputs are attributed to final products as far as possible using the stoichiometric demand but the remaining inputs are assigned to the products on a simple mass basis.