4.1. Overview
The main tool employed is system dynamics modelling. For designing the system dynamics model, we use systems analysis. We analyse the system using stock-and-flow charts and causal loop diagrams. The mass balance expressed differential equations resulting from the flow charts and the causal loop diagrams were numerically solved using the STELLA® Architect modelling environment (Senge 1990, Sverdrup et al. 2022). We use causal loop diagrams for mapping out where the causalities are, to find intervention points in the system, and to propose policy interventions. The Integrated Assessment Model WORLD7 was used for this study (Sverdrup and Olafsdottir 2019). The workflow was as follows:
- Estimate the available gallium resource that can be extracted using valid mining methods, considering the different yields and estimating the total geological deposit-to-supplied gallium approach.
- Use the WORLD7 integrated modelling framework to generate gallium demand from the production of consumer goods and technological infrastructures.
- Identify the available sources of technology elements and the estimate the available amounts that can be extracted from those deposits, considering extraction technologies and the cut-off caused by resource qualities and costs of extraction as related to the market price dynamics.
- Run the WORLD7 model to assess the supply sustainability from the first use of the technology metals to about 2200.
- Evaluate the model simulations with respect to result validity, and risk for future aspects of scarcity.
- Evaluate how future policies that would result from the EU Imaginaries would grip into the gallium system.
The WORLD7 integrated assessment model was used for earlier assessments supply for silver (Sverdrup et al., 2014b), copper, zinc, lead (Sverdrup et al., 2015, 2019), aluminium (Sverdrup et al., (2015a), platinum group metals (Sverdrup and Ragnarsdottir 2016), wolfram (Sverdrup et al., 2017c), molybdenum and rhenium (Sverdrup et al., 2018b), tin (Olafsdottir and Sverdrup 2018), nickel (Olafsdottir and Sverdrup 2020), indium (Sverdrup et al., 2023). Further publications near completion after this are studies on tellurium, selenium, yttrium, antimony and bismuth, The source metal reserves and resources estimates for the relevant metals are based on geological estimates, the interpretation of geological data, and the allocation of extractable amounts according to ore quality, stratified with extraction costs, and as revised in our earlier studies for copper, zinc, lead, bauxite, nickel, molybdenum and wolfram (Phillips and Edwards 1976, Olafsdottir and Sverdrup 2018 (Sn), 2020 (Ni), Sverdrup and Olafsdottir 2019 (markets), Sverdrup et al., 2014a (Ag), 2015 (Al), 2017 (W), 2018 (Mo), 2019 (Ca,Zn,Pb), 2023 (In), 2024 (Ge).).
4.2. Resource estimations
4.2.1. Dependencies and cross-links
Figure 2 shows how the different technology metals are almost all of them dependent on primary extraction of a major resource such as hydrocarbons, metals or phosphate. All the 10 big metals and the minor metals indicated with yellow colour have their own primary mines, for all those in blue colour, extraction is dominated by secondary extraction. This complicated system is contained inside the WORLD7 model.
4.2.2. Basis for estimating how much can be extracted from ore deposits
Gallium is extracted mainly from Bayer Liquid from processing bauxite to alumina (about 60%) and zinc (about 40%) (Nassar et al., 2015). A few coal mines extract some gallium from coal and some production has been done from coal fly ash, and potentially, more is available. Gallium can be from secondary extraction during the refining process of primary metals like copper, zinc and lead. Recycled mother metals have very little content of gallium. Gallium is only available if the ore is hydrometallurgical processed and little technology metals come out with heap leaching methods. Only a few studies make detailed studies of the available resources of the technology metals. We have identified a few that were helpful for this study concerning: The size of the extractable gallium resource was discussed by Frenzel et al., (2016a,b, 2017), Lu et al., (2017), Paradis (2015), Panoussi et al., 2015, Wang et al., (2011) and Jaskula (2019). Statistics and data was supplied by USGS (2015, 2017, 2018, 2022). Aspects of the extraction methods and different degrees of recycling was discussed by Brown et al., (2014), Moskalyk (2003, 2004), Redlinger et al., (2015). No earlier studies on gallium involve any real feedbacks from market dynamics.
Estimating the demand is particularly uncertain and was discussed by Goe and Gaustad (2014), Gibson and Hayes (2011), Dehnavi (2013), Weeks (1973) and Licht et al., (2015). The basic approach is to assume a certain percentage growth per year and let it expand exponentially. This is a fairly short term and naive approach and is generally not based in any fundamental system dynamics knowledge of the gallium system. Another approach was to let it expand with GDP. The more sophisticated approaches trace the demand back to specific technology needs, and derive estimates from that.
4.2.3. Extractability and yields
One major source of difference between the available resource estimates in the literature are the differences (or lack of) assessment of actual industrial extractability. That a deposit has a certain amount of metal does not mean that it can all be extracted. The extraction pathway for a metal in general is shown in Figure 1. We have looked at many assessments to see if they seem to converge on a similar resource base for gallium (We reviewed Werner et al., 2017, Yellishetty et al., 2017, USGS 2022, Brown et al., 2015, Frenzel 2016, Mudd et al., 2014, 2017, Nassar et al., 2015, Sverdrup and Olafsdottir 2020, for gallium resource estimates). Yield is defined as being made of several components: Access yield: The part of the deposits that will be available for this kind of extraction.
Some deposits lack physical or legal access, some have a composition that prevents extraction or the extraction operation do not have the infrastructure to extract the technology metal when the operation is running Reuter et al., (2013a,b); (YA). The substrate yield is the fraction of the potential in the source material that will be used for extraction, in many mines, the refining residuals are simply thrown away; (YS). When the gallium is taken out, first there is an extraction where gallium is separated from the other metals present (YE) and then it its refined and into pure gallium (YR), see Figure 3. Some methods, such as heap leach do not readily give such a secondary substrate that contains gallium or other metals that can be extracted. The refining yield is the fraction of the gallium recovered from the refining substrate; (YR). Some bauxites have good gallium contents, but too much silica to be interesting for alumina production. Then gallium will not be extracted. Some coals goes straight to a use where the gallium will not be extracted from the ashes. The extraction cut-off is dependent on technology, extraction costs and the metal price at the time.
4.2.4. Resource and extractable amounts estimation.
The recoverable resources are estimated (Krautkrämer 1988, Sverdrup and Olafsdottir 2019, 2020):
Gallium resource = Mother metal resource * XGa * Y (1)
Gallium production = Mother metal production * XGa * Y (2)
XGa is the fraction gallium in the material, and where the yield Y is the yield (Krautkrämer 1988, Sverdrup and Olafsdottir 2020, Sverdrup et al., 2023). This is defined as:
Y= YA * YE * YR (3)
The refining yield YR will be a function of the extractive efficiency when treating the ore shipped to the refinery. The material contained below the cut-off grade is lost with the waste (Krautkrämer 1988, Sverdrup and Olafsdottir 2020). The extraction yield YE is:

Y is the overall yield, the amount metal extracted divided by the total metal content in the original ore. The extraction cut-off is determined by the technology used for extraction, combined with several cost aspects of extraction. Gallium can be extracted from the waste liquid when bauxite is processed to alumina (Bayer process) and if the extraction plant has the necessary infrastructure for it. Some Russian and Chinese coal deposits are known to contain significant amounts of gallium. The different estimates come from different sources, not using the same background material, and they are thus not always consistent. For gallium extraction before 1950 was very small. Yields from refining residuals are far higher than the access yields and enrichment yields, suggesting that investment in technical ability for gallium extraction appear to be missing. Possibly because on the individual process step level, each process is difficult to make profitable, even if gallium is very important on the whole-system strategic level.
4.2.5 Long term sustainable supply of gallium.
Sustainability is defined as “..sufficient for the needs of the present and future generations” according to the Brundtland definition. The future has many more generations than the present. If the time from invention of writing is counted, then that would be 5,000 years or about 150 generations. If we count from the invention of agriculture and the rise of cities, it is 10,000 years or 330 generations. If the industrial revolution started 1840, that is 180 years ago, then it is 6 generations. The total available resource must be estimated as follows:
Available amount = extractable + recycled (5)
This can be used to estimate the annual average supply for the time period assumed to be appropriate for length of the future.

This way of estimating the long term average supply sets a final date for the resource, and after this time it will potentially no longer be available at all. Take note that “sufficient need” is not necessarily the same as “want” or “demand”. The results are reported later.