Research Article 
Corresponding author: Dariya Yu. Semenova ( dysemenova@bk.ru ) Academic editor: Yury Kazansky
© 2024 Ulugbek T. Mirkhusanov, Dariya Yu. Semenova, Vladimir V. Kharitonov.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Mirkhusanov UT, Semenova DYu, Kharitonov VV (2024) Forecasting the cost and volume of uranium mining for different world nuclear energy development scenarios. Nuclear Energy and Technology 10(2): 131137. https://doi.org/10.3897/nucet.10.130485

The paper presents a new analytical methodology for predicting the volume and cost of natural uranium production depending on uranium resources and scenarios for the development of traditional nuclear energy. The proposed methodology is based on a mathematical model of the dynamic process of exhaustion of fossil resources previously developed at MEPhI and uses the parameters of the explored mass of the fossil resource, the annual volume of production and the set rate of production growth. The three parameters known at the beginning of forecasting make it possible to describe the change in the resource base over time and solve a number of economic problems related to the extraction of valuable minerals. The paper provides forecasts of the NPP’s demand for natural uranium, depending on the scenarios for the development of global nuclear energy developed by the World Nuclear Association (WNA), uranium resources and volumes of its production with different costs for 2021–2022. It is shown that at a low rate (1.8%/year) of the installed capacity of nuclear power plants, uranium resources will last for more than a century, but the contribution of nuclear energy to electricity production will continuously decrease from the current 10%. Under high scenarios for the development of nuclear energy (>5%/year), which is possible under the conditions of intensification of the “green energy transition”, the peak of uranium production may occur before the middle of this century. Based on these data, forecasts of the dynamics of uranium exhaustion and annual production volumes at fields with different costs are presented until the second half of this century, depending on the initial production growth rates determined by the scenario of nuclear energy development.
natural uranium, cost of uranium mining, nuclear energy development scenario, uranium production
It will be no exaggeration to say (following the authors
Based on different scenarios, global production of electricity will grow until 2050, the growth rate to be not less than 2%/year. With nuclear generation of electricity growing at a rate of not less than 2%/year, as is the case in recent decades, the contribution of nuclear power to global electricity production will go down. According to the scenario from the International Energy Agency (IEA) published in October 2022 (World Energy Outlook 2022), nuclear generation of electricity will grow until 2040, with a growth rate of about 1.8%/year, while electricity generation by wind and solar power plants will increase at a rate of 9% to 12% per year (Fig.
The WNA reports identify three global scenarios, that is, lowrate, baserate, and highrate scenarios (
In accordance with the IAEA classification of uranium resources, the core criterion is the probable cost of uranium mining (
Global uranium resources (kt) with different cost of production as of 2021 (
Production cost  Reasonably assured resources (RAR)  Inferred resources (IR)  Recoverable resources (RAR+IR) 

<$40/kgU  457  319  776 
<$80/kgU  1211  780  1991 
<$130/kgU  3815  2264  6079 
<$260/kgU  4688  3229  7917 
Resources and production of uranium in the cost category of below 260 $/kgU by countries of the world as of 2022 (
Country  Uranium resources in 2021 R, kt  Uranium production in 2022 Р, kt/year  Capacity in 2022 kt/year  Cumulative uranium production for 1945–2022 Q, kt  Uranium demand, kt/year 

Australia  1960  4.55  6.81  241   
Kazakhstan  875  21.23  29.06  350   
Canada  865  7.35  16.54  554  1.48 
Russia  657  2.51  3.10  378*+91  6.28 
Namibia  510  5.61  8.90  159   
Niger  468  2.02  2.02  157   
South Africa  445  0.20  0.77  166  0.28 
Brazil  277        0.34 
China  245  1.70  1.92  54  11.3 
India  221  0.60  0.61    1.41 
Ukraine  185  0.10  1.65  25  1.57 
Uzbekistan  131  3.30  3.50  77   
USA  112  0.075    378  18.05 
Others  967  0.11  0.34  557**  24.94*** 
Total  7918  49.36  76.20  3185  65.65 
It also follows from Table
A MEPhI paper of
According to the MEPhI model, the dynamics of annual production, G (t), in year t>0 (as from the forecast start time) is described by the analytical expression
$G\left(t\right)={G}_{0}\frac{(2+\theta {)}^{2}\mathrm{exp}(T)}{\left(\mathrm{exp}\right(T)+1+\theta {)}^{2}}$ . (1)
Here, θ = k_{0}T_{0} = k_{0}M_{0}/G_{0} is the dimensionless parameter that characterizes the raw material depletion rate; Т_{0}=М_{0}/G_{0} is the depletion period of the raw material resource, M_{0}, in the event of stable annual production, G_{0}, (referred to in foreign literature as “ReservestoProduction” or “R/P ratio”); and T=(k_{0}+2/T_{0})t is the dimensionless parameter that characterizes the forecast time. According to (1), with k_{0}>0, the diagram of G (t) is bellshaped: the production grows initially at a rate of k_{0}, and then the production rate, k=(dG/dt)/G, slows down and becomes equal to zero (k=0) at a certain time point, t_{M}, as the mineral production reaches the peak, G_{M}:
${G}_{M}={G}_{0}\frac{(2+\theta {)}^{2}}{4(1+\theta )};\phantom{\rule{0.5em}{0ex}}{t}_{M}=\frac{\theta}{{k}_{0}(2+\theta )}\mathrm{ln}(1+\theta )$ . (2)
The annual production decreases thereafter due to the further depletion of the resource. The model suggests that there will be no new deposits in future. If otherwise, the resource amount needs to be changed for a new value at this point. That is, the model takes into account longterm trends rather than shortterm production declines and increases due to all kinds of current circumstances. For Kazakhstan, for instance, as shown in Table
To illustrate how the resource depletion model can be used, Fig.
Dynamics of the annual oil and natural gas production worldwide (10^{9} t/year and 10^{12} m^{3}/year respectively) with the initial rate of production growth rate being k_{0}=1%/year with initial data shown in Table
Proven resources and annual production of oil and natural gas by countries of the world for 2020*(BP2021) (Statistical Review of World Energy 2021)
Countries  Oil  Natural gas  

Resource M, 10^{9} t  Production G, 10^{9} t/year  Depletion period Т_{0}=M/G, years  Resource M, 10^{12} m^{3}  Production G, 10^{12} m^{3}/year  Depletion period Т_{0}=M/G, years  
USA+Canada  8.2 + 27.1 = 35.3  0.965  36.6  12.6 + 2.4 = 15.0  1.080  13.9 
Western Europe  1.8  0.167  10.8  3.2  0.219  14.6 
Russia  14.8  0.524  28.2  37.4  0.638  58.6 
Middle East  113.2  1.297  87.3  75.8  0.687  110.4 
World total  244.4  4.165  58.7  188.1  3.854  48.8 
The doubled oil and gas resources (dashed lines in Fig.
It follows from Fig.
Uranium production cost, unlike uranium market price, is a more stable quantity while uranium market prices are highly volatile due to varying severalfold under the influence of either the demand growth expectations or following the volatility of prices for oil, gas and other energy sources. Thus, in 2007, on the eve of the world economic crisis of 2008‒2009, the uranium prices reached the historical peak of 345 $/kgU (133 $/lbU_{3}O_{8}). There was another price peak (148 $/kgU) observed in 2011, just before the Fukushima nuclear accident in Japan, after which the market prices dropped to reach the minimum of 57 $/kgU (22 $/lbU_{3}O_{8}) in 2017. At the same time, there have been no major changes in the uranium production technology, output or cost. In a longer term, however, due to the exhaustion of cheap deposits and development of more remote (expensive) deposits with the use of more advanced (and expensive) technologies, the cost of uranium production will grow to affect inevitably the market prices. Accordingly, forecasting the uranium production cost is fundamental to identifying the trends for the change in the market prices for natural uranium and, therefore, for the NPP electricity cost fuel component.
The cost of different deposits varies in the limits of С_{0}≤С≤С_{м} where the minimum cost is С_{0}≈16 $/kgU (Karatau, Kazakhstan (
We shall express the uranium production cost dynamics as the most common function, g (C,t), that describes the annual uranium output (kg/year) for all deposits with a production cost of not more than С ($/kgU) in year t as from the forecast start. That is, value g (C,t) is the cumulative annual output for all deposits in a cost range from the smallest cost to С, quantity C varying between the minimum value and the maximum value as determined above. The initial form of this function (with t=0) is known to be g (C,t=0)≡g_{0}(С) and is shown in Fig.
Influence of uranium production cost, С, ($/kgU) on timedependent change in uranium resources, m (C,t), (2021‒2070), Mt U (a) and annual uranium production, g (C, t), ktU/year (b), with the initial production growth rate of k_{0}=4.1%/year which corresponds to the WNA23 base scenario (
Having such initial data as m_{0}(С), g_{0}(С) and k_{0}I, and using expression (1), we find the sought solution for the dynamics of uranium production with a different cost in the following form
$g(C,t)={g}_{0}\left(C\right)\frac{(2+\theta {)}^{2}\mathrm{exp}(T)}{{\left[\mathrm{exp}\left(T\right)+1+\theta \right]}^{2}}$ . (3)
Here, dimensionless groups θ(C) and T(C), which depend on the uranium production cost, are determined by the following expressions:
$\theta \left(C\right)=\frac{{k}_{0}\left(C\right){m}_{0}\left(C\right)}{{g}_{0}\left(C\right)};\phantom{\rule{0.5em}{0ex}}T\left(C\right)=\left(1+\frac{2}{\theta \left(C\right)}\right){k}_{0}\left(C\right)\xb7t$
The timedependent change in the balance of inplace resources, m(C, t), with the cost of production in a range between the minimum cost and С is determined by the following expression
$m(C,t)={m}_{0}\left(C\right){\int}_{t=0}^{t}g(C,t)dt={m}_{0}\left(C\right)\frac{2+\theta}{\mathrm{exp}\left(T\right)+1+\theta}$
Therefore, since the initial functions of the resource, m_{0}(С), and of the output, g_{0}(С), are known (see Fig.
Dynamics of uranium production with different cost (initial rate of k_{0}=4.1%/year) which corresponds to the WNA23 base scenario (
The results presented in Figs
The results that justify the reliability of the proposed methodology, that is, the estimated depletion dynamics for different mineral resources, are presented in detail in
Forecasting the cost of uranium production is fundamental to identifying the trends for the change in the market prices for natural uranium and, thus, for the fuel component of the nuclear electricity cost.
Based on the mineral resources depletion model developed by MEPhI, this paper shows for the first time how global annual uranium production changes over time depending on the cost of production with the predefined uranium resources and scenarios of the global nuclear power evolution (and with initial uranium production growth rates). The uranium production peak is expected to occur in 10 years for cheap deposits (below 40 $/kgU), while production will be half as small, as compared with 2022, by the middle of this century with the initial production growth rate being about 4%/year (the base scenario from the World Nuclear Association). For expensive deposits, production will increase until the middle of the century with the equally rapid decline in production thereafter. With lowrate scenarios of nuclear power evolution (less than 2%/year), conventional uranium resources in the production cost category of below 260 $/kgU will suffice for more than a century but its contribution to electricity generation will decrease continuously from the current 10%. With highrate scenarios of nuclear power evolution, the uranium production peak is expected to be reached by the middle of this century.
Since the major suppliers of natural uranium for the world market are countries with no domestically deployed NPPs, and the major uranium consumers are economically developed countries (“Golden Billion” countries) with practically no domestic uranium resources, one can expect competition to grow in the world uranium market with a potential for an increase in the event of NPP construction in uranium producing countries.