Hubbert Model Research Articles

Combination prediction and error analysis of conventional gas production in Sichuan Basin

The accurate prediction of the trend of natural gas production changes plays an important role in the formulation of development planning plans. The conventional gas exploration and development in Sichuan Basin has a long history. Based on the development of conventional natural gas production, the article uses the Hubbert model, Gauss model, and GM (1, N) model to predict conventional natural gas production, and then the Shapley value method is used to allocate the weight values of the three models, and a combination model for conventional gas production prediction is established. Finally, residual analysis and precision test are carried out on the prediction results. The results show that: 1) The combination model established using the Shapley value method can effectively combine the advantages of various models and improve the accuracy of prediction. And the standardized residual of the combined model is the lowest, the prediction is closest to the actual value, and the accuracy test is the best, indicating that the combined model has the highest accuracy. 2) After using a combination model for prediction, conventional gas production will peak in 2046, with a peak production of 412 × 108 m3, with a stable production period of (2038–2054) years, a stable production period of 17 years, and a stable production period of 389 × 108 m3, the predicted results of the combined model have a longer stable production period, and the trend of production changes is more stable. The use of combination model provides a reference for the field of natural gas prediction, while improving the accuracy of prediction results and providing better guidance for production planning.

U.S. shale oil production and trend estimation: Forecasting a Hubbert model

AbstractScarcity and growth analyses about energy include forecasting extraction rates of non‐renewable resources while taking into account technological progression. One mechanism, Moore's (1965) Law of technological improvement, encompasses experience enhanced steady cost reductions. Alternatively, synthesis technological change refers to unforeseen innovative breakthroughs. These trends relate to the Hubbert (1956, 1962) Curve of U.S shale oil extraction in the U.S. Lower 48 contiguous states. Price effects, drilling rigs and the price‐to‐drilling rig relationship are analyzed. Results show we are at peak U.S. shale oil, and could experience comprehensive decline. This implies Catton's (1982) “Age of Exuberance,” and “Carrying Capacity” drawdown.

Applicability of Hubbert model to global mining industry: Interpretations and insights

The Hubert’s model has been introduced in 1956 as a phenomenological description of the time evolution of US and world oil fields production. It has since then acquired a vast notoriety as a conceptual approach to resource depletion. It is often invoked nowadays in the context of the energy transition to question the limitations induced by the finitude of mineral stocks. Yet, its validity is often controversial despite its popularity. This paper offers a pedagogical introduction to the model, assesses its ability to describe the current evolution of 20 mining elements, and discusses the nature and robustness of conclusions drawn from Hubbert’s model considered either as a forecast or as a foresight tool. We also propose a novel way to represent graphically these conclusions as a “Hubbert’s map” which offers direct visualization of their main features.

Studies of natural gas production prediction and risk assessment for tight gas in Sichuan Basin

After a new round of tight gas geological evaluation was launched in 2018, a new chapter of tight gas exploration and development has been opened in the Sichuan Basin. In order to make better planning work, it is very important to study the variation rule and risk assessment of tight gas production. In this paper, the peak production is predicted by Ward model. Based on the prediction results, Hubbert and Gauss models were established to study the variation law of tight gas production, and the accuracy and prediction results of the models were determined by the degree of fitting and correlation coefficient. By studying the relationship between URR and production, it is concluded that the production increases in a step, and the future production of tight gas is simulated from the perspective of realization probability. Finally, the risk assessment matrix is established to study the difficulty degree of achieving the production target. The results are as follows: 1) Hubbert model has higher accuracy in predicting tight gas production change. The peak year of tight gas is 2042, the peak production is (86−106)×108m3/a, and the final URR recovery degree is about 60%. 2) The realization probability of production is calculated, and the possibility of reaching the target value is evaluated from the perspective of risk, so as to guide the production of tight gas, and finally promote the formulation of tight gas development planning in the Sichuan Basin.

Gas production prediction and risk quantification of shale gas reservoirs in Sichuan Basin based on Gauss prediction model and Monte Carlo probability method

The shale gas exploration and development potential in the Sichuan Basin is huge. Production prediction and risk quantification are important in planning of natural gas resources. Hubbert and Gauss models are used to predict the growth trend of production in the gas reservoir. Based on the prediction results, the Monte Carlo simulation is used to calculate the probability of production realization. The evaluation matrix of risk level is established by using indices of production realization probability and dispersion degree for assessing the risk level of shale gas production. The results show that: 1) when URR is at the same growth rate, Gauss model has a more stable yield growth trend than Hubbert model, and the correlation coefficients of Gauss model are all higher than that of Hubbert model. This means that the production prediction results of the Gauss model have higher accuracy. 2) According to the Gauss model, the shale gas will reach peak production of (280–460) × 108 m3/a in 2042 and will have stable production from 2037 to 2047. By the end of the stable production stage, the URR exploitation degree is about 60%; 3) The Monte Carlo method can be used to obtain the production realization probability for each year. The risk level evaluation matrix can be established by taking the probability of realization and the dispersion degree as evaluation indices, which can provide the systematization of the risk levels. This study is helpful to deepen the understanding of natural gas exploration and development. And it is of great significance to gas field development planning and production index realization.

A dynamic model for liquid fossil fuel production based on gross product/ERoEI coupling

Since 1940, many attempts to model oil production have been proposed. These approaches, using increasing complexity, consider growing and decay of production independently of external, time-varying, causes. It is here proposed to extend the production equation by a dynamic dependency between oil and Energy Return on Energy Invested (ERoEI). The model is based on mass and energy conservation and can be applied to all extracted liquid fossil fuels. After comparison with oil extraction and ERoEI dynamics, it highlights the existence of an external, controlling parameter: the investment rate, which account for the re-investment in newly operated liquid fuel sources. Its dynamic provides explanations about the oil shock and some explanations about the peak prediction issues of the Hubbert model. Studying this evolution suggests an attempt to control the oil production in order to sustain a globally linear production, starting around 1943: at short time scale (shorter than 28–36 years), the investment rate evolved linearly. However, in order to keep a linearly growing production at long time scale, the investment rate had to evolve exponentially: this was achieved through a piecewize linear control, where the investment rate and its derivative doubled every 28–36 years. The link between this control and the oil shocks suggests the next oil shock will occur around 2035–2040.The model also allows to highlight a major issue in liquid fossil fuel production: even if gross product can be controlled and keeps growing linearly, net product, which account for the energy delivered by the oil industry to the consumer, can decrease before the gross product peaks, due to the decay of ERoEI. At this point, the energy benefit of the oil industry will inevitably decrease and oil production will slow down. Based on the present model and a sensibility study on its parameters, this tipping point will happen between 2026 and 2039. Net product of fossil liquid fuels could therefore keep growing linearly until this point, where a steep decay is expected. Hence production will be strongly asymmetric regarding the peak, contrary to the prediction suggested by Hubbert's model. Production will finally be close to zero around 2063–2072.

Studies on natural gas production prediction and risk quantification of Sinian gas reservoir in Sichuan Basin

The Sinian gas reservoir in the Sichuan Basin has the potential for natural gas exploration and development. Production prediction and risk quantification are important in planning of natural gas resources. Ultimate recoverable reserves (URRs) of Sinian gas reservoir are estimated. Hubbert and Gauss models are used to predict the growth trend of production in the gas reservoir. Based on the prediction results, the Monte Carlo simulation is used to calculate the probability of production realization. The evaluation matrix of risk level is established by using indices of production realization probability and dispersion degree for assessing the risk level of natural gas production. The results show that: (1) compared to the Hubbert model, the production prediction results of the Gauss model have higher accuracy. The Sinian gas reservoir will reach peak production of left( {140 - 285} right) times 10^{8} {text{m}}^{3} /{text{a}} in 2036 and will have stable production from 2032 to 2040. By the end of the stable production stage, the URR exploitation degree is about 60% and (2) the Monte Carlo method can be used to obtain the production realization probability for each year. The risk level evaluation matrix can be established by taking the probability of realization and the dispersion degree as evaluation indices, which can provide the systematization of the risk levels. The study can help to better understand the guiding significance for the natural gas exploration and development.

Assessing cobalt supply sustainability through production forecasting and implications for green energy policies

Transitioning to a decarbonized and circular economy is paramount for climate change mitigation and sustainable development. In this paper we assess the global production trends of cobalt, an energy-transition metal (ETM), and its supply sustainability. Accurate production forecasting of ETMs is essential to understand the dynamics of energy supply security and adequately plan for a change from fossil fuel energy to renewable energy production. Evaluations of market concentrations demonstrate that cobalt is a high-risk market characterized by production fluctuations and supply-chain complexities. We forecast the cobalt production using several methods. Results from both of the Auto Regressive Integrated Moving Average (ARIMA) and Holt's methods show a linear increase in world cobalt production for the short term, while a Hubbert model predicts a world production decline beginning in the late 2010s. These predictions, coupled with geopolitical, socio-environmental, and techno-economic influences on the market, reinforce the concern regarding cobalt supply sustainability. Although alternative avenues for sourcing cobalt, such as secondary urban mining and stockpiling exist, they are unlikely to become major suppliers in the short term, which highlights the need to accurately forecast primary production. Increasing interests in critical raw materials (CRMs) in policy spheres also heightens the necessity to anticipate the future of cobalt supply as governmental entities acknowledge the imbalance of CRMs in international trade. Well-researched and well-designed policies, that incorporate environmental sustainability and non-discriminatory economic growth, can facilitate an equitable shift to a greener and more circular economy. At the forefront of this shift should be ethical environmental and resource governance that recognizes the inequalities in socio-economic development and energy-transition, and mandates for a just transition towards a low carbon future.

A hybrid assessment model for mineral resource availability potentials

Traditional mineral resource availability assessment methods always have strong assumptions and limitations on application. Both the physical mechanism of the Hubbert model and the economic mechanism of the Hotelling model can evaluate only specific dimensions of the availability of mineral resources. Therefore, we propose a hybrid model that could explain mineral resource availability from geological factors to the metal market. In this model, mineral resource availability will be assessed by two indicators in a coordinate system. One is the marginal effect of mining technology, which is calculated by the Cobb-Douglas production function. Another is the price elasticity ratio of reserve and production. Meanwhile, we apply this model to assess 13 kinds of strategic minerals in China. Among them, the availability potential of gold, tin and lead is large in the future, while that of iron, aluminum and copper is relatively small. In addition, zirconium, chromium, lithium, cobalt, tungsten and nickel are technology-based strategic minerals, while molybdenum is a market-oriented strategic mineral. Moreover, we put forward the classified management policy based on empirical results.

Studies on natural gas reserves multi-cycle growth law in Sichuan Basin based on multi-peak identification and peak parameter prediction

Research on predicting the growth trend of natural gas reserves will help provide theoretical guidance for natural gas exploration in Sichuan Basin. The growth trend of natural gas reserves in Sichuan Basin is multi-cycle and complex. The multi-cyclic peak is screened by the original multi-cyclic peak judgment standard. Metabolically modified GM(1,3) gray prediction method is used to predict the multi-cycle model parameters. The multi-cycle Hubbert model and Gauss model are used to predict the growth trend of natural gas reserves. The research results show that: (1) The number of cycles of natural gas reserves curve during 1956–2018 is 13. Natural gas reserves will maintain the trend of rapid growth in the short term. (2) Metabolism modified GM(1,3) gray prediction model can improve the accuracy of model prediction. The prediction accuracy of Hubbert model is higher than that of Gauss model. By 2030, the cumulative proven level of natural gas will reach 52.34%. The Sichuan Basin will reach its peak of proven lifetime reserves in the next few years.

Establishment and application of prediction model of natural gas reserve and production in Sichuan Basin

Research on predicting the growth trend of natural gas reserves and production will help provide a scientific basis for natural gas exploration and development. The metabolically improved modified weight coefficient GM(1,n) method is applied to the multi-cycle Hubbert model to predict the trend of new proven natural gas reserves in the Sichuan Basin. The ultimate recoverable reserves (URR) is introduced as a boundary condition in the production-time series to predict the natural gas production growth. The research results show that: (1) The annual newly added proven natural gas reserves of the Sichuan Basin maintain a multi-cycle growth trend, which will reach the peak reserves in 2034, at which time the proven rate of natural gas will reach 36%. (2) Based on the predicted results of proven reserves, the final recoverable reserves of natural gas are estimated to be 5.25-5.75times {10}^{12}{m}^{3}. The production in 2035 will reach 750-810times {10}^{8}{mathrm{m}}^{3}/mathrm{a}, and production will grow rapidly. The exploration and development of natural gas in the basin will be prospective for a long time.

A cycle‐jumping method for multicyclic Hubbert modeling of resource production

AbstractThe amount of ultimately recoverable resources and/or timing of peak production have been the central purpose of numerous studies. One broadly applied method is Hubbert modeling, subsequently extended as multicyclic Hubbert modeling. This paper explores a modification to conventional multicyclic Hubbert modeling that we term “cycle‐jumping” wherein the overlap of multiple curves is limited and explicitly accounted for. The model is designed in a way that each curve is described by the same three parameters as a multicyclic Hubbert model, and every two curves are connected through an explicit transition. The transition width indicates the time of the shift from one curve to the next and is controlled by a weighting parameter for the respective curves. Cycle‐jumping provides a superior data fit compared to the conventional cycle‐addition model and, more important, reflects historical production data more realistically as socioeconomic and political factors important to resource production vary in time.Recommendations for Resource Managers Conventional multicyclic Hubbert modeling poorly reflects transitions in production trends. Cycle‐jumping with a finite transition period practically and mathematically provides a superior model for historical resource production by limiting the overlap of multiple curves. Cycle‐jumping with a finite transition period reflects more realistically the production profile affected by external factors including capturing inherent asymmetry in different cycles.

A Copula–Hubbert Model for Co(By)-Product Minerals

Production of major minerals and co(by)-product minerals is highly connected. For example, almost 95% of indium production can be derived from zinc mining and processing. In this paper, a Copula–Hubbert model for co(by)-product minerals is proposed and applied for predicting zinc and indium production in the world. Unlike the Hubbert model, a copula function to joint multiple logistic distributions in the Copula–Hubbert model makes the minerals’ production more accurate. Because of geological and mining information asymmetric relationships among mineral deposits, the model is more appropriate to by-product minerals. The empirical result shows that the peak of zinc may arrive in 2030 nearly; however, the peak of indium may reach after 2050. In the future, the peak value and peak date of indium can be affected by the development and utilization efficiency of zinc mining and processing. Finally, some directions on this model are introduced.

Renewable Energy: Volume 1: Requirements and Sources

This book reviews the past and present energy use of society and its future needs. A breakdown of current energy sources shows that approximately 80% of the world's primary energy comes from fossil fuels. The book provides an assessment of the needs to change the way in which energy is produced and utilized. The reasons for change fall into two broad categories; diminishing resources and environmental impact. The Hubbert model is described as a means of projecting availability of fossil fuel energy resources in the future. The environmental impact of fossil fuel use is described, with particular emphasis on global climate change. The major options for carbon-free energy are presented. These options include hydroelectric energy and solar energy for both thermal applications and the production of electricity, wind energy, and biofuels. Renewable energy options that range from residential wind turbines and photovoltaics for electricity and solar thermal heating systems to grid scale facilities, such as off-shore wind farms and hydroelectric installations, are discussed. The production of biofuels as a replacement for fossil fuels used for transportation is also presented. The book also provides evidence for the need to develop energy storage technologies. Energy storage is essential for most forms of renewable energy because the thermal or electrical energy produced by such sources is generally not available when it is needed, nor is it sufficiently portable for transportation applications.

Coal production and consumption analysis, and forecasting of related carbon emission: evidence from China

Carbon dioxide (CO2) formed during coal combustion is responsible for over half of the increase in the greenhouse effect, globally. It is crucial to conduct a comprehensive analysis and accurate prediction for coal production and consumption to optimize coal utilization and control emissions. However, several unstable factors inhibit the accurate forecasting of coal. Therefore, taking into account both effect and efficiency of prediction, the Hubbert model is applied in this study to forecast China’s peak coal production, peak year, and future production. Additionally, a combined model, with weights determined by a flower pollination algorithm and no-negative-constraint theory, is proposed to forecast coal consumption, which is superior to that of all individual models. Subsequently, accounting for the vital effect of CO2 from coal combustion on economic issues, correlation analysis and an environmental Kuznets curve (EKC) are applied to quantitatively examine the relationship among coal consumption, economic development, and carbon emissions. The results of this estimation suggest that, compared to the US, China’s economic development relies more on coal consumption; however, the EKC indicates that China has still not reached the ‘inflection point’. Accordingly, it is essential for policymakers to balance the relationship among coal utilization, economic development, and the environment.

Research on a Model of Oil Production Forecast Based on Technical Development and Dynamic Change of Reserves

The Hubbert model is widely used in forecasting the oil production. However, many scholars compared the history data to the data calculated by Hubbert model and got the conclusion that the Hubbert model was not suitable for forecasting oil production. In this paper, the Hubbert model is modified and the technical progress is considered in the model. An oil production forecast system is presented, which can be used to analyze the technical progress and dynamic change of reserves. This forecast system is decomposed into three models, namely the technical model, dynamic reserves model and production forecast model. The purpose of this paper is to show the powerful effect of technical progress and dynamic reserves on oil production. It is an innovative view that less research focus on this side. Furthermore, seismic technology, exploration theory, drilling technology and oil production technology are considered in technical model. These models are used to forecast world oil production from 2018 to 2030.

A critique of Hubbert’s model for peak oil

In 1956, Shell Oil Company geologist M. King Hubbert published a model for the growth and decline over time of the production rates of oil extracted from the land mass of the continental US. Employing an estimate for the amount of ultimately recoverable oil and a logistic curve for the oil production rate, he accurately predicted a peak in US oil production for 1970. His arguments and the success of his prediction have been much celebrated, and the original paper has 1400 publication citations to date. The theory of “peak oil” (and subsequently, of natural resource scarcity in general) has consequently become associated with Hubbert and “Hubbert” curves and models. However, his prediction for the timing of a world peak oil production rate and the subsequent predictions of many others have proven inaccurate. We revisit the Hubbert model for oil extraction and provide an analysis of it and several variants in the language of (time) autonomous differential equations.

China’s Rare Earths Production Forecasting and Sustainable Development Policy Implications

Because of their unique physical and chemical properties, Rare earth elements (REEs) perform important functions in our everyday lives, with use in a range of products. Recently, the study of China’s rare earth elements production has become a hot topic of worldwide interest, because of its dominant position in global rare earth elements supply, and an increasing demand for rare earth elements due to the constant use of rare earth elements in high-tech manufacturing industries. At the same time, as an exhaustible resource, the sustainable development of rare earth elements has received extensive attention. However, most of the study results are based on a qualitative analysis of rare earth elements distribution and production capacity, with few studies using quantitative modeling. To achieve reliable results with more factors being taken into consideration, this paper applies the generic multivariant system dynamics model to forecast China’s rare earth elements production trend and Hubbert peak, using Vensim software based on the Hubbert model. The results show that the peak of China’s rare earth elements production will appear by 2040, and that production will slowly decline afterwards. Based on the results, the paper proposes some policy recommendations for the sustainable development of China’s—and the world’s—rare earth elements market and rare earth-related industries.

Oil production and abrupt institutional change: the multi-cyclic Hubbert model and the case of Iraq

Iraq, one of the world's leading crude oil producers with the fifth largest share of proven global oil reserves, recently ranked as the second-largest producer among Organization of the Petroleum Exporting Countries (OPEC) members. Nevertheless, performance of the upstream subsector in terms of oil production volume has been subject to severe disruptions for more than four decades. The main sources for these fluctuations are multi-institutional changes caused by nationalization, wars and United Nations sanctions. This article applies to the Iraqi case an extended version of the multi-cycle Hubbert model, developed by Reynolds and Kolodziej in 2008 and 2009. This econometrics model explores and attempts to quantify statistically the relationship between oil production and multi-institutional changes within Iraq. Findings indicate the negative and significant impacts of abrupt institutional change on the performance of the oil industry where this adverse impact varies in magnitude from one episode to another. As Iraq is still yet in the midst of a turbulent transition, the article also discusses the major challenges of the post-2003 era, associated with the present and potential future development of the Iraqi oil-producing sector. This is especially with regard to the increasing economic and political fragmentation that stems from the absence of a unified oil policy.

Where is the future of China’s biogas? Review, forecast, and policy implications

This paper discusses the history and present status of different categories of biogas production in China, most of which are classified into rural household production, agriculture-based engineering production, and industry-based engineering production. To evaluate the future biogas production of China, five models including the Hubbert model, the Weibull model, the generalized Weng model, the H–C–Z model, and the Grey model are applied to analyze and forecast the biogas production of each province and the entire country. It is proved that those models which originated from oil research can also be applied to other energy sources. The simulation results reveal that China’s total biogas production is unlikely to keep on a fast-growing trend in the next few years, mainly due to a recent decrease in rural household production, and this greatly differs from the previous goal set by the official department. In addition, China’s biogas production will present a more uneven pattern among regions in the future. This paper will give preliminary explanation for the regional difference of the three biogas sectors and propose some recommendations for instituting corresponding policies and strategies to promote the development of the biogas industry in China.