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25 pages, 6500 KiB  
Article
Production Forecasting at Natural Gas Wells
by Alina Petronela Prundurel, Ioana Gabriela Stan, Ion Pană, Cristian Nicolae Eparu, Doru Bogdan Stoica and Iuliana Veronica Ghețiu
Processes 2024, 12(5), 1009; https://doi.org/10.3390/pr12051009 - 15 May 2024
Cited by 2 | Viewed by 1533
Abstract
In Romania, natural gas production is concentrated in two large producers, OMV Petrom and Romgaz. However, there are also smaller companies in the natural gas production area. In these companies, the deposits are mostly mature, or new deposits have low production capacity. Thus, [...] Read more.
In Romania, natural gas production is concentrated in two large producers, OMV Petrom and Romgaz. However, there are also smaller companies in the natural gas production area. In these companies, the deposits are mostly mature, or new deposits have low production capacity. Thus, the production forecast is very important for the continued existence of these companies. The model is based on the pressure variation in the gas reservoir, and the exponential model with production decline is currently used by gas and oil producers. Following the variation in the production of the gas wells, we found that in many cases, the Gaussian and Hubbert forecast models are more suitable for simulating the production pattern of gas wells. The models used to belong to the category of poorly conditioned models, with little data, usually called gray models. Papers published in this category are based on data collected over a period of time and provide a forecast of the model for the next period. The mathematical method can lead to a very good approximation of the known data, as well as short-term forecasting in the continuation of the time interval, for which we have these data. The neural network method requires more data for the network learning stage. Increasing the number of known variables is conducive to a successful model. Often, we do not have this data, or obtaining it is expensive and uneconomical for short periods of possible exploitation. The network model sometimes captures a fairly local pattern and changing conditions require the model to be remade. The model is not valid for a large category of gas wells. The Hubbert and Gauss models used in the article have a more comprehensive character, including a wide category of gas wells whose behavior as evolutionary stages is similar. The model is adapted according to practical observations by reducing the production growth period; the layout is asymmetric around the production peak; and the production range is reduced. Thus, an attempt is made to replace the exponential model with the Hubbert and Gauss models, which were found to be in good agreement with the production values. These models were completed using the Monte Carlo method and matrix of risk evaluation. A better appreciation of monthly production, which is an important aspect of supply contracts, and cumulative production, which is important for evaluating the utility of the investment, is ensured. In addition, we can determine the risk associated with the realization of production at a certain moment of exploitation, generating a complete picture of the forecast over the entire operating interval. A comparison with production results on a case study confirms the benefits of the forecasting procedure used. Full article
(This article belongs to the Section Energy Systems)
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Figure 1

Figure 1
<p>The stages of making the article.</p>
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<p>The time variation model for the production of a gas well expressed in the monthly gas flow due to the decrease in the pressure in the reservoir (exponential model), for each of the three initial flow hypotheses (start/end flow values): case A—High Estimation (17,194/327 mScm/month), case B—Best Estimation (10,030/309 mScm/month), and case C—Low Estimation (2865/230 mScm/month).</p>
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<p>Cumulative production variation in the three cases of analysis of a gas well based on the exponential model (end flow values): case A—High Estimation (430.48 MScm), case B—Best Estimation (248.23 MScm), and case C—Low Estimation (67.44 MScm).</p>
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<p>Comparison of actual and anticipated production results: (<b>a</b>) actual production of five natural gas wells from zone 1; (<b>b</b>) production forecast of the natural gas wells from zone 1.</p>
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<p>Prediction of natural gas production: (<b>a</b>) symmetric Gauss and Hubbert models; (<b>b</b>) Gauss and asymmetric Hubbert models; (<b>c</b>) Gauss and symmetrical Hubbert models with a reduced production growth interval; (<b>d</b>) Gauss and asymmetric Hubbert models with a reduced production growth interval.</p>
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<p>Prediction of natural gas production: (<b>a</b>) symmetric Gauss and Hubbert models; (<b>b</b>) Gauss and asymmetric Hubbert models; (<b>c</b>) Gauss and symmetrical Hubbert models with a reduced production growth interval; (<b>d</b>) Gauss and asymmetric Hubbert models with a reduced production growth interval.</p>
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<p>Assessing the risk of achieving natural gas production using the risk matrix. The risk levels are in order from I to IV, with level I representing the lowest risk and level IV representing the highest risk.</p>
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<p>The models used to make the production forecast at the analyzed gas well, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math> (PNG, Production of Natural Gas).</p>
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<p>Variation in the production at natural gas wells in the oil field of which the exemplified well is a part (PNG, Production of Natural Gas).</p>
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<p>Identification of operational areas on the production forecast (PNG, Production of Natural Gas).</p>
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<p>Risk matrix in the production forecast phase at the gas well.</p>
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<p>The graphical tests used to establish the normal distribution for the monthly production value variable Q: (<b>a</b>) normal probability plot; and (<b>b</b>) histogram plot.</p>
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<p>The influence of production on the probability of realization in the phase of slow production decline at a gas well: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>).</p>
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<p>The influence of production on the probability of realization in the phase of slow production decline at a gas well: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>).</p>
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<p>Comparison between production values and theoretical forecasting models: (<b>a</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> <mo>;</mo> </mrow> </semantics></math> (<b>b</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.6</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>; and (<b>c</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.7</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>, (PNG, Production of Natural Gas).</p>
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<p>Comparison between production values and theoretical forecasting models: (<b>a</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.5</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> <mo>;</mo> </mrow> </semantics></math> (<b>b</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.6</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>; and (<b>c</b>) Gauss model, symmetric/asymmetric Hubbert models, and production values, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>0.7</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>0.69</mn> <mo>;</mo> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mn>0.72</mn> </mrow> </semantics></math>, (PNG, Production of Natural Gas).</p>
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21 pages, 7187 KiB  
Article
How US Suppliers Alter Their Extraction Rates and What This Means for Peak Oil Theory
by Theodosios Perifanis
Energies 2022, 15(3), 821; https://doi.org/10.3390/en15030821 - 24 Jan 2022
Cited by 4 | Viewed by 2767
Abstract
Hubbert suggests that oil extraction rates will have an exponentially increasing course until they reach their highest level and then they will suddenly decline. This best describes the well-acclaimed Peak Oil Theory or Peak Oil. We research whether the theory is validated in [...] Read more.
Hubbert suggests that oil extraction rates will have an exponentially increasing course until they reach their highest level and then they will suddenly decline. This best describes the well-acclaimed Peak Oil Theory or Peak Oil. We research whether the theory is validated in seven US plays after the shale revolution. We do so by applying two well-established methodologies for asset bubble detection in capital markets on productivity rates per day (bbl/d). Our hypothesis is that if there is a past or an ongoing oil extraction rate peak then Hubbert’s model is verified. If there are multiple episodes of productivity peaks, then it is rejected. We find that the Peak Theory is not confirmed and that shale production mainly responds to demand signals. Therefore, the oil production curve is flattened prolonging oil dependency and energy transition. Since the US production is free of geological constraints, then maximum productivity may not ever be reached due to lower demand levels. Past market failures make the US producers more cautious with productivity increases. Our period is between January 2008 and December 2021. Full article
(This article belongs to the Section C: Energy Economics and Policy)
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Figure 1
<p>Ultimate global oil production (Hubbert’s original calculations) [<a href="#B2-energies-15-00821" class="html-bibr">2</a>].</p>
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<p>Ultimate US production (Hubbert’s original calculations) [<a href="#B2-energies-15-00821" class="html-bibr">2</a>].</p>
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<p>WTI Futures prices (USD/bbl) and total production (Mbbl/d) of the seven regions.</p>
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<p>PWY (2011), Anadarko region, productivity explosions.</p>
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<p>PWY (2011), Appalachia region, productivity explosions.</p>
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<p>PWY (2011), Bakken region, productivity explosions.</p>
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<p>PWY (2011), Eagle Ford region, productivity explosions.</p>
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<p>PWY (2011), Haynesville region, productivity explosions.</p>
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<p>PWY (2011), Niobrara region, productivity explosions.</p>
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<p>PWY (2011), Permian region, productivity explosions.</p>
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<p>PSY (2015), Anadarko region, productivity explosions.</p>
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<p>PSY (2015), Appalachia region, productivity explosions.</p>
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<p>PSY (2015), Bakken region, productivity explosions.</p>
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<p>PSY (2015), Eagle Ford region, productivity explosions.</p>
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<p>PSY (2015), Haynesville region, productivity explosions.</p>
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<p>PSY (2015), Niobrara region, productivity explosions.</p>
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<p>PSY (2015), Permian region, productivity explosions.</p>
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10557 KiB  
Article
The Future of Sustainable Energy Production in Pakistan: A System Dynamics-Based Approach for Estimating Hubbert Peaks
by Syed Aziz Ur Rehman, Yanpeng Cai, Nayyar Hussain Mirjat, Gordhan Das Walasai, Izaz Ali Shah and Sharafat Ali
Energies 2017, 10(11), 1858; https://doi.org/10.3390/en10111858 - 13 Nov 2017
Cited by 34 | Viewed by 7218
Abstract
This paper presents an effort pertaining to the simulation of the future production in Pakistan of different primary energy resources, i.e., coal, natural gas and crude oil, thereby constructing Hubbert peaks. In this context, the past 45 years’ production data of primary energy [...] Read more.
This paper presents an effort pertaining to the simulation of the future production in Pakistan of different primary energy resources, i.e., coal, natural gas and crude oil, thereby constructing Hubbert peaks. In this context, the past 45 years’ production data of primary energy resources of Pakistan have been analyzed and simulated using a generic STELLA (Systems Thinking, Experimental Learning Laboratory with Animation) model. The results show that the Hubbert peak of Pakistan’s crude oil production has been somehow already achieved in 2013, with the highest production of 4.52 million toe, which is 1.51 times the production in 2000. Similarly, the natural gas peak production is expected in 2024 with a production of 32.70 million toe which shall be 1.96-fold the extraction of the resource in the year 2000. On the other hand, the coal production in the country has been historically very low and with a constant production rate that is gradually picking up, the peak production year for the coal is anticipated to be in the year 2080 with an estimated production of 134.06 million. Based on the results of this study, which provide a greater understanding of future energy patterns, it is recommended that an energy security policy be devised for the country to ensure sustained supplies in the future. Full article
(This article belongs to the Section L: Energy Sources)
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Figure 1
<p>Percent share of fuels in the total energy mix: 1992–2015 [<a href="#B11-energies-10-01858" class="html-bibr">11</a>,<a href="#B12-energies-10-01858" class="html-bibr">12</a>,<a href="#B13-energies-10-01858" class="html-bibr">13</a>,<a href="#B14-energies-10-01858" class="html-bibr">14</a>,<a href="#B15-energies-10-01858" class="html-bibr">15</a>].</p>
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<p>Historical share of energy consumption in different sectors [<a href="#B11-energies-10-01858" class="html-bibr">11</a>,<a href="#B12-energies-10-01858" class="html-bibr">12</a>,<a href="#B13-energies-10-01858" class="html-bibr">13</a>,<a href="#B14-energies-10-01858" class="html-bibr">14</a>,<a href="#B15-energies-10-01858" class="html-bibr">15</a>].</p>
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<p>Map of the major coal, oil and natural gas production sites in Pakistan.</p>
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<p>Coal consumption (demand) across various sector in Pakistan.</p>
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<p>Natural gas consumption across various sectors (1992–2014).</p>
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<p>Exploratory and development wells drilled in Pakistan.</p>
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<p>Oil and petroleum products consumption across various sectors (1992–2014).</p>
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<p>The STELLA interface depicting the Hubbert production as a flow.</p>
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<p>Historical Supply, production, consumption and import of coal (ktoe).</p>
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<p>Coal past vs. cumulative production in million tons.</p>
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<p>Coal Hubbert production peaks under multiple probabilities.</p>
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<p>Historical supply, production, and consumption of natural gas (ktoe).</p>
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<p>Hubbert and cumulative production peak for natural gas (Million toe).</p>
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<p>Natural gas past and cumulative production (million toe).</p>
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<p>Historical supply, production, consumption and import of oil and petroleum products.</p>
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<p>Past and cumulative production for oil (million toe).</p>
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<p>Hubbert and cumulative production peak for oil (Million toe).</p>
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1176 KiB  
Article
China’s Rare Earths Production Forecasting and Sustainable Development Policy Implications
by Xibo Wang, Mingtao Yao, Jiashuo Li, Kexue Zhang, He Zhu and Minsi Zheng
Sustainability 2017, 9(6), 1003; https://doi.org/10.3390/su9061003 - 10 Jun 2017
Cited by 37 | Viewed by 7798
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Section Environmental Sustainability and Applications)
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<p>A generic Vensim diagram. Note: R vs P is reserves to production ratio; resv is reserves; prd is production.</p>
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<p>Three scenarios of China’s REEs Hubbert peak.</p>
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<p>Sensitivity analysis for intrinsic growth rate ‘a’.</p>
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10012 KiB  
Article
The Use of Empirical Methods for Testing Granular Materials in Analogue Modelling
by Domenico Montanari, Andrea Agostini, Marco Bonini, Giacomo Corti and Chiara Del Ventisette
Materials 2017, 10(6), 635; https://doi.org/10.3390/ma10060635 - 9 Jun 2017
Cited by 45 | Viewed by 7486
Abstract
The behaviour of a granular material is mainly dependent on its frictional properties, angle of internal friction, and cohesion, which, together with material density, are the key factors to be considered during the scaling procedure of analogue models. The frictional properties of a [...] Read more.
The behaviour of a granular material is mainly dependent on its frictional properties, angle of internal friction, and cohesion, which, together with material density, are the key factors to be considered during the scaling procedure of analogue models. The frictional properties of a granular material are usually investigated by means of technical instruments such as a Hubbert-type apparatus and ring shear testers, which allow for investigating the response of the tested material to a wide range of applied stresses. Here we explore the possibility to determine material properties by means of different empirical methods applied to mixtures of quartz and K-feldspar sand. Empirical methods exhibit the great advantage of measuring the properties of a certain analogue material under the experimental conditions, which are strongly sensitive to the handling techniques. Finally, the results obtained from the empirical methods have been compared with ring shear tests carried out on the same materials, which show a satisfactory agreement with those determined empirically. Full article
(This article belongs to the Special Issue Granular Materials)
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Graphical abstract

Graphical abstract
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<p>Microscope picture of the pure Q-sand (<b>a</b>) and pure K-feldspar sand (<b>b</b>). Note the strong differences in terms of grain size, grain size distribution, and grain roundness.</p>
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<p>Grain-size distribution curve for the pure Q-sand (<b>red line</b>) and the pure K-feldspar sand (<b>yellow line</b>).</p>
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<p>(<b>a</b>) Deformation pure-simple shear apparatus (‘Tosi machine’, modified after Montanari et al. [<a href="#B46-materials-10-00635" class="html-bibr">46</a>]); and (<b>b</b>) basic model set-up used to evaluate the angle of internal friction.</p>
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<p>Schematic cartoon showing the measuring procedure of the angle of repose (modified after de Campos and Ferreira [<a href="#B50-materials-10-00635" class="html-bibr">50</a>]).</p>
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<p>Example of an ideal heap shape compared to the actual heap shape (here for the 50 Quartz—50 K-feldspar mixture). The strong deviation from the ideal shape indicates a high cohesion.</p>
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<p>Cross sections of the extensional models used to determine the internal friction angle for the different sand mixtures. The white bar on the lower right angle of each panel indicates the moving metal basal sheet acting as a velocity discontinuity. The table in the right bottom panel summarizes the dip angles of faults on the right and left side of the VD (see text for details).</p>
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<p>Evaluation of the angle of repose using the ‘fixed base cone’ method. The red number on the right top of each panel indicates the measured angle.</p>
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<p>Graph showing the variation of the angle of internal friction as a function of the granular mixture composition as measured with the adopted empirical methods.</p>
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<p>Variation of bulk density as a function of the granular mixture composition.</p>
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<p>Variation of the Hausner ratio (blue dots) and the volume variation (red dots) as a function of the granular mixture composition.</p>
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<p>The ring-shear apparatus used in this study and an example of the test results. The curves on the right referr to different applied normal stress ranging from 1.8 kPa (blue line) to 4.4 kPa (green line).</p>
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244 KiB  
Article
The Birth of Homo Colossus: Energy Consumption and Pre-Familiarization in Joel Barlow’s Vision of Columbus
by Matthew Pangborn
Humanities 2016, 5(2), 39; https://doi.org/10.3390/h5020039 - 3 Jun 2016
Cited by 1 | Viewed by 5415
Abstract
Although Raymond De Young points out the current response to energy descent he terms localization “is not globalization in reverse”, the writers of modernity’s energy ramp-up used many of the same techniques De Young proposes for adapting to the downslope of M. King [...] Read more.
Although Raymond De Young points out the current response to energy descent he terms localization “is not globalization in reverse”, the writers of modernity’s energy ramp-up used many of the same techniques De Young proposes for adapting to the downslope of M. King Hubbert’s fossil-fuels peak. Among these is pre-familiarization, the construction of mental models that “help people to feel at home in a place they have not yet inhabited.” Long before William Catton’s depiction of the West’s outsized energy user as Homo colossus, for example, Joel Barlow provided early national Americans with a reflection of themselves as gigantic consumers of the continent’s bounty in his 1787 Vision of Columbus. In the epic poem, Barlow puts in place foundational elements of the myth of progress that will develop with an increasingly extravagant energy consumption: a refutation of the classical republican model of history as cyclical; a conflation of the process of resource extraction with that of production; a characterization of this “production” as the natural trait of the knowledgeable, moral Western subject; the pairing of this characterization with a racialized discourse; and an assertion of climate melioration that anticipates by two centuries the counter-arguments of anthropogenic climate-change denialists. The poem invites its reader to inhabit the skin of a lofty and distanced observer of natural life, drawing on the earlier century’s infatuation with the prospect view, to help the reader become “pre-familiarized” with an idea of him- or herself fitting an economic model of endless growth. In the work, therefore, might be found not only the blueprints for an as-yet inchoate Anthropocene, but also the design of a new humanity to go along with it. Full article
(This article belongs to the Special Issue Energy Use and the Humanities)
1010 KiB  
Review
Ten Reasons to Take Peak Oil Seriously
by Robert J. Brecha
Sustainability 2013, 5(2), 664-694; https://doi.org/10.3390/su5020664 - 12 Feb 2013
Cited by 15 | Viewed by 12524
Abstract
Forty years ago, the results of modeling, as presented in The Limits to Growth, reinvigorated a discussion about exponentially growing consumption of natural resources, ranging from metals to fossil fuels to atmospheric capacity, and how such consumption could not continue far into [...] Read more.
Forty years ago, the results of modeling, as presented in The Limits to Growth, reinvigorated a discussion about exponentially growing consumption of natural resources, ranging from metals to fossil fuels to atmospheric capacity, and how such consumption could not continue far into the future. Fifteen years earlier, M. King Hubbert had made the projection that petroleum production in the continental United States would likely reach a maximum around 1970, followed by a world production maximum a few decades later. The debate about “peak oil”, as it has come to be called, is accompanied by some of the same vociferous denials, myths and ideological polemicizing that have surrounded later representations of The Limits to Growth. In this review, we present several lines of evidence as to why arguments for a near-term peak in world conventional oil production should be taken seriously—both in the sense that there is strong evidence for peak oil and in the sense that being societally unprepared for declining oil production will have serious consequences. Full article
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<p>Data from the US Energy Information Administration [<a href="#B6-sustainability-05-00664" class="html-bibr">6</a>]; the relative shares of different liquid fuels in 2011.</p>
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<p>World supply of conventional crude oil (bottom curve) and total liquids, including biofuels, oil sands, shale oil, natural gas liquids and refinery processing gain (top curve). Data from US Energy Information Administration, International Energy Statistics [<a href="#B6-sustainability-05-00664" class="html-bibr">6</a>].</p>
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<p>Yearly average Brent crude oil price from 1990–2011. Data from BP Statistical Review of World Energy, 2012. Data are in $US<sub>2011</sub></p>
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<p>(<b>a</b>) Correlation between world oil consumption and world GDP, both plotted as logarithms. (<b>b</b>) Scaled GDP and oil production (left-hand axis) and oil price (right-hand axis).</p>
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<p>Cumulative production of oil from the continental US, together with a logistic curve fit to the data. The lower dashed curve is the fit that would have been found in 1980 using data to that point. The upper dot-dash curve is the current projection.</p>
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<p>Fits to actual production data for world conventional crude oil production. <b>(a)</b> World cumulative production (Gb) data (yellow squares) with logistic function fits for 5.5%/year initial growth rate and 2,000 Gb (red, lower curve) and 3,000 Gb (green, upper curve) ultimate recovery. <b>(b)</b> Yearly world crude oil production (Gb/year) with parameters corresponding to the curves in <b>(a)</b>. The (purple) curve in the right-hand panel represents a 7.5%/year exponential growth rate that continued for the first century of oil production.</p>
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<p>Oil and gas cost indices and the real price of oil. Oil capital cost index from EIA [<a href="#B52-sustainability-05-00664" class="html-bibr">52</a>], scaled to 100 for the year 2000, and from IHS Cambridge Energy Research Associates [<a href="#B53-sustainability-05-00664" class="html-bibr">53</a>]. Oil price (right-hand axis) is from BP.</p>
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<p>Saudi Arabia output of petroleum. Production is given by the (blue) diamonds, rig count by the (red) squares.</p>
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<p>Possible production trajectories under assumptions of growth rates that reflect past history <b>(a)</b> or for significantly more rapid growth rates <b>(b)</b>. Total conventional ultimately recoverable resource (URR) is 2,500 Gb (OPEC, Rest of the World (ROW), enhanced oil recovery (EOR), Arctic); URR for oil sands and shale oil assumed to be 1,000 Gb each. Included in shale is light, tight oil, although that is a recognized to be a different unconventional source.</p>
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<p>Cost availability curves.(a) schematic marginal production cost curves. In this representation, extraction costs for each individual resource contribute to an overall curve that increases much more rapidly than one would expect from a “rational” extraction sequence, always proceeding from the cheapest available resource to the next most expensive, <span class="html-italic">etc</span>. Concrete results from the deterministic logistic model of extraction of different resource grades is shown in <b>(b)</b>. A linear increase in costs would be predicted from a perfectly sequential extraction of resources; the output of the model shows that the average cost is close to that linear approximation, but the marginal cost is usually much higher.</p>
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<p>Yearly production (blue squares) and the reserves-to-production ratio (red triangles) for the UK and Norway</p>
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<p>Yearly production from <b>(a)</b> Norway and <b>(b)</b> Mexico (both with blue diamonds), together with projections by the EIA for future production from various volumes of the International Energy Outlook, as labeled.</p>
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<p>Yearly production of anthracite in the U.S.</p>
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<p>Production of coal in England. Historical production is shown in three segments: up to 1865, when W.S. Jevons wrote The Coal Question; from 1865 to 1912, when his son wrote about coal, and then production after 1912. The triangles show projections made by H.S. Jevons in 1912 using careful geological and socioeconomic projections.</p>
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Article
A Simple Interpretation of Hubbert’s Model of Resource Exploitation
by Ugo Bardi and Alessandro Lavacchi
Energies 2009, 2(3), 646-661; https://doi.org/10.3390/en20300646 - 13 Aug 2009
Cited by 53 | Viewed by 36505
Abstract
The well known “Hubbert curve” assumes that the production curve of a crude oil in a free market economy is “bell shaped” and symmetric. The model was first applied in the 1950s as a way of forecasting the production of crude oil in [...] Read more.
The well known “Hubbert curve” assumes that the production curve of a crude oil in a free market economy is “bell shaped” and symmetric. The model was first applied in the 1950s as a way of forecasting the production of crude oil in the US lower 48 states. Today, variants of the model are often used for describing the worldwide production of crude oil, which is supposed to reach a global production peak (“peak oil”) and to decline afterwards. The model has also been shown to be generally valid for mineral resources other than crude oil and also for slowly renewable biological resources such as whales. Despite its widespread use, Hubbert’s modelis sometimes criticized for being arbitrary and its underlying assumptions are rarely examined. In the present work, we use a simple model to generate the bell shaped curve curve using the smallest possible number of assumptions, taking also into account the “Energy Return to Energy Invested” (EROI or EROEI) parameter. We show that this model can reproduce several historical cases, even for resources other than crude oil, and provide a useful tool for understanding the general mechanisms of resource exploitation and the future of energy production in the world’s economy. Full article
(This article belongs to the Special Issue Energy Economics)
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<p>Qualitative solutions of the model described in the present paper. The three parameters shown are 1) the production rate (upper curve), 2) the amount of resource available (middle curve) and 3) the accumulated capital (lower curve).</p>
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<p>Oil production in the US lower 48 states, fitted using the model developed in the present paper (data courtesy of Mr. Colin Campbell).</p>
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<p>Gold production and number of miners during the “Gold Rush” in California fitted using the LV model developed here. The data are from [<a href="#B22-energies-02-00646" class="html-bibr">22</a>].</p>
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<p>LV model fitting of gold production in South Africa. In this case, the resource is the gold itself, while the amount of ore mined can be assumed to be proportional to the effort (i.e., the capital) placed by the gold industry in extraction. Data are from [<a href="#B23-energies-02-00646" class="html-bibr">23</a>].</p>
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<p>Data for whaling in 19<sup>th</sup> century fitted by the model developed in the present study. In this case, the resource is whale oil, while a measure of the capital invested in production can be taken as proportional to the total tonnage of the whaling vessels. Data are from [<a href="#B26-energies-02-00646" class="html-bibr">26</a>].</p>
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<p>Fitting of the data for oil discovery in the US 48 lower states and of the number of wildcats. In this case, the number of wildcats is proportional to the capital used by the oil industry in the effort of discovering the resource (oil wells). Data by courtesy of Messrs. Colin Campbell and Jean Laherrere.</p>
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<p>Fitting of the data for oil discovery in Norway and of the number of wildcats. In this case, the number of wildcats is proportional to the capital used by the oil industry in the effort of discovering the resource, oil wells. Data by courtesy of Messrs. Colin Campbell and Jean Laherrere.</p>
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313 KiB  
Article
North American Natural Gas Supply Forecast: The Hubbert Method Including the Effects of Institutions
by Douglas B. Reynolds and Marek Kolodziej
Energies 2009, 2(2), 269-306; https://doi.org/10.3390/en20200269 - 22 May 2009
Cited by 36 | Viewed by 15988
Abstract
In this article, the U.S. and southern Canadian natural gas supply market is considered. An important model for oil and natural gas supply is the Hubbert curve. Not all regions of the world are producing oil or natural gas following a Hubbert curve, [...] Read more.
In this article, the U.S. and southern Canadian natural gas supply market is considered. An important model for oil and natural gas supply is the Hubbert curve. Not all regions of the world are producing oil or natural gas following a Hubbert curve, even when price and market conditions are accounted for. One reason is that institutions are affecting supply. We investigate the possible effects of oil and gas market institutions in North America on natural gas supply. A multi-cycle Hubbert curve with inflection points similar to the Soviet Union’s oil production multi-cycle Hubbert curve is used to determine North American natural gas discovery rates and to analyze how market specific institutions caused the inflection points. In addition, we analyze the latest shale natural gas projections critically. While currently, unconventional resources of natural gas suggest that North American natural gas production will increase without bound, the model here suggests a peak in North American natural gas supplies could happen in 2013. Full article
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<p>Oil production from the Piper field in the North Sea. Note how it is not time dependent.</p>
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<p>A Quandt Likelihood Ratio over time.</p>
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<p>Four Cycle Hubbert Curve.</p>
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<p>Five Cycle Hubbert curve.</p>
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<p>Forecast Consumption.</p>
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<p>(a) Forecast consumption over time.</p>
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