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Mass and energy-capital conservation equations to study price evolution of non-renewable energy resources, Part III - Energy supply curve
No full textThe price evolution of non-renewable resources versus the consumption rate is investigated with the aim of constructing the energy supply curve. The case studied is without accumulation nor depletion of the resources and the mass and energy-capital conservation equations are solved under the condition of the same mass flow rate of extraction and sale. The energy supply curve of extracted resource is dependent on the newly defined parameter, RINE, Rate of Interest of Non-extracted resources on the Extraction rate. The energy supply curve of sold resource is dependent on the newly defined parameter, RISE, Rate of Interest of Sold resources on the Extraction rate, in case the rate of interest of non-extracted resources, r(N), is nil. In general, the energy supply curve of sold resource is dependent also on two dimensionless parameters, Dimensionless Critical Initial Price of Sold resources. i.e. DCIPS, and Dimensionless Critical Initial Price Extreme of Sold resources, i.e. DOPES. The energy supply curve of sold resources is investigated under different relations between three parameters, i.e. extraction rate and interest rates of non-extracted and extracted/sold resources. New trends are observed in the economic market of non-renewable energy resources. The energy supply curve of the difference between sold and extracted resource is also obtained and is dependent on two dimensionless parameters, Critical Initial Price Difference i.e. CIPD, and Critical Extreme of the Initial Price Difference, i.e. CEIPD. Finally, the predictions obtained with the present approach are compared to the real evolution of the world price of oil and the European price of gas versus the world consumption during the last three decades, i.e. from 1980 until 2005 for oil and from 1984 until 2005 for gas. taking into account inflation, discount and prime rates of the economic market. The agreement is acceptable but, more important, the trend is correctly predicted. The price difference between sold and extracted resources is also investigated versus the dimensionless mass flow rate of extraction. The evolution is dependent on four parameters: RINE, RISE, DCIPS, and DCIPES. (C) 2008 Elsevier Ltd. All rights reserved
Mass and energy-capital conservation equations to study the price evolution of non-renewable energy resources. Part II - Extension to resources sold to the market
No full textThe time evolution of the price of resources sold to the market and of the price difference, between sold and extracted resources, is investigated in case of no accumulation of the resources; i.e. when the resources are extracted and sold to the market at the same mass flow rate. The price evolution of sold resources varies with time according to the relation between the price increase factor, PIF, of sold and extracted resources. The price evolutions of sold resources and price difference are investigated according to the relation between extraction rate and interest rate of extracted and sold resources. The price of sold resources and the price difference increase with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is greater than the critical price of sold resources, which depends on the initial price of extracted resources and the interest rate of non-extracted and extracted resources. The price of sold resources and the price difference decrease with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is smaller than the critical price of sold resources. The other cases are discussed extensively in the paper. (c) 2005 Elsevier Ltd. All rights reserved
A New Theory to Forecast the Price of Non Renewable Energy Resources with Mass and Energy-Capital Conservation Equations.
Full text linkThe mass and energy-capital conservation equations are employed to study the time evolution of mass and price of non-renewable energy resources, extracted and sold to the market, in case of no-accumulation and no-depletion; i.e. when the resources are extracted and sold to the market at the same mass flow rate. The Hotelling rule for non-renewable resources, i.e. an exponential increase of the price at the rate of the current interest multiplied the time, is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is unity. The mass and energy-capital conservation equations are solved jointly to investigated the time evolution of the extracted resources. The parameter PIFE, “Price Increase Factor of Extracted resources”, is the difference between the interest rate of capital, typically the inflation rate, and the mass flow rate of extraction of non-renewable resources. The price of the extracted resources increases if PIFE is greater than zero, i.e. the mass flow rate of extraction is smaller than the inflation rate. The price is constant if PIFE is zero, i.e. the mass flow rate of extraction is equal to the inflation rate. The price is decreasing with time if PIFE is smaller than zero, i.e. the mass flow rate of extraction is greater than the inflation rate. The price of selling resources varies with time according to the relation between the parameters PIFE and PIFS, “Price Increase Factor of Selling resources”, which is the difference between the extraction rate and the interest rates of selling resources, prime or discount rate. The price of selling resources increases with time if the initial price is greater than CIPS, “Critical Initial Price of Sold resources”, which depends on the initial price of extracted resources, the interest rate of non-extracted resources, and the difference between PIFS and PIFE or is greater than CIPES, “Critical Initial Price Extreme of Selling resources”, which depends on the initial price of extracted resources, the interest rate of non-extracted resources, and PIFS. The price of selling resources increases temporarily with time if the interest rates of non-extracted and extracted resources are equal, i.e. PIFE is equal to PIFS, and the initial price is greater than CIPES, “Critical Initial Price Extreme of Selling resources”. The price evolutions of the difference between selling and extracted resources are investigated according to the relation between extraction rate and interest rate of extracted and selling resources. The price difference increases with time if PIFS is greater than PIFE of the extracted resources and the initial price is greater than the critical price of selling resources, which depends on the initial price of extracted resources and the interest rate of non-extracted and extracted resources. The price difference decreases with time if PIFS is greater than PIFE and the initial price is smaller than the critical price of selling resources. The other cases are discussed extensively in the paper. The price evolution of non-renewable resources versus the consumption rate is investigated with the aim of constructing the energy supply curve. The case studied is without accumulation nor depletion of the resources and the mass and energy-capital conservation equations are solved under the condition of the same mass flow rate of extraction and sale. The energy supply curve of extracted resource is dependent on the new parameter, RINE, “Rate of Interest of Non-extracted resources on the Extraction rate”. The energy supply curve of selling resource is dependent on the new parameter, RISE, “Rate of Interest of Sold resources on the Extraction rate”, in case the rate of interest of non-extracted resources, rN, is nil. The energy supply curve of selling resources is dependent also on two dimensionless parameters, “Dimensionless Critical Initial Price of Sold resources”, i.e. DCIPS, and “Dimensionless Critical Initial Price Extreme of Sold resources”, i.e. DCIPES. The energy supply curve of selling resources is investigated under different relations between three parameters, i.e. extraction rate and interest rates of extracted and selling resources. New trends are observed in the economic market of non-renewable energy resources. The energy supply curve of the difference between selling and extracted resource is dependent on two dimensionless parameters, “Critical Initial Price Difference”, i.e. CIPD, and “Critical Extreme of the Initial Price Difference”, i.e. CEIPD. The price difference between selling and extracted resources is investigated versus the dimensionless mass flow rate of extraction. The evolution is dependent on four parameters: RINE, RISE, DCIPS, and DCIPES
Remarks on the paper “Mass and energy-capital conservation equations to Forecast monthly oil price”
Full text linkThe mass and energy-capital conservation equations have been used at the beginning of 2013 to forecast the monthly oil price up to December 2013. The approach of the interest rates has employed an interest rate equal to the arithmetic average between the prime and the discount rates. The present short communication comments the comparison between the forecast made during the middle of the 2013 and the real oil prices, as registered today, at the beginning of 2014
Mass and energy-capital conservation equations to study the price evolution of non-renewable energy resources. Part I-Generalization of the Hotelling rule
No full textMass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called "Price Increase Factor", PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (c) 2005 Elsevier Ltd. All rights reserved
Mass and energy-capital conservation equations for the time evolution of non-renewable energy resources
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Forecasting the Time Evolution of the Oil Price During Months of Negative Inflation Rate
No full textMass conservation equation is employed to study the time evolution of the mass of oil in a reservoir, according to the mass flow rate of extraction, and to define the critical mass flow rate of extraction, which is the value exhausting the reservoir in an infinite time. The price evolution with time of the resources extracted and sold to the market is investigated in case of no-accumulation and no-depletion of the resources; i.e. when the resources are extracted and sold to the market at the same mass flow rate. The total energy conservation equation is transformed into a capital per time conservation equation which allows to study the price evolution with time, which is dependent on the following parameters. The price evolution with time of the extracted resource is dependent on the parameter PIFE, “Price Increase Factor of Extracted resource”, which is the difference between the basic interest rate of the capital, e.g. the inflation rate, and the mass flow rate of extraction. The price evolution with time of the sold resource is dependent on the parameter PIFS, “Price Increase Factor of Sold resource”, which is the difference between the interest rate of the capital, discount or prime rate, and the mass flow rate of extraction. The parameter CIPS, “Critical Initial Price of Sold resource”, depends on the initial price of the extracted resource, on the interest rate of non-extracted resource, and on the difference between PIFS and PIFE. The parameter CIPES, “Critical Initial Price Extreme of Sold resource”, depends on the initial price of the extracted resources, on the interest rate of non-extracted resource, and PIFS. The time evolution of the oil price during the eight months of 2009 when the inflation rate was negative, and following the economic crisis of 2008, is investigated introducing a new category of cases, i.e. the negative inflation rate. The paper presents and discuss the results of the forecasting for several different values of the interest rate of the capital, prime and discount rate, with the conclusion that the present theory can forecast the evolution of the oil price with a reasonable confidence using the prime and discount rates as extreme limits
Heat Transfer of Newtonian Fluids in Laminar Flow in Vertical Tubes with Constant Wall Temperature
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