## theory of production | economics | britannica

theory of production, in economics, an effort to explain the principles by which a business firm decides how much of each commodity that it sells (its outputs or products) it will produce, and how much of each kind of labour, raw material, fixed capital good, etc., that it employs (its inputs or factors of production) it will use. The theory involves some of the most fundamental principles of economics. These include the relationship between the prices of commodities and the prices (or wages or rents) of the productive factors used to produce them and also the relationships between the prices of commodities and productive factors, on the one hand, and the quantities of these commodities and productive factors that are produced or used, on the other.

The various decisions a business enterprise makes about its productive activities can be classified into three layers of increasing complexity. The first layer includes decisions about methods of producing a given quantity of the output in a plant of given size and equipment. It involves the problem of what is called short-run cost minimization. The second layer, including the determination of the most profitable quantities of products to produce in any given plant, deals with what is called short-run profit maximization. The third layer, concerning the determination of the most profitable size and equipment of plant, relates to what is called long-run profit maximization.

However much of a commodity a business firm produces, it endeavours to produce it as cheaply as possible. Taking the quality of the product and the prices of the productive factors as given, which is the usual situation, the firms task is to determine the cheapest combination of factors of production that can produce the desired output. This task is best understood in terms of what is called the production function, i.e., an equation that expresses the relationship between the quantities of factors employed and the amount of product obtained. It states the amount of product that can be obtained from each and every combination of factors. This relationship can be written mathematically as y = f (x1, x2, . . ., xn; k1, k2, . . ., km). Here, y denotes the quantity of output. The firm is presumed to use n variable factors of production; that is, factors like hourly paid production workers and raw materials, the quantities of which can be increased or decreased. In the formula the quantity of the first variable factor is denoted by x1 and so on. The firm is also presumed to use m fixed factors, or factors like fixed machinery, salaried staff, etc., the quantities of which cannot be varied readily or habitually. The available quantity of the first fixed factor is indicated in the formal by k1 and so on. The entire formula expresses the amount of output that results when specified quantities of factors are employed. It must be noted that though the quantities of the factors determine the quantity of output, the reverse is not true, and as a general rule there will be many combinations of productive factors that could be used to produce the same output. Finding the cheapest of these is the problem of cost minimization.

in which p1 denotes the price of a unit of the first variable factor, r1 denotes the annual cost of owning and maintaining the first fixed factor, and so on. Here again one group of terms, the first, covers variable cost (roughlydirect costs in accounting terminology), which can be changed readily; another group, the second, covers fixed cost (accountants overhead costs), which includes items not easily varied. The discussion will deal first with variable cost.

The principles involved in selecting the cheapest combination of variable factors can be seen in terms of a simple example. If a firm manufactures gold necklace chains in such a way that there are only two variable factors, labour (specifically, goldsmith-hours) and gold wire, the production function for such a firm will be y = f (x1, x2; k), in which the symbol k is included simply as a reminder that the number of chains producible by x1 feet of gold wire and x2 goldsmith-hours depends on the amount of machinery and other fixed capital available. Since there are only two variable factors, this production function can be portrayed graphically in a figure known as an isoquant diagram (Figure 1). In the graph, goldsmith-hours per month are plotted horizontally and the number of feet of gold wire used per month vertically. Each of the curved lines, called an isoquant, will then represent a certain number of necklace chains produced. The data displayed show that 100 goldsmith-hours plus 900 feet of gold wire can produce 200 necklace chains. But there are other combinations of variable inputs that could also produce 200 necklace chains per month. If the goldsmiths work more carefully and slowly, they can produce 200 chains from 850 feet of wire; but to produce so many chains more goldsmith-hours will be required, perhaps 130. The isoquant labelled 200 shows all the combinations of the variable inputs that will just suffice to produce 200 chains. The other two isoquants shown are interpreted similarly. It is obvious that many more isoquants, in principle an infinite number, could also be drawn. This diagram is a graphic display of the relationships expressed in the production function.

## egypt to begin project to convert sand into solar panels - al-monitor: the pulse of the middle east

The Egypt-based Enara groupfor renewable energy services signed on Dec. 28, 2020, a cooperation protocol with the Chinese Chint energy company to establish a project aimed at locally manufacturing solar panels from silica-rich sand a first in Egypt.

Mohammad Adel, project development manager at Enara, told Al-Monitor over the phone that cooperation with the Chinese company will mark a quantum leap in the field of solar energy in Egypt, considering that the company has great experience in this field and has already installed threesolar energy stations in the Benban solar power complex in Aswan governorate.

Adel saidthat the Enara group is seeking to boost local manufacturing, localize modern technology and exchange global experiences in the fields of energy and agriculture by using new and renewable energy sources. He said the group is also seeking the governments contribution in its development plan to boost the Egyptian economy.

Enara signed acooperation protocol on Jan. 25 with the National Organization for Military Production (NOMP),affiliated with the Ministry of Military Production,and the Nasser Social Bank with the aim of funding small clients and prompting them to use solar energy in the agricultural sector.

Sherif el-Gabaly, chairman of the board of directors of Enara, told Al-Monitor over the phone that he was happy about the fruitful cooperation with the Ministry of Military Production and the Ministry of Social Solidarity, as it would benefit the agricultural sector in Egypt.

Gabaly said that one of the most important current goals of the Enara group was the generation and distribution of electricity to the agricultural sector, especially considering that it represents one of the most important sources of national income and is responsible for achieving food security, meeting local needs of food commodities, diversifying production and maximizing the added value of agricultural production.

Gabaly explained that the companys projects include investments in the infrastructure and renewable energy sectors, and pointed out that it obtained a loan of \$200 million from several international financial and financing institutions, as it cooperates with the European Bank for Reconstruction and Development, the African Development Bank and the World Bank.

Minister of State for Military Production Mohammed Ahmed Morsi said during the signing of the protocol with the NOMPand the Nasser Social Bank that the agreement aims at benefiting from the energy overcapacity in the Ministry of Military Production units and subsidiary companies in order to implement national development and service projects for various ministries and agencies in the country to ultimately serve citizens.

He pointed out that the protocol aims at exploiting the partnership between the NOMP and Enara as a consortium with the aim of implementing and equipping water wells to be fueled by solar energy through the military production companies supplying the necessary equipment for solar energy systems such as solar panels and stabilizers.

In a statement issued on Jan. 25 by the Ministry of Solidarity on itswebsite, Morsi explained that the mission of the consortium under this protocol is to provide an integrated technical and financial offer to small and medium investors in the agricultural sector in order to invest in the use of solar energy in the agricultural sector by operating water pumps using solar energy instead of diesel and other fuels.

He indicated that the project aims at selling, supplying, installing and operating 1,000 wells as a start to provide a source of electricity that is economically, environmentally and socially feasible.

Morsi continued that the program includes the provision of five different capacities for solar irrigation systems with the possibility of adjusting the capacity in line with the different water needs of agricultural investors. Within the framework of this project, he said, solar energy irrigation systems will be promoted.

Asked about the funding of projects undertaken by young investors, Mohammad Ashmawy, chairman of the board of directors at Nasser Social Bank, toldAl-Monitor that the bank will fund small and medium-sized projects for solar energy irrigation systems provided that the funding is paid to the consortium that includes the NOMPand Enara. The funding will allow the consortium to implement the investors projects in terms of design, supply, installation and operation contracts of solar-powered irrigation systems.

Energy projects in Egypt have come to represent a great priority in recent years in terms of filling the electric power generation deficit. Over the past years, the government has worked to exploit natural resources to generate electric energy, especially solar energy, as many projects were opened in several regions of the governorates of the country.

In November 2020, the Egyptian Minister of Electricity and Renewable Energy Mohamed Shakersaid duringthe International Conference of the Institute of National Planning titled Energy and Sustainable Development that Egypts electricity production has doubled since 2014, bringing the total electricity production by the end of 2019 to 28,000 megawatts (MW).

The complex, located 30 kilometers (19 miles) north of Aswan city in Upper Egypt, includes 32 solar power plants with a production capacity of 1,465 MW, i.e., about 90% of the Aswan High Dams total production capacity. The complex covers an area of 37 square kilometers (14 miles) where the sun shines throughout the year. The \$2.4 billion project is being carried out by 39 specialized companies.

Mohammad Saad el-Din,head of the Energy Committee at the Federation of Egyptian Industries, told Al-Monitor that Egypts plan for the coming period aims at optimally utilizing solar energy especially in light of large untapped areas in the country where such projects could be implemented.

He explained that Egypt consumes about 26 gigawatts (GW) per year and has a surplus of 6-8 GW,and interconnection power lines with Saudi Arabia and Sudan are currently being built to invest such surplus.

## the allure of triso nuclear fuel explained

Tristructural isotropic (TRISO) particle fuel has long been used in high-temperature gas-cooled nuclear reactors, but it is seeing a resurgence as a result of other applications. Modern TRISO fuel designs are under consideration for an assortment of advanced reactors, including high-temperature reactors and microreactors, and even as accident-tolerant fuel for light water reactors.

In October 2020, when the U.S. Department of Energy (DOE) announced it chose TerraPower and X-energy to each receive \$80 million in initial federal funding under the agencys Advanced Reactor Demonstration Program (ARDP) to build their two distinct advanced nuclear reactors and begin operating them within seven years, the advanced reactor community was abuzz about the agencys larger scope for X-energy. Under the award, Rockville, Marylandbased X-energy will deliver a commercial four-unit power plant (likely in Washington state) based on its Xe-100 reactor designan 80-MWe/200-MWth pebble-bed high-temperature gas-cooled reactor (HTGR). But X-energy will also leverage the award to deliver a commercial-scale fuel fabrication facility for its proprietary TRISO-X TRi-structural ISOtropic (TRISO) particle fuel, technology it developed under the 2015 DOE Advanced Gas Reactor (AGR) Fuel Qualification Program. As some industry observers noted, the award re-establishes a longstanding commitment by the DOE to render the U.S. into a technology purveyor of the specialized nuclear fuel form that is expected to quickly gain traction around the world as new advanced reactor designs emerge on the global power scene.

As the DOE explained to POWER in February, TRISO is essentially a robust, microencapsulated fuel form developed originally for use in HTGRs in the 1950s. Modern particleswhich can be about the size of a poppy seedtypically consist of a spherical fissile kernel sheathed by several layers of pyrocarbon (PyC) and a silicon carbide (SiC) layer. These particles can then be packed together into different forms, most prominently cylindrical pellets or billiard ballsized spherical fuel forms, called pebbles, using a resinated graphite matrix material (Figure 1).

1. This U.S. Department of Energy (DOE) graphic shows different TRi-structural ISOtropic (TRISO) particle fuel forms. On the right is a micrograph of a coated particle with exposed kernel and coating layers. Also shown are examples of spherical (pebble) and cylindrical (compact) fuel forms, and prismatic graphite blocks. Source: DOE

Perhaps TRISOs biggest benefit is that each particle acts as its own containment system thanks to its triple-coated layers, the DOE explained. This allows them to retain fission products under all reactor conditions. TRISO particles are also especially robust. TRISO fuels are structurally more resistant to neutron irradiation, corrosion, oxidation, and high temperatures (the factors that most impact fuel performance) than traditional reactor fuels, the agency said. And most importantly, they are safe. Simply put,TRISO particles cannot melt in a reactorand can withstand extreme temperatures that are well beyond the threshold of current nuclear fuels, it said.

While several exotic kernel compositions and different matrix materials have been proposed to date, so far, the DOEs TRISO fuel qualification efforts have focused on what it calls conventional TRISO particles. These have a kernel composed of a mixture of uranium carbide and uranium oxide, which the industry colloquially refers to as uranium oxycarbide (UCO).

When the uranium in a uranium dioxide (UO 2) molecule splits, the oxygen ions released can react with carbon in the pyrolytic layers to form carbon monoxide (CO) gas, the DOE said. At very high burnup, the accumulated CO gas may exert excessive pressure on the particle coatings and cause them to fail. The UCO mixture limits the amount of free oxygen released from the kernel, enabling higher burnups to be achieved, as has been confirmed during post-irradiation examination of TRISO fuel, it said.

Because TRISO enables a high temperature output in advanced reactor designs, it could potentially boost the use of nuclear energy beyond electricity generation into energy sectors, for example, that are currently dominated by fossil fuels such as process heat, oil shale and sand reprocessing, petroleum refining, desalination, and hydrogen production. Meanwhile, owing to TRISOs fuel form flexibility, and despite its origin and historic use in HTGRs, the conventional particle design could be well-suited to several types of advanced, high-temperature reactors (HTRs), including the fluoride saltcooled HTRs, and microreactors. More exotic compositions (that still retain the fundamental TRISO coating structure) are also being considered as accident-tolerant fuel for light water reactors.

The modern TRISO particle has evolved through a series of improvements in particle design, coating layer properties, and kernel composition. According to the DOE, the concept of nuclear fuel microspheres with refractory coatings to contain fission products can be traced to the early years of the nuclear age, when they were developed for the 20-MWth Dragon reactor, a prismatic-core HTGR that achieved critically in the UK in 1964. The first fuel charge included fissile particles consisting of several consecutive layers of pyrocarbon with different properties, and fertile particles with both PyC and SiC coating layers formed into annular cylinders, the DOE noted.

Peach Bottom 1, an experimental 115-MWth prismatic HTGR in York County, Pennsylvania, that reached criticality in 1966, used pyrocarbon-only coated particles. However, that reactor also contained fuel test elements in which a large number of different types of particles were irradiated, including TRISO particles with various kernel types, and post-irradiation examination of these elements yielded a large amount of data on fuel performance, the DOE said. Other reactors that bolstered TRISO research and development include the 1967-completed 46-MWth Arbeitsgemeinschaft Versuchsreaktor (AVR) unit in Germanythe first pebble-bed reactor design. AVR initially used the two-layered bi-structural isotropic (BISO) particle design before adopting TRISO as a standard fuel for the remainder of its operational years, which ended in the late 1980s.

During the 1970s, TRISO coatings grew more sophisticated, gaining from advances in fabrication technology, SiC and pyrocarbon coating properties, coated particle irradiation performance, fuel performance modeling, and fission product release observations. The robustness of these new fuel forms was put to test at the Fort Saint Vrain HTGR in Colorado, which operated between 1976 and 1989.

2. Fuel loading at the Shidaowan high-temperature gas-cooled reactor pebble-bed module (HTR-PM) in China, slated to begin in April 2021, will involve putting 870,000 spherical TRISO fuel elements into the two small reactors that will drive a single 210-MWe turbine. Courtesy: China National Nuclear Corp. (CNNC)

HTGR fuel development has since burgeoned in Germany, China, Japan, South Africa, France, Russia, and South Korea. China, notably, has made remarkable progress to develop TRISO-coated particle fuel for its Shidaowan HTGR pebble-bed module (HTR-PM), a Generation IV reactor. Fuel loading (Figure 2) at that project is expected to begin this April.

Several high-temperature reactor developers have leveraged data from DOE-supported AGR TRISO fuel experiments. In tandem, the DOE has been working to establish a pilot-scale TRISO fuel manufacturing capability in the U.S. Initially, the fabrication process was a joint activity between the Idaho National Laboratory (INL), Oak Ridge National Laboratory (ORNL), and an industrial fuel vendor, BWX Technologies (BWXT).

BWXT toldPOWERit worked with the DOE for more than 15 years under the AGR program to develop and manufacture TRISO-coated kernels at its specialty fuel facility in Lynchburg, Virginia, to support the governments vision of developing passively safe, compact nuclear reactors capable of economically generating electricity and hydrogen before it ceased TRISO production in the spring of 2017. Last November, however, the company said its Nuclear Operations Group had completed its TRISO nuclear fuel line restart project, which means the companys Lynchburg, Virginia, facility is now actively producing the fuel again.BWXT said restarting its existing TRISO fuel production capability and increasing its capacity would position the company to meet emergent client interests in Department of Defense microreactors, space reactors, and civil advanced reactors. By co-locating the TRISO production line with other existing uranium processing capabilities, BWXT has a vertically integrated facility capable of handling all TRISO-related needs from feedstock preparation through uranium recovery and purification, it said.

The DOE is also working with Kairos Power, developer of a fluoride saltcooled high-temperature reactor (FHR). Similar to a molten salt reactor, FHRs use solid TRISO fuel instead of liquid fuel dissolved in the coolant. [Kaiross] design would use TRISO fuel in a pebble form with a fluoride-lithium-beryllium (FLiBe) salt coolant to allow high temperature output by the FHR, the DOE said. In addition, the previous extensive DOE TRISO fuel qualification studies would shorten the timeline to demonstrate this reactor type. The DOE has backed the development of the Kairos design through an assortment of funding opportunities, including via Gateway for Accelerated Innovation in Nuclear (GAIN) vouchers and other industry partnership awards, it noted.

X-energy, too, has long had the DOEs backing. X-energys TRISO-X fuel pebbles, which build off the AGR experiments, comprise pebbles that contain thousands of specially coated TRISO fuel particles. These particles seal uranium particles in a protective coating, are virtually indestructible, retain the waste inside, and make meltdown impossible while releasing no carbon emissions. The entire process releases even less carbon than wind or solar, the DOE said. The inherent safety of the design would allow a fabrication facility to be constructed within 500 meters of factories or urban areas, it suggested.

For now, X-energy continues to run a TRISO-X fuel fabrication pilot line at the ORNL Uranium Building, co-located within the ORNL AGR TRISO Fuel laboratory area.The TRISO-X pilot line reportedly has full production size (engineering-scale) fabrication equipment to make UCO kernels, coat them with a buffer layer, two PyC layers, and the SiC layer that acts as a fission product containment barrier for the fuel.The same pilot line production equipment could be used in X-energys commercial TRISO-X fuel fabrication facility that the DOE is funding under the ARDP program.

Ultra Safe NuclearCorp. (USNC), another notable TRISO fuel developer, is spearheading development of its proprietary Fully Ceramic Microencapsulated (FCM) fuel, which consists of coated nuclear fuel particles embedded inside a dense and fully sealed SiC matrix. The specific coated fuel particles are TRISO microspheres that provide micro-encapsulation of the fuel with multiple pyrocarbon and a SiC coating layer, USNC CEO Francesco Venneri explained to POWER. Using FCM technology, an additional layer of protection against radionuclide release is added by taking advantage of SiC as the matrix for these coated fuel particles. This macro-encapsulation further enhances radionuclide retention capability of the fuel, and allows for design and deployment of ultra-safe nuclear energy systems.

USNC, notably, in September opened a new facility in Salt Lake City, Utah, to support the development of its FCM fuel and materials that will be used in its own Micro-Modular Reactors (MMR), as well as other nuclear reactors, including gas-cooled reactors, light water reactors, CANDU reactors, and molten saltcooled reactors.

## solar pv power | sciencedirect

Solar PV Power: Design, Manufacturing and Applications from Sand to Systems details developments in the solar cell manufacturing process, including information from system design straight through to the entire value chain of Solar PV Manufacturing. In addition, the book includes aspects of ground mounted grid connected solar PV systems and optimization for solar PV plants, economic analyses, and reliability and performance. The advances and processes of solar product technology and reliability, along with the performance of solar PV plants and operational and maintenance aspects with advance diagnostic techniques are also presented, making this an ideal resource. With rapid change in the manufacturing process, it is crucial for solar cells and solar PV modules to adapt to new developments in solar products, especially with regard to reliability, financial aspects and performance.

Solar PV Power: Design, Manufacturing and Applications from Sand to Systems details developments in the solar cell manufacturing process, including information from system design straight through to the entire value chain of Solar PV Manufacturing. In addition, the book includes aspects of ground mounted grid connected solar PV systems and optimization for solar PV plants, economic analyses, and reliability and performance. The advances and processes of solar product technology and reliability, along with the performance of solar PV plants and operational and maintenance aspects with advance diagnostic techniques are also presented, making this an ideal resource.

With rapid change in the manufacturing process, it is crucial for solar cells and solar PV modules to adapt to new developments in solar products, especially with regard to reliability, financial aspects and performance.

Solar PV Power: Design, Manufacturing and Applications from Sand to Systems details developments in the solar cell manufacturing process, including information from system design straight through to the entire value chain of Solar PV Manufacturing. In addition, the book includes aspects of ground mounted grid connected solar PV systems and optimization for solar PV plants, economic analyses, and reliability and performance. The advances and processes of solar product technology and reliability, along with the performance of solar PV plants and operational and maintenance aspects with advance diagnostic techniques are also presented, making this an ideal resource. With rapid change in the manufacturing process, it is crucial for solar cells and solar PV modules to adapt to new developments in solar products, especially with regard to reliability, financial aspects and performance.

Solar PV Power: Design, Manufacturing and Applications from Sand to Systems details developments in the solar cell manufacturing process, including information from system design straight through to the entire value chain of Solar PV Manufacturing. In addition, the book includes aspects of ground mounted grid connected solar PV systems and optimization for solar PV plants, economic analyses, and reliability and performance. The advances and processes of solar product technology and reliability, along with the performance of solar PV plants and operational and maintenance aspects with advance diagnostic techniques are also presented, making this an ideal resource.

With rapid change in the manufacturing process, it is crucial for solar cells and solar PV modules to adapt to new developments in solar products, especially with regard to reliability, financial aspects and performance.

## mechanical properties of the clayey-silty sediment-natural gas hydrate mixed system - sciencedirect

Mechanical properties of hydrate-bearing strata are crucial to evaluate hydrate production related geohazards. However, the mechanical parameters of the hydrate reservoirs in the Shenhu area of the South China Sea have been rarely reported. In this paper, the sediments from the top of the hydrate reservoirs in the Shenhu area are taken to analyze the triaxial shearing behaviors of clayey-silty sediments containing tetrahydrofuran (THF) hydrates. The results indicate that the stressstrain curves of THF hydrate-bearing clayey-silty sediments show strain-hardening failure characteristics under a relatively low hydrate mass fraction (16.7%). Triaxial shearing strength, tangent modulus, and cohesion force increase with the increase of hydrate less fraction. However, prime results from pure THF hydrates reveal a brittle failure mode, which is totally different from that when hydrate mass fraction is more than 16.7%. Therefore, hydrate fraction (either mass fraction or volume fraction), rather than hydrate saturation, is strongly recommended to characterize the content of hydrate within clayey-silty sediments. The clayey-silty sediment-hydratemixed system is suggested to be divided into pure sediment, hydrate-bearing sediment (HBS), sediment-bearing hydrate (SBH), and pure hydrate, for which a universally applicable mechanical property evaluation method is thus established.

Project supported by the National Natural Science Foundation of China Research on the Response Characteristics and Main Controlling Factors of Static Cone Penetration Test of Hydrate Reservoirs in the Shenhu Area of the South China Sea (No. 41976074), and Shandong Provincial Taishan Scholars Special Expert Project (No. ts201712079).

## multiphase flow behavior of layered methane hydrate reservoir induced by gas production

Yilong Yuan, Tianfu Xu, Xin Xin, Yingli Xia, "Multiphase Flow Behavior of Layered Methane Hydrate Reservoir Induced by Gas Production", Geofluids, vol. 2017, Article ID 7851031, 15 pages, 2017. https://doi.org/10.1155/2017/7851031

Gas hydrates are expected to be a potential energy resource with extensive distribution in the permafrost and in deep ocean sediments. The marine gas hydrate drilling explorations at the Eastern Nankai Trough of Japan revealed the variable distribution of hydrate deposits. Gas hydrate reservoirs are composed of alternating beds of sand and clay, with various conditions of permeability, porosity, and hydrate saturation. This study looks into the multiphase flow behaviors of layered methane hydrate reservoirs induced by gas production. Firstly, a history matching model by incorporating the available geological data at the test site of the Eastern Nankai Trough, which considers the layered heterogeneous structure of hydrate saturation, permeability, and porosity simultaneously, was constructed to investigate the production characteristics from layered hydrate reservoirs. Based on the validated model, the effects of the placement of production interval on production performance were investigated. The modeling results indicate that the dissociation zone is strongly affected by the vertical reservoirs heterogeneous structure and shows a unique dissociation front. The beneficial production interval scheme should consider the reservoir conditions with high permeability and high hydrate saturation. Consequently, the identification of the favorable hydrate deposits is significantly important to realize commercial production in the future.

Natural gas hydrate (NGH) is solid crystalline compound in which gas molecules are encaged inside the lattices of ice crystals under proper thermodynamic conditions [1, 2]. In nature, the dominant gas in NGH is methane, which forms at low temperature and high pressure with extensive distribution in the permafrost and in deep marine sediments [1, 3, 4]. The evaluation results show that the global quantity of hydrocarbon gas hydrates varies widely between 1015 and 1018 STm3 (ST represents the standard conditions) [2, 5]. As an unconventional energy resource, the exploitation of NGH has attracted significant interest around the world [6].

Gas production from hydrate-bearing sediments (HBS) could be realized by dissociating solid-state hydrate into fluid phases (e.g., gas and water). Multiple methods have been proposed and employed to decompose hydrate for gas recovery from the HBS, such as depressurization, thermal stimulation, gas exchange, and the use of hydration inhibitors (such as salts and alcohols) [2, 58]. The above methods have been compared in terms of energy efficiency, economic and technological feasibility, and environmental performance [1, 4, 9, 10]. Past laboratory and field tests and numerical studies showed that depressurization is the most potential method for gas recovery from HBS, while the other methods may be suitable for enhancing recovery or reservoir stimulation [4, 11, 12]. The obvious advantages of depressurization method include its simplicity and technical effectiveness [2, 13].

In order to seek the most technically and economically feasible method for production from the hydrate deposits, numerical simulation was considered the best way to achieve this objective. Moridis et al. [1, 2] investigated the gas production potential from Class 1 and Class 2 hydrate deposits through depressurization. They found that large volumes of gas can be produced at high rates for long times from Class 1 hydrate deposits by using conventional technology. Li et al. [14] investigated the effects of confined formation permeability on the gas production potential from marine hydrate deposit. They indicated that the hydrate deposit with impermeable boundaries was expected to be the potential gas production target. Huang et al. [15] investigated the effects of geologic conditions on the hydrate dissociation and gas production through depressurization. Their results indicated that permeability, porosity, and initial hydrate saturation have significant effects on gas production performance. Hou et al. [16] numerically investigated the production characteristics of gas hydrate deposits by cyclic hot water stimulation with a separated-zone horizontal well. They indicated that the method combining depressurization and thermal stimulation can improve the hydrate production effectively. Based on the latest geological data in the Eastern Nankai Trough, the long-term production behavior was investigated by Sun et al. [17] and Konno et al. [4]. Both of their results indicated that the gas production rate is expected to increase with time and the simulated water recovery rate cannot match field measured data. In addition, the geomechanical behaviors (such as seafloor subsidence and sand production) of the marine HBS induced by gas production have been widely studied [3, 7, 1821]. The geomechanical analysis indicated that the spatial evolution of the temperature, pressure, hydrate saturation, and gas saturation is the most relevant to the geomechanical behavior of HBS.

The above research has properly promoted the development of gas production from hydrate deposits; however, most of previous numerical studies assume homogeneous reservoirs with a single layer due to absence of substantial geological structure and field test data, resulting in inaccurate estimation of gas productivity and reservoir characteristics. In fact, the marine gas hydrate drilling explorations at the Eastern Nankai Trough of Japan and in Shenhu area of the South China Sea revealed the variable distribution of hydrate deposits. Gas hydrate reservoirs are composed of alternating beds of sand and clay in sediments with various conditions of permeability, porosity, and hydrate saturation [22, 25]. Consequently, the development of suitable geological model is critical to identify the dissociation layers and dissociation front induced by depressurization, which are key factors to ensure the success of the next long-term offshore production test [3, 4, 19, 22]. Additionally, the sensitivity analyses of gas production potential in previous studies were concentrated on production pressure, reservoir permeability, porosity, hydrate saturation, thickness, and initial temperature and pressure of HBS [11, 12, 14, 15, 26], whereas comprehensive studies related to the effects of well production interval on gas recovery have been reported sparsely, which are important for the optimization of gas production and reducing the water production rate.

In this paper, we extensively used the borehole geophysical logging, seismic interpretation, and core analyses at the production test site of the Eastern Nankai Trough reported previously by Japanese investigators. A more realistic reservoir model, which considers the layered heterogeneous structure of hydrate saturation, permeability, and porosity, was constructed to improve the simulation accuracy. The model we developed was validated by comparing the simulation results with actual test data of well production. The reservoirs responses and multiphase movement behaviors of water and gas during the production test were analyzed and discussed in detail. Furthermore, we use the validated model to investigate the effects of the placement of production interval on the production performance. Overall, this work may provide a useful method and some feasible suggestions for the subsequent test and future commercial production under similar reservoir conditions.

The Eastern Nankai Trough is the most potential resource-rich area of gas hydrates in Japan [22, 27]. In this area, the total amount of CH4 gas contained in HBS was estimated at an average value of 1.1 1012m3, most of which was reserved in the 16 methane hydrate concentrated zones (MHCZs) [4, 22, 28]. MHCZ was characterized as sand-dominant methane hydrate with high saturation [4]. The AT1 site within the -MHCZ, located in the north slope of Daini Atsumi Knoll area, is the 2013 production test site [22, 29]. The area of -MHCZ is about 12km2 with the water depth ranging from 857 to 1405m [22, 28]. The thickness of MHCZ is dozens of meters, which is composed of turbidite channel-type sediments [22].

In 2012, the production well (AT1-P), two monitoring wells (AT1-MC and AT1-MT1), and sampling well (AT1-C) were drilled at the AT1 site [22, 29]. The well locations and their trajectories projected in the horizontal section are shown in Figure 1. The extensive logging programs were conducted at wells AT1-P, MC, and MT1 in 2012 to evaluate reservoir properties and to determine the production interval [22, 28]. In addition, pressure coring was conducted at well AT1-C to collect essential geological and geochemical data and to correct in situ formation parameters [22, 30].

Figure 2 shows the detailed resistivity images at three wells (AT1-P, MC, and MT1) at the AT1 site. As shown in Figure 2, the target MHCZ (Unit IV) has a gross thickness of 61m [22]. On the basis of lithological structure, the MHCZ is divided into three major subzones [22, 23]. Unit IV-1 is composed of thin alternating beds of sand and mud in the upper part and sand layers with thicknesses of 3070cm. Unit IV-2 also contains alternations of sand and silt in the middle part but with lower hydrate saturation. Unit IV-3 is composed of sand-dominant layers in the lower part with high hydrate saturation, and the thicknesses of sand layers range from dozens of centimeters to 2m.

Figure 3 shows the depth profiles of hydrate saturation, porosity, absolute permeability, and resistivity image. Hydrate saturation (Figure 3(a)) was estimated by using the Archie equation [31]. The validity of the derived saturation was confirmed by the pressure core data [22]. The porosities (Figure 3(b)) mainly ranging from 0.4 to 0.5 were determined from the density log. These are validated by the core derived porosities, which were measured under in situ confining pressure [22, 23]. The absolute permeability (intrinsic permeability, Figure 3(c)) was estimated by using the Kozeny-Carman model and calibrated with the core data collected from hydrate reservoirs at the Eastern Nankai Trough [23, 24].

In this study, the TOUGH+HYDRATE simulator was used to investigate the multiphase flow behavior of layered methane hydrate reservoir induced by gas production. This code can model the nonisothermal hydration reaction, multiphase behavior, and flow of fluids and heat under conditions typical in geological media containing gas hydrates [1, 2, 5]. It includes both an equilibrium and a kinetic model of hydrate formation and dissociation [5]. The model accounts for heat and up to four mass components (i.e., H2O, CH4, hydrate, and water-soluble inhibitors such as salts or alcohols). These components are partitioned among four possible phases (i.e., gas, liquid, ice, and hydrate) [2, 5]. The model can describe all possible hydrate dissociation mechanisms, such as depressurization, thermal stimulation, and salting-out effects.

The geometry of the axisymmetric cylinder 2D model (RZ2D model) was constructed for the latter history matching simulation as shown in Figure 4. The model size in R-direction is 1000m to avoid the boundary effects. The total thickness of the entire model is 100m with the thickness of MHCZ being 61m. The production well with a radius of 0.1m is located in the center of the cylinder [29, 32]. Production interval was 38m from the top of the MHCZ for expecting the lower part of MHCZ as sealing layer to prevent water production [22]. Because the radius distance of 1000m can effectively avoid the boundary effects in 6-day production test, there is no flow of fluids and heat through the lateral boundary. The top of the silt-dominant zone and the bottom of the water-bearing zone are designed as constant temperature and pressure boundaries [17]. For simulation of the varied depressurization processes (Section 3.5), the time-independent Dirichlet boundary (e.g., constant pressure) conditions are applied to the production well.

Previous studies had indicated that the critical process occurs within a limited range around the production well [1, 2, 7]. Therefore, the grids are refined surrounding the well with the minimum interval of 0.1m. The grid sizes increase with the distance to the well, which reach a size of 75m at the lateral boundary. The discretization for each fine layer at the vertical Z-direction is 0.5m. Figure 5 shows the corresponding grids used in the simulations. The simulation domain was discretized into 200 100 grids in R- and Z-directions.

The initial reservoir pressure was assigned in line with the hydrostatic pressure, which was computed according to the water depth and a pressure-adjusted saline water density [7, 17]. The initial temperature was specified to be 4C at the seafloor [11, 17, 23]. The temperature profile was assigned to vary linearly as a function of depth with a geothermal gradient of 0.03C/m. The initial hydrate saturation was varied in each fine layer and assumed to be horizontally uniform as shown in Figure 6(a).

Table 1 presents the main modeling parameters and physical properties for the AT1 site sediments at the Eastern Nankai Trough. These were based on the geophysical well logs and core samples analyses from published papers [4, 17, 22, 23, 27, 28]. The permeability and porosity are based on the logging data of AT1-MC and the pressure core data of AT1-C as shown in Figure 3. Hydrate saturations obtained from geophysical logging data were validated by those evaluated by pressure core analysis. The wellbore is simulated as a pseudoporous medium with porosity, permeability, capillary pressure, and low irreducible gas saturation of 1.0, 1.0 108m2, 0MPa, and 0.005, respectively. Earlier studies had shown the validity of this approximation [33, 34]. The composite thermal conductivity, relative permeability, and capillary pressure models are employed commonly in numerical simulations on gas production from hydrate deposits [2, 7, 17, 18]. The corresponding parameters for relative permeability and capillary pressure were determined from the field test data by Moridis and Reagan [34]. The changes of effective permeability and capillary pressure are consistent with the porosity and phase saturation during the simulation.

Well-to-well correlation between three wells (AT1-P, MC, and MT1) shown in Figure 2 exhibited that lateral continuity of these sand layers is fairly good, and the 3D seismic survey suggests the widespread deposits of the turbidite sediments beyond several kilometers [11, 22, 23]. Consequently, the reservoir properties were assumed to be uniform in each fine layer. Figure 6 shows the cross-sectional views of the initial hydrate saturation, porosity, and absolute permeability in the model.

The method used to decompose the solid hydrate was depressurization, which had been successfully applied at the Mallik site, Canada, in 2007 and 2008 [19, 37, 38]. Figure 7 shows the depressurization processes both in field test and in this simulation, which lasted for about 6 days. As shown in Figure 7, the wellbore pressure of production well was decreased from approximately 13MPa to about 4MPa during the first day and then remained almost stable for 5 days [29]. In the morning of the 6th day, sudden water rate increase was observed followed by strong sand production to the surface, and then the flow test was terminated [29]. During the stable production period, the volumetric rates of gas and water were approximately 20,000 and 200m3/d, and the cumulative volume produced at the well during the period of 6 days was 119,500m3 and 1,250m3, respectively [4, 17, 29].

By decreasing the wellbore pressure of production well, gas and water flowed into the well due to the pressure gradient of the reservoir. Figure 8 indicates the evolution of the volumetric rate of (a) the model-predicted CH4 production in the well , (b) site measured CH4 production in the well , and (c) gas released from hydrate dissociation (). As shown in Figure 8, the predicted volumetric rates of gas production match well with the measured data by site test. The accumulated volume of gas trapped () in 6 days is 122,861m3; both and are basically consistent with the field data observed.

Initially and increase quickly because of the significant decrease of borehole pressure during the first day (Figure 7). In the following days, both and begin oscillating around a coarsely invariable value, which clarify the struggle between the impacts of temperature and pressure on hydrate decomposition and gas production [3]. Decreasing pressure causes hydrate decomposition with the increase in and . The endothermic nature of hydrate decomposition results in temperature decline and makes further decomposition not easy, resulting in decrease in and . Note that the dramatic changes of at about 2.5 days are due to the wellbore pressure disturbance (Figure 7), which indicates that the decomposition of hydrate is extremely sensitive to production pressure. Further consideration of the difference between and suggests that the released gas cannot be trapped completely and most of which still remained in the hydrate reservoirs. Consequently, the optimization of well configuration and production strategies are needed to improve the gas recovery efficiency.

Figure 9 shows the evolution of volumetric rates of simulated () and measured () water production in the well. The predicted water production rate is about 300m3/d, which is slightly higher than that of site measured rate of 200m3/d. This may be because the geomechanical response during depressurization production from the HBS is not considered in our model, which means that the reservoir compression has immediate effects on decreases in formation porosity and intrinsic permeability and then on the fluid-flow behavior [3, 19]; the well completion methods used at the field relate to prevent water from reservoir flow into the production well as explained by Yamamoto et al. [29] and Sun et al. [17]; (3) the exposure of clay minerals of marine deposit to fresh water (released from hydrate dissociation) can induce swelling and structural weakening [7, 18]; (4) the complex and inevitable horizontal heterogeneity in each fine layer is also neglected in our model. In fact, these factors mentioned above have little effect on gas production, because gas viscosity is much smaller than that of water and gas slippage effects in the low-permeability deposits exist [5]. As a consequence, the predicted gas production rates are basically consistent with the site measured data, while the predicted water production rates are higher than that in the field.

The stable depressurization and gas production at the AT1 site of the Eastern Nankai Trough proved that hydrate decomposition by depressurization is applicable even in the marine sediments. Over and above the absolute criteria of and to evaluate the production potential, the cumulative water/gas ratio provides a relative criterion to evaluate the overall operation performance of the system, which is defined as [7]

Figure 10 indicates the evolution of the simulated during the 6-day production test at the AT1 site, which declines monotonically with time. This is because of continuous improvement of the gas production. In the early stage, drops rapidly because of significant hydrate dissociation in the reservoir and gas recovery at the production well (Figure 8). With time advancing, the stability of gas and water output results in slight changes of . Consequently, reaches very low levels of 20 in less than 1 day and is further reduced to kg of H2O/STm3 of CH4 at 6 days.

During the offshore production test, two monitoring wells (AT1-MT1 and MC) were designed for monitoring thermal disturbance around the production well (AT1-P). Figure 11 shows the monitored and simulated temperature changes at the location of the monitoring well AT1-MT1 on day 5. Measured data indicate that temperature decreases broadly occurred in the upper MHCZ and slightly in the lower MHCZ, which are mainly controlled by the location of production interval (Figure 4). The maximum changes of temperature reach the value of 0.6C [4, 39]; such a temperature decrease cannot be explained purely from the heat conduction (significantly long time is needed) according to Kanno et al. [39]. Therefore, the hydrate dissociations occurred at the location of the well AT1-MT1. The model-predicted temperature changes at well AT1-MT1 match well with the measured data, especially in the silt-dominated zone that showed slight change of temperature for both measured and simulated results.

For the multiphase flow system induced by depressurization, the dynamic evolutions of reservoir properties including pressure, temperature, hydrate, and gas saturation should be analyzed in detail. This is crucial knowledge for the later long-term production test of marine gas hydrate. In addition, the evolution of these variables is important to determine the geomechanical behaviors (such as sand production) in the Eastern Nankai Trough, which are key factors to ensure the success of the offshore production test.

Figure 12 indicates the evolution of pressure in the hydrate reservoir due to depressurization. White dashed lines show the position of the top and bottom of the MHCZ. Because the fine sand layers with high hydrate saturation and permeability are hydraulically confined by silt/mud layers in MHCZ, depressurization is anticipated to be quickly and effectively propagated in the horizontal direction. In the early stage, the low pressure at the production well and the low effective permeability of MHCZ create a high pressure gradient near the production well. This pressure gradient extends laterally along the radial direction and tends to be stable with the gradual pressure diffusion. As hydrate dissociation results in increase of effective permeability, depressurization occurs more rapidly in the dissociated region. Due to the transmitted nature of pressure (e.g., even when fluid flow is restricted), the disturbance region of pressure is obviously larger than that of other reservoir properties (Figures 1315). The effect of depressurization in the hydrate reservoir propagates laterally over 150m during the 6-day production test.

The decrease in pore-water pressure (Figure 12) drives the hydrate to dissociate around the well in the production interval (Figure 13). As mentioned above, hydrate dissociation increases the effective permeability of the deposits. This process and the anisotropic permeability conditions accelerate the pressure decrease in the radial direction. Consequently, the hydrate dissociates more in the radial direction than in the vertical direction (Figure 13). Overall, the dissociation zone is strongly affected by the vertical reservoir heterogeneity and shows a unique dissociation front. The spatial distribution of hydrate saturation indicates that hydrate has completely dissociated within a few meters around the well. Comparison with the initial hydrate distribution indicates the extent of dissociation zone within 35m during the 6-day production test.

The temperature reduction is strongly related to the hydrate dissociation because of the endothermic function of hydrate dissociation (Figure 14). The spatial distribution of low temperature shows vertical heterogeneity as well. This is because of the drastic dissociation in the fine sand layers (with high hydrate saturation and high permeability) resulting in significant temperature decreases, whereas the silt-dominant zones with low hydrate saturation undergo slight temperature decreases. Generally, the evolution of low temperature region can reveal the dissociation performance directly.

Figure 15 indicates the spatial distribution of gas saturation in the reservoir due to depressurization. The evolution of spatial distribution of free gas is very important for us to understand the gas production behaviors and to evaluate the formation of secondary hydrate [17]. As the depressurization begins, there gradually forms a gas bank around and below the production well with the maximum gas saturation of 0.22. With time advancing, the region of gas zone gradually enlarges (Figure 15). Gas accumulation is observed around and below the production interval because of continuing hydrate dissociation. However, results of Rutqvist and Moridis [7] indicate that gas accumulation occurred under the bottom of the confined overburden, which results by buoyancy. This phenomenon did not occur in our modeling results, because the hydrate deposits in the case of the Eastern Nankai Trough are composed of alternating beds of sand and clay; thus, the low-permeability sealing formations can effectively prevent gas from migrating upward. This is very important for hydrate exploitation from marine sediments because lack of a confining overburden could result in gas diffusion into the sea floor [7].

The design of production interval is recognized as a significant factor that affects the performance of hydrate exploitation [12, 17]. The production interval of 38m from the top of the MHCZ (total thickness of 61m) was employed at the AT1 site of the Eastern Nankai Trough (Figure 16, Case A). For effective depressurization, the lower part of the MHCZ (i.e., with high hydrate saturation) was considered as sealing formation to block water production from the underlying water-bearing zones [22, 28]. Both the site test data and the modeling results indicate the effectiveness of this production interval design by depressurization at marine hydrate deposits. However, the significant gas accumulation is observed at the lower part of the MHCZ and could not sufficiently transport to the production well (Figure 15). This suggests that the gas recovery schemes should be optimized for the subsequent production test.

In this study, three different cases (Figure 16) with different locations of production interval are designed to investigate the effects of placement of production interval on gas production performance. The purpose is to provide some feasible suggestions for the subsequent site test and future large-scale exploitation of gas hydrate. For the convenience of comparison, all of the thermophysical properties of the hydrate reservoirs and production method remain unchanged.

Figure 17 indicates the evolution of model-predicted volumetric rates of gas () and water () production from hydrate reservoirs under different locations of production interval (Figure 16). As shown in Figure 17(a), the gas production rate in Case C is significantly higher than that in Case A and Case B. The average values of in Case A, Case B, and Case C are about 20477, 20692, and 24307STm3/d, and the accumulated volumes of gas trapped () in 6 days are 122,861, 124,151, and 145,843m3, respectively. On the other side, in Case B and Case C is significantly lower than that in Case A. The predicted average values of in Case A, Case B, and Case C are approximately 292, 207, and 231m3/d, respectively.

Figure 18 shows the evolution of model-predicted during the 6-day production test under different locations of production interval. As mentioned above, drops rapidly in the early stage because of the significant hydrate dissociation and gas production (Figure 17(a)). The predicted average values of in Case A, Case B, and Case C are approximately 15.7, 10.8, and 9.9kg of H2O/STm3 of CH4, respectively. Obviously, lower indicates higher energy efficiency and economic efficiency of gas hydrate production from marine sediments, because lifting large water volumes to the surface could burden gas production with the cost. Particularly, the disposal of produced low-salinity water (released from hydrate dissociation) may pose environmental damage if released near the sea floor without mixing with sea water at suitable ratios [7].

Both the absolute criteria and relative criteria discussed earlier illustrate the obvious superiority of Case C, in which the production interval is located at the bottom of the MHCZ. This can be explained by the characteristic of flow-related reservoir properties, as shown in Figure 19. The main reasons include the following: the lower part of MHCZ is composed of thick sand-dominant layers with high initial hydrate saturation and permeability (Figures 3 and 6); the pressure drops rapidly around production interval causing significant hydrate decomposition and gas production; (2) the extent of hydrate dissociation zone is enlarged due to hydrate dissociation which increases the effective permeability and accelerates the pressure reduction in the radial direction; (3) the fluid flow from bottom formations with higher temperature promotes the hydrate dissociation occurring in deeper sediments significantly; (4) the actual reservoir structure with low-permeability silt/mud layers in hydrate deposits can block the water flow through the formation into production well effectively. The simulation results suggest that the favorable production interval scheme should consider the reservoir conditions with high permeability and high hydrate saturation in the subsequent field test and future commercial production. Furthermore, the production behaviors of the hydrate reservoir highly depend on the structure of lithofacies and reservoir properties such as the hydrate saturation and sediments permeability.

By incorporating the available geological data at the offshore production test site of the Eastern Nankai Trough, a multiphase fluid-flow model was constructed to investigate the gas production performance from the layered hydrate reservoirs by depressurization. The performance affected by the placement of production interval was discussed. Based on the numerical simulations, the following conclusions can be drawn:(1)The numerical model can match reasonably well with site-observed data of gas recovery. However, a slight deviation occurs between the predicted and measured water production rates. This is mainly due to the geomechanical responses such as reservoir compression, well completion method, clay minerals swelling, and lateral heterogeneity in each fine layer, which are not considered in our model.(2)Because the fine sand layers with high hydrate saturation are hydraulically confined by silt/mud layers in MHCZ, depressurization is anticipated to be rapidly and effectively propagated, leading to fast hydrate dissociation in the radial direction. As hydrate dissociation results in an increase of effective permeability, this process and the anisotropic permeability conditions accelerate the pressure reduction and hydrate dissociation in the radial direction. Overall, the dissociation zone is strongly affected by the vertical reservoir heterogeneity and shows a unique dissociation front.(3)The actual reservoir structure with low-permeability silt/mud layers in hydrate reservoirs can block the water flow through the formation into production well. Gas accumulation is observed around and below the production interval, because the low-permeability sealing formations can effectively prevent gas from migrating upward.(4)The location of production interval is significantly important for the optimization of gas recovery and reduction of water production. The beneficial production interval scheme should consider the reservoir conditions with high permeability and high initial hydrate saturation. Consequently, the identification of favorable hydrate sediments is significantly important to realize commercial production in the future.

Copyright 2017 Yilong Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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