{"id":657,"date":"2020-02-11T09:44:27","date_gmt":"2020-02-11T08:44:27","guid":{"rendered":"http:\/\/yvcharron.com\/?page_id=657"},"modified":"2021-03-20T11:07:49","modified_gmt":"2021-03-20T10:07:49","slug":"co2-geothermal-loop-motor-cycle","status":"publish","type":"page","link":"https:\/\/yvcharron.com\/index.php\/co2-geothermal-loop-motor-cycle\/","title":{"rendered":"CO2 geothermal loop – Motor cycle"},"content":{"rendered":"\n

1_Introduction<\/strong><\/h2>\n\n\n\n

Heat\nis currently recovered from the ground by conventional geothermal production\nsystems extracting hot water stored at large depth. In most cases, water is\navailable at medium temperature (between 50 to 100 \u00b0C depending on reservoir\ncharacteristics) which is sufficiently high to supply heating to residential\nareas. In other cases, water pressure and temperature are considerably greater\nproviding high pressure steam together with hot water. In these cases, energy\nmay be recovered by the use of a steam turbine. Following treatment, water is\ndisposed at the surface or re-injected into the ground depending on water\nproperties and local regulation.<\/p>\n\n\n\n

Carbon\ndioxide is detrimental to the environment. As a consequence, this gas is\noccasionally injected into the ground for long time storage.<\/p>\n\n\n\n

Carbon\ndioxide storage and heat available into the ground are two parameters that have\nto be considered for energy supply. This could be performed by using a\ngeothermal loop extracting the gas from a storage cavity, energy and heat being\nrecovered on the surface with the gas re-injected into the ground. Operating\nsuch a system with any gas would not provide necessarily any benefit when the\nenergy required to re-inject the gas may be more or less equivalent to the\nenergy recovered at the surface.<\/p>\n\n\n\n

Carbon dioxide thermodynamic properties are determinant to provide a positive energy balance in a geothermal loop<\/p>\n\n\n\n

2_Description\nof the system<\/strong><\/h2>\n\n\n\n

The system consists in a carbon dioxide geothermal loop including at ground surface a gas expander with cooling devices, a well for injecting the dense fluid into a reservoir and a second well supplying a hot pressurised gas to the expander<\/strong>. In between these two wells, carbon dioxide is stored in a high pressure and high temperature reservoir.<\/p>\n\n\n\n

Following\ngas cooling (below 30 \u00b0C) downstream the expander, carbon dioxide is either in\na liquid or a super critical phase condition characterized by a large\nvolumetric mass (approx. 1000 kg\/m3). The fluid is discharged, through the\ninjection well, into the high pressure and high temperature reservoir where\nheat is progressively transferred to the newly injected fluid. Production and\ninjection wells are sufficiently remote in order that the newly injected carbon\ndioxide mass does not reach the production well in a too short time therefore\nat a temperature lower than the reservoir temperature. Carbon dioxide is\nsupplied by the production well at a high temperature (for instance 150 \u00b0C) in\na gas phase condition with a medium volumetric mass (for instance 500 kg\/m3).<\/p>\n\n\n\n

Considering the difference in volumetric masses, the pressure at the production well is significantly greater than the one at the injection well, the difference in pressures increasing with the well length and the reservoir temperature. This difference in pressure may be used to activate an expander<\/strong> transmitting energy to a load: an electric generator or a mechanical machine (compressor or pump).<\/p>\n\n\n\n

The cooling provided by gas expansion being not sufficient to reach liquid condition, the gas is further cooled in one or several external cooling devices.<\/p>\n\n\n\n

\"Schematic<\/figure><\/div>\n\n\n\n

3_\nReservoir characteristics<\/strong><\/h2>\n\n\n\n

An\nindication of reservoir temperature is given by:<\/p>\n\n\n\n

https:\/\/www.sciencedirect.com\/topics\/engineering\/reservoir-temperature<\/a>. According to this document, the reservoir temperature could be estimated by adding the surface temperature to a temperature gradient ranging from 0.5 \u00b0C (minimum) to 0.9 \u00b0C (maximum) per 30 m.<\/strong> This gradient would be valid for most reservoirs. However, there are anomalies where this gradient may be considerably larger. The gas expansion (according to an isentropic process) occurring during its displacement from the reservoir to the surface is not discussed in this document.<\/span><\/p>\n\n\n\n

According to: https:\/\/en.wikipedia.org\/wiki\/Petroleum_reservoir<\/a>; organic elements buried in depths of 1000 to 6000 m present a temperature ranging from 60 to 150 \u00b0C<\/span>.<\/p>\n\n\n\n

According to: https:\/\/petrowiki.org\/Reservoir_pressure_and_temperature<\/a>, Reservoir temperature is governed primarily by the reservoir\u2019s proximity to the earth\u2019s mantle and by the relative heat exchange capacities and thermal conductivities of the formations forming the lithostatic sequence that includes the reservoir.<\/span><\/p>\n\n\n\n

According to: https:\/\/link.springer.com\/article\/10.1007\/s13202-016-0275-1<\/a>\u00a0 \u201cInvestigation of reservoir temperature in a gas reservoir in Middle East: case study\u201d; the temperature would be 260 \u00b0F at 11\u00a0000 ft representing a temperature gradient of 1.8\u00b0F per 100 ft<\/strong> that is 33 \u00b0C per 1\u00a0000 m<\/strong>.<\/span><\/p>\n\n\n\n

The field of Elgin \u2013 Franklin<\/strong><\/span> https:\/\/fr.wikipedia.org\/wiki\/Elgin-Franklin_(gisement)<\/a> is usually called \u00ab\u00a0HP\/HT\u00a0\u00bb (\u201cHigh Pressure & High Temperature\u201d) due to its uncommon reservoir characteristics. The reservoir depth is 6\u00a0100 m while the temperature exceeds, in some parts, 200 \u00b0C and the pressure is of the order of 1\u00a0150 bar.<\/span><\/p>\n\n\n\n

4_\nCarbon dioxide thermodynamic properties<\/strong><\/h2>\n\n\n\n

Carbon\ndioxide thermodynamic properties may be presented on a Mollier diagram\nproviding pressure variation versus enthalpy for several temperature\nconditions. On this diagram, entropy and specific volume lines are also usually\nrepresented. See, for instance, Mollier diagram for carbon dioxide (R744) from http:\/\/frederic.benet.free.fr\/<\/a>.<\/p>\n\n\n\n

The\ncarbon dioxide geothermal loop operates under the following thermodynamic\nconditions:<\/p>\n\n\n\n

The\ngas is firstly extracted from a reservoir through a production well. As the gas\nrises in the production well, the gas is expanded in an isentropic process<\/strong> (Temperature reduction).<\/p>\n\n\n\n

At\nthe surface, the gas is expanded in a turbine (an expander) providing\nmechanical energy. The gas expansion being carried out with some losses, this\nprocess is irreversible and called polytropic<\/strong>.\nIt is characterised by an isentropic efficiency<\/strong>\nslightly lower than 1. <\/p>\n\n\n\n

Before\nits re injection, the fluid is cooled down at constant pressure until it\nreaches the liquid or super critical condition. This is an isobaric process<\/strong>.<\/p>\n\n\n\n

Following\ncooling, the fluid is re injected into the reservoir. As the fluid flows down,\nthe pressure rises due to the monometric head without a significant change in\nthe fluid temperature. This is an isothermal\nprocess<\/strong>.<\/p>\n\n\n\n

In\nthe reservoir, the fluid flows from the injection to the production wells\nreceiving heat from the ambient media at a constant pressure. This is an isobaric process.<\/strong><\/p>\n\n\n\n

Carbon dioxide\u00a0<\/strong>hydrate<\/strong><\/a> or carbon dioxide clathrate<\/strong>\u00a0is a snow-like crystalline substance composed of water ice and carbon dioxide (It is normally a Type I gas<\/span>\u00a0clathrate<\/a>). The clathrate formation occurs below approximately 283K (10\u00a0C). It is therefore important not to operate the geothermal loop and more particularly the injection well below 10 \u00b0C in order to avoid the formation of carbon dioxide hydrates and therefore the plugging of the injection well. See <\/span>https:\/\/en.wikipedia.org\/wiki\/Carbon_dioxide_clathrate<\/a>. <\/p>\n\n\n\n

5_\nExample of geothermal loop<\/strong><\/h2>\n\n\n\n

An example\nof geothermal loop is described in the attached document (PDF).<\/p>\n\n\n\n

It was\nstudied based on the following operating conditions: Reservoir pressure and\ntemperature, respectively, 319 bar abs and 180 \u00b0C; injection and production\nwell length: 2 750 m; injection and production well diameter,\nrespectively, 150 mm and 250 mm; carbon dioxide mass flow rate: 100 kg\/s; expander\nisentropic efficiency: 85 %; expander discharge pressure: 80 bar abs; gas\ncooling before injection into the reservoir: 10\u00b0C (limit for hydrate formation).<\/p>\n\n\n\n

The\ncarbon dioxide leaves the reservoir with a pressure of 319 bar abs and a\ntemperature of 180\u00b0C and reaches the surface with a pressure of 203 bar abs.\nDue to the gas expansion in the production well (pressure decrease), the\ntemperature at the surface is reduced to 135\u00b0C. As an average, the gas\nvolumetric mass in the production well is of the order of 400 kg\/m3.<\/p>\n\n\n\n

Through\nthe expander, the gas is cooled down to 62 \u00b0C (57.6 \u00b0C for an isentropic\nexpansion) then cooled in a final step by an external fluid down to 10\u00b0C. This\nprovides a volumetric mass of 900 kg\/m3 at the injection wellhead and of the\norder of 1000 kg\/m3 at the bottom of the well. The wellhead pressure is 78 bar\nabs, i.e. 2 bar below the expander outlet pressure.<\/p>\n\n\n\n

An isentropic expansion through the expander provides an energy unit of 43.2 kJ\/kg. Applying an isentropic efficiency of 85 %, the energy provided by the expander is 36.7 kJ\/kg. The heating rate dissipated during the final cooling process is 236 kJ\/kg. The total heating rate transmitted by the reservoir to the gas is therefore 273 kW, the expander delivering only 13.4 % of that power. The thermodynamic operation of the motor cycle is represented on the Mollier diagram below.<\/p>\n\n\n\n

\"Pressure<\/figure><\/div>\n\n\n\n

6_\nParameter analysis <\/strong><\/h2>\n\n\n\n

For\ndetails concerning the parameter analysis see the attached document (PDF).<\/p>\n\n\n\n

6.1_ Post expansion cooling<\/strong><\/h4>\n\n\n\n

Calculation\nhas been carried out to determine the effect of the post cooling i.e. the\ntemperature at the injection wellhead on the operation of the geothermal loop.\nThis calculation has been performed for 10, 20 and 30 \u00b0C. In a general manner,\nthe volumetric mass decreases in both the injection and the production well\nproviding some sort of compensating effect.<\/p>\n\n\n\n

The\ndifference in performance is relatively small for post cooling temperatures of\n10 and 20\u00b0C. In that instance, the production wellhead pressure is only reduced\nfrom 203 to 191 bar and the expander pressure ratio is only reduced from 1 \/\n2.54 to 1 \/ 2.39.<\/p>\n\n\n\n

The effect of the post cooling becomes important above\n20\u00b0C<\/strong>, particularly in the lower pressure sections of the\ninjection and production wells. When the post cooling temperature is increased\nfrom 20 to 30\u00b0C, the expansion pressure ratio is reduced from 1 \/ 2.39 to 1 \/\n2.15. This corresponds to a significant reduction in the expander power supply.<\/p>\n\n\n\n

6.2_ Expander outlet pressure<\/strong><\/h4>\n\n\n\n

The\ncase analysed in section 5 refers to an expander outlet pressure of 80 bar abs.\nThis parameter was diminished to analyse its effect down to 46 bar where it\napproaches the dew point line. It has to be noted that this calculation was\nperformed keeping constant the expander inlet conditions (199 bar abs and 135\n\u00b0C).<\/p>\n\n\n\n

By\nreducing this parameter from 80 bar, the energy per unit mass delivered by the\nexpander increases significantly. The variation is relatively linear down to 60\nbar below which the variation is quasi exponential.<\/p>\n\n\n\n

The\npressure at the injection wellhead decreases as the expander outlet pressure\nreduces. It is relatively small down to 60 bar becoming relatively important\nbelow that value. It is quasi exponential below 50 bar compromising the\noperation of the geothermal loop.<\/p>\n\n\n\n

6.3_ Well pipe length<\/strong><\/h4>\n\n\n\n

To\nevaluate the impact on the expander energy supply, injection and production\npipe lengths have been increased by 20 % (from 2 750 to 3 300 m)\nkeeping the reservoir temperature unchanged.<\/p>\n\n\n\n

The\npipe length being greater, the manometric head in the injection well is also\ngreater. It is increased by 21 % (from 240 bar to 291 bar). Concerning the\nproduction well, the pipe length and the fluid volumetric mass (greater\nreservoir pressure) being both greater, the manometric head is also considerably\ngreater. It is increased by 34 % (from 115 to 155 bar) while the differential\ntemperature is increased by 19 % (from 44.8 to 53.5 \u00b0C) due to gas expansion\nfrom the reservoir to the surface. <\/p>\n\n\n\n

At\nthe expander inlet, the temperature is reduced from 135 (2 750 m) to\n126.5\u00b0C (3 300 m).while the pressure ratio is increased from 1 \/ 2.49 to 1\n\/ 2.63. As a result, the expander energy supply is increased by 14 %.<\/p>\n\n\n\n

6.4_ Loop mass flow rate<\/strong><\/h4>\n\n\n\n

Basic\ncalculation has been performed with a mass flow rate of 100 kg\/s but could be\nextended to any mass flow rate with some adaptation of the equipment and\napplying for some corrections, particularly, regarding energy losses. It has to\nbe noted that the pipe diameters selected below do not correspond necessarily to\na standard size.<\/p>\n\n\n\n

For\na 100 kg\/s mass flow rate<\/strong>, equipment\nsizing does not present major difficulties (150 and 250 mm diameter for\ninjection and production wells). The power provided by the expander is\nrelatively small (isentropic 4.32 MW) by comparison with the residual heat (post\ncooling) which could present a major constraint if it cannot be exploited.<\/p>\n\n\n\n

For\na 1 000 kg\/s mass flow rate <\/strong>(4 000\nm3\/hr at injection wellhead), the power provided by the expander is significant\n(isentropic 44 MW) and pipe diameters are still of a reasonable size (475 and\n790 mm in this calculation). Same comment concerning post cooling. <\/p>\n\n\n\n

For\na 10 000 kg\/s mass flow rate<\/strong>,\nthe power provided by the expander is quite important (isentropic 460 MW) and\nthe cooling duty is also hugged (2.36 GW \u2013 equivalent to two nuclear power\nplants). This case would require several injection and production wells located\nat a large distance from one another and an extended reservoir. This\nconfiguration could be of interest for a large urban area or number of\ninhabitants.<\/p>\n\n\n\n

Pipe\ndiameters have to be selected sufficiently large in order to minimize pressure\nlosses in injection and production wells. If an injection well diameter was\nreduced by 20 %, the corresponding reservoir pressure would be reduced by 10 %\nand the column differential pressure by 14 % (to be considered as a limit). If a\nproduction well diameter was reduced by 30 %, the corresponding wellhead\npressure would be reduced by 6 % and the column differential pressure would be\nincreased by 9 % (to be considered as a limit). Beyond these diameter\nreductions, the operation of the geothermal loop would be compromised.<\/p>\n\n\n\n

6.5_ Reservoir temperature<\/strong><\/h4>\n\n\n\n

The\ncalculation has been performed in two cases of reservoir temperature (180 and\n150 \u00b0C) keeping constant the expander pressure ratio (approx. 1 \/ 2.48).\nDespite the expander pressure ratio was kept approximately constant, the power\nsupplied by the expander is considerably reduced: 19.9 MW instead of 36.7 MW\n(46 % less) by reducing the reservoir temperature from 180 to 150\u00b0C. The expander\nenergy relative to the post cooling duty is also reduced: 13.4 % in the hot\ncase and 9.6 % in the cold case.<\/p>\n\n\n\n

This highlights the importance of the reservoir temperature.<\/strong><\/p>\n\n\n\n

Concerning the parameter analysis, further details may be found in the following document (PDF). <\/p>\n\n\n\n

\"PDF<\/a><\/figure><\/div>\n\n\n\n

7_ Secondary circuit<\/strong><\/h2>\n\n\n\n

Section\n5 indicates that energy of 43.2 kJ\/kg and residual heat of 236 kJ\/kg may be\nextracted for every mass unit of produced carbon dioxide. These energy and heat\nare obtained for inlet and outlet pressures, of respectively, 199 and 80 bar\nabs and an inlet temperature of 135\u00b0C (\u201cHT\u201d on figure below). Based on an\nisentropic efficiency of 85 %, the outlet temperature is 62 \u00b0C (\u201cMHT\u201d). The\nresidual heat is therefore available at this relatively high temperature.<\/p>\n\n\n\n

The\nprocess fluid is cooled down before its reinjection into the storage reservoir.\nIt has been shown in section 6.1 that the efficiency of the geothermal loop is\nreduced by 6.4 % by increasing the injection temperature from 10 \u00b0C to 20 \u00b0C\n(17 % in the case of 30 \u00b0C).<\/p>\n\n\n\n

It\nis assumed in the following that a cooling media is available at a relatively\nlow temperature. Consequently, these two heat sources at a different\ntemperature may be used to activate a motor cycle (\u201cSecondary circuit\u201d). The\nefficiency of the motor cycle is dependent on the temperature difference. As an\nexample, for a 10\u00b0C cold source, the Carnot efficiency is 15 %. Calculations\nhave been performed with cold sources of plus 6.8 and minus 6.8 \u00b0C. <\/p>\n\n\n\n

The\nmotor cycle includes an evaporator, an expander, a pump, a condenser and a\nrefrigerant flowing in that order. From the evaporator, the refrigerant removes\nheat from the main fluid (inlet temperature 60 \u00b0C). Operating the motor cycle\nat a relatively high pressure (80 bars in the present case) the refrigerant\nenters into the expander where gas expansion occurs producing energy and\ncooling. At its outlet, the gas enters into the condenser where it is cooled by\nan external media and liquefied. At the condenser outlet, the liquid is\npressurised to the evaporator pressure to initiate another refrigerant cycle. <\/p>\n\n\n\n

\"Operation<\/figure><\/div>\n\n\n\n

_<\/p>\n\n\n\n

Cooling\nmedia between 10 and 20 \u00b0C <\/strong><\/h5>\n\n\n\n

Temperature\nat this level may be encountered in many circumstances: atmospheric air,\naquifers, water from the sea surface (cold or temperate seas) or pumped from the\nthermocline in the case of tropical seas. Calculations have not been performed\nin that temperature range but some order of magnitude may be deduced from the\ntheoretical Carnot efficiency values (See PDF) and the two calculations\nperformed below at two low temperatures: plus 6.8 and minus 6.8\u00b0C. It has to be\nnoted that the Carnot efficiency is relatively proportional to the hot and cold\ntemperature difference.<\/p>\n\n\n\n

Calculations\nhave been performed using the CoolPack software developed\nby the Department of Mechanical Engineering (MEK)<\/a>,\nSection of Thermal Energy (TES)<\/a> at the Technical University of\nDenmark (DTU).<\/p>\n\n\n\n

Cooling\nmedia at plus 6.8 \u00b0C <\/strong><\/h5>\n\n\n\n

The\ncycle is operated with pure carbon dioxide in order to avoid the formation of\nhydrates (temperature below 10\u00b0C). The \u201c2nd<\/sup> circuit\u201d expander\noperates with inlet pressure and temperature of, respectively, 80 bar abs and\n60\u00b0C and an outlet pressure of 40 bar abs corresponding to an outlet\ntemperature of 6.9\u00b0C close to the dew point line.<\/p>\n\n\n\n

The\n\u201c2nd<\/sup> circuit\u201d absorbs the heat (236 kJ\/kg) provided by the process\nfluid through the evaporator while the expander supplies 22.0 kJ\/kg (pumping\nenergy taken into account) and releases the rest of the heat through the\ncondenser. For a Carnot efficiency of 16 %, actual efficiency is 9.3%. This energy\nrepresents 51 % of the main expander energy. Calculation was performed with a\ncooling temperature of 6.8 \u00b0C. This indicates that an extra cooling is required\nor that this cooling is permitted only for reduced periods of time (seasonal\nconditions) or in specific areas (case of North Sea – Sea temperature often\nclose to 4\u00b0C).<\/p>\n\n\n\n

The\nstudy has been performed only with pure carbon dioxide. Other refrigerant\nfluids could be investigated to evaluate their respective benefit.<\/p>\n\n\n\n

To\nget further details concerning operation of the motor cycle at 6.8 \u00b0C and minus\n6.8 \u00b0C see the attached document (PDF).<\/p>\n\n\n\n

8_ Merging\nmain and secondary circuits<\/strong><\/h2>\n\n\n\n

This\ncase is briefly discussed in the attached document. There are some reservoir\nconditions where the energy of the main expander is significantly lower than\nthe one of the secondary circuit. In that case, it may be preferable to use a\nsingle expansion system: the secondary circuit one.<\/p>\n\n\n\n

9_ Conclusion<\/strong><\/h2>\n\n\n\n

A\ngeothermal loop may be operated with carbon dioxide without any pressurizing\nequipment. To the contrary, a geothermal\nloop may produce mechanical energy<\/strong> when site conditions are present. This\nenergy is accompanied with a significant amount of heat. <\/p>\n\n\n\n

The\nlarge difference in manometric heads between the injection well, characterized\nby a large volumetric mass of the fluid (of the order of 1 000 kg\/m3) and\nthe production well, characterized by a medium volumetric mass of the fluid (of\nthe order of 400 kg\/m3) permits the operation of a geothermal loop due to the\nexistence of a large pressure difference between the two wells.<\/p>\n\n\n\n

The efficiency of the geothermal loop increases with the\nreservoir temperature, the reservoir pressure and the well length<\/strong>.\nThis indicates that only specific areas are suitable for producing heat and\nenergy in an efficient way. If only heat is required, the application field of\nthe technology is considerably wider.<\/p>\n\n\n\n

Calculations\nin different reservoir configurations indicate that 10 to 15 % of the capted reservoir heat may be converted into\nmechanical energy<\/strong>. <\/p>\n\n\n\n

The\nresidual heat<\/strong> may be used to provide\nheating to residential areas<\/strong> if they\nare present in close vicinity. If it is not the case, a fraction of that heat\nmay be converted to mechanical energy in a second\nmotor cycle circuit<\/strong>. The efficiency of that loop is of the order of 10 %\n(approximately 50 to 60 % of the Carnot efficiency). The operation of the second\ncircuit was analysed with pure carbon dioxide operating at low temperature\n(around 0\u00b0C, only available in specific areas or for reduced time intervals).\nIt is possible that this second circuit would operate more efficiently with\nanother refrigerant. This may be tested in a near future.\n\nAs an overall, the\nmain geothermal loop and the second motor cycle circuit may convert 15 to 20%\nof the capted heat into mechanical energy.\n\n\n\n<\/p>\n\n\n\n

This study was performed by Yves CHARRON in 2020. For any question use form below:<\/p>\n\n\n\n

http:\/\/yvcharron.com\/index.php\/contact\/<\/a> or<\/p>\n\n\n\n

\"yves<\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"

1_Introduction Heat is currently recovered from the ground by conventional geothermal production systems extracting hot water stored at large depth. In most cases, water is available at medium temperature (between 50 to 100 \u00b0C depending on reservoir characteristics) which is sufficiently high to supply heating to residential areas. In other cases, water pressure and temperature…
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In most cases, water is available at medium temperature (between 50 to 100 \u00b0C depending on reservoir characteristics) which is sufficiently high to supply heating to residential areas. 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