Compression\nof carbon dioxide may present some difficulties in various areas. Carbon\ndioxide does not behave as an ideal gas; therefore, good knowledge of its\nthermodynamic properties is required. Attention should be paid to the relative\ngas velocity at the blade edges to avoid sonic losses and inside hydraulic cell\nchannels to limit choke losses. Attention is required at low temperature to\navoid the formation of carbonate hydrates and not to cool the gas at a too low\ntemperature to avoid liquid formation especially during the compression of the\nfluid in a single phase condition. Above the critical point, the fluid behaves\nin terms of compressibility in between a gas and a liquid phase; therefore,\nhydraulic cells with adapted internal geometry are required to get an optimum\npressure coefficient. Operability of a compression train may be of concern in\nterms of flow and running speed range around the design point. Special\nmaterials are required to take into account the aggressiveness of wet carbon\ndioxide (sour gas), the presence of hydrogen sulphide and also the occurrence\nof very low temperature following a sudden depressurisation of the compression\nfacilities.<\/p>\n\n\n\n
The benefit of a two phase compression system is sometimes questioned. This document investigates on the relative advantage of this mode of compression.<\/p>\n\n\n\n
.<\/p>\n\n\n\n
COMPRESSION SYSTEM ISSUES <\/strong><\/h2>\n\n\n\n1 – Single phase flow – Sonic losses<\/strong><\/h3>\n\n\n\nThe speed of sound is the distance travelled per unit time by a <\/strong><\/em>sound wave<\/strong><\/em><\/a> as it propagates through an elastic<\/strong><\/em><\/a> medium. Its value depends strongly on the temperature as well as the medium through which the sound wave propagates. At 20 C, the speed of sound in air is about 343 metres per second.<\/p>\n\n\n\nIn fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The ratio of the speed of an object to the speed of sound in the fluid is called the object’s Mach Number. Objects moving at speeds greater than Mach1<\/em> are said to be traveling at supersonic<\/em><\/strong><\/a> speeds.<\/p>\n\n\n\nConcerning rotodynamic compressors, internals have to be designed according to the local relative gas velocity to limit losses occurring when this gas velocity approaches the speed of sound. These losses are designated by sonic losses<\/strong>.<\/p>\n\n\n\nThe sound velocity reduces considerably\nwith the temperature. In the case of carbon dioxide, at 25 bar abs, it is 200\nm\/s at minus 20 \u00b0C and 320 m\/s at 170 \u00b0C. The sound velocity varies to the\nopposite of the pressure with a variation particularly important at low\ntemperature but relatively small at high temperature. The sound velocity is\napproximately equal to 270 m\/s at the critical point. At 50 bar, the sound\nvelocity is increased approximately from 210 m\/s at 20 \u00b0C to 245 m\/s at 50 \u00b0C.<\/p>\n\n\n\n
Attention must therefore be paid when operating a compressor with carbon dioxide at low temperature and medium pressure.<\/strong> For further details see attached PDF (See before “Conclusion” section) and also: <\/p>\n\n\n\n https:\/\/en.wikipedia.org\/wiki\/Speed_of_sound<\/a><\/p>\n\n\n\n![\"Carbon](\"http:\/\/yvcharron.com\/wp-content\/uploads\/2020\/06\/image-2.png\")
<\/figure><\/div>\n\n\n\n2 – Single phase flow – Choke losses<\/strong><\/h3>\n\n\n\nChoked flow is a compressible flow effect<\/strong>. When it occurs, the fluid velocity (the flow rate) is considerably limited. It is associated with the venturi effect<\/strong><\/em><\/a> , that is, when a fluid flows through a constriction (such as the throat of a convergent \u2013 divergent nozzle) the fluid velocity increases causing the static pressure to decrease. Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure for a fixed upstream pressure and temperature.<\/p>\n\n\n\nFor homogeneous fluids, the physical point at which the choking occurs, for adiabatic conditions, is when the exit plane velocity is at sonic condition; i.e., at a Mach number<\/em><\/strong><\/a> of 1. At choked flow, the mass flow rate can only be increased by increasing the density (or the pressure) upstream the choke point <\/p>\n\n\n\nThe critical pressure ratio is established according to the isentropic factor. In the case of nitrogen the critical pressure is equal to 0.528 the upstream total (stagnation) pressure. The choke flow rate is a function of the restriction characteristics: the upstream total pressure and temperature, the molecular weight and the isentropic factor. The lower are the pressure and the temperature, the lower is the critical mass flow rate.<\/strong><\/p>\n\n\n\nFor\nfurther details see the attached PDF and: https:\/\/en.wikipedia.org\/wiki\/Choked_flow<\/a><\/p>\n\n\n\nIn the case of a rotodynamic compressor (axial or centrifugal), the chocked flow limit may be designated by overload.<\/strong><\/p>\n\n\n\n3 – Two phase flow – Sonic characteristics<\/strong><\/h3>\n\n\n\nSeveral numerical expressions are available to\ncalculate the sound velocity for a two phase mixture. Nguyen has proposed a\nmodel where the gas phase is homogenously dispersed in the liquid phase. This\nmodel has been used to analyse the characteristics of the sound velocity\naccording to the gas \u2013 liquid mixture characteristics.<\/p>\n\n\n\n
When the gas volume fraction tends, respectively, towards 1 and 0, the two phase sound velocity tends, respectively, towards the gas and the liquid sound velocity. In between, the sound velocity is reduced being smaller than the lowest (the gas) sound velocity.<\/strong><\/p>\n\n\n\nAt\na low pressure (low gas volumetric mass), the two phase sound velocity may\nreduce to 20 m\/s (that is 10 times smaller than the gas sound velocity). At\nmedium pressure (of the order of 50 bar) the sound velocity is increased to 100\nm\/s. The two phase sound velocity approaches the gas sound velocity for a\npressure greater than 150 bar.<\/p>\n\n\n\n
For further details see the attached PDF (Before “Conclusion” section) with graph showing the characteristics of the sound velocity of a carbon dioxide gas \u2013 liquid mixture. See also: https:\/\/pastel.archives-ouvertes.fr\/pastel-00005234\/document<\/a> <\/p>\n\n\n\n4 – Hydrates <\/strong><\/h3>\n\n\n\nCarbon dioxide <\/strong>hydrate<\/strong><\/a> or carbon dioxide\nclathrate<\/strong> is a snow-like crystalline substance composed of water ice\nand carbon dioxide. It is normally a Type I gas clathrate<\/a>. In the case of pure\ncarbon dioxide and at low pressure, clathrate formation occurs below 283K\n(10 C). See https:\/\/en.wikipedia.org\/wiki\/Carbon_dioxide_clathrate<\/a>.<\/p>\n\n\n\nThe temperature threshold (temperature at which hydrate formation occurs) increases slightly with the pressure: 10\u00b0C at 50 bar abs and 12\u00b0C at 150 bar abs.<\/strong><\/p>\n\n\n\nThe temperature threshold increases with the fraction of associated components: 13\u00b0C at 50 bar abs and 16\u00b0C at 250 bar abs in the case of a mixture containing 5 per cent of methane.<\/p>\n\n\n\n
5 – Flow surging <\/strong><\/h3>\n\n\n\nSeveral cases\nof flow surging are considered in the present document.<\/p>\n\n\n\n
5.a – Rotating stall<\/strong> is a local disruption of airflow permitting the compressor to continue to provide a positive gas flow but with reduced effectiveness. The rotating stall arising at an air foil (or blade) may propagate to the air foils around it.<\/p>\n\n\n\nIt may be briefly\ndescribed in the following way: A flow perturbation causes a blade to reach a stalled condition at an\ninstant before other blades mounted in the same cascade (same row of blades).\nThe stalled blade does not produce a sufficient pressure rise to maintain the\nflow around it. As a consequence, an effective flow blockage develops which is\ntransmitted transversally<\/strong> to the\nblades around it. The stall propagates downward relative to the blade row rotation\nat a rate about half the rotational speed.<\/p>\n\n\n\nFor further details see: https:\/\/www.sciencedirect.com\/topics\/engineering\/rotating-stall<\/a>. Also Nuovo Pigone paper: https:\/\/core.ac.uk\/download\/pdf\/188800045.pdf<\/a><\/p>\n\n\n\nSometimes, a rotating stall is\nassimilated to an approach to a surge flow condition as a result of a\nsignificant increase in rotor vibrations.<\/p>\n\n\n\n
5.b – Compressor surge <\/strong>is a form of aerodynamic instability in axial or radial (centrifugal) compressors. The term describes a violent air flow oscillating in the axial direction<\/strong> of a compressor. The axial component of fluid velocity varies periodically and may even become negative.<\/p>\n\n\n\nThe surge flow may be\ndescribed by considering the shape of the pressure coefficient curve of a single\ncompression stage (hydraulic cell). By reducing the flow from the design point,\nthe pressure coefficient increases until it passes through a maximum then\nreduces if the flow is further decreased. By decreasing the flow below the\nmaximum of the pressure coefficient, the compression stage losses its capability\nto push the flow forward (toward compressor exit) resulting in a backward flow.\nThe flow is then violently increased and progressively reduced (to reach the\noperating condition) until it generates a second backward flow. This generates\na pumping system (oscillating phenomenon) with a frequency of the order of 1Hz.<\/p>\n\n\n\n
For\ngeneral information on stall and surge see: https:\/\/en.wikipedia.org\/wiki\/Compressor_stall<\/a> and https:\/\/en.wikipedia.org\/wiki\/Surge_in_compressors<\/a><\/p>\n\n\n\nFor\nother unsteady flow fields see: https:\/\/hal.archives-ouvertes.fr\/hal-01296905\/document<\/a><\/p>\n\n\n\n6 – Centrifugal compressor operability<\/strong><\/h3>\n\n\n\nIn\na rotodynamic compressor (axial or centrifugal), the pressure ratio and the temperature\nratio are a function of the manometric head transmitted by the hydraulic cell\nto the gas and the gas characteristics (compressibility factor, isentropic factor and molecular weight). The\nmanometric head of a hydraulic stage is the product of a pressure coefficient\n(a function of the relative flow) and the square of the peripheral velocity of the\nimpeller.<\/p>\n\n\n\n
In the attached PDF three gases have been analysed and compared<\/strong>: a light molecular weight (hydrogen), a medium molecular weight (methane) and a large molecular weight (carbon dioxide) plotting in each case the manometric head and pressure ratio of a compressor unit versus the relative flow.<\/p>\n\n\n\nIn this document, the case of a hydrogen compressor<\/strong> including 10\nstages is analysed. It is shown that, the compression ratio for each stage\nbeing relatively small, the manometric head and pressure ratio curves versus\nthe relative volume flow are relatively flat providing an extremely large\noperating range in terms of rotating speed and volume flow.<\/p>\n\n\n\nThe case of a methane\ncompressor<\/strong> with 10 stages is then analysed. It is shown that the\ncompression ratio for the overall compressor is considerably larger with\nmethane (8 at the design point) compared to hydrogen (1.25 at design point) the\nmanometric head and pressure ratio curves versus the relative volume flow being\nsharper. The operating range in terms of rotating speed and volume flow is\nconsiderably reduced.<\/p>\n\n\n\nThe case of a carbon dioxide compressor<\/strong> with 5 stages is then analysed (the number of stages had to be reduced to take into account the considerable increase in pressure ratio based on the same manometric head per stage). Despite the significant reduction in the number of stages, the compressor pressure ratio is significantly greater with carbon dioxide compared to methane<\/strong>. Similarly, tthe temperature ratio is greater in the carbon dioxide case<\/strong>, the temperature limitation occurring at 5 % above the design speed (25 % in the methane case). The flow range is also considerably smaller with carbon dioxide than with methane <\/strong>at maximum and minimum speed even after a significant reduction in the speed range (2\/3 in carbon dioxide compared to the methane case).<\/p>\n\n\n\nSee attached PDF for the details concerning the overall performance curves (See before “Conclusion” section).<\/p>\n\n\n\n
7 – Materials <\/strong><\/h3>\n\n\n\nSome details concerning the material\nrequirements may be found in the SPE 36 600 document \u201cSleipner West CO2\ndisposal, CO2 injection into a shallow underground aquifer\u201d. Authors are from\nStatoil and Sintef.<\/p>\n\n\n\n
Materials are selected on the following basis: a) Corrosion potential<\/strong> of wet carbon dioxide; b) Low yield<\/strong> requirement in presence of hydrogen sulphide; c) Material brittleness<\/strong> in case of sudden compression loop depressurisation: risk of temperature lowering below minus 50\u00b0C. <\/p>\n\n\n\n.<\/p>\n\n\n\n
THERMODYNAMIC PROPERTIES<\/strong><\/h2>\n\n\n\nKnowledge of thermodynamic properties is\nrequired to calculate the sonic velocity, the occurrence of a choke flow and\nthe compression features of a fluid.<\/p>\n\n\n\n
Thermodynamic calculation was performed by using the CoolPack software. It has been developed by the<\/span>\u00a0Department of Mechanical Engineering (MEK)<\/a>, Section of\u00a0Thermal Energy (TES)<\/a>\u00a0at the Technical University of Denmark (DTU): https:\/\/www.ipu.dk\/products\/pack-calculation-pro\/<\/a><\/p>\n\n\n\nUsing this software, the following have been\ncalculated versus the actual pressure and temperature : a) The specific heat at\nconstant pressure (Cp); b) The specific heat at constant volume (Cv); c) The\nisentropic factor in the case of an ideal gas (Cp\/Cv); d) The isentropic factor\nin the case of a real gas; e) The volumetric mass (density); f) The\ncompressibility factor; g) The enthalpy and h) The entropy.<\/p>\n\n\n\n
These results are presented on figures 3.1 (a&b), 3.2 (a&b), 3.3 (a&b) and 3.4 in the attached PDF (See before “Conclusion” section).<\/p>\n\n\n\n
.<\/p>\n\n\n\n
ONE APPLICATION CASE<\/strong><\/h2>\n\n\n\nA compression calculation has been performed on a carbon dioxide flow leaving an amine treatment unit at a pressure slightly above 1 bar abs. The injection pressure was taken to 150 bar in the present exemple.<\/p>\n\n\n\n
The\ngas is suctioned by the first compressor section at a temperature of\napproximately 30\u00b0C. The gas outlet temperature is limited to 180 \u00b0C in the\npresent study. Following each compression stage, the gas is cooled down to a\ntemperature of 30 \u00b0C to provide sufficient margin with the temperature\ncorresponding to hydrate formation, particularly, in the case of a gas mixture\ncontaining methane (See hydrate section). Between each compression stage, a\npressure loss of 10 % of the actual pressure is considered to take into account\nintermediate losses between compressor sections.<\/p>\n\n\n\n
The\ncompression ratio for each stage is of the order of 4 and four sections are\nrequired to bring the gas at a pressure of the order of 100 bar. At this\npressure level, following cooling, the gas enters into a dense phase condition<\/strong> with a volumetric mass of the order of 750\nkg\/m3. It has to be noted that following the first three cooling\u2019s, the\nvolumetric mass is considerably smaller, respectively, of the order of 6, 24\nand 75 kg\/m3 at the outlet of, respectively, the first, the second and the\nthird cooling stage.<\/p>\n\n\n\n![\"CO2](\"http:\/\/yvcharron.com\/wp-content\/uploads\/2020\/06\/image-3.png\")
.<\/figcaption><\/figure><\/div>\n\n\n\nTWO PHASE FLOW COMPRESSION<\/strong><\/h2>\n\n\n\nAs\nshown on the above figure, carbon dioxide compression is started in gas phase\nat a pressure slightly above 1 bar abs and at a temperature of 30 \u00b0C. Should\nthe temperature be significantly lower, there is no possibility for liquid\nformation (at least not below minus 50 \u00b0C).<\/p>\n\n\n\n
Above\n40 bar abs, the temperature has to be controlled carefully to avoid the\nformation of carbon hydrates (temperature to be above 20 \u00b0C providing 5 \u00b0C\ntemperature margin in case of presence of methane in the carbon dioxide\nmixture) and also to avoid the liquefaction of carbon dioxide when using a\ncompressor handling only a gas phase.<\/p>\n\n\n\n
Carbon dioxide could be partially liquefied, without any risk of hydrate formation, at a temperature of 20 \u00b0C in view of using a two phase flow compressor (pump). This temperature corresponds to a liquefaction pressure of approximately 60 bar abs. The compression could operate in two phase flow up to 73 bar abs corresponding to the critical pressure above which the fluid is in dense phase condition (single phase). The pressure range in two phase flow is therefore relatively narrow.<\/strong><\/p>\n\n\n\nIn addition, there is a major difficulty in controlling the volume flow crossing the two phase flow pump as the liquefaction occurs at a single point condition in terms of pressure for a given temperature value (<\/strong>case of every pure fluid). This would induce a lack of knowledge (therefore control) in the gas and liquid fractions therefore in the total volume flow. This total volume flow could vary in the volumetric mass ratio of the liquid and gas phases that is of the order of 6.<\/p>\n\n\n\nIf the fluid mixture was made of a least two pure components<\/strong>, the gas-liquid phase fractions would be represented by an envelope and not by a single line (pure component). In this last case the gas and liquid fractions could be controlled during the two phase compression.<\/strong><\/p>\n\n\n\nAs a result of these two points, the two phase flow compression (pumping) of carbon dioxide does not present a significant advantage as the domain of operation is extremely small and the liquefaction process is practically out of control.<\/p>\n\n\n\n
Concerning two phase flow pump design and performance see<\/span>: http:\/\/yvcharron.com\/index.php\/two-phase-flow-pumps\/<\/a><\/p>\n\n\n\n.<\/p>\n\n\n\n
For more details on carbon dioxide compression with formula and graphs get document below in pdf format.<\/strong><\/p>\n\n\n\n
The speed of sound is the distance travelled per unit time by a <\/strong><\/em>sound wave<\/strong><\/em><\/a> as it propagates through an elastic<\/strong><\/em><\/a> medium. Its value depends strongly on the temperature as well as the medium through which the sound wave propagates. At 20 C, the speed of sound in air is about 343 metres per second.<\/p>\n\n\n\n In fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The ratio of the speed of an object to the speed of sound in the fluid is called the object’s Mach Number. Objects moving at speeds greater than Mach1<\/em> are said to be traveling at supersonic<\/em><\/strong><\/a> speeds.<\/p>\n\n\n\n Concerning rotodynamic compressors, internals have to be designed according to the local relative gas velocity to limit losses occurring when this gas velocity approaches the speed of sound. These losses are designated by sonic losses<\/strong>.<\/p>\n\n\n\n The sound velocity reduces considerably\nwith the temperature. In the case of carbon dioxide, at 25 bar abs, it is 200\nm\/s at minus 20 \u00b0C and 320 m\/s at 170 \u00b0C. The sound velocity varies to the\nopposite of the pressure with a variation particularly important at low\ntemperature but relatively small at high temperature. The sound velocity is\napproximately equal to 270 m\/s at the critical point. At 50 bar, the sound\nvelocity is increased approximately from 210 m\/s at 20 \u00b0C to 245 m\/s at 50 \u00b0C.<\/p>\n\n\n\n Attention must therefore be paid when operating a compressor with carbon dioxide at low temperature and medium pressure.<\/strong> For further details see attached PDF (See before “Conclusion” section) and also: <\/p>\n\n\n\n https:\/\/en.wikipedia.org\/wiki\/Speed_of_sound<\/a><\/p>\n\n\n\n Choked flow is a compressible flow effect<\/strong>. When it occurs, the fluid velocity (the flow rate) is considerably limited. It is associated with the venturi effect<\/strong><\/em><\/a> , that is, when a fluid flows through a constriction (such as the throat of a convergent \u2013 divergent nozzle) the fluid velocity increases causing the static pressure to decrease. Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure for a fixed upstream pressure and temperature.<\/p>\n\n\n\n For homogeneous fluids, the physical point at which the choking occurs, for adiabatic conditions, is when the exit plane velocity is at sonic condition; i.e., at a Mach number<\/em><\/strong><\/a> of 1. At choked flow, the mass flow rate can only be increased by increasing the density (or the pressure) upstream the choke point <\/p>\n\n\n\n The critical pressure ratio is established according to the isentropic factor. In the case of nitrogen the critical pressure is equal to 0.528 the upstream total (stagnation) pressure. The choke flow rate is a function of the restriction characteristics: the upstream total pressure and temperature, the molecular weight and the isentropic factor. The lower are the pressure and the temperature, the lower is the critical mass flow rate.<\/strong><\/p>\n\n\n\n For\nfurther details see the attached PDF and: https:\/\/en.wikipedia.org\/wiki\/Choked_flow<\/a><\/p>\n\n\n\n In the case of a rotodynamic compressor (axial or centrifugal), the chocked flow limit may be designated by overload.<\/strong><\/p>\n\n\n\n Several numerical expressions are available to\ncalculate the sound velocity for a two phase mixture. Nguyen has proposed a\nmodel where the gas phase is homogenously dispersed in the liquid phase. This\nmodel has been used to analyse the characteristics of the sound velocity\naccording to the gas \u2013 liquid mixture characteristics.<\/p>\n\n\n\n When the gas volume fraction tends, respectively, towards 1 and 0, the two phase sound velocity tends, respectively, towards the gas and the liquid sound velocity. In between, the sound velocity is reduced being smaller than the lowest (the gas) sound velocity.<\/strong><\/p>\n\n\n\n At\na low pressure (low gas volumetric mass), the two phase sound velocity may\nreduce to 20 m\/s (that is 10 times smaller than the gas sound velocity). At\nmedium pressure (of the order of 50 bar) the sound velocity is increased to 100\nm\/s. The two phase sound velocity approaches the gas sound velocity for a\npressure greater than 150 bar.<\/p>\n\n\n\n For further details see the attached PDF (Before “Conclusion” section) with graph showing the characteristics of the sound velocity of a carbon dioxide gas \u2013 liquid mixture. See also: https:\/\/pastel.archives-ouvertes.fr\/pastel-00005234\/document<\/a> <\/p>\n\n\n\n Carbon dioxide <\/strong>hydrate<\/strong><\/a> or carbon dioxide\nclathrate<\/strong> is a snow-like crystalline substance composed of water ice\nand carbon dioxide. It is normally a Type I gas clathrate<\/a>. In the case of pure\ncarbon dioxide and at low pressure, clathrate formation occurs below 283K\n(10 C). See https:\/\/en.wikipedia.org\/wiki\/Carbon_dioxide_clathrate<\/a>.<\/p>\n\n\n\n The temperature threshold (temperature at which hydrate formation occurs) increases slightly with the pressure: 10\u00b0C at 50 bar abs and 12\u00b0C at 150 bar abs.<\/strong><\/p>\n\n\n\n The temperature threshold increases with the fraction of associated components: 13\u00b0C at 50 bar abs and 16\u00b0C at 250 bar abs in the case of a mixture containing 5 per cent of methane.<\/p>\n\n\n\n Several cases\nof flow surging are considered in the present document.<\/p>\n\n\n\n 5.a – Rotating stall<\/strong> is a local disruption of airflow permitting the compressor to continue to provide a positive gas flow but with reduced effectiveness. The rotating stall arising at an air foil (or blade) may propagate to the air foils around it.<\/p>\n\n\n\n It may be briefly\ndescribed in the following way: A flow perturbation causes a blade to reach a stalled condition at an\ninstant before other blades mounted in the same cascade (same row of blades).\nThe stalled blade does not produce a sufficient pressure rise to maintain the\nflow around it. As a consequence, an effective flow blockage develops which is\ntransmitted transversally<\/strong> to the\nblades around it. The stall propagates downward relative to the blade row rotation\nat a rate about half the rotational speed.<\/p>\n\n\n\n For further details see: https:\/\/www.sciencedirect.com\/topics\/engineering\/rotating-stall<\/a>. Also Nuovo Pigone paper: https:\/\/core.ac.uk\/download\/pdf\/188800045.pdf<\/a><\/p>\n\n\n\n Sometimes, a rotating stall is\nassimilated to an approach to a surge flow condition as a result of a\nsignificant increase in rotor vibrations.<\/p>\n\n\n\n 5.b – Compressor surge <\/strong>is a form of aerodynamic instability in axial or radial (centrifugal) compressors. The term describes a violent air flow oscillating in the axial direction<\/strong> of a compressor. The axial component of fluid velocity varies periodically and may even become negative.<\/p>\n\n\n\n The surge flow may be\ndescribed by considering the shape of the pressure coefficient curve of a single\ncompression stage (hydraulic cell). By reducing the flow from the design point,\nthe pressure coefficient increases until it passes through a maximum then\nreduces if the flow is further decreased. By decreasing the flow below the\nmaximum of the pressure coefficient, the compression stage losses its capability\nto push the flow forward (toward compressor exit) resulting in a backward flow.\nThe flow is then violently increased and progressively reduced (to reach the\noperating condition) until it generates a second backward flow. This generates\na pumping system (oscillating phenomenon) with a frequency of the order of 1Hz.<\/p>\n\n\n\n For\ngeneral information on stall and surge see: https:\/\/en.wikipedia.org\/wiki\/Compressor_stall<\/a> and https:\/\/en.wikipedia.org\/wiki\/Surge_in_compressors<\/a><\/p>\n\n\n\n For\nother unsteady flow fields see: https:\/\/hal.archives-ouvertes.fr\/hal-01296905\/document<\/a><\/p>\n\n\n\n In\na rotodynamic compressor (axial or centrifugal), the pressure ratio and the temperature\nratio are a function of the manometric head transmitted by the hydraulic cell\nto the gas and the gas characteristics (compressibility factor, isentropic factor and molecular weight). The\nmanometric head of a hydraulic stage is the product of a pressure coefficient\n(a function of the relative flow) and the square of the peripheral velocity of the\nimpeller.<\/p>\n\n\n\n In the attached PDF three gases have been analysed and compared<\/strong>: a light molecular weight (hydrogen), a medium molecular weight (methane) and a large molecular weight (carbon dioxide) plotting in each case the manometric head and pressure ratio of a compressor unit versus the relative flow.<\/p>\n\n\n\n In this document, the case of a hydrogen compressor<\/strong> including 10\nstages is analysed. It is shown that, the compression ratio for each stage\nbeing relatively small, the manometric head and pressure ratio curves versus\nthe relative volume flow are relatively flat providing an extremely large\noperating range in terms of rotating speed and volume flow.<\/p>\n\n\n\n The case of a methane\ncompressor<\/strong> with 10 stages is then analysed. It is shown that the\ncompression ratio for the overall compressor is considerably larger with\nmethane (8 at the design point) compared to hydrogen (1.25 at design point) the\nmanometric head and pressure ratio curves versus the relative volume flow being\nsharper. The operating range in terms of rotating speed and volume flow is\nconsiderably reduced.<\/p>\n\n\n\n The case of a carbon dioxide compressor<\/strong> with 5 stages is then analysed (the number of stages had to be reduced to take into account the considerable increase in pressure ratio based on the same manometric head per stage). Despite the significant reduction in the number of stages, the compressor pressure ratio is significantly greater with carbon dioxide compared to methane<\/strong>. Similarly, tthe temperature ratio is greater in the carbon dioxide case<\/strong>, the temperature limitation occurring at 5 % above the design speed (25 % in the methane case). The flow range is also considerably smaller with carbon dioxide than with methane <\/strong>at maximum and minimum speed even after a significant reduction in the speed range (2\/3 in carbon dioxide compared to the methane case).<\/p>\n\n\n\n See attached PDF for the details concerning the overall performance curves (See before “Conclusion” section).<\/p>\n\n\n\n Some details concerning the material\nrequirements may be found in the SPE 36 600 document \u201cSleipner West CO2\ndisposal, CO2 injection into a shallow underground aquifer\u201d. Authors are from\nStatoil and Sintef.<\/p>\n\n\n\n Materials are selected on the following basis: a) Corrosion potential<\/strong> of wet carbon dioxide; b) Low yield<\/strong> requirement in presence of hydrogen sulphide; c) Material brittleness<\/strong> in case of sudden compression loop depressurisation: risk of temperature lowering below minus 50\u00b0C. <\/p>\n\n\n\n .<\/p>\n\n\n\n Knowledge of thermodynamic properties is\nrequired to calculate the sonic velocity, the occurrence of a choke flow and\nthe compression features of a fluid.<\/p>\n\n\n\n Thermodynamic calculation was performed by using the CoolPack software. It has been developed by the<\/span>\u00a0Department of Mechanical Engineering (MEK)<\/a>, Section of\u00a0Thermal Energy (TES)<\/a>\u00a0at the Technical University of Denmark (DTU): https:\/\/www.ipu.dk\/products\/pack-calculation-pro\/<\/a><\/p>\n\n\n\n Using this software, the following have been\ncalculated versus the actual pressure and temperature : a) The specific heat at\nconstant pressure (Cp); b) The specific heat at constant volume (Cv); c) The\nisentropic factor in the case of an ideal gas (Cp\/Cv); d) The isentropic factor\nin the case of a real gas; e) The volumetric mass (density); f) The\ncompressibility factor; g) The enthalpy and h) The entropy.<\/p>\n\n\n\n These results are presented on figures 3.1 (a&b), 3.2 (a&b), 3.3 (a&b) and 3.4 in the attached PDF (See before “Conclusion” section).<\/p>\n\n\n\n .<\/p>\n\n\n\n A compression calculation has been performed on a carbon dioxide flow leaving an amine treatment unit at a pressure slightly above 1 bar abs. The injection pressure was taken to 150 bar in the present exemple.<\/p>\n\n\n\n The\ngas is suctioned by the first compressor section at a temperature of\napproximately 30\u00b0C. The gas outlet temperature is limited to 180 \u00b0C in the\npresent study. Following each compression stage, the gas is cooled down to a\ntemperature of 30 \u00b0C to provide sufficient margin with the temperature\ncorresponding to hydrate formation, particularly, in the case of a gas mixture\ncontaining methane (See hydrate section). Between each compression stage, a\npressure loss of 10 % of the actual pressure is considered to take into account\nintermediate losses between compressor sections.<\/p>\n\n\n\n The\ncompression ratio for each stage is of the order of 4 and four sections are\nrequired to bring the gas at a pressure of the order of 100 bar. At this\npressure level, following cooling, the gas enters into a dense phase condition<\/strong> with a volumetric mass of the order of 750\nkg\/m3. It has to be noted that following the first three cooling\u2019s, the\nvolumetric mass is considerably smaller, respectively, of the order of 6, 24\nand 75 kg\/m3 at the outlet of, respectively, the first, the second and the\nthird cooling stage.<\/p>\n\n\n\n As\nshown on the above figure, carbon dioxide compression is started in gas phase\nat a pressure slightly above 1 bar abs and at a temperature of 30 \u00b0C. Should\nthe temperature be significantly lower, there is no possibility for liquid\nformation (at least not below minus 50 \u00b0C).<\/p>\n\n\n\n Above\n40 bar abs, the temperature has to be controlled carefully to avoid the\nformation of carbon hydrates (temperature to be above 20 \u00b0C providing 5 \u00b0C\ntemperature margin in case of presence of methane in the carbon dioxide\nmixture) and also to avoid the liquefaction of carbon dioxide when using a\ncompressor handling only a gas phase.<\/p>\n\n\n\n Carbon dioxide could be partially liquefied, without any risk of hydrate formation, at a temperature of 20 \u00b0C in view of using a two phase flow compressor (pump). This temperature corresponds to a liquefaction pressure of approximately 60 bar abs. The compression could operate in two phase flow up to 73 bar abs corresponding to the critical pressure above which the fluid is in dense phase condition (single phase). The pressure range in two phase flow is therefore relatively narrow.<\/strong><\/p>\n\n\n\n In addition, there is a major difficulty in controlling the volume flow crossing the two phase flow pump as the liquefaction occurs at a single point condition in terms of pressure for a given temperature value (<\/strong>case of every pure fluid). This would induce a lack of knowledge (therefore control) in the gas and liquid fractions therefore in the total volume flow. This total volume flow could vary in the volumetric mass ratio of the liquid and gas phases that is of the order of 6.<\/p>\n\n\n\n If the fluid mixture was made of a least two pure components<\/strong>, the gas-liquid phase fractions would be represented by an envelope and not by a single line (pure component). In this last case the gas and liquid fractions could be controlled during the two phase compression.<\/strong><\/p>\n\n\n\n As a result of these two points, the two phase flow compression (pumping) of carbon dioxide does not present a significant advantage as the domain of operation is extremely small and the liquefaction process is practically out of control.<\/p>\n\n\n\n Concerning two phase flow pump design and performance see<\/span>: http:\/\/yvcharron.com\/index.php\/two-phase-flow-pumps\/<\/a><\/p>\n\n\n\n .<\/p>\n\n\n\n For more details on carbon dioxide compression with formula and graphs get document below in pdf format.<\/strong><\/p>\n\n\n\n<\/figure><\/div>\n\n\n\n2 – Single phase flow – Choke losses<\/strong><\/h3>\n\n\n\n
3 – Two phase flow – Sonic characteristics<\/strong><\/h3>\n\n\n\n
4 – Hydrates <\/strong><\/h3>\n\n\n\n
5 – Flow surging <\/strong><\/h3>\n\n\n\n
6 – Centrifugal compressor operability<\/strong><\/h3>\n\n\n\n
7 – Materials <\/strong><\/h3>\n\n\n\n
THERMODYNAMIC PROPERTIES<\/strong><\/h2>\n\n\n\n
ONE APPLICATION CASE<\/strong><\/h2>\n\n\n\n
TWO PHASE FLOW COMPRESSION<\/strong><\/h2>\n\n\n\n
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