{ "version": 1, "topic": "FA04", "title": "Ramey wellbore temperature profiles and heat transfer assumptions", "createdAt": "2026-10-24", "case": { "title": "Ramey Wellbore Liquid Temperature Profile Calculator", "premise": "Fixed controls: Inlet liquid absolute temperature = 300 K; Undisturbed formation temperature at inlet = 290 K; Signed formation gradient along flow = 0.03 K/m; Distance along flow = 2000 m; Constant liquid mass flow rate = 5 kg/s; Liquid specific heat capacity = 4200 J/(kg.K); Tubing inside radius (U reference area) = 0.03 m; Outer radius at formation heat-transfer interface = 0.1 m; Overall wellbore coefficient excluding formation = 20 W/(m2.K); Formation thermal conductivity = 2.5 W/(m.K); Formation thermal diffusivity = 0.000001 m2/s.", "formula": "tD=alpha*t/rw^2, with t in seconds. F=0.5*ln(4*tD)-0.290. Resistance per length R'=1/(2*pi*ri*U)+F/(2*pi*k). Relaxation length A=mass_rate*cp*R'. U=0 is the insulated limit.; Earth temperature=Te0+G*s. dT/ds=(earth-T)/A. T=Te0+G*s-G*A+(T0-Te0+G*A)*exp(-s/A). Net liquid heat gain=mass_rate*cp*(T-T0); positive means heating. Heat to formation per length=(T-earth)/R'.", "variables": "Elapsed steady injection or production time is varied within the supported input range. Ramey's approximate single-phase incompressible-liquid case at one fixed operating time, with constant flow rate, heat capacity, U and formation thermal properties. Radial formation conduction and quasi-steady wellbore heat transfer; linear geothermal background along one uniform interval. It does not solve an early-time thermal transient or arbitrary injection/shut-in history.", "steps": [ { "label": "Define the baseline", "calculation": "Elapsed steady injection or production time (day) = 30", "explanation": "Fixed controls: Inlet liquid absolute temperature = 300 K; Undisturbed formation temperature at inlet = 290 K; Signed formation gradient along flow = 0.03 K/m; Distance along flow = 2000 m; Constant liquid mass flow rate = 5 kg/s; Liquid specific heat capacity = 4200 J/(kg.K); Tubing inside radius (U reference area) = 0.03 m; Outer radius at formation heat-transfer interface = 0.1 m; Overall wellbore coefficient excluding formation = 20 W/(m2.K); Formation thermal conductivity = 2.5 W/(m.K); Formation thermal diffusivity = 0.000001 m2/s." }, { "label": "Select the relation", "calculation": "tD=alpha*t/rw^2, with t in seconds. F=0.5*ln(4*tD)-0.290. Resistance per length R'=1/(2*pi*ri*U)+F/(2*pi*k). Relaxation length A=mass_rate*cp*R'. U=0 is the insulated limit.; Earth temperature=Te0+G*s. dT/ds=(earth-T)/A. T=Te0+G*s-G*A+(T0-Te0+G*A)*exp(-s/A). Net liquid heat gain=mass_rate*cp*(T-T0); positive means heating. Heat to formation per length=(T-earth)/R'.", "explanation": "Elapsed steady injection or production time is varied within the supported input range. Ramey's approximate single-phase incompressible-liquid case at one fixed operating time, with constant flow rate, heat capacity, U and formation thermal properties. Radial formation conduction and quasi-steady wellbore heat transfer; linear geothermal background along one uniform interval. It does not solve an early-time thermal transient or arbitrary injection/shut-in history." }, { "label": "Substitute the values", "calculation": "days = 30 day; with the fixed controls above, the workflow evaluates Outlet liquid temperature = 303.87118 K; Effective conductance per unit length = 2.13754099 W/(m.K)", "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation." }, { "label": "Read the result", "calculation": "Outlet liquid temperature (K) = 303.87118; Effective conductance per unit length (W/(m.K)) = 2.13754099", "explanation": "No gas/steam, phase change, pressure profile, Joule-Thomson effect, viscosity update, frictional heating, axial conduction, multiple coupled strings, thermal recovery reservoir simulation or hydraulic feedback is included. Verify that the fluid remains liquid at actual local pressure and temperature separately. The thermal and hydraulic workflows are not automatically coupled. Software limits: inlet and entire undisturbed formation interval 200-600 K, |G| <= 0.1 K/m, time >= 7 days and tD >= 100, positive conductivity/diffusivity/heat capacity and outer thermal radius greater than tubing inside radius. The line-source expression uses Ramey's rounded constant 0.290; it is not an exact early-time cylindrical solution or a field-accuracy guarantee." } ], "result": "Outlet liquid temperature (K) = 303.87118; Effective conductance per unit length (W/(m.K)) = 2.13754099", "interpretation": "No gas/steam, phase change, pressure profile, Joule-Thomson effect, viscosity update, frictional heating, axial conduction, multiple coupled strings, thermal recovery reservoir simulation or hydraulic feedback is included. Verify that the fluid remains liquid at actual local pressure and temperature separately. The thermal and hydraulic workflows are not automatically coupled. Software limits: inlet and entire undisturbed formation interval 200-600 K, |G| <= 0.1 K/m, time >= 7 days and tD >= 100, positive conductivity/diffusivity/heat capacity and outer thermal radius greater than tubing inside radius. The line-source expression uses Ramey's rounded constant 0.290; it is not an exact early-time cylindrical solution or a field-accuracy guarantee.", "control": "Elapsed steady injection or production time (day)", "columns": [ "Elapsed steady injection or production time (day)", "Outlet liquid temperature (K)", "Effective conductance per unit length (W/(m.K))" ], "rows": [ [ 14, 304.0717572220799, 2.254447723771561 ], [ 21, 303.96253250262646, 2.1907054184218113 ], [ 30, 303.87117970248505, 2.137540988337812 ], [ 60, 303.7051692801215, 2.041271045282504 ], [ 120, 303.55280157279395, 1.9532989414092186 ] ], "baseline": 2, "rowNotes": [ "Elapsed steady injection or production time (day) = 14. Outlet liquid temperature (K): 304.071757; Effective conductance per unit length (W/(m.K)): 2.25444772.", "Elapsed steady injection or production time (day) = 21. Outlet liquid temperature (K): 303.962533; Effective conductance per unit length (W/(m.K)): 2.19070542.", "Elapsed steady injection or production time (day) = 30. Outlet liquid temperature (K): 303.87118; Effective conductance per unit length (W/(m.K)): 2.13754099.", "Elapsed steady injection or production time (day) = 60. Outlet liquid temperature (K): 303.705169; Effective conductance per unit length (W/(m.K)): 2.04127105.", "Elapsed steady injection or production time (day) = 120. Outlet liquid temperature (K): 303.552802; Effective conductance per unit length (W/(m.K)): 1.95329894." ], "provenance": "Original recorded synthetic cases solved with the site's ramey-liquid-temperature-profile engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.", "questions": [ { "question": "Reproduce the baseline Outlet liquid temperature (K) without rounding intermediate values.", "answer": "days = 30 day; with the fixed controls above, the workflow evaluates Outlet liquid temperature = 303.87118 K; Effective conductance per unit length = 2.13754099 W/(m.K). Outlet liquid temperature (K) = 303.87118. No gas/steam, phase change, pressure profile, Joule-Thomson effect, viscosity update, frictional heating, axial conduction, multiple coupled strings, thermal recovery reservoir simulation or hydraulic feedback is included. Verify that the fluid remains liquid at actual local pressure and temperature separately. The thermal and hydraulic workflows are not automatically coupled. Software limits: inlet and entire undisturbed formation interval 200-600 K, |G| <= 0.1 K/m, time >= 7 days and tD >= 100, positive conductivity/diffusivity/heat capacity and outer thermal radius greater than tubing inside radius. The line-source expression uses Ramey's rounded constant 0.290; it is not an exact early-time cylindrical solution or a field-accuracy guarantee." }, { "question": "Compare the first and last recorded scenarios. Which input changes?", "answer": "Elapsed steady injection or production time (day) changes from 14 to 120. Other controls remain as stated in the premise. Outlet liquid temperature (K) changes from 304.071757 to 303.552802." }, { "question": "What would be needed to apply this example to a different physical system?", "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Elapsed steady injection or production time is varied within the supported input range. Ramey's approximate single-phase incompressible-liquid case at one fixed operating time, with constant flow rate, heat capacity, U and formation thermal properties. Radial formation conduction and quasi-steady wellbore heat transfer; linear geothermal background along one uniform interval. It does not solve an early-time thermal transient or arbitrary injection/shut-in history. No gas/steam, phase change, pressure profile, Joule-Thomson effect, viscosity update, frictional heating, axial conduction, multiple coupled strings, thermal recovery reservoir simulation or hydraulic feedback is included. Verify that the fluid remains liquid at actual local pressure and temperature separately. The thermal and hydraulic workflows are not automatically coupled. Software limits: inlet and entire undisturbed formation interval 200-600 K, |G| <= 0.1 K/m, time >= 7 days and tD >= 100, positive conductivity/diffusivity/heat capacity and outer thermal radius greater than tubing inside radius. The line-source expression uses Ramey's rounded constant 0.290; it is not an exact early-time cylindrical solution or a field-accuracy guarantee." } ] }, "recorded": { "kind": "workflow", "workflow": "ramey-liquid-temperature-profile", "parameter": "days", "runs": [ { "inputs": { "T0": 300, "Te0": 290, "G": 0.03, "L": 2000, "m": 5, "cp": 4200, "r_i": 0.03, "r_w": 0.1, "U": 20, "k": 2.5, "alpha": 0.000001, "days": 14 }, "result": { "outputs": [ { "label": "Outlet liquid temperature", "value": 304.0717572220799, "unit": "K" }, { "label": "Liquid temperature change", "value": 4.071757222079896, "unit": "K" }, { "label": "Net heat gained by liquid", "value": 85.50690166367781, "unit": "kW" }, { "label": "Outlet undisturbed formation temperature", "value": 350, "unit": "K" }, { "label": "Effective conductance per unit length", "value": 2.254447723771561, "unit": "W/(m.K)" }, { "label": "Long-time formation function", "value": 2.8008771367755565, "unit": "dimensionless" }, { "label": "Formation dimensionless time", "value": 120.95999999999998, "unit": "dimensionless" }, { "label": "Maximum energy-balance temperature discrepancy", "value": 6.252776074688882e-13, "unit": "K" } ], "columns": [ "Distance along flow (m)", "Liquid temperature (K)", "Undisturbed formation temperature (K)", "Heat to formation per length (W/m)", "Net heat gained by liquid (kW)" ], "rows": [ [ 0, 300, 290, 22.54447723771561, 0 ], [ 40, 299.9597230345678, 291.2, 19.748337656150685, -0.8458162740764692 ], [ 80, 299.9247606302668, 292.4, 16.964179474830903, -1.5800267643971324 ], [ 120, 299.8950900143126, 293.6, 14.191951353704043, -2.203109699435686 ], [ 160, 299.87068851150167, 294.8, 11.431602172709518, -2.7155412584649525 ], [ 200, 299.8515335437932, 296, 8.683081030834416, -3.1177955803426016 ], [ 240, 299.83760262989284, 297.2, 5.946337245175828, -3.410344772250312 ], [ 280, 299.82887338483806, 298.4, 3.221320350005985, -3.593658918400706 ], [ 320, 299.8253235195856, 299.6, 0.5079800958418902, -3.6682060887025045 ], [ 360, 299.82693084060014, 300.8, -2.193733551481343, -3.63445234739703 ], [ 400, 299.8336732494452, 302, -4.883870411733684, -3.492861761650545 ], [ 440, 299.84552874237585, 303.2, -7.5624800912078705, -3.2438964101071974 ], [ 480, 299.8624754099324, 304.4, -10.229611983635301, -2.888016391419285 ], [ 520, 299.88449143653696, 305.6, -12.885315271096163, -2.4256798327238016 ], [ 560, 299.9115551000911, 306.8, -15.52963892492545, -1.8573428980867561 ], [ 600, 299.94364477157467, 308, -18.162631706618605, -1.1834597969319702 ], [ 640, 299.980738914648, 309.2, -20.784342168727555, -0.4044827923922867 ], [ 680, 300.02281608525357, 310.4, -23.394818655758904, 0.47913779032489856 ], [ 720, 300.0698549312217, 311.6, -25.994109305063184, 1.4669535556556639 ], [ 760, 300.1218341918762, 312.8, -28.582262047723187, 2.558518029399977 ], [ 800, 300.1787326976422, 314, -31.15932460943884, 3.753386650486277 ], [ 840, 300.24052936965626, 315.2, -33.72534451140594, 5.05111676278142 ], [ 880, 300.3072032193774, 316.4, -36.280369071192844, 6.451267606925684 ], [ 920, 300.3787333482001, 317.6, -38.824445403613396, 7.953400312202404 ], [ 960, 300.45509894706885, 318.8, -41.35762042159518, 9.557077888445804 ], [ 1000, 300.5362792960945, 320, -43.87994083704515, 11.26186521798462 ], [ 1040, 300.6222537641724, 321.2, -46.391453161710324, 13.067329047620376 ], [ 1080, 300.7130018086015, 322.4, -48.89220370803622, 14.973037980631887 ], [ 1120, 300.808502974706, 323.6, -51.38223859002038, 16.978562468826343 ], [ 1160, 300.9087368954579, 324.8, -53.8616037240625, 19.083474804615435 ], [ 1200, 301.01368329110136, 326, -56.33034482981187, 21.287349113128528 ], [ 1240, 301.123321968779, 327.2, -58.78850743101001, 23.589761344359207 ], [ 1280, 301.2376328221595, 328.4, -61.23613685632977, 25.990289265350043 ], [ 1320, 301.3565958310666, 329.6, -63.67327824021215, 28.48851245239888 ], [ 1360, 301.48019106111013, 330.8, -66.09997652369736, 31.084012283312802 ], [ 1400, 301.6083986633185, 332, -68.51627645525436, 33.77637192968842 ], [ 1440, 301.74119887377225, 333.2, -70.92222259160636, 36.56517634921721 ], [ 1480, 301.8785720132401, 334.4, -73.31785929855154, 39.45001227804215 ], [ 1520, 302.02049848681594, 335.6, -75.70323075178155, 42.43046822313471 ], [ 1560, 302.16695878355733, 336.8, -78.07838093769585, 45.50613445470401 ], [ 1600, 302.3179334761258, 338, -80.44335365421361, 48.67660299864184 ], [ 1640, 302.4734032204287, 339.2, -82.79819251158048, 51.94146762900226 ], [ 1680, 302.63334875526226, 340.4, -85.14294093317334, 55.30032386050749 ], [ 1720, 302.79775090195676, 341.6, -87.47764215630075, 58.75276894109197 ], [ 1760, 302.96659056402257, 342.8, -89.80233923299997, 62.298401844473915 ], [ 1800, 303.13984872679816, 344, -92.11707503083154, 65.93682326276144 ], [ 1840, 303.3175064570995, 345.2, -94.42189223366908, 69.66763559908975 ], [ 1880, 303.49954490287064, 346.4, -96.7168333424873, 73.49044296028342 ], [ 1920, 303.6859452928365, 347.6, -99.00194067614463, 77.40485114956635 ], [ 1960, 303.8766889361565, 348.8, -101.27725637216383, 81.41046765928616 ], [ 2000, 304.0717572220799, 350, -103.54282238750962, 85.50690166367781 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Temperature (K)", "includeZero": false, "series": [ { "name": "Liquid", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 300, 299.9597230345678, 299.9247606302668, 299.8950900143126, 299.87068851150167, 299.8515335437932, 299.83760262989284, 299.82887338483806, 299.8253235195856, 299.82693084060014, 299.8336732494452, 299.84552874237585, 299.8624754099324, 299.88449143653696, 299.9115551000911, 299.94364477157467, 299.980738914648, 300.02281608525357, 300.0698549312217, 300.1218341918762, 300.1787326976422, 300.24052936965626, 300.3072032193774, 300.3787333482001, 300.45509894706885, 300.5362792960945, 300.6222537641724, 300.7130018086015, 300.808502974706, 300.9087368954579, 301.01368329110136, 301.123321968779, 301.2376328221595, 301.3565958310666, 301.48019106111013, 301.6083986633185, 301.74119887377225, 301.8785720132401, 302.02049848681594, 302.16695878355733, 302.3179334761258, 302.4734032204287, 302.63334875526226, 302.79775090195676, 302.96659056402257, 303.13984872679816, 303.3175064570995, 303.49954490287064, 303.6859452928365, 303.8766889361565, 304.0717572220799 ] }, { "name": "Undisturbed formation", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 290, 291.2, 292.4, 293.6, 294.8, 296, 297.2, 298.4, 299.6, 300.8, 302, 303.2, 304.4, 305.6, 306.8, 308, 309.2, 310.4, 311.6, 312.8, 314, 315.2, 316.4, 317.6, 318.8, 320, 321.2, 322.4, 323.6, 324.8, 326, 327.2, 328.4, 329.6, 330.8, 332, 333.2, 334.4, 335.6, 336.8, 338, 339.2, 340.4, 341.6, 342.8, 344, 345.2, 346.4, 347.6, 348.8, 350 ] } ] }, "warnings": [ "Single-phase incompressible liquid at one fixed operating time, using the long-time radial line-source approximation. Constant rate, heat capacity and thermal properties; U is based on tubing inside area and excludes the separate formation resistance.", "Use a signed formation gradient along the direction of flow: positive for hotter surroundings downstream, negative for colder. No pressure, viscosity, phase change, steam, gas expansion, shut-in history, frictional heating or thermal feedback to the hydraulic solvers is computed." ] } }, { "inputs": { "T0": 300, "Te0": 290, "G": 0.03, "L": 2000, "m": 5, "cp": 4200, "r_i": 0.03, "r_w": 0.1, "U": 20, "k": 2.5, "alpha": 0.000001, "days": 21 }, "result": { "outputs": [ { "label": "Outlet liquid temperature", "value": 303.96253250262646, "unit": "K" }, { "label": "Liquid temperature change", "value": 3.962532502626459, "unit": "K" }, { "label": "Net heat gained by liquid", "value": 83.21318255515564, "unit": "kW" }, { "label": "Outlet undisturbed formation temperature", "value": 350, "unit": "K" }, { "label": "Effective conductance per unit length", "value": 2.1907054184218113, "unit": "W/(m.K)" }, { "label": "Long-time formation function", "value": 3.003609690829639, "unit": "dimensionless" }, { "label": "Formation dimensionless time", "value": 181.43999999999994, "unit": "dimensionless" }, { "label": "Maximum energy-balance temperature discrepancy", "value": 5.684341886080801e-13, "unit": "K" } ], "columns": [ "Distance along flow (m)", "Liquid temperature (K)", "Undisturbed formation temperature (K)", "Heat to formation per length (W/m)", "Net heat gained by liquid (kW)" ], "rows": [ [ 0, 300, 290, 21.907054184218115, 0 ], [ 40, 299.9608594014762, 291.2, 19.192462160845665, -0.8219525689992224 ], [ 80, 299.92687868143986, 292.4, 16.48917391123397, -1.53554768976295 ], [ 120, 299.89803635375256, 293.6, 13.79714236558323, -2.1412365711962593 ], [ 160, 299.87431102174634, 294.8, 11.116320650097194, -2.6394685433269274 ], [ 200, 299.85568137785054, 296, 8.446662086165263, -3.0306910651385692 ], [ 240, 299.8421262032208, 297.2, 5.788120189550081, -3.315349732363188 ], [ 280, 299.8336243673696, 298.4, 3.1406486695782245, -3.493888285237915 ], [ 320, 299.83015482779865, 299.6, 0.5042014283343944, -3.566748616228324 ], [ 360, 299.83169662963223, 300.8, -2.121267440140793, -3.5343707777230975 ], [ 400, 299.83822890525215, 302, -4.735803650651763, -3.39719298970482 ], [ 440, 299.8497308739349, 303.2, -7.339452727642092, -3.1556516473670513 ], [ 480, 299.86618184148927, 304.4, -9.932260005988617, -2.8101813287254345 ], [ 520, 299.88756119989654, 305.6, -12.514270631789694, -2.3612148021726966 ], [ 560, 299.9138484269512, 306.8, -15.085529563151963, -1.8091830340252955 ], [ 600, 299.9450230859039, 308, -17.64608157097287, -1.1545151960175417 ], [ 640, 299.9810648251055, 309.2, -20.195971239720837, -0.39763867278497855 ], [ 680, 300.0219533776526, 310.4, -22.73524296821056, 0.4610209307047626 ], [ 720, 300.0676685610351, 311.6, -25.263940970376712, 1.4210397817366243 ], [ 760, 300.118190276784, 312.8, -27.782109276043748, 2.481995812463822 ], [ 800, 300.1734985101222, 314, -30.289791731692514, 3.6434687125665164 ], [ 840, 300.23357332961575, 315.2, -32.78703200122346, 4.905039921930779 ], [ 880, 300.2983948868266, 316.4, -35.27387356671726, 6.266292623358595 ], [ 920, 300.3679434159671, 317.6, -37.7503597291922, 7.7268117353089005 ], [ 960, 300.442199233556, 318.8, -40.21653360935702, 9.286183904675624 ], [ 1000, 300.52114273807564, 320, -42.67243814836275, 10.94399749958842 ], [ 1040, 300.6047544096305, 321.2, -45.118116108550325, 12.699842602240835 ], [ 1080, 300.6930148096075, 322.4, -47.55361007419478, 14.55331100175789 ], [ 1120, 300.78590458033744, 323.6, -49.97896245224704, 16.50399618708633 ], [ 1160, 300.883404444758, 324.8, -52.394215473071654, 18.551493339918295 ], [ 1200, 300.9854952060781, 326, -54.79941119118309, 20.695399327640075 ], [ 1240, 301.0921577474435, 327.2, -57.194591485977455, 22.93531269631308 ], [ 1280, 301.20337303160403, 328.4, -59.57979806246176, 25.27083366368464 ], [ 1320, 301.31912210058226, 329.6, -61.95507245198014, 27.701564112227516 ], [ 1360, 301.4393860753431, 330.8, -64.32045601293673, 30.227107582205576 ], [ 1400, 301.5641461554654, 332, -66.67598993151631, 32.84706926477298 ], [ 1440, 301.6933836188143, 333.2, -69.02171522240084, 35.56105599510079 ], [ 1480, 301.8270798212154, 334.4, -71.35767272948449, 38.36867624552383 ], [ 1520, 301.96521619613026, 335.6, -73.68390312658369, 41.26954011873539 ], [ 1560, 302.10777425433264, 336.8, -76.00044691814618, 44.26325934098543 ], [ 1600, 302.2547355835872, 338, -78.30734443995588, 47.34944725533131 ], [ 1640, 302.4060818483284, 339.2, -80.60463585983554, 50.52771881489696 ], [ 1680, 302.56179478934155, 340.4, -82.89236117834584, 53.7976905761725 ], [ 1720, 302.7218562234448, 341.6, -85.17056022948181, 57.158980692340265 ], [ 1760, 302.88624804317215, 342.8, -87.43927268136699, 60.611208906615055 ], [ 1800, 303.05495221645896, 344, -89.69853803694335, 64.15399654563811 ], [ 1840, 303.22795078632726, 345.2, -91.94839563465979, 67.78696651287237 ], [ 1880, 303.40522587057336, 346.4, -94.18888464915682, 71.50974328204057 ], [ 1920, 303.58675966145654, 347.6, -96.42004409194865, 75.32195289058734 ], [ 1960, 303.77253442538887, 348.8, -98.64191281210222, 79.22322293316626 ], [ 2000, 303.96253250262646, 350, -100.85452949691425, 83.21318255515564 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Temperature (K)", "includeZero": false, "series": [ { "name": "Liquid", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 300, 299.9608594014762, 299.92687868143986, 299.89803635375256, 299.87431102174634, 299.85568137785054, 299.8421262032208, 299.8336243673696, 299.83015482779865, 299.83169662963223, 299.83822890525215, 299.8497308739349, 299.86618184148927, 299.88756119989654, 299.9138484269512, 299.9450230859039, 299.9810648251055, 300.0219533776526, 300.0676685610351, 300.118190276784, 300.1734985101222, 300.23357332961575, 300.2983948868266, 300.3679434159671, 300.442199233556, 300.52114273807564, 300.6047544096305, 300.6930148096075, 300.78590458033744, 300.883404444758, 300.9854952060781, 301.0921577474435, 301.20337303160403, 301.31912210058226, 301.4393860753431, 301.5641461554654, 301.6933836188143, 301.8270798212154, 301.96521619613026, 302.10777425433264, 302.2547355835872, 302.4060818483284, 302.56179478934155, 302.7218562234448, 302.88624804317215, 303.05495221645896, 303.22795078632726, 303.40522587057336, 303.58675966145654, 303.77253442538887, 303.96253250262646 ] }, { "name": "Undisturbed formation", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 290, 291.2, 292.4, 293.6, 294.8, 296, 297.2, 298.4, 299.6, 300.8, 302, 303.2, 304.4, 305.6, 306.8, 308, 309.2, 310.4, 311.6, 312.8, 314, 315.2, 316.4, 317.6, 318.8, 320, 321.2, 322.4, 323.6, 324.8, 326, 327.2, 328.4, 329.6, 330.8, 332, 333.2, 334.4, 335.6, 336.8, 338, 339.2, 340.4, 341.6, 342.8, 344, 345.2, 346.4, 347.6, 348.8, 350 ] } ] }, "warnings": [ "Single-phase incompressible liquid at one fixed operating time, using the long-time radial line-source approximation. Constant rate, heat capacity and thermal properties; U is based on tubing inside area and excludes the separate formation resistance.", "Use a signed formation gradient along the direction of flow: positive for hotter surroundings downstream, negative for colder. No pressure, viscosity, phase change, steam, gas expansion, shut-in history, frictional heating or thermal feedback to the hydraulic solvers is computed." ] } }, { "inputs": { "T0": 300, "Te0": 290, "G": 0.03, "L": 2000, "m": 5, "cp": 4200, "r_i": 0.03, "r_w": 0.1, "U": 20, "k": 2.5, "alpha": 0.000001, "days": 30 }, "result": { "outputs": [ { "label": "Outlet liquid temperature", "value": 303.87117970248505, "unit": "K" }, { "label": "Liquid temperature change", "value": 3.871179702485051, "unit": "K" }, { "label": "Net heat gained by liquid", "value": 81.29477375218607, "unit": "kW" }, { "label": "Outlet undisturbed formation temperature", "value": 350, "unit": "K" }, { "label": "Effective conductance per unit length", "value": 2.137540988337812, "unit": "W/(m.K)" }, { "label": "Long-time formation function", "value": 3.181947162799005, "unit": "dimensionless" }, { "label": "Formation dimensionless time", "value": 259.19999999999993, "unit": "dimensionless" }, { "label": "Maximum energy-balance temperature discrepancy", "value": 3.410605131648481e-13, "unit": "K" } ], "columns": [ "Distance along flow (m)", "Liquid temperature (K)", "Undisturbed formation temperature (K)", "Heat to formation per length (W/m)", "Net heat gained by liquid (kW)" ], "rows": [ [ 0, 300, 290, 21.375409883378122, 0 ], [ 40, 299.96180729893695, 291.2, 18.72872223339516, -0.8020467223241212 ], [ 80, 299.92864565873447, 292.4, 16.0927886822165, -1.4984411665761854 ], [ 120, 299.9004946370386, 293.6, 13.467565533472536, -2.089612622189293 ], [ 160, 299.87733387455756, 294.8, 10.853009268342804, -2.57598863429115 ], [ 200, 299.85914309472383, 296, 8.249076544833025, -2.9579950107994932 ], [ 240, 299.8459021033583, 297.2, 5.6557241970576175, -3.236055829475731 ], [ 280, 299.83759078833543, 298.4, 3.0729092345239044, -3.410593444955907 ], [ 320, 299.83418911924986, 299.6, 0.5005888414192514, -3.4820284957530134 ], [ 360, 299.8356771470844, 300.8, -2.0612796240979208, -3.450779911227073 ], [ 400, 299.84203500387935, 302, -4.612738630606146, -3.3172649185337377 ], [ 440, 299.85324290240277, 303.2, -7.153830474124548, -3.081899049541846 ], [ 480, 299.86928113582314, 304.4, -9.684597278813317, -2.74509614771398 ], [ 520, 299.89013007738225, 305.6, -12.205080997672734, -2.3072683749726934 ], [ 560, 299.9157701800698, 306.8, -14.715323413238295, -1.7688262185345138 ], [ 600, 299.94618197629944, 308, -17.215366138273776, -1.1301784977117109 ], [ 640, 299.98134607758624, 309.2, -19.705250616460535, -0.3917323706889988 ], [ 680, 300.021243174225, 310.4, -22.185018123084877, 0.4461066587248297 ], [ 720, 300.0658540349704, 311.6, -24.65470976572198, 1.3829347343786935 ], [ 760, 300.115159506718, 312.8, -27.114366484917557, 2.418349641077725 ], [ 800, 300.1691405141868, 314, -29.564029054866598, 3.551950797922359 ], [ 840, 300.22777805960305, 315.2, -32.003738084089136, 4.78333925166413 ], [ 880, 300.29105322238536, 316.4, -34.433534016103565, 6.112117670092516 ], [ 920, 300.35894715883103, 317.6, -36.853457130096814, 7.537890335451607 ], [ 960, 300.4314411018035, 318.8, -39.26354754159228, 9.060263137873505 ], [ 1000, 300.5085163604215, 320, -41.66384520311496, 10.678843568851107 ], [ 1040, 300.59015431974905, 321.2, -44.05438990485339, 12.393240714729984 ], [ 1080, 300.67633644048703, 322.4, -46.43522127531941, 14.203065250227722 ], [ 1120, 300.7670442586656, 323.6, -48.80637878200555, 16.10792943197714 ], [ 1160, 300.8622593853383, 324.8, -51.1679017320382, 18.10744709210411 ], [ 1200, 300.9619635062772, 326, -53.51982927283047, 20.201233631820912 ], [ 1240, 301.06613838166925, 327.2, -55.86220039273031, 22.388906015054204 ], [ 1280, 301.17476584581414, 328.4, -58.19505392166676, 24.670082762096857 ], [ 1320, 301.2878278068226, 329.6, -60.51842853179484, 27.044383943274113 ], [ 1360, 301.4053062463171, 330.8, -62.83236273813472, 29.511431172658718 ], [ 1400, 301.5271832191329, 332, -65.13689489921174, 32.070847601790774 ], [ 1440, 301.65344085302047, 333.2, -67.43206321769185, 34.72225791342987 ], [ 1480, 301.7840613483495, 334.4, -69.71790574101442, 37.46528831533942 ], [ 1520, 301.9190269778135, 335.6, -71.99446036202383, 40.29956653408294 ], [ 1560, 302.058320086136, 336.8, -74.26176481959678, 43.224721808856145 ], [ 1600, 302.2019230897784, 338, -76.51985669926808, 46.24038488534649 ], [ 1640, 302.34981847664756, 339.2, -78.76877343385455, 49.34618800959868 ], [ 1680, 302.5019888058062, 340.4, -81.00855230407441, 52.54176492193034 ], [ 1720, 302.6584167071837, 341.6, -83.23923043916588, 55.826750850857195 ], [ 1760, 302.81908488128767, 342.8, -85.46084481750256, 59.20078250704097 ], [ 1800, 302.9839760989178, 344, -87.67343226720652, 62.663498077274255 ], [ 1840, 303.1530732008801, 345.2, -89.87702946675836, 66.21453721848212 ], [ 1880, 303.32635909770187, 346.4, -92.07167294560631, 69.85354105173923 ], [ 1920, 303.5038167693492, 347.6, -94.25739908477058, 73.5801521563335 ], [ 1960, 303.6854292649444, 348.8, -96.43424411744692, 77.39401456383217 ], [ 2000, 303.87117970248505, 350, -98.60224412960743, 81.29477375218607 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Temperature (K)", "includeZero": false, "series": [ { "name": "Liquid", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 300, 299.96180729893695, 299.92864565873447, 299.9004946370386, 299.87733387455756, 299.85914309472383, 299.8459021033583, 299.83759078833543, 299.83418911924986, 299.8356771470844, 299.84203500387935, 299.85324290240277, 299.86928113582314, 299.89013007738225, 299.9157701800698, 299.94618197629944, 299.98134607758624, 300.021243174225, 300.0658540349704, 300.115159506718, 300.1691405141868, 300.22777805960305, 300.29105322238536, 300.35894715883103, 300.4314411018035, 300.5085163604215, 300.59015431974905, 300.67633644048703, 300.7670442586656, 300.8622593853383, 300.9619635062772, 301.06613838166925, 301.17476584581414, 301.2878278068226, 301.4053062463171, 301.5271832191329, 301.65344085302047, 301.7840613483495, 301.9190269778135, 302.058320086136, 302.2019230897784, 302.34981847664756, 302.5019888058062, 302.6584167071837, 302.81908488128767, 302.9839760989178, 303.1530732008801, 303.32635909770187, 303.5038167693492, 303.6854292649444, 303.87117970248505 ] }, { "name": "Undisturbed formation", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 290, 291.2, 292.4, 293.6, 294.8, 296, 297.2, 298.4, 299.6, 300.8, 302, 303.2, 304.4, 305.6, 306.8, 308, 309.2, 310.4, 311.6, 312.8, 314, 315.2, 316.4, 317.6, 318.8, 320, 321.2, 322.4, 323.6, 324.8, 326, 327.2, 328.4, 329.6, 330.8, 332, 333.2, 334.4, 335.6, 336.8, 338, 339.2, 340.4, 341.6, 342.8, 344, 345.2, 346.4, 347.6, 348.8, 350 ] } ] }, "warnings": [ "Single-phase incompressible liquid at one fixed operating time, using the long-time radial line-source approximation. Constant rate, heat capacity and thermal properties; U is based on tubing inside area and excludes the separate formation resistance.", "Use a signed formation gradient along the direction of flow: positive for hotter surroundings downstream, negative for colder. No pressure, viscosity, phase change, steam, gas expansion, shut-in history, frictional heating or thermal feedback to the hydraulic solvers is computed." ] } }, { "inputs": { "T0": 300, "Te0": 290, "G": 0.03, "L": 2000, "m": 5, "cp": 4200, "r_i": 0.03, "r_w": 0.1, "U": 20, "k": 2.5, "alpha": 0.000001, "days": 60 }, "result": { "outputs": [ { "label": "Outlet liquid temperature", "value": 303.7051692801215, "unit": "K" }, { "label": "Liquid temperature change", "value": 3.7051692801214813, "unit": "K" }, { "label": "Net heat gained by liquid", "value": 77.8085548825511, "unit": "kW" }, { "label": "Outlet undisturbed formation temperature", "value": 350, "unit": "K" }, { "label": "Effective conductance per unit length", "value": 2.041271045282504, "unit": "W/(m.K)" }, { "label": "Long-time formation function", "value": 3.5285207530789777, "unit": "dimensionless" }, { "label": "Formation dimensionless time", "value": 518.3999999999999, "unit": "dimensionless" }, { "label": "Maximum energy-balance temperature discrepancy", "value": 5.684341886080801e-13, "unit": "K" } ], "columns": [ "Distance along flow (m)", "Liquid temperature (K)", "Undisturbed formation temperature (K)", "Heat to formation per length (W/m)", "Net heat gained by liquid (kW)" ], "rows": [ [ 0, 300, 290, 20.41271045282504, 0 ], [ 40, 299.96352399747974, 291.2, 17.8887277906938, -0.765996052925459 ], [ 80, 299.9318462468115, 292.4, 15.374539661136097, -1.4312288169581393 ], [ 120, 299.9049481279649, 293.6, 12.870108055622774, -1.9960893127376949 ], [ 160, 299.88281109316597, 294.8, 10.375395113120382, -2.4609670435146427 ], [ 200, 299.8654166666171, 296, 7.8903631195178585, -2.8262500010413305 ], [ 240, 299.85274644421776, 297.2, 5.414974507057851, -3.092324671427093 ], [ 280, 299.8447820932859, 298.4, 2.9491918537672293, -3.259576040995796 ], [ 320, 299.8415053522811, 299.6, 0.49297788289212124, -3.328387602096825 ], [ 360, 299.8428980305285, 300.8, -1.9537045376650795, -3.2991413589017498 ], [ 400, 299.8489420079436, 302, -4.3908923959082395, -3.172217833184277 ], [ 440, 299.85961923475855, 303.2, -6.818622536305953, -2.94799607007036 ], [ 480, 299.8749117312492, 304.4, -9.236931660348498, -2.6268536437668217 ], [ 520, 299.89480158746306, 305.6, -11.6458563271034, -2.209166663275653 ], [ 560, 299.91927096294904, 306.8, -14.045432953766708, -1.6953097780701114 ], [ 600, 299.9483020864872, 308, -16.435697816215193, -1.0856561837684353 ], [ 640, 299.9818772558207, 309.2, -18.816687049553327, -0.3805776277657742 ], [ 680, 300.0199788373874, 310.4, -21.18843664866072, 0.41955558513507185 ], [ 720, 300.06258926605403, 311.6, -23.550982468735512, 1.3143745871346937 ], [ 760, 300.10969104485025, 312.8, -25.904360225836474, 2.3035119418552767 ], [ 800, 300.1612667447043, 314, -28.24860549742325, 3.386601638789841 ], [ 840, 300.2172990041792, 315.2, -30.583753722894294, 4.56327908776342 ], [ 880, 300.2777705292107, 316.4, -32.90984020412236, 5.83318111342527 ], [ 920, 300.3426640928458, 317.6, -35.22690010598803, 7.195945949761381 ], [ 960, 300.41196253498185, 318.8, -37.53496845691146, 8.65121323461892 ], [ 1000, 300.4856487621077, 320, -39.83408014938234, 10.198624004261717 ], [ 1040, 300.563705747045, 321.2, -42.124269940486776, 11.837820687944825 ], [ 1080, 300.64611652869075, 322.4, -44.40557245243316, 13.568447102505843 ], [ 1120, 300.732864211761, 323.6, -46.678022173075604, 15.390148446981241 ], [ 1160, 300.82393196653555, 324.8, -48.94165345643442, 17.30257129724663 ], [ 1200, 300.9193030286032, 326, -51.19650052321683, 19.305363600667704 ], [ 1240, 301.01896069860857, 327.2, -53.442597461333584, 21.398174670779895 ], [ 1280, 301.12288834199967, 328.4, -55.679978226413866, 23.580655181993055 ], [ 1320, 301.231069388776, 329.6, -57.908676642320074, 25.85245716429614 ], [ 1360, 301.34348733323884, 330.8, -60.12872640165689, 28.213233998015653 ], [ 1400, 301.4601257337408, 332, -62.34016106628311, 30.66264040855731 ], [ 1440, 301.5809682124381, 333.2, -64.54301406781715, 33.200332461200276 ], [ 1480, 301.7059984550424, 334.4, -66.73731870814338, 35.8259675558902 ], [ 1520, 301.8352002105744, 335.6, -68.92310815991534, 38.53920442206209 ], [ 1560, 301.96855729111803, 336.8, -71.10041546705718, 41.33970311347867 ], [ 1600, 302.10605357157607, 338, -73.26927354526312, 44.227125003097456 ], [ 1640, 302.2476729894259, 339.2, -75.42971518249549, 47.20113277794377 ], [ 1680, 302.393399544477, 340.4, -77.58177303947987, 50.26139043401713 ], [ 1720, 302.543217298629, 341.6, -79.7254796501993, 53.40756327120846 ], [ 1760, 302.6971103756306, 342.8, -81.86086742238545, 56.63931788824232 ], [ 1800, 302.8550629608397, 344, -83.98796863800958, 59.95632217763347 ], [ 1840, 303.0170593009844, 345.2, -86.10681545376946, 63.3582453206721 ], [ 1880, 303.18308370392464, 346.4, -88.21743990157618, 66.84475778241739 ], [ 1920, 303.35312053841506, 347.6, -90.3198738890385, 70.41553130671616 ], [ 1960, 303.52715423386866, 348.8, -92.41414919994453, 74.0702389112418 ], [ 2000, 303.7051692801215, 350, -94.500297494743, 77.8085548825511 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Temperature (K)", "includeZero": false, "series": [ { "name": "Liquid", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 300, 299.96352399747974, 299.9318462468115, 299.9049481279649, 299.88281109316597, 299.8654166666171, 299.85274644421776, 299.8447820932859, 299.8415053522811, 299.8428980305285, 299.8489420079436, 299.85961923475855, 299.8749117312492, 299.89480158746306, 299.91927096294904, 299.9483020864872, 299.9818772558207, 300.0199788373874, 300.06258926605403, 300.10969104485025, 300.1612667447043, 300.2172990041792, 300.2777705292107, 300.3426640928458, 300.41196253498185, 300.4856487621077, 300.563705747045, 300.64611652869075, 300.732864211761, 300.82393196653555, 300.9193030286032, 301.01896069860857, 301.12288834199967, 301.231069388776, 301.34348733323884, 301.4601257337408, 301.5809682124381, 301.7059984550424, 301.8352002105744, 301.96855729111803, 302.10605357157607, 302.2476729894259, 302.393399544477, 302.543217298629, 302.6971103756306, 302.8550629608397, 303.0170593009844, 303.18308370392464, 303.35312053841506, 303.52715423386866, 303.7051692801215 ] }, { "name": "Undisturbed formation", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 290, 291.2, 292.4, 293.6, 294.8, 296, 297.2, 298.4, 299.6, 300.8, 302, 303.2, 304.4, 305.6, 306.8, 308, 309.2, 310.4, 311.6, 312.8, 314, 315.2, 316.4, 317.6, 318.8, 320, 321.2, 322.4, 323.6, 324.8, 326, 327.2, 328.4, 329.6, 330.8, 332, 333.2, 334.4, 335.6, 336.8, 338, 339.2, 340.4, 341.6, 342.8, 344, 345.2, 346.4, 347.6, 348.8, 350 ] } ] }, "warnings": [ "Single-phase incompressible liquid at one fixed operating time, using the long-time radial line-source approximation. Constant rate, heat capacity and thermal properties; U is based on tubing inside area and excludes the separate formation resistance.", "Use a signed formation gradient along the direction of flow: positive for hotter surroundings downstream, negative for colder. No pressure, viscosity, phase change, steam, gas expansion, shut-in history, frictional heating or thermal feedback to the hydraulic solvers is computed." ] } }, { "inputs": { "T0": 300, "Te0": 290, "G": 0.03, "L": 2000, "m": 5, "cp": 4200, "r_i": 0.03, "r_w": 0.1, "U": 20, "k": 2.5, "alpha": 0.000001, "days": 120 }, "result": { "outputs": [ { "label": "Outlet liquid temperature", "value": 303.55280157279395, "unit": "K" }, { "label": "Liquid temperature change", "value": 3.5528015727939533, "unit": "K" }, { "label": "Net heat gained by liquid", "value": 74.60883302867302, "unit": "kW" }, { "label": "Outlet undisturbed formation temperature", "value": 350, "unit": "K" }, { "label": "Effective conductance per unit length", "value": 1.9532989414092186, "unit": "W/(m.K)" }, { "label": "Long-time formation function", "value": 3.87509434335895, "unit": "dimensionless" }, { "label": "Formation dimensionless time", "value": 1036.7999999999997, "unit": "dimensionless" }, { "label": "Maximum energy-balance temperature discrepancy", "value": 2.8421709430404007e-13, "unit": "K" } ], "columns": [ "Distance along flow (m)", "Liquid temperature (K)", "Undisturbed formation temperature (K)", "Heat to formation per length (W/m)", "Net heat gained by liquid (kW)" ], "rows": [ [ 0, 300, 290, 19.532989414092185, 0 ], [ 40, 299.9650930089972, 291.2, 17.120846895827597, -0.7330468110587844 ], [ 80, 299.9347720385778, 292.4, 14.717662246713878, -1.3697871898658036 ], [ 120, 299.909020057836, 293.6, 12.323402200300574, -1.9105787854436471 ], [ 160, 299.88782009911273, 294.8, 9.938033613677419, -2.3557779186326684 ], [ 200, 299.8711552577611, 296, 7.561523467015438, -2.7057395870174332 ], [ 240, 299.8590086919122, 297.2, 5.1938388631100505, -2.9608174698436187 ], [ 280, 299.85136362224216, 298.4, 2.8349470269255064, -3.121363932914619 ], [ 320, 299.84820333173957, 299.6, 0.4848153051410968, -3.1877300334690517 ], [ 360, 299.84951116547444, 300.8, -1.856588834300082, -3.1602655250367775 ], [ 400, 299.8552705303673, 302, -4.189297802642695, -3.0393188622865637 ], [ 440, 299.8654648949599, 303.2, -6.513343890766628, -2.8252372058415176 ], [ 480, 299.8800777891859, 304.4, -8.828759269635116, -2.518366427095714 ], [ 520, 299.89909280414344, 305.6, -11.135575990738868, -2.1190511129878473 ], [ 560, 299.9224935918673, 306.8, -13.433825986540754, -1.6276345707868245 ], [ 600, 299.95026386510324, 308, -15.72354107091738, -1.0444588328319924 ], [ 640, 299.98238739708233, 309.2, -18.004752939599328, -0.36986466127098083 ], [ 680, 300.01884802129615, 310.4, -20.2774931706104, 0.3958084472191672 ], [ 720, 300.0596296312732, 311.6, -22.541793224704424, 1.2522222567371273 ], [ 760, 300.1047161803559, 312.8, -24.797684445800382, 2.199039787474362 ], [ 800, 300.1540916814784, 314, -27.045198061417324, 3.2359253110465147 ], [ 840, 300.2077402069454, 315.2, -29.284365183105514, 4.36254434585345 ], [ 880, 300.2656458882115, 316.4, -31.515216806877888, 5.578563652441688 ], [ 920, 300.32779291566163, 317.6, -33.737783813638984, 6.883651228894279 ], [ 960, 300.3941655383924, 318.8, -35.95209696961152, 8.277476306239805 ], [ 1000, 300.46474806399345, 320, -38.158186926763975, 9.75970934386254 ], [ 1040, 300.5395248583312, 321.2, -40.35608422323308, 11.330022024955612 ], [ 1080, 300.61848034533136, 322.4, -42.545819283748294, 12.988087251958632 ], [ 1120, 300.7015990067642, 323.6, -44.72742242005136, 14.733579142047859 ], [ 1160, 300.7888653820292, 324.8, -46.900923831316625, 16.566173022613214 ], [ 1200, 300.8802640679411, 326, -49.06635360456979, 18.48554542676277 ], [ 1240, 300.97577971851706, 327.2, -51.22374171510276, 20.491374088858265 ], [ 1280, 301.07539704476375, 328.4, -53.37311802689013, 22.58333794003869 ], [ 1320, 301.1791008144658, 329.6, -55.5145122930021, 24.761117103782055 ], [ 1360, 301.2868758519755, 330.8, -57.64795415601516, 27.024392891485093 ], [ 1400, 301.3987070380018, 332, -59.77347314842442, 29.37284779803815 ], [ 1440, 301.5145793094018, 333.2, -61.89109869305115, 31.80616549743831 ], [ 1480, 301.6344776589718, 334.4, -64.00086010345049, 34.32403083840728 ], [ 1520, 301.75838713523973, 335.6, -66.10278658431687, 36.92612984003432 ], [ 1560, 301.88629284225823, 336.8, -68.19690723188849, 39.6121496874228 ], [ 1600, 302.01817993939835, 338, -70.28325103435019, 42.38177872736537 ], [ 1640, 302.15403364114405, 339.2, -72.36184687223482, 45.23470646402512 ], [ 1680, 302.29383921688765, 340.4, -74.4327235188228, 48.1706235546406 ], [ 1720, 302.437581990726, 341.6, -76.49590964054023, 51.18922180524635 ], [ 1760, 302.5852473412571, 342.8, -78.55143379735605, 54.29019416639943 ], [ 1800, 302.73682070137784, 344, -80.59932444317745, 57.473234728934585 ], [ 1840, 302.8922875580824, 345.2, -82.63960992624328, 60.73803871973013 ], [ 1880, 303.05163345226117, 346.4, -84.672318489517, 64.0843024974846 ], [ 1920, 303.2148439785007, 347.6, -86.69747827107761, 67.51172354851491 ], [ 1960, 303.3819047848845, 348.8, -88.7151173045082, 71.02000048257474 ], [ 2000, 303.55280157279395, 350, -90.72526351928549, 74.60883302867302 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Temperature (K)", "includeZero": false, "series": [ { "name": "Liquid", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 300, 299.9650930089972, 299.9347720385778, 299.909020057836, 299.88782009911273, 299.8711552577611, 299.8590086919122, 299.85136362224216, 299.84820333173957, 299.84951116547444, 299.8552705303673, 299.8654648949599, 299.8800777891859, 299.89909280414344, 299.9224935918673, 299.95026386510324, 299.98238739708233, 300.01884802129615, 300.0596296312732, 300.1047161803559, 300.1540916814784, 300.2077402069454, 300.2656458882115, 300.32779291566163, 300.3941655383924, 300.46474806399345, 300.5395248583312, 300.61848034533136, 300.7015990067642, 300.7888653820292, 300.8802640679411, 300.97577971851706, 301.07539704476375, 301.1791008144658, 301.2868758519755, 301.3987070380018, 301.5145793094018, 301.6344776589718, 301.75838713523973, 301.88629284225823, 302.01817993939835, 302.15403364114405, 302.29383921688765, 302.437581990726, 302.5852473412571, 302.73682070137784, 302.8922875580824, 303.05163345226117, 303.2148439785007, 303.3819047848845, 303.55280157279395 ] }, { "name": "Undisturbed formation", "x": [ 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000 ], "y": [ 290, 291.2, 292.4, 293.6, 294.8, 296, 297.2, 298.4, 299.6, 300.8, 302, 303.2, 304.4, 305.6, 306.8, 308, 309.2, 310.4, 311.6, 312.8, 314, 315.2, 316.4, 317.6, 318.8, 320, 321.2, 322.4, 323.6, 324.8, 326, 327.2, 328.4, 329.6, 330.8, 332, 333.2, 334.4, 335.6, 336.8, 338, 339.2, 340.4, 341.6, 342.8, 344, 345.2, 346.4, 347.6, 348.8, 350 ] } ] }, "warnings": [ "Single-phase incompressible liquid at one fixed operating time, using the long-time radial line-source approximation. Constant rate, heat capacity and thermal properties; U is based on tubing inside area and excludes the separate formation resistance.", "Use a signed formation gradient along the direction of flow: positive for hotter surroundings downstream, negative for colder. No pressure, viscosity, phase change, steam, gas expansion, shut-in history, frictional heating or thermal feedback to the hydraulic solvers is computed." ] } } ] } }