{ "version": 1, "topic": "FA08", "title": "Explore gas slip and its effect on a thermal pressure profile", "createdAt": "2026-10-24", "case": { "title": "Slip-Aware Hydrocarbon Thermal Pressure Profile Calculator", "premise": "Fixed controls: Inlet absolute pressure = 5 MPa(a); Inlet equilibrium temperature = 330 K; Pipe inside diameter = 0.1 m; Total mass flow rate = 1 kg/s; Distance along flow = 50 m; Prescribed inside-area heat-transfer coefficient = 100 W/(m2.K); Constant surrounding absolute temperature = 300 K; Prescribed Darcy friction factor = 0.02 dimensionless; Prescribed vertical drift distribution coefficient = 1.2 dimensionless; Methane feed mole fraction = 0.5 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.05 dimensionless.", "formula": "G=mass rate/pipe area; wg is local PR equilibrium vapor mass fraction, not molar beta. jg=G*wg/rhog and jl=G*(1-wg)/rhol. alpha=jg/[C0*(jg+jl)+vd], ug=jg/alpha, ul=jl/(1-alpha). HEM fixes C0=1, vd=0. Holdup density=alpha*rhog+(1-alpha)*rhol. Momentum flux M=G*(wg*ug+(1-wg)*ul), total specific static/kinetic energy E=h+0.5*(wg*ug^2+(1-wg)*ul^2).; Implicit trapezoidal balance: d(p+M)/ds=-fD*G^2/(2*D*holdup_density)-holdup_density*g*sin(theta). dE/ds=pi*D*U/mass_rate*(Te-T)-g*sin(theta). Slip profile is vertical upward only. Solve both for p and T using SciPy bounded least squares, then repeat at 10 and 20 steps and audit integrated heat, friction, elevation and flux changes.", "variables": "Prescribed upward gas drift speed is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.", "steps": [ { "label": "Define the baseline", "calculation": "Prescribed upward gas drift speed (m/s) = 0.2", "explanation": "Fixed controls: Inlet absolute pressure = 5 MPa(a); Inlet equilibrium temperature = 330 K; Pipe inside diameter = 0.1 m; Total mass flow rate = 1 kg/s; Distance along flow = 50 m; Prescribed inside-area heat-transfer coefficient = 100 W/(m2.K); Constant surrounding absolute temperature = 300 K; Prescribed Darcy friction factor = 0.02 dimensionless; Prescribed vertical drift distribution coefficient = 1.2 dimensionless; Methane feed mole fraction = 0.5 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.05 dimensionless." }, { "label": "Select the relation", "calculation": "G=mass rate/pipe area; wg is local PR equilibrium vapor mass fraction, not molar beta. jg=G*wg/rhog and jl=G*(1-wg)/rhol. alpha=jg/[C0*(jg+jl)+vd], ug=jg/alpha, ul=jl/(1-alpha). HEM fixes C0=1, vd=0. Holdup density=alpha*rhog+(1-alpha)*rhol. Momentum flux M=G*(wg*ug+(1-wg)*ul), total specific static/kinetic energy E=h+0.5*(wg*ug^2+(1-wg)*ul^2).; Implicit trapezoidal balance: d(p+M)/ds=-fD*G^2/(2*D*holdup_density)-holdup_density*g*sin(theta). dE/ds=pi*D*U/mass_rate*(Te-T)-g*sin(theta). Slip profile is vertical upward only. Solve both for p and T using SciPy bounded least squares, then repeat at 10 and 20 steps and audit integrated heat, friction, elevation and flux changes.", "explanation": "Prescribed upward gas drift speed is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots." }, { "label": "Substitute the values", "calculation": "v_d = 0.2 m/s; with the fixed controls above, the workflow evaluates Outlet absolute pressure = 4.89813048 MPa(a); Outlet equilibrium temperature = 319.951783 K", "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation." }, { "label": "Read the result", "calculation": "Outlet absolute pressure (MPa(a)) = 4.89813048; Outlet equilibrium temperature (K) = 319.951783", "explanation": "Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Short uniform interval 0.1-500 m, interior 0.101-9.99 MPa(a), 181-449 K, phase speed <=100 m/s and acceleration determinant >=0.5. Vertical upward only, C0=1-1.5 and vd=0-3 m/s supplied by the user; no regime-dependent fit or countercurrent flow. A failed trial or refinement rejects the entire profile. Constant prescribed U, Darcy factor and surroundings; no transient formation/wall thermal history, changing area, fittings, reactions, water, heavy ends, metastable phase delay or two-way reservoir coupling. Slip calculations require vapor/liquid coexistence with mass quality strictly between 0.001 and 0.999 at every trial; constant C0/drift parameters cannot be extended through a disappearing phase. HEM alone permits single-phase continuation. Numerical closure does not establish a field-valid physical correlation." } ], "result": "Outlet absolute pressure (MPa(a)) = 4.89813048; Outlet equilibrium temperature (K) = 319.951783", "interpretation": "Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Short uniform interval 0.1-500 m, interior 0.101-9.99 MPa(a), 181-449 K, phase speed <=100 m/s and acceleration determinant >=0.5. Vertical upward only, C0=1-1.5 and vd=0-3 m/s supplied by the user; no regime-dependent fit or countercurrent flow. A failed trial or refinement rejects the entire profile. Constant prescribed U, Darcy factor and surroundings; no transient formation/wall thermal history, changing area, fittings, reactions, water, heavy ends, metastable phase delay or two-way reservoir coupling. Slip calculations require vapor/liquid coexistence with mass quality strictly between 0.001 and 0.999 at every trial; constant C0/drift parameters cannot be extended through a disappearing phase. HEM alone permits single-phase continuation. Numerical closure does not establish a field-valid physical correlation.", "control": "Prescribed upward gas drift speed (m/s)", "columns": [ "Prescribed upward gas drift speed (m/s)", "Outlet absolute pressure (MPa(a))", "Outlet equilibrium temperature (K)" ], "rows": [ [ 0, 4.917123614880913, 320.0224640333165 ], [ 0.1, 4.907038344189558, 319.98496159402396 ], [ 0.2, 4.898130482021152, 319.95178320658385 ], [ 0.3, 4.890204317134573, 319.92221750387483 ], [ 0.4, 4.883105031320047, 319.8957011848083 ] ], "baseline": 2, "rowNotes": [ "Prescribed upward gas drift speed (m/s) = 0. Outlet absolute pressure (MPa(a)): 4.91712361; Outlet equilibrium temperature (K): 320.022464.", "Prescribed upward gas drift speed (m/s) = 0.1. Outlet absolute pressure (MPa(a)): 4.90703834; Outlet equilibrium temperature (K): 319.984962.", "Prescribed upward gas drift speed (m/s) = 0.2. Outlet absolute pressure (MPa(a)): 4.89813048; Outlet equilibrium temperature (K): 319.951783.", "Prescribed upward gas drift speed (m/s) = 0.3. Outlet absolute pressure (MPa(a)): 4.89020432; Outlet equilibrium temperature (K): 319.922218.", "Prescribed upward gas drift speed (m/s) = 0.4. Outlet absolute pressure (MPa(a)): 4.88310503; Outlet equilibrium temperature (K): 319.895701." ], "provenance": "Original recorded synthetic cases solved with the site's hydrocarbon-slip-thermal-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 absolute pressure (MPa(a)) without rounding intermediate values.", "answer": "v_d = 0.2 m/s; with the fixed controls above, the workflow evaluates Outlet absolute pressure = 4.89813048 MPa(a); Outlet equilibrium temperature = 319.951783 K. Outlet absolute pressure (MPa(a)) = 4.89813048. Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Short uniform interval 0.1-500 m, interior 0.101-9.99 MPa(a), 181-449 K, phase speed <=100 m/s and acceleration determinant >=0.5. Vertical upward only, C0=1-1.5 and vd=0-3 m/s supplied by the user; no regime-dependent fit or countercurrent flow. A failed trial or refinement rejects the entire profile. Constant prescribed U, Darcy factor and surroundings; no transient formation/wall thermal history, changing area, fittings, reactions, water, heavy ends, metastable phase delay or two-way reservoir coupling. Slip calculations require vapor/liquid coexistence with mass quality strictly between 0.001 and 0.999 at every trial; constant C0/drift parameters cannot be extended through a disappearing phase. HEM alone permits single-phase continuation. Numerical closure does not establish a field-valid physical correlation." }, { "question": "Compare the first and last recorded scenarios. Which input changes?", "answer": "Prescribed upward gas drift speed (m/s) changes from 0 to 0.4. Other controls remain as stated in the premise. Outlet absolute pressure (MPa(a)) changes from 4.91712361 to 4.88310503." }, { "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. Prescribed upward gas drift speed is varied within the supported input range. Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots. Every flash trial must remain at 180-450 K and 0.1-10 MPa absolute, with consistent mole fractions summing to one. Near-critical, vanishing-phase or failed closure states are rejected. Single-phase states are not given an invented vapor quality. Independent engine agreement is not experimental validation. Instantaneous equilibrium and the documented steady balance only. No machinery efficiency, transient behavior, separator sizing, phase residence time, mechanical safety approval or claimed field calibration. A rejected or unbracketed root is not extrapolated into an unsupported range. Short uniform interval 0.1-500 m, interior 0.101-9.99 MPa(a), 181-449 K, phase speed <=100 m/s and acceleration determinant >=0.5. Vertical upward only, C0=1-1.5 and vd=0-3 m/s supplied by the user; no regime-dependent fit or countercurrent flow. A failed trial or refinement rejects the entire profile. Constant prescribed U, Darcy factor and surroundings; no transient formation/wall thermal history, changing area, fittings, reactions, water, heavy ends, metastable phase delay or two-way reservoir coupling. Slip calculations require vapor/liquid coexistence with mass quality strictly between 0.001 and 0.999 at every trial; constant C0/drift parameters cannot be extended through a disappearing phase. HEM alone permits single-phase continuation. Numerical closure does not establish a field-valid physical correlation." } ] }, "recorded": { "kind": "workflow", "workflow": "hydrocarbon-slip-thermal-profile", "parameter": "v_d", "runs": [ { "inputs": { "p_in": 5, "T_in": 330, "D": 0.1, "m": 1, "L": 50, "U": 100, "Te": 300, "f_D": 0.02, "C_0": 1.2, "v_d": 0, "z1": 0.5, "z2": 0.15, "z3": 0.15, "z4": 0.1, "z5": 0.05, "z6": 0.05 }, "result": { "outputs": [ { "label": "Outlet absolute pressure", "value": 4.917123614880913, "unit": "MPa(a)" }, { "label": "Outlet equilibrium temperature", "value": 320.0224640333165, "unit": "K" }, { "label": "Net heat into fluid", "value": -38.8248925831455, "unit": "kJ/kg" }, { "label": "Maximum pressure refinement difference", "value": 5.962223266209321e-7, "unit": "MPa difference" }, { "label": "Maximum temperature refinement difference", "value": 0.0007066332809699816, "unit": "K difference" }, { "label": "Integrated energy residual", "value": 7.203198038041592e-10, "unit": "J/kg" }, { "label": "Integrated momentum residual", "value": 1.5279510989785194e-9, "unit": "Pa" } ], "columns": [ "Distance (m)", "Pressure (MPa(a))", "Temperature (K)", "Momentum flux (Pa)", "Static enthalpy plus kinetic energy (J/kg)", "Holdup density (kg/m3)", "Friction gradient (Pa/m)", "Heat input gradient (J/(kg.m))", "Gas void fraction (-1 = unassigned single phase)", "Maximum phase speed (m/s)", "Static enthalpy (J/kg)" ], "rows": [ [ 0, 5, 330, 137.70844657779912, -128843.7949913199, 164.39524138157864, 9.861227883808208, -942.4777960769379, 0.7610095534444118, 1.564352304086811, -128844.52668261106 ], [ 2.5, 4.995940862053926, 329.41318695477275, 136.8250370654661, -131201.46201211296, 164.80167586300453, 9.836908088392354, -924.0425205577723, 0.7601234628701742, 1.5581551743911846, -131202.1842542004 ], [ 5, 4.991871871650936, 328.83643976416266, 135.96913299883508, -133513.43612929512, 165.2016428487954, 9.813092111687952, -905.92347318778, 0.7592538098423904, 1.5521038191310035, 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-163218.3914371978, 170.43552792379205, 9.511742991767976, -669.188922432418, 0.7480732060457133, 1.4772166054528904, -163218.9994650741 ], [ 45, 4.925555971570802, 320.86699106268134, 125.34804317773798, -164898.83903805143, 170.73452661476625, 9.495085560141165, -655.5558582504356, 0.747444950870542, 1.4731828555764663, -164899.44177948954 ], [ 47.5, 4.921343334856505, 320.44087590849983, 124.84210993821357, -166545.51180570314, 171.02746245293915, 9.478822377566912, -642.1690558708367, 0.7468303967254754, 1.4692571540389576, -166546.10943472455 ], [ 50, 4.917123614880913, 320.0224640333165, 124.35146531153161, -168159.02007446467, 171.3143899752795, 9.46294668247853, -629.0242591383301, 0.7462294662922747, 1.4654378428802006, -168159.61275954472 ] ], "chart": { "xLabel": "Distance along flow (m)", "yLabel": "Pressure (MPa(a))", "includeZero": false, "series": [ { "name": "Pressure", "x": [ 0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, 35, 37.5, 40, 42.5, 45, 47.5, 50 ], "y": [ 5, 4.995940862053926, 4.991871871650936, 4.987793187151035, 4.983704966436492, 4.979607366941201, 4.975500545930676, 4.971384660310201, 4.967259866491932, 4.963126320422767, 4.958984177440519, 4.954833592294633, 4.950674719147983, 4.946507711468358, 4.942332721997607, 4.938149902571762, 4.933959404354501, 4.929761377586885, 4.925555971570802, 4.921343334856505, 4.917123614880913 ] } ] }, "warnings": [ "C1-C6 PR, zero kij, instantaneous local phase equilibrium. Constant inside-area U, surroundings and prescribed Darcy factor; no automatic boiling/friction/formation-history closure. Slip option uses supplied constant C0 and drift speed only for vertical upward co-current flow; it is not a calibrated regime map. No transient slugging, capillarity or nonequilibrium mass transfer. Both pressure and total energy include changing phase velocities; friction is not added as an external heat source. A 10/20-step refinement and integrated balance audit are numerical checks, not field validation." ] } }, { "inputs": { "p_in": 5, "T_in": 330, "D": 0.1, "m": 1, "L": 50, "U": 100, "Te": 300, "f_D": 0.02, "C_0": 1.2, "v_d": 0.1, "z1": 0.5, "z2": 0.15, "z3": 0.15, "z4": 0.1, "z5": 0.05, "z6": 0.05 }, "result": { "outputs": [ { "label": "Outlet absolute pressure", "value": 4.907038344189558, "unit": "MPa(a)" }, { "label": "Outlet equilibrium temperature", "value": 319.98496159402396, "unit": "K" }, { "label": "Net heat into fluid", "value": -38.7937145277007, "unit": "kJ/kg" }, { "label": "Maximum pressure refinement difference", "value": 7.323178889961923e-7, "unit": "MPa difference" }, { "label": "Maximum temperature refinement difference", "value": 0.0007085386965286489, "unit": "K difference" }, { "label": "Integrated energy residual", "value": 5.093170329928398e-10, "unit": "J/kg" }, { "label": "Integrated momentum residual", "value": 8.440110832452774e-10, "unit": "Pa" } ], "columns": [ "Distance (m)", "Pressure (MPa(a))", "Temperature (K)", "Momentum flux (Pa)", "Static enthalpy plus kinetic energy (J/kg)", "Holdup density (kg/m3)", "Friction gradient (Pa/m)", "Heat input gradient (J/(kg.m))", "Gas void fraction (-1 = unassigned single phase)", "Maximum phase speed (m/s)", "Static enthalpy (J/kg)" ], "rows": [ [ 0, 5, 330, 140.5222868706165, -128843.71964760766, 184.4409457428464, 8.789474223026644, -942.4777960769379, 0.7152854869967158, 1.6643523040868111, -128844.52668261106 ], [ 2.5, 4.995451295373672, 329.4109828327829, 139.5458847309326, -131201.3001127333, 184.91950055491276, 8.766727864895996, -923.973276023263, 0.7142976597300237, 1.6583316450859658, -131202.09661294977 ], [ 5, 4.990890981452861, 328.83206941091885, 138.59965469130572, -133513.01605087615, 185.39012811405007, 8.744472830182719, -905.7861744913365, 0.7133288924514798, 1.6524570360341257, -133513.8023744465 ], [ 7.5, 4.9863192525482365, 328.26313495461005, 137.68254587289456, 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A 10/20-step refinement and integrated balance audit are numerical checks, not field validation." ] } }, { "inputs": { "p_in": 5, "T_in": 330, "D": 0.1, "m": 1, "L": 50, "U": 100, "Te": 300, "f_D": 0.02, "C_0": 1.2, "v_d": 0.4, "z1": 0.5, "z2": 0.15, "z3": 0.15, "z4": 0.1, "z5": 0.05, "z6": 0.05 }, "result": { "outputs": [ { "label": "Outlet absolute pressure", "value": 4.883105031320047, "unit": "MPa(a)" }, { "label": "Outlet equilibrium temperature", "value": 319.8957011848083, "unit": "K" }, { "label": "Net heat into fluid", "value": -38.719378281684484, "unit": "kJ/kg" }, { "label": "Maximum pressure refinement difference", "value": 0.0000010239110146414987, "unit": "MPa difference" }, { "label": "Maximum temperature refinement difference", "value": 0.0007137352919244222, "unit": "K difference" }, { "label": "Integrated energy residual", "value": 2.1100277081131935e-9, "unit": "J/kg" }, { "label": "Integrated momentum residual", "value": 1.1350493878126144e-9, "unit": "Pa" } ], 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