Pipeline Optimization Project: Engineering Calculations for Heat Transfer and Energy Efficiency (Case Study Sample)

Oil Distribution Design Design Criteria Mass Flow Rate (M) kg/s 44 Specific Heat (Cp) J/kg-k 1930 T∞1-Permafrost Temp (°C) -4 Ts2- Outside insulation Temp (°C) 0 Length of Pipe (meters) 32000 Insolation Thermo Conductivity (W/m°C) 0.036 h(i) - Inside heat transfer coefficient (W/m²K) 113 h(o) - outside heat transfer coefficient (W/m²K) 7.2 Pip Pipe inner Diameter (mm) 428.66 Pipe inner Diameter (meters) 0.42866 Pipe outside Diameter (mm) 457.2 Pipe outside Diameter (meters) 0.4572 D(o) of insulation (m) D2 0.8 Thermal Conductivity W/m-°C 0.036 Insulation Thickness (δ) 0.1714 Area A(i) - Inside Area of the Pipe (m²) 1.346675107 A(o) - Outside Area of the Pipe w/ insulation (m²) 2.513274123 Heat Transfer Coefficient [1/h(i)A(i)] Inside Convective Resistance (m²-°C/W) 0.006571412 [1/h(o)A(o)] Outside Convective Resistance (m²- °C/W) 0.055262133 [δ/(k(A(i)+A(o))/2)] Insulation Resistance (m²-°C/W) 2.466929396 Overall Heat Transfer Coefficient U ((W/m²°C) 0.293649354 Inlet Temperature Conduction from inner pipe to Insulation 8.66124E-05 Conduction from insulation to Permafrost 1158116.716 Inlet Temperature 100 Temperature Distribution Let "A" be (U*PI*D)/(M*cp) 4.65674E-06 C=-ln(T+4°C) -4.647341159 Length of Travel (Meters) Temperature 0 100.31 1000 99.82 2000 99.34 3000 98.86 4000 98.38 5000 97.91 6000 97.43 7000 96.96 8000 96.49 9000 96.03 10000 95.56 11000 95.10 12000 94.64 13000 94.18 14000 93.72 15000 93.27 16000 92.82 17000 92.37 18000 91.92 19000 91.47 20000 91.03 21000 90.59 22000 90.15 23000 89.71 24000 89.28 25000 88.84 26000 88.41 27000 87.98 28000 87.56 29000 87.13 30000 86.71 31000 86.29 32000 85.87 Electrical Results Total Pressure Drop 3529948.211 Pump Work (Includes loss) 170849493.4 Pump electricity power (pump work /efficiency) 227799324.6 Heating power needed 635.3932338 Heater electricity (Heating power/efficiency) 668.8349829 Total electricity (watts) 227799993.4 Total electricity (watts) per day 2636.573998 Cost Results Electrical Cost ($/hr) 0.24 Pump electricity power (pump work /efficiency) Heater electricity (Heating power/efficiency) ingPipe thickness (mm)14.27ingPipe thickness (mm)14.27 0.02 Pipe Rougness 0.000045 Cross Sectional Area Cross-sectional area of pipe (m²) 0.144316438 Specific Gravity of Crude Oil at 30° respect to Temperature Empirical Formula Velocity (m/s) Reynold' Specific Gravity Density (kg/m^3) Viscosity (Pa.s) 0.821 820.81 0.050525811 0.371445764 2586.6 640080685800 0.821 821.10 0.052269158 0.371315764 2500.3 0.821 821.38 0.054064137 0.371186459 2417.3 0.822 821.67 0.055911987 0.371057844 2337.4 0.822 821.95 0.057813965 0.370929915 2260.5 0.822 822.23 0.059771354 0.370802667 2186. 0.823 822.51 0.061785456 0.370676098 2115.2 0.823 822.79 0.063857593 0.370550202 2046.6 0.823 823.07 0.06598911 0.370424976 1980.5 0.823 823.35 0.068181374 0.370300416 1916.8 0.824 823.62 0.070435774 0.370176518 1855.4 0.824 823.90 0.072753718 0.370053278 1796.3 0.824 824.17 0.075136639 0.369930691 1739.3 0.824 824.44 0.077585991 0.369808755 1684.4 0.825 824.71 0.080103249 0.369687465 1631.5 0.825 824.98 0.082689912 0.369566818 1580.5 0.825 825.25 0.0853475 0.36944681 1531.2 0.826 825.52 0.088077555 0.369327436 1483.8 0.826 825.78 0.090881642 0.369208693 1438.0 0.826 826.05 0.093761348 0.369090578 1393.8 0.826 826.31 0.096718284 0.368973087 1351.2 0.827 826.57 0.099754081 0.368856216 1310.1 0.827 826.83 0.102870394 0.368739961 1270.4 0.827 827.09 0.106068901 0.368624319 1232.1 0.827 827.35 0.1093513 0.368509287 1195.1 0.828 827.61 0.112719316 0.36839486 1159.4 0.828 827.86 0.116174691 0.368281035 1124.9 0.828 828.12 0.119719195 0.368167809 1091.6 0.828 828.37 0.123354617 0.368055178 1059.4 0.829 828.62 0.127082771 0.367943139 1028.4 0.829 828.87 0.13090549 0.367831688 998.37 0.829 829.12 0.134824634 0.367720822 969.34 0.829 829.37 0.138842082 0.367610537 941.30 Pressure Drop s Number Friction ΔP ( 1/2*fD*density*V^2* 43301 0.024742492 0 70279 0.025596209 3379.970847 55689 0.02647521 6989.650457 63902 0.027380102 10839.06581 65413 0.028311501 14938.55763 53654 0.029270035 19298.78682 59147 0.03025634 23930.74095 20375 0.031271066 28845.74072 12391 0.03231487 34055.44655 32145 0.033388422 39571.86514 81144 0.034492401 45407.35609 65237 0.035627499 51574.63853 94407 0.036794415 58086.7978 82577 0.037993863 64957.29215 47425 0.039226564 72199.95945 10208 0.040493253 79829.02394 95594 0.041794674 87859.10296 31503 0.043131582 96305.21374 48959 0.044504743 105182.7802 81942 0.045914936 114507.6397 67256 0.047362947 124296.0498 44395 0.048849577 134564.6953 55423 0.050375636 145330.6947 44854 0.051941945 156611.6073 59543 0.053549336 168425.4396 48578 0.055198653 180790.6528 63179 0.056890751 193726.1688 56604 0.058626495 207251.3773 84054 0.060406761 221386.1427 02588 0.062232438 236150.8106 10391 0.064104424 251566.2146 99372 0.066023628 267653.683 14316 0.067990973 284435.0454 Oil Distribution Design Design Criteria Mass Flow Rate (M) kg/s 44 Specific Heat (Cp) J/kg-k 1930 T∞1-Permafrost Temp (°C) -4 Ts2- Outside insulation Temp (°C) 0 Length of Pipe (meters) 32000 Insolation Thermo Conductivity (W/m°C) 0.036 h(i) - Inside heat transfer coefficient (W/m²K) 113 h(o) - outside heat transfer coefficient (W/m²K) 7.2 Pip Pipe inner Diameter (mm) 477.82 Pipe inner Diameter (meters) 0.47782 Pipe outside Diameter (mm) 508 Pipe outside Diameter (meters) 0.508 D(o) of insulation (m) D2 0.8 Thermal Conductivity W/m-°C 0.036 Insulation Thickness (δ) 0.146 Area A(i) - Inside Area of the Pipe (m²) 1.501115802 A(o) - Outside Area of the Pipe w/ insulation (m²) 2.513274123 Heat Transfer Coefficient [1/h(i)A(i)] Inside Convective Resistance (m²-°C/W) 0.00589532 [1/h(o)A(o)] Outside Convective Resistance (m²- °C/W) 0.055262133 [δ/(k(A(i)+A(o))/2)] Insulation Resistance (m²-°C/W) 2.020509035 Overall Heat Transfer Coefficient U ((W/m²°C) 0.320018181 Inlet Temperature Conduction from inner pipe to Insulation 7.15706E-05 Conduction from insulation to Permafrost 1158116.716 Inlet Temperature 83 Temperature Distribution Let "A" be (U*PI*D)/(M*cp) 5.6569E-06 C=-ln(T+4°C) -4.464610017 Length of Travel (Meters) Temperature 0 82.89 1000 82.40 2000 81.91 3000 81.43 4000 80.94 5000 80.46 6000 79.99 7000 79.51 8000 79.04 9000 78.57 10000 78.11 11000 77.65 12000 77.18 13000 76.73 14000 76.27 15000 75.82 16000 75.37 17000 74.92 18000 74.48 19000 74.03 20000 73.59 21000 73.15 22000 72.72 23000 72.29 24000 71.86 25000 71.43 26000 71.00 27000 70.58 28000 70.16 29000 69.74 30000 69.33 31000 68.91 32000 68.50 Results Total Pressure Drop 7641381.846 Pump Work (Includes loss) 369842881.3 Pump electricity power (pump work /efficiency) 493123841.8 Heating power needed 633.0261024 Heater electricity (Heating power/efficiency) 666.3432656 Total electricity (watts) 493124508.1 Total electricity (watts) per day 5707.459585 ingPipe thickness (mm)15.09ingPipe thickness (mm)15.09 0.02 Pipe Rougness 0.000045 Cross Sectional Area Cross-sectional area of pipe (m²) 0.179315788 Specific Gravity of Crude Oil at 30° respect to Temperature Empirical Formula Velocity (m/s) Reynold' Specific Gravity Density (kg/m^3) Viscosity (Pa.s) 0.831 831.14 0.17103945 0.295230381 685.49 640080381000.831 0.832 0.832 0.832 0.833 0.833 0.833 0.833 0.834 0.834 0.834 0.835 0.835 0.835 0.835 0.836 0.836 0.836 0.836 0.837 0.837 0.837 0.837 0.838 0.838 0.838 0.838 0.839 0.839 0.839 0.839 0.840 831.43 831.72 832.00 832.29 832.57 832.86 833.14 833.42 833.70 833.97 834.25 834.52 834.79 835.06 835.33 835.60 835.86 836.13 836.39 836.65 ...