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["Exam TPG4245, Autumn 2022, Prof. Milan Stanko.",null,null,"Input"]
[null,null,null,"Calculated"]
[null,null,null,"Solver adjusted"]
["Reservoir pressure, pR","[bara]",400]
["Productivity Index, J","[Sm3/d/bar]",10]
["Bubble point pressure (pb) @TR","[bara]",253,"<--Task 1",null,null,null,null,null,"Task 1 - Explanation -->","The bubble point pressure of the oil is found by examining the black oil tables given in the tab \"PVT\" and determining at which pressure Rs becomes constant"]
["Reservoir GOR","[Sm3/Sm3]",100,null,null,null,null,null,null," -->","Since the reservoir is undersaturated oil, the producing GOR is equal to the saturation Rs (100)"]
[null,null,null,null,null,null,null,null,null," -->"]
[null,null,null,null,null,null,null,null,null," -->"]
["Task 2",null,null,null,null,null,null,null,null,"Task 2 - Explanation -->","Assume the flowing bottom-hole pressure"]
["TPR column","pwf (IPR)","qo ","pwf (TPR)","pwf (TPR)-pwf (IPR)",null,null,null,null," -->","Use the composite IPR equation to calculate oil rate. (VBA function \"CompositeIPR_qo\")"]
["[-]","[bara]","[Sm3/d]","[bara]","[bar]",null,null,null,null," -->","Use the interpolation VBA function (\"tabinterpol\"), the oil rate calculated above and the TPR table for GOR=100, to determine flowing bottom-hole pressure. "]
[2,271.29298869260242,{"$f":"CompositeIPR_qo($C$4,B13,$C$6,$C$5)","v":1287.0701130739758},{"$f":"tabinterpol(Data!C13,A13,TPR!$A$8:$B$27)","v":271.29298830608388},{"$f":"D13-B13","v":-3.8651853628834942E-7},null,null,null,null," -->","These two flowing bottom-hole pressures should be the same for natural flow."]
[null,null,null,null,null,null,null,null,null," -->","Substract the available flowing bottom-hole pressure (calculated with IPR) from the required  flowing bottom-hole pressure (calculated from TPR). This gives a pressure difference"]
["Task 3",null,null,null,null,null,null,null,null," -->","Use solver or goal seek to change assumed flowing bottom-hole pressure until  the pressure difference is equal to zero"]
["Skin factor, initial","[-]",3,null,null,null,null,null,null,"Task 3 - Explanation  -->","After inspecting the analytical expression of J, multiply the J provided by (8-0.75-3) and divide by (8-0.75+0) to calculate the new J. "]
["Skin factor, new","[-]",0,null,null,null,null,null,null," -->","Repeat the procedure described in task 2 to calculate the new equilibrium rate."]
["ln(re/rw)","[-]",8,null,null,null,null,null,null," -->","The new equilibrium rate is significantly higher than the rate found in task 2."]
["New productivity index, J","[Sm3/d/bar]",{"$f":"C5*(C18-0.75+C16)/(C18-0.75+C17)","v":14.137931034482758},null,null,null,null,null,null," -->"]
[null,null,null,null,null,null,null,null,null," -->"]
["TPR column","pwf (IPR)","qo ","pwf (TPR)","pwf (TPR)-pwf (IPR)",null,null,null,null," -->"]
["[-]","[bara]","[Sm3/d]","[bara]","[bar]",null,null,null,null," -->"]
[2,274.97805959298466,{"$f":"CompositeIPR_qo($C$4,B23,$C$6,$C$19)","v":1767.551571271596},{"$f":"tabinterpol(Data!C23,A23,TPR!$A$8:$B$27)","v":274.97805955946296},{"$f":"D23-B23","v":-3.3521700970595703E-8},null,null,null,null," -->"]
[null,null,null,null,null,null,null,null,null," -->"]
["Task 4",null,null,null,null,null,null,null,null,"Task 4 - Explanation -->","Set flowing bottom-hole pressure to pb at TR (253 bara)"]
["ESP hydraulic efficiency ","[-]",0.6,null,null,null,null,null,null," -->","Use the composite IPR equation to calculate oil rate. (VBA function \"CompositeIPR_qo\")"]
[null,null,null,null,null,null,null,null,null," -->","Use the interpolation VBA function (\"tabinterpol\"), the oil rate calculated above and the TPR table for GOR=100, to determine flowing bottom-hole pressure. "]
["TPR column","pwf (IPR)","qo ","pwf (TPR)","pwf (TPR)-pwf (IPR)","Bo@psuc","qo@psuc","ESP power",null," -->","Substract the available flowing bottom-hole pressure (calculated with IPR) from the required  flowing bottom-hole pressure (calculated from TPR). This gives the required pump delta pressure."]
["[-]","[bara]","[Sm3/d]","[bara]","[bar]","[-]","[m3/d]","[W]",null," -->","Calculate the oil volume factor Bo at the inlet of the pump, by using the available flowing bottom-hole pressure, the interpolation VBA function (\"tabinterpol\") and the PVT table provided in table \"PVT\""]
[2,{"$f":"C6","v":253},{"$f":"CompositeIPR_qo($C$4,B30,$C$6,$C$5)","v":1470},{"$f":"tabinterpol(Data!C30,A30,TPR!$A$8:$B$27)","v":272.47551343105391},{"$f":"D30-B30","v":19.475513431053912},{"$f":"tabinterpol(B30,4,PVT!A5:I35)","v":1.29131},{"$f":"F30*C30","v":1898.2257},{"$f":"ESP_power(E30,G30,C26)","v":71313.503309262567},null," -->","Calculate the volumetric rate of oil at the inlet of the pump with the oil volume factor calculated in the previous step and the standard conditions oil rate --> qo = qo_sc*Bo"]
[null,null,null,null,null,null,null,null,null," -->","Calculate the ESP power by using the VBA function \"ESP_power\", and input the volumetric oil rate at inlet, pump delta pressure anc hydraulic efficiency"]
["Task 5",null,null,null,null,null,null,null,null,"Task 5 - Explanation -->","Repeat task 2 but using all TPR curves provided in the tab \"TPR\""]
["TPR column","Tubing Rp (with gas lift)","pwf (IPR)","qo ","pwf (TPR)","pwf (TPR)-pwf (IPR)","qg - gas lift",null,null," -->","For all results, estimate the required gas lift rate by qo_sc*(GOR-100)"]
["[-]","[-]","[bara]","[Sm3/d]","[bara]","[bar]","[Sm3/d]",null,null," -->","The largest oil production is found for a tubing Rp of 400 and a gas lift rate of 5.3E05 Sm3/d"]
[2,100,271.29294070247357,{"$f":"CompositeIPR_qo($C$4,C35,$C$6,$C$5)","v":1287.0705929752644},{"$f":"tabinterpol(Data!D35,A35,TPR!$A$8:$F$27)","v":271.29299103055331},{"$f":"E35-C35","v":5.0328079737482767E-5},{"$f":"D35*(B35-$C$7)","v":0},null,null," -->","This alternative seems much better than using ESP"]
[3,200,239.49073825310325,{"$f":"CompositeIPR_qo($C$4,C36,$C$6,$C$5)","v":1601.485895078727},{"$f":"tabinterpol(Data!D36,A36,TPR!$A$8:$F$27)","v":239.4913716292113},{"$f":"E36-C36","v":6.3337610805547229E-4},{"$f":"D36*(B36-$C$7)","v":160148.5895078727},null,null," -->"]
[4,400,220.8705370946852,{"$f":"CompositeIPR_qo($C$4,C37,$C$6,$C$5)","v":1770.8933961167052},{"$f":"tabinterpol(Data!D37,A37,TPR!$A$8:$F$27)","v":220.87096183113783},4.2473645262930404E-4,531268.01883501152,null,null," -->"]
[5,600,222.78862091153366,{"$f":"CompositeIPR_qo($C$4,C38,$C$6,$C$5)","v":1754.0756994532994},{"$f":"tabinterpol(Data!D38,A38,TPR!$A$8:$F$27)","v":222.7885484788535},-7.2432680155998241E-5,877037.8497266497,null,null," -->"]
[6,800,229.0276291151321,{"$f":"CompositeIPR_qo($C$4,C39,$C$6,$C$5)","v":1698.366503990148},{"$f":"tabinterpol(Data!D39,A39,TPR!$A$8:$F$27)","v":229.02707947768909},-5.4963744301517181E-4,1188856.5527931035,null,null," -->"]
[null,null,null,null,null,{"$f":"SUMSQ(F35:F39)","v":8.9144707597652209E-7},null,null,null," -->"]
["Task 6",null,null,null,null,null,null,null,null,"Task 6 - Explanation -->","Set pressure at TVD=0 m to 100 bara"]
["Tubing inner diameter, d","[m]",{"$f":"4.5*25.4/1000","v":0.1143},null,null,null,null,null,null," -->","Calculate black oil properties at that pressure by using the pressure, the interpolation VBA function (\"tabinterpol\") and the PVT table provided in table \"PVT\". Use the proper column number!!!"]
["Tubing cross section area, A","[m2]",{"$f":"((C42)^2)*PI()*0.25","v":1.0260826451724329E-2},null,null,null,null,null,null," -->","Calculate oil and gas local volumetric rates by using the black oil properties, the oil and gas standard conditions rates and the VBA functions  \"qg_local” and “qo_local"]
["Tubing wall roughness","[m]",1.0000000000000001E-5,null,null,null,null,null,null," -->","Calculate superficial oil and gas velocities from the oil and gas volumetric rates. Remember changing units!!!"]
["Tubing inclination angle from horizontal","[deg]",90,null,null,null,null,null,null," -->","Calculate the non-slip gas volume fraction (lambdag) by qg/(qg+qo)"]
["Well oil rate at standard conditions, qo","[Sm3/d]",{"$f":"C13","v":1287.0701130739758},null,null,null,null,null,null," -->","As there is no slip (homogeneous flow) then void fraction ɛ is equal to lambdag "]
["Well gas rate at standard conditions, qg","[Sm3/d]",{"$f":"C46*$C$7","v":128707.01130739758},null,null,null,null,null,null," -->","Use the drift flux model, the VBA function \"dpdx_mpf\" with the proper input (void fraction, superficial velocities, densities, viscosities, pipe diameter, roughness and inclination) to compute pressure gradient."]
[null,null,null,null,null,null,null,null,null," -->","Calculate pressure at the next point in the tubing by substracting dpdx*delta L"]
[null,null,null,null,null,null,null,null,null," -->","Repeat for all depth by dragging the top row down. Ensure cells that must be frozen are frozen."]
[]
[null,null,null,"BO table column->",2,3,4,5,6,7,8,9]
[null,"TVD [m]","T [C]","p[bara]","Rs [Sm3/Sm3]","rs [Sm3/Sm3]","Bo [m3/Sm3]","Bg [m3/Sm3]","deng [kg/m3]","viscg [cp]","deno [kg/m3]","viso [cp]","qo [m3/d]","qg[m3/d]","uso [m/s]","usg [m/s]","lambdag[-]","ɛ - void fraction [-]","dp/dx [bara/m]"]
[null,0,80,100,{"$f":"tabinterpol($D53,E$51,PVT!$A$5:$I$35)","v":33.630456434837591},{"$f":"tabinterpol($D53,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D53,G$51,PVT!$A$5:$I$35)","v":1.1079782218523553},{"$f":"tabinterpol($D53,H$51,PVT!$A$5:$I$35)","v":1.052534719631942E-2},{"$f":"tabinterpol($D53,I$51,PVT!$A$5:$I$35)","v":87.95118322079847},{"$f":"tabinterpol($D53,J$51,PVT!$A$5:$I$35)","v":1.5309437490460582E-2},{"$f":"tabinterpol($D53,K$51,PVT!$A$5:$I$35)","v":786.17920069483307},{"$f":"tabinterpol($D53,L$51,PVT!$A$5:$I$35)","v":0.99106433572939301},{"$f":"qo_local(E53,F53,G53,$C$47,$C$46)","v":1426.0456552830135},{"$f":"qg_local(E53,F53,H53,$C$47,$C$46)","v":899.09890207274452},{"$f":"M53/(3600*24*$C$43)","v":1.6085602972539716},{"$f":"N53/(3600*24*$C$43)","v":1.0141714550449152},{"$f":"P53/(P53+O53)","v":0.38668516296261318},{"$f":"Q53","v":0.38668516296261318},{"$f":"dpdx_mpf($C$44,L53,J53,K53,I53,O53,P53,$C$42,$C$45,R53)","v":-5.3038838103765674E-2}]
[null,500,80,{"$f":"D53+(B53-B54)*S53","v":126.51941905188283},{"$f":"tabinterpol($D54,E$51,PVT!$A$5:$I$35)","v":43.404640053009757},{"$f":"tabinterpol($D54,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D54,G$51,PVT!$A$5:$I$35)","v":1.1327339590099648},{"$f":"tabinterpol($D54,H$51,PVT!$A$5:$I$35)","v":8.0865038894134787E-3},{"$f":"tabinterpol($D54,I$51,PVT!$A$5:$I$35)","v":114.2408726967746},{"$f":"tabinterpol($D54,J$51,PVT!$A$5:$I$35)","v":1.6654279093270039E-2},{"$f":"tabinterpol($D54,K$51,PVT!$A$5:$I$35)","v":776.95694505063852},{"$f":"tabinterpol($D54,L$51,PVT!$A$5:$I$35)","v":0.90268543544577373},{"$f":"qo_local(E54,F54,G54,$C$47,$C$46)","v":1457.9080247056877},{"$f":"qg_local(E54,F54,H54,$C$47,$C$46)","v":589.03870390713769},1.6445006209314634,{"$f":"N54/(3600*24*$C$43)","v":0.6644277265182772},{"$f":"P54/(P54+O54)","v":0.2877645498406875},{"$f":"Q54","v":0.2877645498406875},{"$f":"dpdx_mpf($C$44,L54,J54,K54,I54,O54,P54,$C$42,$C$45,R54)","v":-5.9643100557148707E-2}]
[null,1000,80,{"$f":"D54+(B54-B55)*S54","v":156.3409693304572},{"$f":"tabinterpol($D55,E$51,PVT!$A$5:$I$35)","v":55.209646152341058},{"$f":"tabinterpol($D55,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D55,G$51,PVT!$A$5:$I$35)","v":1.1639957877149547},{"$f":"tabinterpol($D55,H$51,PVT!$A$5:$I$35)","v":6.467386141793029E-3},{"$f":"tabinterpol($D55,I$51,PVT!$A$5:$I$35)","v":142.86802543525766},{"$f":"tabinterpol($D55,J$51,PVT!$A$5:$I$35)","v":1.8403332154204165E-2},{"$f":"tabinterpol($D55,K$51,PVT!$A$5:$I$35)","v":765.4573683425956},{"$f":"tabinterpol($D55,L$51,PVT!$A$5:$I$35)","v":0.811657637651376},{"$f":"qo_local(E55,F55,G55,$C$47,$C$46)","v":1498.1441901119183},{"$f":"qg_local(E55,F55,H55,$C$47,$C$46)","v":372.83398332041588},1.6898864737240669,{"$f":"N55/(3600*24*$C$43)","v":0.42055171292341875},{"$f":"P55/(P55+O55)","v":0.19927222487927104},{"$f":"Q55","v":0.19927222487927104},{"$f":"dpdx_mpf($C$44,L55,J55,K55,I55,O55,P55,$C$42,$C$45,R55)","v":-6.4873333894854099E-2}]
[null,1500,80,188.77763627788426,{"$f":"tabinterpol($D56,E$51,PVT!$A$5:$I$35)","v":69.076838973866685},{"$f":"tabinterpol($D56,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D56,G$51,PVT!$A$5:$I$35)","v":1.2021751977478283},{"$f":"tabinterpol($D56,H$51,PVT!$A$5:$I$35)","v":5.389565227696601E-3},{"$f":"tabinterpol($D56,I$51,PVT!$A$5:$I$35)","v":171.34902906656635},{"$f":"tabinterpol($D56,J$51,PVT!$A$5:$I$35)","v":2.0468651297052883E-2},{"$f":"tabinterpol($D56,K$51,PVT!$A$5:$I$35)","v":751.79373333592355},{"$f":"tabinterpol($D56,L$51,PVT!$A$5:$I$35)","v":0.7219445962261487},{"$f":"qo_local(E56,F56,G56,$C$47,$C$46)","v":1547.2837677000266},{"$f":"qg_local(E56,F56,H56,$C$47,$C$46)","v":214.50618551454147},1.7453152555721312,{"$f":"N56/(3600*24*$C$43)","v":0.24196008890445267},{"$f":"P56/(P56+O56)","v":0.12175468768178224},0.12175468768178224,{"$f":"dpdx_mpf($C$44,L56,J56,K56,I56,O56,P56,$C$42,$C$45,R56)","v":-6.8650924464939395E-2}]
[null,2000,80,223.10309851035396,{"$f":"tabinterpol($D57,E$51,PVT!$A$5:$I$35)","v":85.000168325411636},{"$f":"tabinterpol($D57,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D57,G$51,PVT!$A$5:$I$35)","v":1.2475021851789678},{"$f":"tabinterpol($D57,H$51,PVT!$A$5:$I$35)","v":4.6674217649645315E-3},{"$f":"tabinterpol($D57,I$51,PVT!$A$5:$I$35)","v":197.70967230160002},{"$f":"tabinterpol($D57,J$51,PVT!$A$5:$I$35)","v":2.2710540734773316E-2},{"$f":"tabinterpol($D57,K$51,PVT!$A$5:$I$35)","v":736.24665126472973},{"$f":"tabinterpol($D57,L$51,PVT!$A$5:$I$35)","v":0.63712393434737313},{"$f":"qo_local(E57,F57,G57,$C$47,$C$46)","v":1605.622778538326},{"$f":"qg_local(E57,F57,H57,$C$47,$C$46)","v":90.108474700865656},1.8111208742547487,{"$f":"N57/(3600*24*$C$43)","v":0.10164114613929427},{"$f":"P57/(P57+O57)","v":5.3138417145252317E-2},5.3138417145252317E-2,{"$f":"dpdx_mpf($C$44,L57,J57,K57,I57,O57,P57,$C$42,$C$45,R57)","v":-7.1170378636136622E-2}]
[null,2500,80,258.68828782842229,{"$f":"tabinterpol($D58,E$51,PVT!$A$5:$I$35)","v":100},{"$f":"tabinterpol($D58,F$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D58,G$51,PVT!$A$5:$I$35)","v":1.2901921614103908},{"$f":"tabinterpol($D58,H$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D58,I$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D58,J$51,PVT!$A$5:$I$35)","v":0},{"$f":"tabinterpol($D58,K$51,PVT!$A$5:$I$35)","v":722.60238537310568},{"$f":"tabinterpol($D58,L$51,PVT!$A$5:$I$35)","v":0.57455973619713263},{"$f":"qo_local(E58,F58,G58,$C$47,$C$46)","v":1660.567771073629},{"$f":"qg_local(E58,F58,H58,$C$47,$C$46)","v":0},1.8730980859925201,0,{"$f":"P58/(P58+O58)","v":0},0,{"$f":"dpdx_mpf($C$44,L58,J58,K58,I58,O58,P58,$C$42,$C$45,R58)","v":-9.7247768657456962E-2}]

{"sheet":"PVT","index":1,"n_rows":35,"n_cols":9,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["T","[C]",80]
["COLUMN:",2,3,4,5,6,7,8,9]
["p","Rs","rs","Bo","Bg","deng","viscg","deno","visco"]
["[bara]","[Sm3/Sm3]","[Sm3/Sm3]","[m3/Sm3]","[m3/Sm3]","[kg/m3]","[cP]","[kg/m3]","[cP]"]
[1,0.59555999999999998,0,1.0355300000000001,1.2276899999999999,0.75144,1.2539E-2,811.73699999999997,1.41903]
[14.758599999999999,5.6726099999999997,0,1.04514,8.2159999999999997E-2,11.2286,1.2692E-2,808.75400000000002,1.33548]
[28.517199999999999,10.0177,0,1.0539000000000001,4.1432999999999998E-2,22.265799999999999,1.2935E-2,805.83900000000006,1.27023]
[42.2759,14.3302,0,1.06301,2.7241000000000001E-2,33.865299999999998,1.3247E-2,802.673,1.2104600000000001]
[56.034500000000001,18.717500000000001,0,1.07267,2.0046000000000001E-2,46.020400000000002,1.3625999999999999E-2,799.21699999999998,1.1541600000000001]
[69.793099999999995,23.221599999999999,0,1.0829599999999999,1.5716999999999998E-2,58.696100000000001,1.4074E-2,795.46400000000006,1.10059]
[83.551699999999997,27.864699999999999,0,1.0939099999999999,1.2845000000000001E-2,71.821299999999994,1.4592000000000001E-2,791.41600000000005,1.0493600000000001]
[97.310299999999998,32.660899999999998,0,1.1055600000000001,1.0817E-2,85.283299999999997,1.5181E-2,787.08100000000002,1.00027]
[111.069,37.6205,0,1.1179300000000001,9.3250999999999994E-3,98.930400000000006,1.5838000000000001E-2,782.46799999999996,0.95318000000000003]
[124.828,42.751800000000003,0,1.13103,8.1942000000000004E-3,112.584,1.6559000000000001E-2,777.58799999999997,0.90800999999999998]
[138.58600000000001,48.061999999999998,0,1.14489,7.3182000000000004E-3,126.06100000000001,1.7333999999999999E-2,772.45500000000004,0.86470000000000002]
[152.345,53.557699999999997,0,1.1595200000000001,6.6277999999999997E-3,139.19300000000001,1.8155000000000001E-2,767.08299999999997,0.82320000000000004]
[166.10300000000001,59.2453,0,1.17493,6.0755000000000002E-3,151.846,1.9009999999999999E-2,761.48599999999999,0.78346000000000005]
[179.86199999999999,65.130799999999994,0,1.1911400000000001,5.6277000000000002E-3,163.92699999999999,1.9890000000000001E-2,755.68100000000004,0.74546000000000001]
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{"sheet":"TPR","index":2,"n_rows":27,"n_cols":9,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["Tubing performance relationship (TPR)"]
["pwh ","[bara]",100]
[]
["COLUMN",2,3,4,5,6]
["Rp (GOR)",100,200,400,600,800,null,2,100]
["qo","pwf","pwf","pwf","pwf","pwf",null,3,200]
["[Sm3/d]","[bara]","[bara]","[bara]","[bara]","[bara]",null,4,400]
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