Modelado numerico
description
Transcript of Modelado numerico
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Los mtodos numricos de la explotacin petroleraRodolfo Camacho VelzquezPemex Exploracin y ProduccinCIMAT, GuanajuatoJunio, 2009
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Problemas de modelos de simulacin comerciales
Propuestas de mejora de estos simuladores (Comportamiento Fractal, Yacimientos Naturalmente Fracturados Vugulares)
ConclusinCONTENIDO
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Problemas de modelos de simulacin comercialesModelo basado en bloques de matriz separados por fracturas uniformemente distribuidas, a una sola escala, y todas interconectadas. No se considera la influencia de los vgulos. Ausencia de modelado adecuado de la geologa de YNF
Alta saturacin residual ha sido medida abajo del contacto agua-aceite en NFR; sin embargo, las simulaciones predicen saturaciones mucho menores
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Problemas de modelos de simulacin comercialesNo se tiene la capacidad de calcular directamente conveccin trmica.
Se introduce un factor de forma, el cual no define una forma de bloque de matriz y representa infinitas posibilidades de tamao de bloque.
Uso de factor de forma constante causa problemas en la simulacin, ya que diferentes lados de los bloques intervienen en diferentes procesos de recuperacin.
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Problemas de modelos de simulacin comerciales Necesario desarrollar tecnologas/modelos para entender mecanismos de interaccin rocafluido, que capturen la complejidad de medio (presencia de bloques de matriz, fracturas, y vgulos, y una distribucin de fracturas, a diferentes escalas, ms realista), y plantear procesos de recuperacin especficos para cada medio fracturado.
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Propuestas de mejora de simuladores (Comportamiento Fractal, Yac. Naturalmente Fracturados Vugulares) COMPORTAMIENTO FRACTAL DEL TRANSITORIO DE PRESIN DE YACIMIENTOS NATURALMENTE FRACTURADOS (YNF)
ANLISIS DE CURVAS DE DECLINACIN CON GEOMETRA FRACTAL
COMPORTAMIENTO DEL TRANSITORIO DE PRESIN Y CURVAS DE DECLINACIN EN YACIMIENTOS CARBONATADOS VUGULARES NATURALEMENTE FRACTURADOS
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PROBLEMAAlgunos Yacimientos Naturalmente Fracturados (YNF) tienen diferentes escalas, pobre conectividad de fracturas y una distribucin espacial desordenada de fracturas. La respuesta de presin de estos yacimientos sigue una ley de potencia en funcin del tiempo.Cmo caracterizar completamente un YNF con geometra fractal usando datos de pruebas de presin?Comportamiento Fractal de Yacimientos Naturalmente Fracturados, SPE 71591
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MOTIVACINMODELADO DE SISTEMAS FRACTALES (ACUA & YORTSOS, 1991)
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MOTIVACINMODELADO DE SISTEMAS FRACTALES (ACUA & YORTSOS, 1991, ACUA et al., 1995)
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MODELO MATEMTICOLa permeabilidad esta determinada en funcin de la siguiente ecuacin:Donde D y son los parmetros fractales, ro es el tamao mnimo considerado en la red (la fractura ms pequea) y ko es una constante de proporcionalidad.
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MODELO MATEMTICOLa ecuacin generalizada d Dimensin Euclidiana de la Matrizdmf Dimensin Fractal de la Red de fracturasB = D--1 Indice de Conductividad de la red de Fracturasw Coeficiente de Interaccin Matriz Fractura
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NUEVOS MODELOSYACIMIENTO CON APORTE DE LA MATRIZ ROCOSA PARA UN MEDIO FRACTAL DE DOBLE POROSIDAD (CHANG Y YORTSOS)
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NUEVOS MODELOSECUACION DE BARKER
YACIMIENTO SIN APORTE DE LA MATRIZ ROCOSA
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NUEVOS MODELOSGENERALIZACION DE LA ECUACION OP (METZLER et al.), ECUACION MGN
YACIMIENTO SIN APORTE DE LA MATRIZ ROCOSA
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ResultadosAnlisis de casos de campo:
datos
76320.00193306.65
76320.00393306.980.00200.33-6.2146081019-1.1086626245
76320.00583307.220.00390.57-5.5467787269-0.5621189182
76320.00813307.650.00621-5.08320598640172.53425579721.06971238650.06738981471.0697123865
76320.01003307.990.00811.34-4.81589121830.292669614170.85507251111.38392608590.32492444971.0327806612
76320.01203308.370.01011.72-4.59521985520.5423242908170.38555511441.72089410660.54284398521.0005198294
76320.01503308.770.01312.12-4.3351430490.7514160887164.47168958142.15457913290.76759540651.0163109118
76320.01813309.130.01622.48-4.12274403690.9082585602144.19581421962.33597219010.848428160.9419242702
76320.02103309.720.01913.07-3.95806694441.1216775616140.76767682932.68866262610.9890439050.8757858717
76320.02503310.040.02313.39-3.76792266181.2208299214126.30358978962.9176129231.07076578980.8606527797
76320.02803310.30.02613.65-3.64581996451.2947271676119.37266368573.11562652251.13643026280.85359630750.65541.92591272840.5192343273
76320.03203310.680.03014.03-3.50323010711.393766376110.36283352073.32192128941.20054331720.8242980867
76320.03603311.110.03414.46-3.3784578951.49514876696.06223359263.27572216451.1865383530.734466853
76320.04003311.460.03814.81-3.26754099711.570697084192.55533065253.5263580971.26026563780.7331305815
76320.04563311.940.04375.29-3.1304071771.665818245987.88366809173.84051629511.34560680940.7259955189
76320.04973312.20.04785.55-3.04072963951.713797927882.06363187943.92264160391.36676530540.706782271
76320.05903312.850.05716.2-2.86295116251.824549292170.40219936644.01996558321.39127334120.6483815457
76320.06603313.290.06416.64-2.7473109151.893111963566.64364638534.27185773351.4520487990.6433520683
76320.07753313.80.07567.15-2.58229899581.967112356755.28699466114.17969679621.43023870710.5845729785
76320.09003314.410.08817.76-2.42928274612.048982334251.87149656434.5698788471.5194866940.5889019133
76320.10103314.890.09918.24-2.31162583772.109000343945.76095411374.53491055231.51180535950.5503532224
76320.11803315.620.11618.97-2.15330339032.193885676144.04882900055.11406904691.63199537830.5701303285
76320.13403316.220.13219.57-2.02419606742.258633205541.80592751995.52256302551.70884206870.5770703266
76320.15103316.570.14919.92-1.90313805722.294552921336.76899096065.4822565521.70151679580.5526468298
76320.16753317.130.165610.48-1.79818003712.349468678939.20998847456.49317409111.87075148530.6195776804
76320.18803317.950.186111.3-1.68147111542.424802725736.139836646.72562359841.90592464960.5951879291
76320.20503318.440.203111.79-1.59405681042.467251714534.5497439197.01705298991.94834332790.5951698889
76320.23003319.090.228112.44-1.47797114972.520917087334.36045180057.83761905552.05893509630.6300336861
76320.25503320.320.253113.67-1.37397061142.615203650731.26176218737.91235200972.06842508390.5788114126
76320.28003320.860.278114.21-1.27977451782.653945942128.30284311357.87102066972.06318774520.5539071548
76320.30503321.530.303114.88-1.1936924952.700018029428.11250000138.52089875012.14252182240.572641045
76320.33003322.120.328115.47-1.1144368392.738902664627.39474671628.98821639762.19591443030.5810094633
76320.35503322.120.353115.47-1.04100397612.738902664620.65093054247.29184357441.98675640490.4713538186
76320.38803322.930.386116.28-0.95165887572.789937360620.92618098998.07959848032.08934217830.4962898329
76320.43003323.730.428117.08-0.84839846592.837908188418.89426966198.08863684212.09046021770.4735735856
76320.46003324.30.458117.65-0.78066777812.870735783417.03971763477.80589464852.05487917240.44226032
76320.51973325.390.517818.74-0.65816621172.930660276818.5900311889.62591814922.26445926770.5136562513
76320.56973326.390.567819.74-0.5659860352.98264703417.798484707610.10597961682.31312728990.5119543879
76320.61973326.970.617820.32-0.48159049853.011605622716.07269493679.92971093182.2955313670.4886668766
76320.71403327.930.712121.28-0.3395369283.057767664514.512595377910.33441916862.33547999110.4856399985
76320.81403329.10.812122.45-0.20813179373.11129061423.111290614212.786122518710.38361009742.34022861090.4625216079
76320.91403330.290.912123.64-0.09200564583.16294019253.162940192511.811790769110.77353436052.37709260450.455733264
76321.01403331.481.012124.830.01202738023.21205259953.212052599512.20012704112.34774857812.51347374510.4972915255
76321.11403332.511.112125.860.10625011983.25269737333.252697373312.183269611413.54901413482.60631378710.5239371282
76321.28103334.191.279127.540.24615670563.31563949333.315639493311.608206009314.84805630652.69786896820.5391451092
76321.41403335.691.412129.040.34507795813.368674193.3686741911.220695595615.84474425062.76283785230.545617915
76321.56403337.171.562130.520.44603106993.41838220643.418382206410.797887959616.86738078162.82538162560.5526664738
76321.74803339.041.746132.390.55738472953.47784973323.477849733211.106215561819.39256299262.96488964170.5987206852
76321.94803340.951.946134.30.66582736993.53514535423.535145354210.201308874519.85276720072.9883434030.5787978776
76322.18103343.072.179136.420.77891194753.59511807433.59511807439.677913416421.08914112563.04875826940.5790538475
76322.33003344.422.328137.770.84505248433.63151513673.63151513679.609662304922.37225481213.10782156670.5923286951
76322.48103345.722.479139.070.90789559113.66535490913.66535490919.186390243322.77398005213.12561865850.5829019722
76322.68103346.992.679140.340.98548091723.69734353253.69734353258.933125717323.93273710913.17524727520.5932755853
76322.93103348.952.929142.31.07469520863.74478708613.74478708617.657606298222.42989460793.11039464983.11039464980.5302575557
76323.08103350.013.079143.361.12463734653.76953735713.76953735717.38526302422.73996337723.12412387783.12412387780.5244456498
76323.33103351.473.329144.821.20270199723.80265446843.80265446846.941702188123.10962075443.14024901373.14024901370.5156095661
76323.58103353.243.579146.591.27511137223.84138592583.84138592587.054608187125.24914816243.2287924193.2287924190.5419435107
76323.88103354.563.879147.911.3556031683.86932425093.86932425096.070657412823.54868716993.15907007243.15907007240.491519248
76324.13103356.124.129149.471.41805946553.90136642523.90136642526.103846782425.20339374923.2269786583.2269786580.5094682383
76324.48103357.854.479151.21.49942213343.9357395323.9357395325.871929473126.30095930283.26960541393.26960541390.5136906114
76324.83103359.84.829153.151.57466011493.97311810483.97311810485.619693673727.13806271963.30093727093.30093727090.5105938423
76325.18103361.55.179154.851.6446312964.00460218674.00460218675.494293497728.4554954543.34834130373.34834130370.5187875197
76325.68103363.985.679157.331.73679276954.04882404694.04882404695.269707661329.92719677923.39876765823.39876765820.5220163401
76326.03103365.656.0291591.79659774594.07753744394.07753744395.170652315931.17437987793.43959659973.43959659970.52837932
76326.53103367.926.529161.271.87626910844.11529032674.11529032674.895169335331.96105010733.46451797733.46451797730.5216427307
76327.03103370.127.029163.471.95005867494.15056735334.15056735334.848046812234.07740584793.52863457963.52863457960.5369057168
76328.08103374.518.079167.862.08928048024.21744675944.21744675944.460826446336.03946294213.58461453093.58461453090.5310855134
76329.08103378.699.079172.042.20597506884.27722152034.27722152034.243688633238.52887346933.65140792053.65140792050.534826117
76330.08103382.610.079175.952.31046397294.3300752294.3300752294.022976162740.54797904133.70248594060.5338772751
76331.08103386.1211.079179.472.40506045064.3753795924.102510670245.45212596613.81665959550.5719406816
76332.08103390.2412.079183.592.49147668644.42592389574.063636363649.085073.89355491520.5872122263
76334.08103396.1714.079189.522.64469142824.4944620643.790041666753.36037562923.97706844110.5960721138
76336.08103402.216.079195.552.7775202924.55964967073.732283884160.01176580034.09454063970.6280666227
76338.08103409.2318.0791102.582.8947565754.6306429823.813908730268.95203732344.23341115160.6721781763
76340.08103416.7220.0791110.072.99967947314.7011165273.474544570569.76572788534.24514288470.6338305432
76342.08103424.1922.0791117.543.09463145974.76677870123.666899503780.96184083294.39397794280.6888024573
76343.08003427.7723.0781121.123.13888411594.79678178973.765693666486.90505500294.46481620090.7175120129
76344.08103431.4824.0791124.833.18134424434.82695281172.897955884869.78016954634.24534986550.5590015985
76361.59403482.341.5921175.653.72791024545.16849337871.6276080867.69563802314.21502174690.3854007289
76362.62703489.3742.6251182.723.75244328165.20795492652.043042898787.08490786154.46688359520.4766030421
76364.87703494.0244.8751187.373.80388307525.23308527161.884759735884.57878162034.43768342690.4513998058
Log-Log
0.331.0697123865
0.571.3839260859
11.7208941066
1.342.1545791329
1.722.3359721901
2.122.6886626261
2.482.917612923
3.073.1156265225
3.393.3219212894
3.653.2757221645
4.033.526358097
4.463.8405162951
4.813.9226416039
5.294.0199655832
5.554.2718577335
6.24.1796967962
6.644.569878847
7.154.5349105523
7.765.1140690469
8.245.5225630255
8.975.482256552
9.576.4931740911
9.926.7256235984
10.487.0170529899
11.37.8376190555
11.797.9123520097
12.447.8710206697
13.678.5208987501
14.218.9882163976
14.887.2918435744
15.478.0795984803
15.478.0886368421
16.287.8058946485
17.089.6259181492
17.6510.1059796168
18.749.9297109318
19.7410.3344191686
20.3210.3836100974
21.2810.7735343605
22.4512.3477485781
23.6413.5490141348
24.8314.8480563065
25.8615.8447442506
27.5416.8673807816
29.0419.3925629926
30.5219.8527672007
32.3921.0891411256
34.322.3722548121
36.4222.7739800521
37.7723.9327371091
39.0722.4298946079
40.3422.7399633772
42.323.1096207544
43.3625.2491481624
44.8223.5486871699
46.5925.2033937492
47.9126.3009593028
49.4727.1380627196
51.228.455495454
53.1529.9271967792
54.8531.1743798779
57.3331.9610501073
5934.0774058479
61.2736.0394629421
63.4738.5288734693
67.8640.5479790413
72.0445.4521259661
75.9549.08507
79.4753.3603756292
83.5960.0117658003
89.5268.9520373234
95.5569.7657278853
102.5880.9618408329
110.0786.9050550029
117.5469.7801695463
121.1267.6956380231
124.8387.0849078615
175.6584.5787816203
182.72
187.37
TIME (hrs)
DP (psi) dpD/dlntD
analisis
-1.1086626245-6.2146081019-6.2146081019-6.2146081019
-0.5621189182-5.5467787269-5.5467787269-5.5467787269
0-5.08320598640.0673898147-5.0832059864
0.292669614-4.81589121830.3249244497-4.8158912183
0.5423242908-4.59521985520.5428439852-4.5952198552
0.7514160887-4.3351430490.7675954065-4.335143049
0.9082585602-4.12274403690.84842816-4.1227440369
1.1216775616-3.95806694440.989043905-3.9580669444
1.2208299214-3.76792266181.0707657898-3.7679226618
1.2947271676-3.64581996451.1364302628-3.6458199645
1.393766376-3.50323010711.2005433172-3.5032301071
1.495148766-3.3784578951.186538353-3.378457895
1.5706970841-3.26754099711.2602656378-3.2675409971
1.6658182459-3.1304071771.3456068094-3.130407177
1.7137979278-3.04072963951.3667653054-3.0407296395
1.8245492921-2.86295116251.3912733412-2.8629511625
1.8931119635-2.7473109151.452048799-2.747310915
1.9671123567-2.58229899581.4302387071-2.5822989958
2.0489823342-2.42928274611.519486694-2.4292827461
2.1090003439-2.31162583771.5118053595-2.3116258377
2.1938856761-2.15330339031.6319953783-2.1533033903
2.2586332055-2.02419606741.7088420687-2.0241960674
2.2945529213-1.90313805721.7015167958-1.9031380572
2.3494686789-1.79818003711.8707514853-1.7981800371
2.4248027257-1.68147111541.9059246496-1.6814711154
2.4672517145-1.59405681041.9483433279-1.5940568104
2.5209170873-1.47797114972.0589350963-1.4779711497
2.6152036507-1.37397061142.0684250839-1.3739706114
2.6539459421-1.27977451782.0631877452-1.2797745178
2.7000180294-1.1936924952.1425218224-1.193692495
2.7389026646-1.1144368392.1959144303-1.114436839
2.7389026646-1.04100397611.9867564049-1.0410039761
2.7899373606-0.95165887572.0893421783-0.9516588757
2.8379081884-0.84839846592.0904602177-0.8483984659
2.8707357834-0.78066777812.0548791724-0.7806677781
2.9306602768-0.65816621172.2644592677-0.6581662117
2.982647034-0.5659860352.3131272899-0.565986035
3.0116056227-0.48159049852.295531367-0.4815904985
3.0577676645-0.3395369282.3354799911-0.339536928
3.11129061423.11129061422.3402286109-0.2081317937
3.16294019253.16294019252.3770926045-0.0920056458
3.21205259953.21205259952.51347374510.0120273802
3.25269737333.25269737332.60631378710.1062501198
3.31563949333.31563949332.69786896820.2461567056
3.368674193.368674192.76283785230.3450779581
3.41838220643.41838220642.82538162560.4460310699
3.47784973323.47784973322.96488964170.5573847295
3.53514535423.53514535422.9883434030.6658273699
3.59511807433.59511807433.04875826940.7789119475
3.63151513673.63151513673.10782156670.8450524843
3.66535490913.66535490913.12561865850.9078955911
3.69734353253.69734353253.17524727520.9854809172
3.74478708613.74478708613.11039464983.1103946498
3.76953735713.76953735713.12412387783.1241238778
3.80265446843.80265446843.14024901373.1402490137
3.84138592583.84138592583.2287924193.228792419
3.86932425093.86932425093.15907007243.1590700724
3.90136642523.90136642523.2269786583.226978658
3.9357395323.9357395323.26960541393.2696054139
3.97311810483.97311810483.30093727093.3009372709
4.00460218674.00460218673.34834130373.3483413037
4.04882404694.04882404693.39876765823.3987676582
4.07753744394.07753744393.43959659973.4395965997
4.11529032674.11529032673.46451797733.4645179773
4.15056735334.15056735333.52863457963.5286345796
4.21744675944.21744675943.58461453093.5846145309
4.27722152034.27722152033.65140792053.6514079205
4.3300752294.3300752293.70248594062.3104639729
4.3753795922.40506045063.81665959552.4050604506
4.42592389572.49147668643.89355491522.4914766864
4.4944620642.64469142823.97706844112.6446914282
4.55964967072.7775202924.09454063972.777520292
4.6306429822.8947565754.23341115162.894756575
4.7011165272.99967947314.24514288472.9996794731
4.76677870123.09463145974.39397794283.0946314597
4.79678178973.13888411594.46481620093.1388841159
4.82695281173.18134424434.24534986553.1813442443
5.16849337873.72791024544.21502174693.7279102454
5.20795492653.75244328164.46688359523.7524432816
5.23308527163.80388307524.43768342693.8038830752
La pendiente en ambos casos es igual a nula diferencia entre las ordenadas de la rectas es de 0.7253 y partiendo de el podemos calcular nu 0.51 que comparado con el nu de las rectas 0.487es una buena aproximacion
Ec. Para la derivada
Ec. Para el ajuste de Delta P
delta
ln (t)
ln (Dp)
Fig xxxxx Field Case No 1 Based on Large Time Analisis
Sheet2
Sheet3
analisis
0.4510756194-5.7763531669-5.7763531669-5.7763531669
1.1939224685-4.9618451302-4.9618451302-4.9618451302
1.6544112781-4.60517018651.7690030883-4.6051701865
1.9699056546-4.3351430492.1291387884-4.335143049
2.2093727113-4.12893600652.34876279-4.1289360065
2.4096441653-3.95284500022.5383675131-3.9528450002
2.5672543911-3.81671282582.6497712744-3.8167128258
2.7087166456-3.68887945432.7602568062-3.6888794543
2.8225686545-3.57198570282.8167134535-3.5719857028
2.9247731846-3.47054745962.8887169389-3.4705474596
3.0101281538-3.37552963512.9635219484-3.3755296351
3.0887671395-3.29683736642.9961098082-3.2968373664
3.1595503588-3.21887582473.0605826349-3.2188758247
3.2232661732-3.1442322823.080163823-3.144232282
3.281662813-3.07694232883.1409954069-3.0769423288
3.3361253849-3.01186165563.1965045237-3.0118616556
3.3870984573-2.95651156053.1983664509-2.9565115605
3.4346321577-2.90042209363.2473753845-2.9004220936
3.5195728344-2.78062089393.2558152178-2.7806208939
3.5584859902-2.73336800913.2665852518-2.7333680091
3.5923685537-2.68677806583.3530909292-2.6867780658
3.6256733782-2.64366794223.3513010466-2.6436679422
3.6908774568-2.56394985713.4233071157-2.5639498571
3.7471483622-2.48771057713.412269314-2.4877105771
3.7723010623-2.45224586753.4091589993-2.4522458675
3.8297277627-2.36233509733.3660008856-2.3623350973
3.8573556041-2.32176791243.3967688938-2.3217679124
3.9054011291-2.23492644453.446831915-2.2349264445
3.9271086428-2.20727491323.4409136137-2.2072749132
3.9708577911-2.13622355573.5178283639-2.1362235557
4.0118683404-2.07068003613.5170277422-2.0706800361
4.05021850424.05021850423.5608028902-2.0024805006
4.08731994734.08731994733.61782187693.6178218769
4.1211487654.1211487653.60212403143.6021240314
4.15198434174.15198434173.65533406433.6553340643
4.17438726994.17438726993.62020392383.6202039238
4.22858403744.22858403743.66964171913.6696417191
4.25390913194.25390913193.75681960563.7568196056
4.30284813684.30284813683.78617065433.7861706543
4.32532399934.32532399933.80754078553.8075407855
4.36805447714.36805447713.86504515923.8650451592
4.38813295314.38813295313.84568886853.8456888685
4.4267609664.4267609663.91532990733.9153299073
4.46337618044.46337618043.95045552983.9504555298
4.49769632774.49769632773.98882399653.9888239965
4.54584471994.54584471994.01162325134.0116232513
4.57357631444.57357631444.0416349524.041634952
4.60426978074.60426978074.06158003044.0615800304
4.63744374654.63744374654.06732617314.0673261731
4.66889587694.66889587694.13725182114.1372518211
4.71303755694.71303755694.18295004294.1829500429
4.74101140894.74101140894.20921580734.2092158073
4.78038320354.78038320354.24547884024.2454788402
4.80500416794.80500416794.2582212114.258221211
4.83992605264.83992605264.28494500874.2849450087
4.87275158674.87275158674.30946029594.3094602959
4.90527477844.90527477844.33720140174.3372014017
4.93583990624.93583990624.37174743724.3717474372
4.97907582524.97907582524.41384728854.4138472885
5.00602468155.00602468154.44004290914.4400429091
5.04432793515.04432793514.45635579594.4563557959
5.07997477225.07997477224.48979049694.4897904969
5.10351828825.10351828824.50613471354.5061347135
5.14598170525.14598170524.55713223724.5571322372
5.16587109925.16587109924.60946980724.6094698072
5.20373192415.20373192414.62862500934.6286250093
5.23601634045.23601634044.6601828874.660182887
5.26883706125.26883706124.67671383124.6767138312
5.30006583715.30006583714.68617781524.6861778152
5.32952529375.32952529374.77099792554.7709979255
5.3573407075.3573407074.74140663184.7414066318
5.38137092175.38137092174.80115337014.8011533701
5.41507765725.41507765724.78551459110.3681093216
5.45116720065.45116720064.79844095580.4350239103
5.48492140715.48492140714.8605204870.4977403842
5.51636797085.51636797084.88518260920.5567545557
5.54580224925.54580224924.90669876410.6124792775
5.57352191755.57352191754.92789490460.6652619771
5.59968042615.59968042614.87188216490.7153977895
5.64788209275.64788209274.98119355280.8087055212
5.65711006655.65711006654.99832595520.8522854019
5.69130495315.69130495315.01183490760.8940451229
5.7309111425.7309111425.13959465370.9726710653
5.74945667815.74945667815.04921259981.009781075
5.78391748585.78391748585.06631122071.0801088171
5.81559214975.81559214975.08292431991.1458138902
5.83059132155.83059132155.09111972471.1771153502
5.85887556745.85887556745.10670646511.2369239045
5.89775808075.89775808075.1252323751.320421617
5.9211761945.9211761945.13473122181.3714598722
5.93977643795.93977643795.21655146461.412692835
5.97421665375.97421665375.15168447091.49047418
5.99982946345.99982946345.33205077621.5271426697
6.0200520046.0200520045.16885818131.5967578593
6.06650244396.06650244395.08689248791.6618785484
6.07292932016.07292932015.18524070841.722963007
6.0962073726.0962073724.96400852691.780546842
6.11798705986.11798705985.18989085591.8349785883
6.1381805156.1381805155.19059373131.8866150002
6.15695779896.15695779895.18605839411.9357443664
6.18268390086.18268390085.17864752942.0051220087
6.19845839116.19845839115.17111604332.0488792361
6.22033168746.22033168745.15628495662.1110613254
6.24011988766.24011988765.1388103742.1696249657
6.2580123562.22505589055.11391535992.2250558905
6.27938409142.29425045625.07816042822.2942504562
6.29371498372.34324707475.04886898212.3432470747
6.31088145062.40506947655.00479622542.4050694765
6.32602424172.46326583414.95743340872.4632658341
6.3395476872.51826082954.90703508482.5182608295
6.35146146722.57040368634.85270410812.5704036863
6.36454419512.63196797374.77887966862.6319679737
6.375757092.68996090524.70326577652.6899609052
6.38548103582.74477421034.62156674992.7447742103
6.39547860292.80735843864.5214019342.8073584386
6.40380595922.86573747694.42108104162.8657374769
6.41101334612.92241398954.39926094052.9224139895
6.41598036592.96455631444.31145812942.9645563144
6.4678695193.64029564373.64029564373.6402956437
6.4649776363.66891141312.99879927013.6689114131
6.46404298373.7259150894-0.62151784593.7259150894
6.4669220273.7843987033.35982843643.784398703
6.47285621083.84179794653.72744276383.8417979465
6.47601806153.89956775993.70066167743.8995677599
6.47849428113.95663492913.39044796923.9566349291
6.48074983464.01466984243.28267330034.0146698424
6.48322966814.07286553054.07286553054.0728655305
6.48539830324.13053344044.13053344044.1305334404
La pendiente en ambos casos es igual a nula diferencia entre las ordenadas de la rectas es de 0.5458 y partiendo de el podemos calcular nu 0.58 que comparadp con el nu de las rectas 0.535es una bastante buena aproximacion
Ec. Para la derivada
Ec. Para el ajuste de Delta P
delta
ln (t)
ln (Dp)
Fig xxxxx Field Case No 1 Based on Large Time Analisis
grafica log-log
1.575.8650035551
3.38.4076229504
5.2310.4726048949
7.1712.6589884607
9.1114.1508016252
11.1315.803900967
13.0316.7218032798
15.0117.9702378901
16.8219.3660580442
18.6320.007552118
20.2921.3399869619
21.9521.7619672154
23.5623.1268760578
25.1124.4469270186
26.6224.4924878179
28.1125.7227389423
29.5825.9407532803
31.0226.2216459724
33.7728.5909698699
35.1128.5398411627
36.3230.6706789658
37.5530.3340035916
40.0830.2398018665
42.428.9624709159
43.4829.8674391021
46.0531.4007543033
47.3431.2154640206
49.6733.7111405869
50.7633.6841615159
53.0335.1914406682
55.2537.2563305088
57.4136.6760528587
59.5838.6804407106
61.6337.3451826188
63.5639.2378451707
6542.8120500269
68.6244.0872512895
70.3845.0395406713
73.9147.7054267215
75.5946.7909060309
78.8950.1656187876
80.4951.9590303303
83.6653.9913579907
86.7855.2364604868
89.8156.9193271387
94.2458.0659846565
96.8958.4006005479
99.9162.6304649998
103.2865.558969997
106.5867.3037400056
111.3969.7891700067
114.5570.684139392
119.1572.5985543219
122.1274.4003239424
126.4676.4931658638
130.6879.1818762332
13582.5865875062
139.1984.7785793675
145.3486.1729045498
149.3189.1027766157
155.1490.5710579687
160.7795.3097617479
164.6100.4308877869
171.74102.3732050913
175.19105.655403387
181.95107.4165031808
187.92108.4379169445
194.19118.0369753175
200.35114.5952817358
206.34121.6506448539
212.16119.7629761877
217.32121.3211250016
224.77129.0913750022
233.03132.3146249971
241.03135.1923750021
248.73138.088516664
256.16130.5664333343
263.36145.648116664
270.34148.1649166653
283.69150.1800499971
286.32170.6465833319
296.28155.8996607165
308.25158.5882500024
314.02161.2448988072
325.03162.5717958373
335.49165.125611331
340.56168.2132256633
350.33169.8186701857
364.22184.2975303798
372.85172.722190912
379.85206.8617666436
393.16175.7140892677
403.36161.8860168537
411.6178.6164391018
431.17143.1665341166
433.95179.4489660605
444.17179.5751406684
453.95178.7625509379
463.21177.4426626501
471.99176.1112756598
484.29173.5186274711
491.99170.5128011537
502.87166.3202854639
512.92160.4785723706
522.18155.8461000401
533.46149.1266918288
541.16142.2282851533
550.53135.2378506361
558.93128.0862811248
566.54118.970988419
573.33110.3068222893
580.88101.653172525
587.4391.9644357193
593.1783.1861644711
599.1381.3906938628
604.1474.5491119814
608.51-13.1031247326
611.5420.0614340909
644.110.5371285402
642.2528.7842521269
641.6541.5726610045
643.540.4740762836
647.3329.6792446801
649.3826.6469127682
650.99-48.9876814959
652.46-49.3228559557
654.08
655.5
Tiempo (hrs)
DP (psi) dpD/dlntD
Hoja1
92640.00583858.83
92640.00893860.40.00311.57-5.77635316690.4510756194
92640.01283862.130.0073.3-4.96184513021.1939224685
92640.01583864.060.015.23-4.60517018651.6544112781586.50035581345.86500355511.76900308831.1214155937
92640.018938660.01317.17-4.3351430491.9699056546641.80327882578.40762295042.12913878841.1726112901
92640.02193867.940.01619.11-4.12893600652.2093727113650.472353399110.47260489492.348762791.1495724363
92640.0253869.960.019211.13-3.95284500022.4096441653659.322315825112.65898846072.53836751311.1373754232
92640.02783871.860.02213.03-3.81671282582.5672543911643.21825577214.15080162522.64977127441.0860170088
92640.03083873.840.02515.01-3.68887945432.7087166456632.156038827115.8039009672.76025680621.0528914702
92640.03393875.650.028116.82-3.57198570282.8225686545595.081967340316.72180327982.81671345350.9941619072
92640.03693877.460.031118.63-3.47054745962.9247731846577.821153883617.97023789012.88871693890.9645860381
92640.043879.120.034220.29-3.37552963513.0101281538566.259007230119.36605804422.96352194840.954463186
92640.04283880.780.03721.95-3.29683736643.0887671395540.744651888320.0075521182.99610980820.9115057913
92640.04583882.390.0423.56-3.21887582473.1595503588533.499673938821.33998696193.06058263490.9057719424
92640.04893883.940.043125.11-3.1442322823.2232661732504.918032894821.76196721543.0801638230.866665361
92640.05193885.450.046126.62-3.07694232883.281662813501.667593369623.12687605783.14099540690.868778214
92640.0553886.940.049228.11-3.01186165563.3361253849496.888760601424.44692701863.19650452370.8696879053
92640.05783888.410.05229.58-2.95651156053.3870984573471.009381149324.49248781793.19836645090.8280083779
92640.06083889.850.05531.02-2.90042209363.4346321577467.686162522625.72273894233.24737538450.8292307847
92640.06783892.60.06233.77-2.78062089393.5195728344418.3992464225.94075328033.25581521780.7681597063
92640.07083893.940.06535.11-2.73336800913.5584859902403.409938023226.22164597243.26658525180.7468426651
92640.07393895.150.068136.32-2.68677806583.5923685537419.838030369728.59096986993.35309092920.787196307
92640.07693896.380.071137.55-2.64366794223.6256733782401.40423575628.53984116273.35130104660.7600490323
92640.08283898.910.07740.08-2.56394985713.6908774568398.320506024730.67067896583.42330711570.7652365011
92640.08893901.230.083142.4-2.48771057713.7471483622365.030127440830.33400359163.4122693140.715424613
92640.09193902.310.086143.48-2.45224586753.7723010623351.217210990730.23980186653.40915899930.6954876234
92640.13904.880.094246.05-2.36233509733.8297277627307.457228383928.96247091593.36600088560.6289353076
92640.10393906.170.098147.34-2.32176791243.8573556041304.459114181529.86743910213.39676889380.63091337350.54581.72598862110.5793780954
92640.11283908.50.10749.67-2.23492644453.9054011291293.46499347931.40075430333.4468319150.6321875237-0.7657178734
92640.11583909.590.1150.76-2.20727491323.9271086428283.776945640631.21546402063.44091361370.61496186010.46485.4005
92640.12393911.860.118153.03-2.13622355573.9708577911285.445728915633.71114058693.51782836390.6356994265
92640.13193914.080.126155.25-2.07068003614.0118683404267.122613144433.68416151593.51702774220.6096680817
92640.14083916.240.13557.41-2.00248050064.05021850424.0502185042260.677338292935.19144066823.56080289020.6129845091
92640.14893918.410.143159.58-1.94421159244.08731994734.0873199473260.351715643137.25633050883.61782187693.61782187690.6253160542
92640.15693920.460.151161.63-1.88981340974.1211487654.121148765242.727020900236.67605285873.60212403143.60212403140.5951006467
92640.16393922.390.158163.56-1.84452753484.15198434174.1519843417244.6580690138.68044071063.65533406433.65533406430.6085657758
92640.17193923.830.166165-1.79516526234.17438726994.1743872699224.835536534237.34518261883.62020392383.62020392380.5745412711
92640.18783927.450.18268.62-1.70374859194.22858403744.2285840374215.592555882439.23784517073.66964171913.66964171910.5718135408
92640.19583929.210.1970.38-1.66073120684.25390913194.2539091319225.32657908642.81205002693.75681960563.75681960560.6082985227
92640.21193932.740.206173.91-1.57939379114.30284813684.3028481368213.911942214544.08725128953.78617065433.78617065430.596499138
92640.21893934.420.213175.59-1.54599373984.32532399934.3253239993211.354015342945.03954067133.80754078553.80754078550.5958399348
92640.23583937.720.2378.89-1.46967597014.36805447714.3680544771207.414898792947.70542672153.86504515923.86504515920.6047081597
92640.24393939.320.238180.49-1.43506452554.38813295314.3881329531196.517874970446.79090603093.84568886853.84568886850.5813257054
92640.25893942.490.253183.66-1.37397061144.4267609664.426760966198.204736417450.16561878763.91532990733.91532990730.599636849
92640.27583945.610.2786.78-1.309333324.46337618044.4633761804192.440853072351.95903033033.95045552983.95045552980.5987442997
92640.29193948.640.286189.81-1.25141387894.49769632774.4976963277188.714987735753.99135799073.98882399653.98882399650.6011731209
92640.31583953.070.3194.24-1.17118298154.54584471994.5458447199178.182130603955.23646048684.01162325134.01162325130.5861254296
92640.32893955.720.323196.89-1.12979340624.57357631444.5735763144176.16628641256.91932713874.0416349524.0416349520.5874633826
92640.34893958.740.343199.91-1.06973332914.60426978074.6042697807169.239244117658.06598465654.06158003044.06158003040.5811829112
92640.36893962.110.3631103.28-1.01307700064.63744374654.6374437465160.838888866758.40060054794.06732617314.06732617310.5654589519
92640.38893965.410.3831106.58-0.95945922734.66889587694.6688958769163.483333330262.63046499984.13725182114.13725182110.5876380653
92640.41893970.220.4131111.39-0.88406558464.71303755694.7130375569158.699999990865.5589699974.18295004294.18295004290.5885534608
92640.43893973.380.4331114.55-0.83678663084.74101140894.7410114089155.400000014767.30374000564.20921580734.20921580730.5875490179
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92640.48893980.950.4831122.12-0.72753160744.80500416794.8050041679146.313681209670.6841393924.2582212114.2582212110.5788088715
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92640.553989.510.5442130.68-0.60843845264.87275158674.8727515867136.71503848274.40032394244.30946029594.30946029590.5693321391
92640.58193993.830.5761135-0.55147402224.90527477844.9052747784132.777583515176.49316586384.33720140174.33720140170.5666160434
92640.61393998.020.6081139.19-0.49741593694.93583990624.9358399062130.21193263279.18187623324.37174743724.37174743720.5688761853
92640.66194004.170.6561145.34-0.42144206264.97907582524.9790758252125.875000008182.58658750624.41384728854.41384728850.5682302704
92640.69394008.140.6881149.31-0.37382110285.00602468155.0060246815123.206771352484.77857936754.44004290914.44004290910.5678024202
92640.74194013.970.7361155.14-0.30638929995.04432793515.0443279351117.066844926586.17290454984.45635579594.45635579590.5554525238
92640.794019.60.7842160.77-0.24309118915.07997477225.0799747722113.622515450589.10277661574.48979049694.48979049690.5542251453
92640.82694023.430.8211164.6-0.19711037435.10351828825.1035182882110.304540212690.57105796874.50613471354.50613471350.5502494409
92640.89194030.570.8861171.74-0.12092546795.14598170525.1459817052107.560954460695.30976174794.55713223724.55713223720.554965423
92640.92394034.020.9181175.19-0.08544896185.16587109925.1658710992109.3899224348100.43088778694.60946980724.60946980720.5732683817
92640.98694040.780.9811181.95-0.01908088785.20373192415.2037319241104.345331863102.37320509134.62862500934.62862500930.5626447106
92641.044046.751.0342187.920.0336281815.23601634045.2360163404102.161480746105.6554033874.6601828874.6601828870.5622360759
92641.10894053.021.1031194.190.0981243985.26883706125.268837061297.3769406038107.41650318084.67671383124.67671383120.553151569
92641.17284059.181.167200.350.15443635335.30006583715.300065837192.9202373131108.43791694454.68617781524.68617781520.5412424105
92641.23784065.171.232206.340.20863886515.32952529375.329525293795.809233212118.03697531754.77099792554.77099792550.5720508642
92641.30084070.991.295212.160.25851069525.3573407075.35734070788.4905650471114.59528173584.74140663184.74140663180.5401361319
92641.35084076.151.345217.320.29639401315.38137092175.381370921790.4465760995121.65064485394.80115337014.80115337010.559776573
92641.45084083.61.445224.770.36810932165.41507765725.415077657282.8809523786119.76297618774.78551459110.5328245593
92641.55084091.861.545233.030.43502391035.45116720065.451167200678.5250000011121.32112500164.79844095580.5206244904
92641.65084099.861.645241.030.49774038425.48492140715.484921407178.4750000011129.09137500224.8605204870.5355821889
92641.75084107.561.745248.730.55675455575.51636797085.516367970875.8249999985132.31462499714.88518260920.5319608612
92641.85084114.991.845256.160.61247927755.54580224925.545802249273.2750000011135.19237500214.90669876410.5277653615
92641.95084122.191.945263.360.66526197715.57352191755.573521917570.996666665138.0885166644.92789490460.5243336751
92642.05084129.172.045270.340.71539778955.59968042615.599680426163.8466666672130.56643333434.87188216490.4829711968
92642.25084142.522.245283.690.80870552125.64788209275.647882092764.8766666656145.6481166644.98119355280.513405889
92642.35084145.152.345286.320.85228540195.65711006655.657110066563.1833333327148.16491666534.99832595520.5174801504
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92642.95084183.862.945325.031.08010881715.78391748585.783917485853.8500000007158.58825000245.06631122070.4879188075
92643.15084194.323.145335.491.14581389025.81559214975.815592149751.2702380944161.24489880725.08292431990.4806250523
92643.25084199.393.245340.561.17711535025.83059132155.830591321550.099166668162.57179583735.09111972470.4773660907
92643.45084209.163.445350.331.23692390455.85887556745.858875567447.9319626504165.1256113315.10670646510.4713430518
92643.75084223.053.745364.221.3204216175.89775808075.897758080744.9167491758168.21322566335.1252323750.4618451092
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92644.94284270.434.937411.61.59675785936.0200520046.02005200435.5912678281175.71408926775.16885818130.4269049788
92645.27542905.2692431.171.66187854846.06650244396.066502443930.7230731143161.88601685375.08689248790.3754575153
92645.60694292.785.6011433.951.7229630076.07292932016.072929320131.8895286822178.61643910185.18524070840.4116060355
92645.938943035.9331444.171.7805468426.0962073726.09620737224.1301400814143.16653411664.96400852690.3223237367
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92646.60284322.046.597463.211.88661500026.1381805156.13818051527.2207277048179.57514066845.19059373130.3876754402
92646.9354330.826.9292471.991.93574436646.15695779896.156957798925.7984400707178.76255093795.18605839410.3787422423
92647.43284343.127.427484.292.00512200876.18268390086.182683900823.891566265177.44266265015.17864752940.3663975359
92647.7654350.827.7592491.992.04887923616.19845839116.198458391122.6970919244176.11127565985.17111604330.3579570228
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92649.25984381.019.254522.182.22505589056.25801235617.9727993802166.32028546395.11391535990.318511405
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92650.42084399.9910.415541.162.34324707476.293714983714.963619783155.84610004015.04886898210.287985254
92651.0854409.3611.0792550.532.40506947656.310881450613.4600595556149.12669182885.00479622540.2708784114
92651.74894417.7611.7431558.932.46326583416.326024241712.1116472783142.22828515334.95743340870.2544652911
92652.41284425.3712.407566.542.51826082956.33954768710.9001249807135.23785063614.90703508480.2387083889
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ln (t)
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Hoja2
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ANLISIS DE CURVAS DE DECLINACIN DE YACIMIENTOS FRACTURADOSCON GEOMETRA FRACTAL
SPE 104009
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SITUACIN Los yacimientos carbonatados contienen ms del 60% del aceite remanente del mundo.Las formaciones geolgicas son heterogneas, con patrones de flujo irregulares y trampas de circulacin. Sin embargo, la mayora de los estudios considera que la geometra Euclideana es aplicable a ambas 1- y 2-.
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1- YACIMIENTO FRACTURADOCURVAS DE DECLINACIN PARA MODELOS OP & MGN, Y LTA, YACIMIENTO LIMITADO
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INFLUENCIA DE reD EN EL MODELO OP, STA & LTA, YACIMIENTO CERRADOYACIMIENTOS DE DOBLE POROSIDAD
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C O N C L U S I O N E SLa produccin de aceite de medios fracturados desordenados muestra comportamientos anmalos que no pueden explicarse mediante la ecuacin de difusin convencional.Las expresiones durante el flujo dominado por la frontera muestran que el comportamiento semilog tpico podra estar representado tambin por el caso fractal ms general. Ambos datos de flujo el transitorio y el dominado por la frontera deberan usarse para caracterizar totalmente un YNF con geometra fractal.
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Comportamiento del Transitorio de Presin y la Curva de Declinacin en Yacimientos Carbonatados Vugulares Naturalmente Fracturados.SPE 77689
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El efecto de los vgulos en la permeabilidad est relacionado con su conectividad. Determinacin de k & en zonas de vgulos a partir de mediciones en ncleos parecen ser pesimistas.Los registros de agujero descubierto se pueden usar para identificar zonas de vgulos; sin embargo, los vgulos no siempre se identifican con registros convencionales debido a la limitada resolucin vertical de las herramientas.M o t i v a c i n
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Proponer un modelo que incluya porosidad vugular alta, y as modelar YNF, permitiendo la posibilidad de flujo a travs de los vgulos. Desarrollar un mtodo para identificar yacimientos vugulares mediante pruebas de pozo y curvas de declinacin. Implementar el nuevo modelo en los simuladores numricos. O b j e t i v o s
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For fractures, triple porositydual permeability model: Model Formulation
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Para los bloques de matriz:FORMULACIN DEL MODELO (cont.)
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For vugs:Model Formulation
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Con j = fracturas o vgulos y kvf = kv si pv > pf y kvf = kf de otro modo. ij= factor de forma de flujo interporoso entre el medio i y el medio j.FORMULACIN DEL MODELO (cont.)
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Relaciones de almacenamiento para fracturas y vgulos:Gasto adimensional:FORMULACIN DEL MODELO (cont.)
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Dimensionless Time, tDDimensionless Pressure, pwDWarren & Root, lmf = 1e-05, wf = 0.01lvf = 0.1,lmv = 1e-06lvf = 0.01,lmv = 1e-06lvf = 0.001,lmv = 1e-06lvf = 1e-05,lmv = 1e-06lmv = 0.001,lvf = 0.1lmv = 0.1,lvf = 0.1Periodo Transitorio, Vgulos sin interconectar, Gasto constante
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Dimensionless Time, tDConnected vugs, wv =1e-03, wf =1e-03, lvf =1e-05, lmv=1e-08Comportamiento Transitorio, Vgulos conectados y no conectados, Gasto ConstanteDimensionless Pressure, pDDimensionless Pressure Derivative, pDlmf =1e-07, k=0.1lmf =0.001, k=0.1lmf =1e-07, k=0.5lmf =0.001, k=0.5lmf =0.001, k=1.0
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Prueba de campo (Transitorio de presin)Field Build-Up
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Ajuste con Curva Tipo con el Grupo Chow, Modelo para vgulos sin conexin.Dimensionless Time, tDpD / (2*pD)Match Point*tm=0.01hourstDm=9000CD= 4500, s= 2wv= 0.2, wf = 0.001, lmf = 1e-07, lvf = 1e-05, lmv = 1e-08wv= 0.001, wf = 1e-04, lmf = 1e-06, lvf = 1e-04, lmv = 1e-07wv= 0.001, wf = 1e-04, lmf = 1e-04, lvf = 1e-04, lmv = 1e-07wv= 0.1, wf = 0.01, lmf = 1e-07, lvf = 1e-04, lmv = 1e-07wv= 0.2, wf = 0.01, lmf = 1e-06, lvf = 1e-06, lmv = 1e-08wv= 0.2, wf = 0.01, lmf = 1e-09, lvf = 1e-06, lmv = 1e-08wv= 0.1, wf = 0.01, lmf = 1e-09, lvf = 1e-06, lmv = 1e-08
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Curva de Declinacin, Vgulos sin conectar (Aislados) Dimensionless Time, tDDimensionless Flow Rate, q wDWarren & Root, lmf = 1e-09, wf = 0.001lvf = 0.1lvf = 0.01lvf = 0.001lvf = 1e-05reD= 2000, wv= 0.1, wf = 0.001, lmf = 1e-09, lmv = 1e-06
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Curvas de declinacin para vgulos conectados y sin conectar, Presin de fondo constantewf =1e-03, wv =1e-01, lmf =1e-03, lvf =1e-05, lmv =1e-06Connected Vugs, k= 0.5, reD= 2000Unconnected Vugs, k= 1.0, reD= 2000Connected Vugs, k= 0.5, reD= 500Unconnected Vugs, k= 1.0, reD= 500Warren & Root, reD= 500Warren & Root, reD= 2000Dimensionless Time, tDDimensionless Flow Rate, qD
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C o n c l u s i o n e sSe formula un modelo nuevo para YVNF, que permite interaccin entre la matriz, los vgulos, y las fracturas.Se presentan soluciones nuevas, para sistemas 3 - 1 & 2-permeabilidades, durante los periodos de flujo dominados por el transitorio y la frontera. Estas expresiones se extienden a soluciones de 2 & 3 .La presencia de vgulos afecta el comportamiento de las pruebas de presin y las curvas de declinacin. El modelo propuesto es importante para caracterizar YVNF y obtener ajustes de historia de buena calidad para estos sistemas.
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C O N C L U S I O N Yacimientos Naturalmente Fracturados
Modelo Comercial
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