Los mtodos numricos de la explotacin petroleraRodolfo Camacho VelzquezPemex Exploracin y ProduccinCIMAT, GuanajuatoJunio, 2009

Problemas de modelos de simulacin comerciales

Propuestas de mejora de estos simuladores (Comportamiento Fractal, Yacimientos Naturalmente Fracturados Vugulares)

ConclusinCONTENIDO

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

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.

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.

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

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

MOTIVACINMODELADO DE SISTEMAS FRACTALES (ACUA & YORTSOS, 1991)

MOTIVACINMODELADO DE SISTEMAS FRACTALES (ACUA & YORTSOS, 1991, ACUA et al., 1995)

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.

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

NUEVOS MODELOSYACIMIENTO CON APORTE DE LA MATRIZ ROCOSA PARA UN MEDIO FRACTAL DE DOBLE POROSIDAD (CHANG Y YORTSOS)

NUEVOS MODELOSECUACION DE BARKER

YACIMIENTO SIN APORTE DE LA MATRIZ ROCOSA

NUEVOS MODELOSGENERALIZACION DE LA ECUACION OP (METZLER et al.), ECUACION MGN

YACIMIENTO SIN APORTE DE LA MATRIZ ROCOSA

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

92640.46893977.980.4631119.15-0.76981226554.78038320354.7803832035150.700000011869.78917000674.24547884024.24547884020.5857253043

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

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92642.75084172.852.745314.021.0097810755.74945667815.749456678156.7940476199155.89966071655.04921259980.4964641128

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

92643.94694231.683.9411372.851.37145987225.9211761945.92117619443.0891553591169.81867018575.13473122180.4554610975

92644.11284238.684.107379.851.4126928355.93977643795.939776437944.8740030143184.29753037985.21655146460.4851850214

92644.4454251.994.4392393.161.490474185.97421665375.974216653738.9084048729172.7221909125.15168447090.4393178119

92644.61084262.194.605403.361.52714266975.99982946345.999829463444.9211219639206.86176664365.33205077620.512846506

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

92646.27084312.786.265453.951.83497858836.11798705986.117987059828.6430911509179.44896606055.18989085590.3953055756

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

92648.26284361.78.257502.872.11106132546.22033168746.220331687421.0147302254173.51862747115.15628495660.3450566299

92648.76084371.758.755512.922.16962496576.24011988766.240119887619.4760481044170.51280115375.1388103740.3324354698

92649.25984381.019.254522.182.22505589056.25801235617.9727993802166.32028546395.11391535990.318511405

92649.92284392.299.917533.462.29425045626.279384091416.1821692418160.47857237065.07816042820.300825877

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

92653.07694432.1613.0711573.332.57040368636.35146146729.7991967872128.08628112484.85270410810.2234076032

92653.90694439.7113.9011580.882.63196797376.36454419518.5583866326118.9709884194.77887966860.2048116451

92654.73694446.2614.7311587.432.68996090526.375757097.4880234531110.30682228934.70326577650.1877786669

92655.5669445215.5611593.172.74477421036.38548103586.532518429101.6531725254.62156674990.1713727473

92656.57194457.9616.5661599.132.80735843866.39547860295.551363067991.96443571934.5214019340.1534966296

92657.56784462.9717.562604.142.86573747696.40380595924.73671361383.18616447114.42108104160.1376935221

92658.59194467.3418.5861608.512.92241398956.41101334614.379116321581.39069386284.39926094050.1337540778

92659.39194470.3719.3861611.542.96455631446.41598036593.845493006974.54911198144.31145812940.1219039016

92678.10894502.9438.1031644.113.64029564376.467869519-0.3438860547-13.1031247326-0.0203429922

92679.2154501.0839.2092642.253.66891141316.4649776360.511651196420.06143409092.99879927010.0312361761

92681.5154500.4841.5092641.653.72591508946.46404298370.01293998780.5371285402-0.62151784590.0008371052

92684.0154502.3344.0092643.53.7843987036.4669220270.654050792328.78425212693.35982843640.0447307725

92686.6154506.1646.6092647.333.84179794656.47285621080.891941097641.57266100453.72744276380.0642217432

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92702.21694514.3362.2111655.54.13053344046.4853983032-0.7928304749-49.3228559557-0.0752446315

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ANLISIS DE CURVAS DE DECLINACIN DE YACIMIENTOS FRACTURADOSCON GEOMETRA FRACTAL

SPE 104009

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-.

1- YACIMIENTO FRACTURADOCURVAS DE DECLINACIN PARA MODELOS OP & MGN, Y LTA, YACIMIENTO LIMITADO

INFLUENCIA DE reD EN EL MODELO OP, STA & LTA, YACIMIENTO CERRADOYACIMIENTOS DE DOBLE POROSIDAD

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.

Comportamiento del Transitorio de Presin y la Curva de Declinacin en Yacimientos Carbonatados Vugulares Naturalmente Fracturados.SPE 77689

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

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

For fractures, triple porositydual permeability model: Model Formulation

Para los bloques de matriz:FORMULACIN DEL MODELO (cont.)

For vugs:Model Formulation

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.)

Relaciones de almacenamiento para fracturas y vgulos:Gasto adimensional:FORMULACIN DEL MODELO (cont.)

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

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

Prueba de campo (Transitorio de presin)Field Build-Up

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

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

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

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.

C O N C L U S I O N Yacimientos Naturalmente Fracturados

Modelo Comercial

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