PROPIEDADESDE LA ROCA(CALIDAD DE ROCA)

RELACIN ENTRE Kr, Pc y Fluidos

RELACIN ENTRE POROSIDAD Y K

Ley de Dupuit for CheimerRelacin Kozeny-CarmanEcuacin de Poiseuille Ecuacin de Winland Ecuacin de Pittman

Efecto Klinkenberg

Fuente: Material Profesores Victor Casas (UCV), Yaraixa Prez (UCV) y Jorge Mendoza (USB).Prof: Yaraixa Prez. Curso 3-2009.

Relacin entre permeabilidad relativa presin capilar y distribucin de fluidos en un yacimientoProf: Yaraixa Prez. Curso 3-2009.

Radio del poro, tamaoFrecuenciaDistribucin del tamao del poro en la zona libre de aguaRadio del poro, tamaoFrecuenciaDistribucin del tamao del poro en la zona con Sw irreducibleRadio del poro, tamaoFrecuenciaDistribucin del tamao del poro en la zona de transicinStanding, 1975)Prof: Yaraixa Prez. Curso 3-2009.Nota importante:http://www.arcfluids.com/undersaturated.htm#6

R35 tamao del puerto (port size)H. D. Winland de Amoco us 322 muestras para desarrollar una relacin emprica entre porosidad permeabilidad y radio de garganta.Encontr que el sistema poral efectivo que domina el flujo a travs de la roca corresponde a una saturacin de Hg de 35%. El radio de garganta correspondiente a esta saturacin se denomina r35 o tamao del puerto.El sistema poral saturado con fluido que no humedece ms all del 35%, no contribuye al flujo, solo contribuye al almacenaje.El r35 puede ser usado para delinear acumulaciones de hidrocarburo comercial en trampas estratigrficas.Prof: Yaraixa Prez. Curso 3-2009.

Caracterizacin de la calidad de roca en base al r35De acuerdo a la ecuacin de Winland existe una relacin entre el tamao del puerto (r35) y la calidad de roca dada por k/ = constantePara un par (k , ) medidos, se puede encontrar cual es el tamao del puerto que domina el flujo para esa rocaDonde:k en mD (aire sin corregir) en %r35 en mProf: Yaraixa Prez. Curso 3-2009.

r35Mismo r35Petrofacie caracterstica de la rocaMegaMacroMesoMicroAbrahamProf: Yaraixa Prez. Curso 3-2009.

F.U.#2 tiene un r35 tres veces ms grande que F.U.#1F.U.#2 alcanza r35 a menor profundidad que F.U.#1, donde el flujo ser el ms eficienteF.U.#2 tiene mejor calidad de roca que F.U.#1F.U.#2 tiene mayor probabilidad de tener menor corte de agua que F.U.#1Con esto se puede construir estoSi no hay datos de Hg( aprox)Prof: Yaraixa Prez. Curso 3-2009.

Pitmann en 1992 extendi el trabajo de Winland al desarrollar un conjunto de ecuaciones empricas que relaciona k, y rgarganta para saturaciones de Hg entre 10% y 75%Ecuaciones de PitmannLog(r10 ) = 0.459 + 0.500 Log(k) - 0.385 Log()Log(r15 ) = 0.333 + 0.509 Log(k) - 0.344 Log()Log(r20 ) = 0.218 + 0.519 Log(k) - 0.303 Log()Log(r25 ) = 0.204 + 0.531 Log(k) - 0.350 Log()Log(r30 ) = 0.215 + 0.547 Log(k) - 0.420 Log()Log(r35 ) = 0.255 + 0.565 Log(k) - 0.523 Log()Log(r40 ) = 0.360 + 0.582 Log(k) - 0.680 Log()Log(r45 ) = 0.609 + 0.608 Log(k) - 0.974 Log()Log(r50 ) = 0.778 + 0.626 Log(k) - 1.205 Log()Log(r55 ) = 0.948 + 0.632 Log(k) - 1.426 Log()Log(r60 ) = 1.096 + 0.648 Log(k) - 1.666 Log()Log(r65 ) = 1.372 + 0.643 Log(k) - 1.979 Log()Log(r70 ) = 1.664 + 0.627 Log(k) - 2.314 Log()Log(r75 ) = 1.880 + 0.609 Log(k) - 2.626 Log()Prof: Yaraixa Prez. Curso 3-2009.

Las ecuaciones de Pitmann permiten construir las curvas de presin capilar a partir de los datos de (k, ) y viceversak = 1200 mD - = 25 %k = 800 mD - = 19 %k = 350 mD - = 17 %Datos InicialesProf: Yaraixa Prez. Curso 3-2009.

Grfico1

17.503348935321.017950662930.4441629592

19.411821522823.444105157834.3683766918

20.841657149525.326423412137.6071076737

22.757810782827.722870904841.3592082459

24.430687129529.847056994544.771181154

26.700322627232.685679358349.1973336809

29.746244083436.372177481154.5598151316

33.641569078840.948926467360.74060367

40.085648147648.571216707271.2721040373

50.354866822660.473483811587.0130482627

65.617812876778.3459250948111.2210614909

91.9686995594107.8404620669147.2440953997

143.4669924309164.290948201213.2766770639

252.4053843747282.3841909284348.8483345261

Sat Hg

Pc (cm Hg)

Curva Capilar (Pitmann)

calidad roca

Log(r35)=0.255+0.565Log(K)-0.523

Log(r45)=0.609+0.608Log(K)-0.974

Set 1Set 2Set 3

r35Porlog kklog kklog kk

16.421.478695828730.10896512651.339698987321.8624579561.050075205911.2221276892

13.541.960937959991.39826672731.821941118566.36530864411.532317337234.0657015437

962.2430315229174.99737043732.1040346815127.0675573711.814410900265.2245212705

82.4431800911277.44703697562.3041832497201.45741161822.0145594684103.4092690618

102.5984273817396.66819653142.4594305403288.02523543092.1698067589147.8450399417

122.7252736541531.21906623522.5862768127385.72413406382.2966530314197.9944567074

142.8325206493680.01837697382.693523808493.76898586252.4039000266253.4545118161

162.9254222223842.21354608672.7864253809611.5407209752.4968015996313.9074330876

183.00736721711017.10834402092.8683703758738.53379929882.5787465944379.0937238271

203.08066951291204.11928727832.9416726715874.32454690812.6520488902448.7959097275

223.14697950521402.74750594983.00798266381018.55072875562.7183588825522.828053418

243.20751578531612.55963804783.0685189441170.89767583182.7788951626601.0286334532

263.26320376481833.17431978453.12420692341331.08847560442.834583142683.255509009

283.31476278062064.2523161123.17576593921498.87680569262.8861421578769.3822413647

303.36276307592305.48911387373.22376623451674.04155567122.9341424532859.2953332444

323.40766435352556.60923592553.26866751211856.382698492.9790437308952.892109592

343.44984262052817.36179137813.31084577912045.71805945463.02122199781050.0790590699

353.47001007112951.27766489693.33101322982142.95588022133.04138944841099.9918018669

calidad roca

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Porosidad (%)

K (mD)

Calidad de Roca

Pitmann

Set 1Set 2Set 3

K mDPor %K mDPor %K mDPor %

Pitmann a diferencia de Winland, propone que los puntos de inflexin de las hiprbolas obtenidas en grficos de la relacin Saturacin de Hg / Presin Capilar en funcin de la Saturacin de Hg, proporcionan el radio de garganta que domina el flujo r40r45 = 18.5 mr45 = 15.1 mr45 = 10.1 mr40 determina la petrofacie caracterstica de la unidad de flujoProf: Yaraixa Prez. Curso 3-2009.

Grfico2

0.57131923940.47578377930.3284701903

0.7727250110.6398196860.4364477303

0.95961659170.78968907980.5318143627

1.09852394150.90178250610.6044603139

1.22796382441.0051242240.6700739008

1.31084558371.070805340.7114206682

1.34470758351.09974169190.733140314

1.33763083091.09892990810.7408553304

1.24732921411.02941625490.7015367467

1.09224794880.90948952390.6320891073

0.91438585610.76583434210.5394661694

0.70676219530.60274222450.4414438475

0.48791710770.42607338240.3282121654

0.29714104630.26559560490.2149931434

Set 1

Set 2

Set 3

Sat Hg

Sat Hg / Pc

Hiperbola de Pitmann

calidad roca

Log(r35)=0.255+0.565Log(K)-0.523

Log(r45)=0.609+0.608Log(K)-0.974

Set 1Set 2Set 3

r35Porlog kklog kklog kk

16.421.478695828730.10896512651.339698987321.8624579561.050075205911.2221276892

13.541.960937959991.39826672731.821941118566.36530864411.532317337234.0657015437

962.2430315229174.99737043732.1040346815127.0675573711.814410900265.2245212705

82.4431800911277.44703697562.3041832497201.45741161822.0145594684103.4092690618

102.5984273817396.66819653142.4594305403288.02523543092.1698067589147.8450399417

122.7252736541531.21906623522.5862768127385.72413406382.2966530314197.9944567074

142.8325206493680.01837697382.693523808493.76898586252.4039000266253.4545118161

162.9254222223842.21354608672.7864253809611.5407209752.4968015996313.9074330876

183.00736721711017.10834402092.8683703758738.53379929882.5787465944379.0937238271

203.08066951291204.11928727832.9416726715874.32454690812.6520488902448.7959097275

223.14697950521402.74750594983.00798266381018.55072875562.7183588825522.828053418

243.20751578531612.55963804783.0685189441170.89767583182.7788951626601.0286334532

263.26320376481833.17431978453.12420692341331.08847560442.834583142683.255509009

283.31476278062064.2523161123.17576593921498.87680569262.8861421578769.3822413647

303.36276307592305.48911387373.22376623451674.04155567122.9341424532859.2953332444

323.40766435352556.60923592553.26866751211856.382698492.9790437308952.892109592

343.44984262052817.36179137813.31084577912045.71805945463.02122199781050.0790590699

353.47001007112951.27766489693.33101322982142.95588022133.04138944841099.9918018669

calidad roca

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Porosidad (%)

K (mD)

Calidad de Roca

Pitmann

Set 1Set 2Set 3

K mDPor %K mDPor %K mDPor %

18.5 m15.1 m10.1 mU.F 1aU.F. 1bU.F 1cPetrofaciesEcuacin de Pitmann r40Todos son mega poros(una U.F.)U.F 2Prof: Yaraixa Prez. Curso 3-2009.

Grfico1

81.364171257257.397870577228.7607557273

182.8740573578129.007415843864.642655499

293.6935880471207.1843945022103.8153454278

411.0276100373289.9569822941145.2907896291

533.4567192038376.3238690238188.5672545429

660.1055137203465.6675076808233.3353015343

790.3746037429557.5650622653279.3830571873

923.8253837307651.7071211079326.5554824151

1060.1217013241747.8565475262374.7337534682

1198.9969682996845.825278444423.8236362549

1340.2341271914945.4601919631473.7484049061

1483.65271486281046.6339814375524.4442689829

1629.1001173151149.2389862296575.8572822106

1776.44543520461253.1828641763627.9411740504

1925.57504746871358.3854619747680.6557815215

2076.3893198021464.7764931969733.9658857081

2228.80010870011572.293777532787.8403294833

2305.57931040891626.4572086173814.9803818082

Porosidad (%)

K (mD)

Calidad de Flujo

calidad roca

Log(r35)=0.255+0.565Log(K)-0.523

Log(r45)=0.609+0.608Log(K)-0.974

Set 1Set 2Set 3

r35Porlog kklog kklog kk

16.421.478695828730.10896512651.339698987321.8624579561.050075205911.2221276892

13.541.960937959991.39826672731.821941118566.36530864411.532317337234.0657015437

962.2430315229174.99737043732.1040346815127.0675573711.814410900265.2245212705

82.4431800911277.44703697562.3041832497201.45741161822.0145594684103.4092690618

102.5984273817396.66819653142.4594305403288.02523543092.1698067589147.8450399417

122.7252736541531.21906623522.5862768127385.72413406382.2966530314197.9944567074

142.8325206493680.01837697382.693523808493.76898586252.4039000266253.4545118161

162.9254222223842.21354608672.7864253809611.5407209752.4968015996313.9074330876

183.00736721711017.10834402092.8683703758738.53379929882.5787465944379.0937238271

203.08066951291204.11928727832.9416726715874.32454690812.6520488902448.7959097275

223.14697950521402.74750594983.00798266381018.55072875562.7183588825522.828053418

243.20751578531612.55963804783.0685189441170.89767583182.7788951626601.0286334532

263.26320376481833.17431978453.12420692341331.08847560442.834583142683.255509009

283.31476278062064.2523161123.17576593921498.87680569262.8861421578769.3822413647

303.36276307592305.48911387373.22376623451674.04155567122.9341424532859.2953332444

323.40766435352556.60923592553.26866751211856.382698492.9790437308952.892109592

343.44984262052817.36179137813.31084577912045.71805945463.02122199781050.0790590699

353.47001007112951.27766489693.33101322982142.95588022133.04138944841099.9918018669

Log(r40)=0.36+0.582Log(K)-0.68

Porlog kklog kklog kk

18.521.910433205281.36417125721.758895780757.39787057721.458800293528.7607557273

15.142.2621521005182.87405735782.1106146759129.00741584381.810519188864.642655499

10.162.4678944651293.69358804712.3163570405207.18439450222.0162615533103.8153454278

82.6138709958411.02761003732.4623335712289.95698229412.1622380841145.2907896291

102.7270991897533.45671920382.5755617651376.32386902382.275466278188.5672545429

122.8196133603660.10551372032.6680759357465.66750768082.3679804486233.3353015343

142.8978329771790.37460374292.7462955525557.56506226532.4462000654279.3830571873

162.9655898911923.82538373072.8140524665651.70712110792.5139569794326.5554824151

183.02535572491060.12170132412.8738183003747.85654752622.5737228131374.7337534682

203.0788180851198.99696829962.9272806604845.8252784442.6271851733423.8236362549

223.12718067241340.23412719142.9756432479945.46019196312.6755477607473.7484049061

243.17133225561483.65271486283.0197948311046.63398143752.7196993439524.4442689829

263.2119477751629.1001173153.06041035041149.23898622962.7603148632575.8572822106

283.24955187241776.44543520463.09801444781253.18286417632.7979189606627.9411740504

303.28456044951925.57504746873.13302302491358.38546197472.8329275378680.6557815215

323.31730878642076.3893198023.16577136181464.77649319692.8656758746733.9658857081

343.34807112032228.80010870013.19653369571572.2937775322.8964382085787.8403294833

353.36278006632305.57931040893.21124264171626.45720861732.9111471545814.9803818082

calidad roca

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Porosidad (%)

K (mD)

Calidad de Flujo R45

Pitmann

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Porosidad (%)

K (mD)

Calidad de Flujo r40

Drenaje 1

Set 1Set 2Set 3

K mDPor %K mDPor %K mDPor %

Prof: Yaraixa Prez. Curso 3-2009.

Prof: Yaraixa Prez. Curso 3-2009.

RELACION

PERMEABILIDAD POROSIDAD

LEY DE

Dupuit-Forcheimer

y

dividiendo q entre A :

INCRUSTAR Draw

_982351159.unknown

_982351419.unknown

_982351496.unknown

_982351259.unknown

RELACION DE CARMAN-KOZENYKozeny (1927) y Carman (1939), derivaron una de las ms populares y fundamentales correlaciones que expresan permeabilidad como funcin de la porosidad y del rea superficial especfica.Prof: Yaraixa Prez. Curso 3-2009.

Supongamos que todos los capilares tienen el mismo radio rAplicando la ecuacin de Poiseuille:Donde n es igual al nmero de capilares presentesLa ecuacin de Darcy es:Donde A es el rea total del tubo incluyendo la matrizes la ley que permite determinar el flujo laminar estacionario V de un lquido incompresible y uniformemente viscoso (tambin denominado fluido newtoniano) a travs de un tubo cilndrico de seccin circular constante. Prof: Yaraixa Prez. Curso 3-2009.

Comparando:ySe tiene:Por definicin la porosidad ser:Prof: Yaraixa Prez. Curso 3-2009.

Despejando A se tiene:y sustituyendo en:Se tiene:k en cm2 en fraccin1 cm2 = 1.013 x 108 DarciesProf: Yaraixa Prez. Curso 3-2009.

Sea el rea superficial especfica de los poros:Sea el rea superficial especfica de los poros con respecto a los granos:Prof: Yaraixa Prez. Curso 3-2009.

Combinando las ecuacionesProf: Yaraixa Prez. Curso 3-2009.

Podemos escribir la ecuacincomo:Prof: Yaraixa Prez. Curso 3-2009.

Finalmente sustituyendo de:se tiene:Relacin Carman-KozenyProf: Yaraixa Prez. Curso 3-2009.

La relacin anterior no toma en cuenta la tortuosidad:FluidoTrayectoria real L0Prof: Yaraixa Prez. Curso 3-2009.

Tomando en cuenta la tortuosidad, la relacin de Carman-Kozeny se puede escribir como:2=constante de KozenyDe acuerdo a Carman 2 se puede aproximar a 5 se mide en el lab (capilaridad)yProf: Yaraixa Prez. Curso 3-2009.

Otras relaciones para rocas clsticasSlichter: dgr = dimetro grano en mm k en darcies en fraccinWyllie & Rose: awr depende de densidad del hidrocarburo Siw saturacin de agua irreducible y Siw en fraccinTimur:mDarcies y Siw en %mDarciesSiw Sb (de modelo D-W)Prof: Yaraixa Prez. Curso 3-2009.

Calidad de la roca en trminos de eficiencia del flujoRelacin de KozenyCualquier familia de rocas con el mismo valor k/tendr la misma eficiencia de flujoProf: Yaraixa Prez. Curso 3-2009.

Prof: Yaraixa Prez. Curso 3-2009.Una unidad de flujo es una subdivisin del yacimiento definida en base a tipos de poros similares. El desempeo o afluencia de una unidad de flujo puede ser inferido de las propiedades de un sistema poral, tales como la geometra y tipo de poros

Grfico1

5050.50.050.005

1001010.10.01

150151.50.150.015

2002020.20.02

250252.50.250.025

3003030.30.03

350353.50.350.035

4004040.40.04

450454.50.450.045

5005050.50.05

550555.50.550.055

6006060.60.06

650656.50.650.065

7007070.70.07

750757.50.750.075

8008080.80.08

850858.50.850.085

9009090.90.09

950959.50.950.095

10001001010.1

105010510.51.050.105

1100110111.10.11

115011511.51.150.115

1200120121.20.12

125012512.51.250.125

1300130131.30.13

135013513.51.350.135

1400140141.40.14

145014514.51.450.145

1500150151.50.15

5000

500

50

5

0.5

Porosidad

Permeabilidad (mD)

Calidad de Flujo

Hoja1

k/phor

50005005050.5

Poros

000000

0.015050.50.050.005

0.021001010.10.01

0.03150151.50.150.015

0.042002020.20.02

0.05250252.50.250.025

0.063003030.30.03

0.07350353.50.350.035

0.084004040.40.04

0.09450454.50.450.045

0.15005050.50.05

0.11550555.50.550.055

0.126006060.60.06

0.13650656.50.650.065

0.147007070.70.07

0.15750757.50.750.075

0.168008080.80.08

0.17850858.50.850.085

0.189009090.90.09

0.19950959.50.950.095

0.210001001010.1

0.21105010510.51.050.105

0.221100110111.10.11

0.23115011511.51.150.115

0.241200120121.20.12

0.25125012512.51.250.125

0.261300130131.30.13

0.27135013513.51.350.135

0.281400140141.40.14

0.29145014514.51.450.145

0.31500150151.50.15

Hoja1

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

5000

500

50

5

0.5

Porosidad

Permeabilidad (mD)

Calidad de Flujo

Hoja2

Hoja3

*Figure 7 (Arps, 1964) shows a generalized relationship between water saturation, relative permeability, and capillary pressure. The diagram shows the difference between critical water saturation (CWS), defined as the water saturation below which the formation will only flow oil or gas, and irreducible water saturation (IWS), defined as the water saturation below which little additional water can be displaced from the formation by a higher capillary injection pressure. It shows that the water saturation at which we start to produce water free oil is not determined by irreducible water saturation, but by the critical water saturation. When Krw is zero (CWS), only oil or gas will be produced regardless of how much mobile water is in the formation. http://www.arcfluids.com/undersaturated.htm#6*Figure 7 (Arps, 1964) shows a generalized relationship between water saturation, relative permeability, and capillary pressure. The diagram shows the difference between critical water saturation (CWS), defined as the water saturation below which the formation will only flow oil or gas, and irreducible water saturation (IWS), defined as the water saturation below which little additional water can be displaced from the formation by a higher capillary injection pressure. It shows that the water saturation at which we start to produce water free oil is not determined by irreducible water saturation, but by the critical water saturation. When Krw is zero (CWS), only oil or gas will be produced regardless of how much mobile water is in the formation. http://www.arcfluids.com/undersaturated.htm#6*H. D. Winland (Amoco Production Company), who was interested in sealing potential, developed an empirical relationship among porosity, air permeability, and the pore aperture corresponding to a mercury saturation of 35% (r35) for a mixed suite of sandstones and carbonates. Winland ran regressions for other percentiles (30, 40, and 50), but the best correlation (highest R) was the 35th percentile. No explanation was given for why the 35th percentile gave the best correlation. His data set included 82 samples (56 sandstone and 26 carbonate) with low permeabilities that were corrected for gas slippage and 240 other samples with uncorrected permeabilities. The Winland equation was used and published by Kolodzie (1980):Log r35 = 0.732 + 0.588 Log Kair - 0.864 Log f(6)where r35 is the pore aperture radius corresponding to the 35th percentile, Kair is uncorrected air permeability (md), and q is porosity (%).

Winland also showed, through several field examples, that r35 could be used to delineate commercial hydrocarbon accumulations of stratigraphic traps. One of Winland's examples was the Terry Sandstone at Spindle Field, Colorado. **********The KozenyCarman equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. It is named after Josef Kozeny and Philip C. Carman. The equation is only valid for laminar flow.The equation is given as[1][2]: where p is the pressure drop, L is the total height of the bed, is the superficial or "empty-tower" velocity, is the viscosity of the fluid, is the porosity of the bed, s is the sphericity of the particles in the packed bed, and Dp is the diameter of the related spherical particle[3]. This equation holds for flow through packed beds with particle Reynolds numbers up to approximately 1.0, after which point frequent shifting of flow channels in the bed causes considerable kinetic energy losses.This equation can be expressed as "flow is proportional to the pressure drop and inversely proportional to the fluid viscosity", which is known as Darcy's law[1].************Una unidad de flujo es una subdivisin del yacimiento definida en base a tipos de poros similares. El desempeo o afluencia de una unidad de flujo puede ser inferido de las propiedades de un sistema poral, tales como la geometra y tipo de poros