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Programa de Adiestramiento 2005
CONTENIDO CAPÍTULO 1 EL SISTEMA DE PRODUCCIÓN 1.1 El Sistema de producción y sus componentes 1.2 Proceso de producción • Recorrido de los fluidos en el sistema
1.3 Capacidad de producción del sistema. • • • •
Curvas de oferta y demanda de energía en el fondo del pozo. Balance de energía y capacidad de producción Optimización del sistema Métodos de producción: Flujo natural y Levantamiento artificial
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Programa de Adiestramiento 2005
• Cálculo del factor de fricción • Definiciones básicas: factor factor Hold-Up, densidad y viscosidad bifásica, bifásica, etc. • Patrones de flujo
3.3 Descripción de correlaciones de flujo multifásico en tuberías • • • • • •
Correlación de Hagedorn & Brown Correlación de Duns & Ros Correlación de Orkiszewski Correlación de Beggs and Brill Ejemplos numéricos Ejemplos con curvas de gradiente ya graficadas
3.4 Construcción de Curva de Demanda de energía • Rangos característicos de la curva de demanda
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Programa de Adiestramiento 2005
CAPÍTULO I
El Sistema de Producción 1.1 El Sistema de producción y sus componentes El sistema de producción está formado por el yacimiento, la completación, el pozo y las facilidades de superficie. El yacimiento es una o varias unidades de flujo del subsuelo creadas e interconectadas por la naturaleza, mientras que la completación (perforaciones ó cañoneo), el pozo y las facilidades de superficie es infraestructura construida por el hombre para la extracción, control, medición, tratamiento y transporte de los fluidos hidrocarburos extraídos de los yacimientos.
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Programa de Adiestramiento 2005
• Recorrido de los fluidos en el sistema Transporte en el yacimiento: El movimiento de los fluidos comienza en el yacimiento a una distancia re del pozo donde la presión es Pws, viaja a través del medio poroso hasta llegar a la cara de la arena o radio del hoyo, rw, donde la presión es Pwfs. En este módulo el fluido pierde energía en la medida que el medio sea de baja capacidad de flujo (Ko.h), presente restricciones en la cercanías del hoyo (daño, S ) y el fluido ofrezca resistencia al flujo (µ o). Mientras mas grande sea el hoyo mayor será el área de comunicación entre el yacimiento y el pozo mejorando el índice de productividad productividad del pozo. La perforación de pozos horizontales aumenta sustancialmente el índice de productividad del pozo.
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Programa de Adiestramiento 2005
Donde:
Py = Pc = Pp = Pl =
Pws – Pwfs Pwfs- Pwf Pwf-Pwh Pwh – Psep
= Caída de presión en el yacimiento, (IPR). = Caída de presión en la completación, (Jones, Blount & Glaze). = Caída de presión en el pozo. (FMT vertical). = Caída de presión en la línea de flujo. (FMT horizontal)
1.3 Capacidad de producción del sistema. La capacidad de producción del sistema está representada a través de la tasa de producción del pozo, y esta es consecuenci consecuenciaa de un perfecto perfecto balanc balancee entre entre la capacidad capacidad de aporte de energía del yacimiento y la demanda de energía de la instalación
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Programa de Adiestramiento 2005
• Balance de energía y capacidad de producción
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Programa de Adiestramiento 2005
el fondo del pozo. La técnica puede usarse para optimizar pozos que producen por flujo natural o por Levantamiento Artificial.
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Programa de Adiestramiento 2005
CAPÍTULO II
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Programa de Adiestramiento 2005
Estados de flujo:
Existen tres estados de flujo dependiendo de cómo es la variación de la presión con tiempo: 1. Flujo No Continuo: dP/dt ≠ 0
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Ecuaciones de flujo para estado
A continuación se presenta la ecuación de Darcy para flujo radial que permite estimar la tasa de producción de petróleo será de
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Programa de Adiestramiento 2005
2.2 Flujo de fluidos en la completación (continuación)
ecuación de Jones, Blount & Glaze quedaría: Ecuación de Sustituyendo a y b la ecuación Jones, Blount & Glaze para cañoneo 1 1 rc 2, 30. 10 - 14 . . Bo 2 . o .( - ) o. o.( Ln ) convencional rp rc rp 2 (continuac…)
Pc =
2
.q +
3
.q
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Programa de Adiestramiento 2005
2.2 Flujo de fluidos en la completación (continuación) Ejercicio propuesto para calcular Pc en una completación con cañoneo convencional
Dada la siguiente información de un pozo cañoneado convencionalmente: K = 5 md Pb = 2830 1pc γg = 0,65 Ø hoyo = 8,75 hp = 15 pie µo = 0,54 cp
Pws = 3500 1pc re = 1500 pies rw = 0,36 pies RGP = 600 pcn/bl Ø casing = 5-1/2" °API = 35
Ty = 190°F h = 25 pies Densidad de tiro = 2 tpp Bo = 1,33 by/bn Pwh = 200 1pc Ø tubería = 2-3/8" OD
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Programa de Adiestramiento 2005
2.2 Flujo de fluidos en la completación (continuación) 1) Tipo de flujo a través del empaque: Se asume que el flujo a través del empaque es lineal y no radial, de allí que se utiliza la ecuación de Darcy para flujo lineal.
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Programa de Adiestramiento 2005
2.2 Flujo de fluidos en la completación (continuación) La ecuación de Jones, Blount & Glaze establece que Ecuación de Jones, Blount & Glaze para Pc Pwfs - Pwf = a q 2 + bq completaciones con empaque Donde: con grava a =
b
9,08 . 10 -13 . .Bo. o . L A 2 o. Bo. L
y 1, 47 . 107
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Programa de Adiestramiento 2005
2.2 Flujo de fluidos en la completación (continuación) Ejercicio propuesto para calcular Pc
Dada la siguiente información de un pozo con empaque con grava: Pwh = 280 1pc Dw = 8000 pies h = 25' pies Ø hoyo = 12-1/4" Ø "liner" = 5-1/2" OD Ø tubería = 4" γg = 0,65 T 190°F
Pws = 3500 1pc Ko = 170 md re = 1500 pies Ø revestidor = 9-5/8" rw = 0,51 pies Tamaño de grava 40-60 (45000 md) °API=35 RGP 600 pcn/bl
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Programa de Adiestramiento 2005
Curva de oferta de
Para obtener la curva de oferta de energía en el fondo del pozo, Pwf vs ql, se le debe sustraer a la IPR para cada tasa de producción, la caída de
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Programa de Adiestramiento 2005
CAPÍTULO III
Flujo Multifásico en Tuberías
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Programa de Adiestramiento 2005
Cálculo de Una vez conocida para una determinada tasa de producción las pérdidas de la presión energía en la línea de flujo, ∆Pl, se puede obtener la presión requerida en el requerida cabezal, Pwh, de la siguiente manera: manera:
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Programa de Adiestramiento 2005
Correlaciones de flujo Entre las correlaciones para flujo multifásico que cubren amplio rango de tasa de producción y todos los tamaños típicos de multifásico mas utilizadas en tuberías tuberías se encuentran, para flujo horizontal: Beegs & Brill,
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Programa de Adiestramiento 2005
Consideraciones teóricas del flujo multifásico en tuberías (continuación…)
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Programa de Adiestramiento 2005
y F3 ' = F3 −
F4 ND
Donde F1, F2, F3 y F4 se obtienen a partir de la siguiente figura, en función de NL.
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Programa de Adiestramiento 2005
NRe b =
1488 ⋅ ρ L ⋅ d ⋅ VsL µL
f 1 ⋅ Vsg ⋅ ND f 2 = se obtiene a partir de la siguiente figura, en función de VsL
2
3
.
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Programa de Adiestramiento 2005
− (Vm − Vs ) + (Vm − Vs )2 + 4 ⋅ Vs ⋅ VsL HL = con Vs = 2 ⋅ Vs
S 1 ⎞ 4
⎛ ρ 1.938 ⋅ ⎜⎜ L ⎟⎟ ⎝ σ L ⎠
(1 + F5 ) ⋅ (NGV 0.982 + F6 ' ) y S= con F6 ' = 0.0029 ⋅ ND + F6 2 (1 + F7 ⋅ NLV )
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Programa de Adiestramiento 2005
ii.
Patrón de Neblina,
en este patrón la fase continua es el gas. Para este patrón, la
ecuación del gradiente de presión total es:
∆P ∆P ⎛ ∆P ⎞ = ( ∆H)E + ( ∆H)f ⎜ ⎟ 144 ⋅ (1 − EK ) ⎝ ∆H ⎠ T
El gradiente de presión por elevación se expresa por la ecuación correspondiente. Duns & Ros supone que no existe deslizamiento en este tipo de patrón, por la cual la
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Programa de Adiestramiento 2005
N we
⎛ ρ g ⋅ Vsg 2 ⎞ ⎟ = 454 ⋅ ξ ⋅ ⎜⎜ σL ⎟ ⎝ ⎠ El valor de ξ puede ser muy pequeño, pero
ξ no puede ser menor que 10-3. d
Luego el procedimiento para calcular f es el siguiente: viii.1
Calcular los números adimensionales de Weber y viscosidad líquida.
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Programa de Adiestramiento 2005
EK = Vsg ⋅
ρ L ⋅ VSL + ρ g ⋅ Vsg 144 ⋅ g c ⋅ P
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Programa de Adiestramiento 2005
⎛ ∆P ⎞ ⎛ ∆P ⎞ ⎛ ∆P ⎞ +B⋅⎜ ⎟ ⎜ ⎟ = A ⋅⎜ ⎟ ⎝ ∆H ⎠ f ⎝ ∆H ⎠ f TAPÓN ⎝ ∆H ⎠ f NEBLINA
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Programa de Adiestramiento 2005
V sg
q L RGL
q o Rs B g
86400 A
t
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Programa de Adiestramiento 2005
NRe =
1488 ⋅ ρ L ⋅ d ⋅ VsL HL ⋅ µ L
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Programa de Adiestramiento 2005
V b, se halla mediante un procedimiento de ensayo y error, ya que V b es función de C1 y C2, además C2 es función de V b.
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Programa de Adiestramiento 2005
S=
0.2997 = 0.3641 2 4 − 0.0523 + 3.182 ⋅ 0.2997 − 0.8725 ⋅ (0.2997 ) + 0.01853 ⋅ (0.2997 )
f tp = f ns ⋅ e S = 0.04296 ⋅ e 0.3641 = 0.06183 2 0.06186 ⋅ 24.584 ⋅ (3.02)2 ⎛ dP ⎞ f tp ⋅ ρ ns ⋅ Vm = = 8.999 ⋅ 10 −3 lpc/pie ⎜ ⎟ = ⎝ dH ⎠ f 144 ⋅ 2 ⋅ g c ⋅ d 144 ⋅ 2 ⋅ 32.174 ⋅ (1.995 ) 12
ρ
V
V
31 7024 3 02 1 74
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Programa de Adiestramiento 2005
•
Ejemplos con curvas de gradiente ya graficadas
Uso de las curvas de gradiente de presión
Cuando no se dispone de simuladores de flujo multifásico en tuberías (Pipesim, Wellflo, Prosper, Naps, etc.) se deben utilizar curvas de gradiente de presión publicadas en la literatura y que representen aceptablemente el flujo multifásico en tuberías, por ejemplo las presentadas por K. Brown en la serie “The Technology of Artificial Lift Methods”. En las siguientes figuras se ilustra el cálculo de la Pwh y Pwf a partir de la Psep. FLUJO HORIZONTAL
Psep Pwh
FLUJO VERTICAL Pwh
Pwf
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Programa de Adiestramiento 2005
Ejercicio propuesto para calcular Pl y Pc
Dada la siguiente información de un pozo que produce por flujo natural Psep = 100 1pcm RAP = 0 RGP = 1000 pcn/bn API = 35 Tsup = 90°F Øtub = 2-7/8" OD Prof.= 7000 pies
Línea de flujo: ØL = 4" L = 6000 pies (sin reductor) γg = 0.65 Tf = 195°F Twh = 195°F Pws = 2200 1pc ql= 600. b/d
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Programa de Adiestramiento 2005
3.4 Construcción de la Curva de Demanda de energía Si se evaluan las Pwh y las Pwf requeridas requeridas para distintas tasas de producción y se grafican v.s. la tasa de producción q, se obtienen las curvas de demanda de energía en el cabezal y fondo del pozo respectivamente. La siguiente figura muestra las curvas de demanda de energía mencionadas, observe para un dado caudal la representación de las pérdidas de presión en la línea, ∆Pl, y en el pozo, ∆Pp.
Ilustración Pwf vs q, Demanda en el fondo del pozo
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Programa de Adiestramiento 2005
Rango de tasas A continuación se presenta rangos óptimos de tasas dados por Brown según tamaño para tuberías de uso común en los pozos petroleros. Los valores de tubería de corresponden a RGL de aproximadamente 2000 pcn/bn: producción RANGO ÓPTIMO Tubería Tasa mínima - Tasa máxima (O.D.) (b/d) - (b/d) 2 3/8” 2 7/8” 3 ½”
200 350 500
-
2500 3000 4000
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Programa de Adiestramiento 2005
CAPÍTULO IV
Capacidad de Producción del Sistema
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Programa de Adiestramiento 2005
Ejercicio propuesto
Determine la capacidad de producción del siguiente pozo capaz de producir por flujo natural:
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Programa de Adiestramiento 2005
En conjunto estas razones están orientadas hacia una explotación eficiente de los yacimientos. Definitivamente estos dispositivos constituyen el medio más efectivo y
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Programa de Adiestramiento 2005
4.1 Capacidad de producción del pozo en flujo natural (continuación)
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Programa de Adiestramiento 2005
4.1 Capacidad de producción del pozo en flujo natural (continuación) Otras correlaciones
Existen otras correlaciones para estimar el comportamiento de
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Programa de Adiestramiento 2005
A continuación se muestra un ejemplo de una curva de Rendimiento de LAG obtenida con el simulador.
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AN A NEXOS An A n álisis Nod lisis Nod al y Flujo Flujo Mul Mul tifásic tifási c o en Tuberia Tu berias s
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(Pws constan constante te en el el límite límite exteri exterior) or) Fluj Flujoo cont contín ínuo uo de un un líqui líquido do (Pws
Pws
Presión Pws Pwfs
P t P Pws t q
cte. Flujo transitorio 0
Flujo permanente
0.00708 Ko.h. Pws Pwfs
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Flujo Flujo semi-co semi-contín ntínuo uo de un un líqui líquido do (Límite (Límite exterior exterior cerrado, cerrado, Pws conocida) conocida)
Pws1
Presión Pws
Pws2 Pws3
P t P t
cte. Flujo transitorio cte. Flujo semi-permanente
Pws1 Pws2 Pws3
Pwfs1
0 00708 Ko h Pws Pwfs
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Curva urvass IPR pa para ra flujo tra transitorio nsitorio •
Ecua cuación ción para para flujo flujo tra transito nsitorio rio • Pozos ozos de petróle petróleo o
k o h p ws
qo
162 .6 µ o Bo log
p wf
k t 2
φ µ o ct r w
3 .23
0 .87 S
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IPR’s pa para ra flu flujo jo tra trans nsito itorio rio •
El tiemp tiempo o requ reque erido rido para para alcanz lcanza ar el esta estado do de flu flujo jo semisemi-con contin tinuo uo,, puede ser ser calcul calcula ado por la ecua ecuación ción t stab ,puede
948 φ µ c r
2
t stab: hr : cps
: fracc. C : lpc-1
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Curvas IPR’s transitorias
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Dife ifere rencia ncia entre h y h p
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EXTENSIÓN DEL TRABAJO DE VOGEL, PARA POZOS CON DAÑO/ESTIMULADOS EFICIENCIA EFICIENCIA DE FLUJO FLUJ O = 1.
EFICIENCIA EFICIENCIA DE FLUJO FLUJ O ( EF ) EF = Jreal / Jideal EF = J / J´ EF<1 POZO CON DAÑO (S>0)
q = J´ (Pws - Pwfs) wfs) q = qb + (qmax-qb). (qmax-qb).[1. [1.-- 0.2 0.2 (Pwfs/ (Pwfs/Pb) Pb) - 0.8 0.8 (Pwfs/ (Pwfs/Pb) Pb)2] q b = J ´ (Pw s - Pb ) (qmax (qmax - qb) = (J´.P (J´.Pb) b) / 1.8 1.8 EFICIENCIA EFICIENCIA DE FLUJO FLUJ O < 1.
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