Nodal Analysis William Vargas October 2000

Introduccin al Anlisis Nodal

8/11/20111Procedimiento de solucin(1) Asume varios Gastos y construye la curva IPR con la ecuacin de afluencia del yacimiento, se calcula pwf.(2) Con los mismos Gastos de 1, se calculan las cadas de presin en la lnea del pozo hasta obtener la presin de cabeza del pozo.(3) Usando el mismo procedimiento y los mismos Gastos del paso 2 y con la correspondiente Pwh determina Pwf(4) Se grafica la curva IPR y la pwf de cada Gasto

Cadas de presin en el sistemaP1 = Pr - Pwfs= Cada en el yacimientoP2 = Pwfs - Pwf= cada en la completacinP3 = Pwf - Pwh = cada en el tubingP4 = Pwh - Psep = cada en la lnea de flujoPrPePwfsPwfP1 = (Pr - Pwfs)P2 = (Pwfs - Pwf)P3 = Pwf - PwhP4 = (Pwh - Psep)PsepGasLiquidoTanquePT = Pr - Psep = cada de presin totalAdapted from Mach et al, SPE 8025, 1979.Pwh8/11/20113Fluid flows from the reservoir to the stock tank because of the pressure gradients within the system. The total pressure drop from the reservoir to the separator is the sum of the individual pressure drops through four different segments: in the reservoir, across the completion, up the wellbore, and through the flowline.It is relatively straightforward to calculate the pressure drop for each of these segments, if we know the flow rate and either the upstream or downstream pressure, and the physical properties of the segment. But we do not know the flow rate - that is what we are trying to find. How do we calculate the flow rate, knowing the reservoir and separator pressures? This is the central question of Nodal Analysis.Given the reservoir pressure and the separator pressure, along with the physical properties of each segment, what is the flow rate at which the well will produce?

Se selecciona la posicin del nodo solucin Nodo en fondo de pozoNode location 1. separator3. Pwh6. Pwf8. Pr14236WV8/11/2011Anlisis nodal con nodo en fondoP1 = Pr - Pwfs= cada en el yacimientoP2 = Pwfs - Pwf= cada en la completacinP3 = Pwf - Pwh = cada en el tubingP4 = Pwh - Psep = cada en la lnea de flujoPrPePwfsPwfP1 = (Pr - Pwfs)P2 = (Pwfs - Pwf)P3 = Pwf - PwhP4 = (Pwh - Psep)PsepGasLiquidoTanquePT = Pr - Psep = cada de presin totalAdapted from Mach et al, SPE 8025, 1979.Pwh8/11/20116How do we determine the right flow rate? We know the separator pressure and the average reservoir pressure.We start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. This pressure is valid only for the assumed flow rate.Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Then we can calculate the bottomhole pressure pwf. Again, this pressure is valid only for the assumed flow rate. The two calculated bottomhole pressures will probably not be the same. If not, then the assumed rate is wrong.Nodal analysis refers to the fact that we have to choose a point or node in the system at which we evaluate the pressure - in this case, the bottom of the wellbore. This point is referred to as the solution point or solution node.7WV8/11/2011Curva de afluencia del pozo

8/11/20117Lets assume that the well is completed open hole, and that the well is neither damaged nor stimulated. In this case, the pressure drop across the completion is zero.For the moment, we ignore the wellbore and the flowline.If the flow rate is 0, the bottomhole pressure pwf will be the same as the average reservoir pressure, pr. As we increase the flow rate, the pressure drop in the reservoir segment increases - causing the bottomhole pressure pwf to decrease. When we graph the flowing bottomhole pressure as a function of flow rate, the result is a curve intersecting the y-axis at the initial reservoir pressure, and intersecting the x-axis at the maximum rate the well would produce if opened to the atmosphere at the perforations.This curve is usually referred to as the inflow curve or the reservoir curve.Until we take into account the pressure drop within the wellbore, this curve tells us very little about the rate at which the well will produce for a given wellhead pressure.8WV8/11/2011Anlisis NodalDos principales componentes

Curva de Afluencia del yacimiento (IPR)Gasto de Petroleo o Gas vs Presin de fondo fluyenteOrdenadas Origen = presin de yacimiento (Dp = 0 q = 0)Abscisa interseccin = Gasto mximo (Dp = pr q = Max)

Curva del sistema (Demanda, entrada al tubing) Componentes de Hidrosttica, friccin y aceleracinCurvas dominadas por presin de cabezal y levantamiento artificial

La interseccin de las dos curvas dan PWF (psi) y Gasto (Bl/d)8/11/201189WV8/11/2011Curva de comportamiento del sistema

8/11/20119Now lets assume that the separator is so close to the wellhead that we may ignore the pressure drop through the flowline.At some low flow rate, perhaps 200 STB/D, the flowing bottomhole pressure may be 1500 psi. In order to increase the flow rate without changing the surface pressure, we have to raise the flowing bottomhole pressure.(At extremely low flow rates, the bottomhole pressure actually falls with increasing flow rate. This is a real phenomenon, and we will address it at some length later in the course. For now, note that the bottomhole pressure for a shut-in well filled with oil is actually higher than the bottomhole pressure for a well flowing a mixture of oil and gas at low rates.)This curve is usually referred to as the outflow curve or the tubing performance curve.Until we take into account the reservoir behavior, this curve also tells us almost nothing about the rate at which the well will produce.10WV8/11/2011Grafico del Sistema

2111 STB/D1957.1 psi8/11/201110The inflow curve describes the relationship between the bottomhole pressure and the flow rate for the reservoir. The outflow curve describes the relationship between the bottomhole pressure and flow rate for the wellbore. When we graph these two curves on the same graph, we refer to this as the system graph. The intersection of the inflow curve and the outflow curve gives the one unique flow rate at which the well will produce for a specified set of reservoir and wellbore properties. The point of intersection will also give the unique bottomhole pressure at which this rate will occur.If we had chosen a different point as our solution node, the shapes of the curves would have been different. The y-coordinate of the intersection of the inflow and outflow curves would have given the pressure at the new solution node. The flow rate at which the curves intersect, however, will be the same no matter where the solution node is taken. Calculated intersection points may differ slightly because of numerical errors.11WV8/11/2011Anlisis NodalInflowPunto de operacinOutflowpresin PWF Gasto Gasto (mmpcd)presin en nodopresin de yacimiento8/11/201111Propiedades de Fluido Oil Viscosidad, Rgp , Punto de burbuja Factor de formacin volumtrica, Densidad Gas Viscosidad, Factor Z, Compresibilidad Densidad

Correlaciones para la IPR e.g. IP-Gas, Backpressure, DarcyGeometria del pozo ej. Vertical, desviado, horizontalPropiedades del yacimiento Presin de yacimiento Permeabilidad Skin (Incluye desviacin, perforacin, dao etc) Caoneo parcialLa curva de afluencia depende de:8/11/201112Anlisis Nodal : UsosEstimacin de Parmetros del yacimiento e.gSkinPermeabilidadPresin de yacimientoEvaluacin de estimulacin Potencial Fracturamiento hidrulicoPrimariamente a travs de la reduccin del skin Estudio de sensibilidad de Parmetros importantes8/11/201113OutflowGastopresin en nodo50-1-3SKINInflow(IPR)qo a 1/ ln re +S rwNote : Log effect10Efecto del Skin en la IPR8/11/201114Efecto de la deplecin de presin en IPROutflowFlowratePressure at Node80412Descenso de presinInflow8/11/201115Propiedades de Fluido Oil Viscosidad, Rgp , Punto de burbuja Factor de formacin volumetrica, Densidad Gas Viscosidad, Factor Z, Compressibilidad DensidadCorrelaciones Usadas e.g. Oil - Duns & Ross, Gas - GrayFriccin Propiedaes de la completacin Dimetro del Tubing Restricciones del Tubing Rugosidad del TubingLa curva del comportamiento del sistema depende de:8/11/201116Efecto del dimetro del tubingInflow(IPR)OutflowGasto (stb/d)presin NodoPara pozo restringido en el tubing2 3/82 7/84 1/23 1/28/11/201117

Solucin en el cabezal del pozoUbicacin nodo 1. separador3. Pwh6. Pwf8. Py1423Procedimiento de solucin paso a paso(1)El primer paso es asumir varios Gastos(2)Se comienza con presin de separacion conocida para entonces calcular la requerida en cabezal para mover ese fluido horizontalmente(3)Usando el mismo Gasto y comenzando desde la presin de yacimiento encontramos la PWF correspondiente (2). (4) Usando la PWF obtenida en 3 se determina la presin de cabezal permisible para este Gasto seleccionado.(5)Se grafica para el mismo gasto seleccionado, la presin de cabezal calculada en el paso 2 vs la presin de cabezal calculada en el paso 4.Nodo solucin en el cabezalP1 = Pr - Pwfs= cada en el yacimiento

P2 = Pwfs - Pwf= cada en la completacinP3 = Pwf - Pwh = cada en el tubingP4 = Pwh - Psep = cada en la lnea de flujoPrPePwfsPwfP1 = (Pr - Pwfs)P2 = (Pwfs - Pwf)P3 = Pwf - PwhP4 = (Pwh - Psep)PsepGasLiquidoTanquePT = Pr - Psep = cada de presin totalAdapted from Mach et al, SPE 8025, 1979.Pwh8/11/201120What if we take the solution node at the wellhead? Again, we know the separator pressure and the average reservoir pressure.As with the bottomhole node, we start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. Finally, we calculate the pressure drop up the wellbore to find the wellhead pressure pwh. This pressure is valid only for the assumed flow rate.Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Again, this pressure is valid only for the assumed flow rate. Graphing inflow and outflow curves for a range of assumed rates allows the solution flow rate and wellhead pressure to be obtained from the intersection of the curves.Grafico del sistema Nodo en cabezal

2050 STB/D500 psi8/11/201121In general, the inflow curve describes the relationship between the pressure at the solution node and the flow rate into the node. For this case, with the solution node at the wellhead, the inflow curve represents the combined performance of the reservoir and tubing system.The outflow curve describes the relationship between the pressure at the solution node and flow rate out of the node. Here, with the solution node taken at the wellhead, the outflow curve is horizontal - we have fixed the wellhead pressure at 500 psi in our input data.The intersection of the curves gives the flow rate (2050 STB/D) and the wellhead pressure (500 psi). The slight discrepancy between this value and the 2111 STB/D calculated using a bottomhole node should not be of concern.

Pressure 100 psiLenght, 1000ftPwhModelaje de flujo Mono / Multifsico

Simulador en estado estacionarioPrograma ejecutableEcuaciones fundamentalesEcuacin de continuidadEcuacin del balance de la energa mecnicaBalance de la energaEcuaciones Fundamentales para un volumen de control Conservacin de la masadM dt= 0 ( )SM tVC ( )+ rVr. n dASC=+0M tVC ( )+ rVr. n dASC rVb. n dA= 0Cambio de masa dentro del volumen de controlTasa del cambio neta del flujo msico que atraviesa la superficie de controlesh + V2 + gZ 2QVC - WVC=( )Sm-h + V2 + gZ 2( )emPor unidad de masa, para un volumen de control con solo una entrada y una salida: esh + V2 + gZ QVC - WVCmm=h + V2 + gZ 2( )S-e( )2Ecuacin de la EnergaCambios de Presin Flujo de Una Fase(dp/dl) = (dp/dl)elev.+ (dp/dl)fric.+ (dp/dl) acc.

= -gsin (elevacional) + -2/2d (friccional) + - x d/dl (aceleracional)donde, = factor de friccin = densidad del fludo = velocidad del fludog = constante gravitacional = ngulo de flujod = dimetro de la tuberaMtodo de Clculo de Cambio de PresinDeterminar la(s) fase(s) presente(s) Determinar el ngulo de inclinacinDeterminar el modelo de flujoCalcular la elevacin, presin de friccin y prdidas o ganancias por aceleracinFases Presentes.00001 < fraccin de volumen de lquido < .99Gas una sola faseMultifsicoLquido una sola faseCorrelaciones de Flujo de Una FaseDisponibleMoody (default)AGA Equacin de Gas SecoPanhandle APanhandle BHazen-WilliamsWeymouthRecomendadaMoodyGradiente de Presin - ImportanciaPozos:Trmino elevacional (85 - 100 %)Trmino frictional (0 - 15 %)

Tuberas:Trmino elevacional (0 - 30%)Trmino friccional (70 - 100 %)

Factores de FriccinNmero de Reynolds (Re) es dado porRe = - d/ Para flujo laminar (Re < 2000) = 64/Re

Para flujo turbulento (Re 6000) -0.5 = 1.74 - 2log((2/d) + (18.7/Re 0.5))

donde, = viscosidad de fluido = rugosidad de la tubera

Rugosidad de la Tubera ()Factores dependientes:(a) Tipo de Material(b) FluidosCorrosivosHidratosDepsitos de parafinas o asfaltenos Slidos presentesVelocidades erosivas(c) Cubrimientos(d) Aos en servicioValores Tpicos de Rugosidad Tipo de Tubera Rugosidad (in) Plsticos, vidrios, etc0.0Tuberas nuevas0.0006Acero comercial 0.0018Tuberas sucias0.009Tubera flexibleDia/250PIPESIM default0.001

Flujo Multifsico Factores AdicionalesEl flujo multifsico es mas complejo

Las prdidas de presin por elevacin son funcin del llamado slip holdup.Las prdidas de presin por friccin son funcin del rgimen de flujo, determinado por la inclinacin del ngulo y las velocidades superficiales del gas y lquidos.

Holdup de Lquido - Definicin Colgamiento o Holdup es definido como el flujo volumtrico de una fase, dividida por el flujo volumtrico total de todas las fases. Holdup con No-resbalamiento (L)Asume que no hay resbalamiento (slip) entre las fases, ej. las fases vijan a la misma velocidad (uG = uL)

Holdup con Resbalamiento (HL)Mas realista, asume que existe resbalamiento entre las fases, ej. las fases vijan a diferentes velocidades (uG uL)

La ltima es usada para determinar las prdidas de presin por elevacin en flujo multifsicoFlujos con Resbalamiento y No-Resbalamiento

Efectos del Resbalamiento SubidaBajadaHLL>vvLG

HLL 45 o < -45 entonces aplica el rgimen de flujo vertical y sus correlaciones de cambio de presin

De otra manera aplica el rgimen de flujo horizontal y sus correlaciones de cambio de presinDefinicin de Velocidad SuperficialEsta es la velocidad a la que una fase fluira si no estubiese presente otra fase dentro de la tubera:Velocidad superficial del lquido (UsL) = qL/A Velocidad superficial del gas (UsG) = qG/A

dondeqL = gasto volumtrico de lquidoqG = gasto volumtrico de gasA = Area transvesal de la tuberaRgimen de Flujo Horizontal

Mapa de Rgimen de Flujo Horizontal de Taitel Dukler1.000.100.0110.075.00.11.010.0900.0100.0IntermittentAnnularStratifiedWavyStratified SmoothBubblyUsL (ft/s)UsG (ft/s)Rgimen de Flujo Vertical

MAPA de Taitel and Dukler para Flujo Vertical

Correlaciones de Flujo MultifsicoCorrelaciones estandar publicadas en la industria:Duns & RosOrkiszewskiHagedorn & BrownBeggs & Brill (original & revised)Mukherjee & BrillGovier, Aziz & FogarasiAGA & FlaniganOliemansGrayAnsari

Correlaciones de Flujo Multifsico (cont.)Correlaciones mecanisticasAnsari XiaoOLGA-SAplicabilidad de las CorrelacionesSistemas de una sola fase - MoodyPozos verticales de aceite Beggs y Brill, Hagedorn & BrownPozos desviados de aceite - Duns & Ros/OLGASPozos de gas y condensado Gray, Ansari, OlgaLneas de tubera de aceite - OliemansLneas de tubera de gas y condensado - BJA Correlation

Q = kh(Pws 2 - Pwf 2)/(1422mTz o(ln(Re/Rw) - 0.75 + S + DQ))) S is the skinD is the rate dependent skin termK is the formation permeabilityh is the formation thicknessm is the liquid or gas viscosityB is the formation volume factorRe is the drainage radiusRw is the wellbore radiusT is the temperatureZ is the z factorPseudo Steady-State Equation / Darcy