WATER INFLUX

Facultad de Petroleo y Gas NaturalPreparo: Ing. Freddy Reynolds ParejaCbba Enero - 2011

Water Influx Muchos reservorios estn limitados en una parte o la totalidad de sus periferias por capas acuferas llamadas acuferosLos acuferos pueden ser tan grandes en comparacin con los reservorios que colindan que parecen infinitas a todos los efectos prcticos o

. Ellos pueden tener un rango hasta los tan pequeo como para ser insignificantes en sus efectos sobre el rendimiento del yacimiento.

Water Influx El propio acufero puede ser totalmente limitado por la roca impermeable para que el reservorio y el acufero juntos forman una unidad cerrada o volumtrica.

Por otra parte, el reservorio puede tener afloramientos en uno o ms lugares donde puede ser repuesto por las aguas superficiales.

Water Influx En respuesta a una cada de presin en el reservorio el acufero reacciona para compensar o retardar la declinacin de la presin, proporcionando una fuente de afluencia de agua por (a) Expansin del agua y la compresin de los poros (b) El flujo de las aguas artesianas que se produce cuando el acufero se eleva a un nivel por encima del yacimiento.

Evaluacion del Water Influx Una parte integral del control normal del reservorio es un programa de evaluacin del influjo del agua activa. La primera fase de la evaluacion es el diagnostico, clasificacion y caracterizacion del empuje de agua. La segunda fase trata de identificar los modelos matemticos aplicables para ayudar en la simulacin del pasado y la prediccin del rendimiento futuro del acufero. Esta fase tambin incluye la estimacin de los parmetros del modelo.La fase final incluye la combinacin de los acuferos y modelos de los yacimientos, en un modelo comn que en ltima instancia, puede predecir el comportamiento del yacimiento y se puede utilizar para optimizar el agotamiento.

Clasificacion de los Acuiferos La nomenclatura del empuje de agua esta basado en la ubicacin de los acuferos con relacin al reservorio. Peripheral water drive: Acufero rodea el reservorio total o parcialmenteEdge water drive: Acufero se alimenta por un solo lado o en el flanco del reservorio

Bottom water drive: Acufero esta debajo del reservorio y lo alimenta desde abajo

Clasificacion de los Acuiferos Clasificaciones basadas en el empuje. (es decir, el pozo que proporciona agua de recarga del acufero al reservorio y poder mitigar la disminucin de la presin del yacimientoStrong acuifero : Acufero en el que el caudal del influjo agua es similar que el caudal de extraccin de fluidos a condiciones de yacimiento. Estos yacimientos se llaman empuje completo de agua y se caracteriza por la pequea disminucin de la presin. Acuferos fuertes son generalmente muy grandes y bien comunicados con el reservorioModerado o debil acuifero: Acufero donde la caudal de recarga del agua es considerablemente inferior al caudal producido del reservorio de lquidos. Estos yacimientos se llaman pulsiones parciales de agua. Se caracteriza por una mayor disminucin de la presin mayor que la de un empuje de agua integral.Inactivo acuifero : Los acuferos sin influjo absoluto durante el agotamiento

Diagnosis del Empuje de Agua Diagnose through: Understanding reservoir geology: identify communicating and noncommunicating pathways. Consult map to identify reservoir trap and impenetratable surfaces by waterStudy performance parameters/variablesWOR history of wells and reservoir: steady rise is an indication of waterdrive. Be careful about water coningHistory of average reservoir pressure: Slower decline than expected is an indicationReservoir Pressure distribution: High pressures exists near reservoir/aquifer boundary. Lower pressures at more distant locations. A pressure contour map is useful.GOR is also an indication. Strong waterdrives have small changes in GORMBE analysis diagnostic plots such as this one for an undesaturated reservoir

Diagnosis via performance plotsUna indicacin fundamental es el aumento de la presin promedio del yacimiento cuando las caudales se reducen.

Propiedades Principales del Acuifero Las propiedades mas importantes del acufero son los siguientes por su importantes para el modelado del influjo de agua y su caracterizacin son:

(1)size and shape (2) permeability (3)porosity (4) water compressibility (5) rock compressibility and (6) water viscosity.

Water Influx Models Los Modelos del influjo de agua son modelos matemticos que simulan y predicen muchas variables, pero lo ms importante es el historial de entrega -volumen o influjo del acufero . Hay varios modelos del acufero muy populares:

Schilthuis model (1936) ( Steady state, ss) van Everdingen and Hurst model (1949, uss)Carter and Tracey model (1960, uss)Small/Pot Aquifer model (Havlena & Odeh, 1963)Fetkovitch model (1971, pss)

Actual Water Influx Dynamics En general, como la deplecion de la presion se origina en el reservorio, debido a las diferencias de presiones entre el reservorio y el aumento del acuifero causado por el influjo de agua. In time, the influx lessens the reservoir pressure decline to the point that the two (reservoir and aquifer) have nearly equal pressures. This interaction causes the water delivery rate to start at zero grow steadily , reach a maximum and then finally decline.

Actual Water Influx Dynamics Los modelos de estado no estacionarios tienen mas exito en la captura de la dinamica real en comparacion de los otros modelos pero a un precio de una mayor complejidad. El modelo de Van Everdingen and Hurst es un metodo (unsteady state) para un estado inestable y es el mas sofisticado que todos los anteriores metodos..Su principal ventaja es su capacidad de capturar la dianamica real del flujo de agua y por lo tanto, esta mas cercano a la realidad. Originalmente su principal desventaja es la necesidad de usar graficos y tablas repetitivamente para un calculo sencillo

Actual Water Influx Dynamics Hoy en dia, facilmente se pueden digitalizar sus graficos y tablas, la necesidad para otras alternativas ha disminuido. Sin embargo, para captar los diferentes mecanismos entre los metodos tambien se podra cubrirlos. The steady state method of Schithuis and Pseudo steady state method of Fetkovitch.

Pot aquifer model Si el acuifero es pequeo, permeabilidad es alta, buenacommunicacion entre el acuifero y los hidrocarburos del reservorioreservorio la transmicion de la disturvancia de la presion es facil y rapida para alcanzar la presion de equilibrio. i.e. la presion promedio en la zona del oil y el acuifero son los mismos.Por la caida de la presion promedio en el sistema reservoir/aquifer , (pi p) , el water en el aquifer se expandera y el influjo en elReservorio con una cantidad de :

Donde B es la constante del acuifero se obtendra como:

Pot aquifer model Recordando que MBE en general

Sustituyendo We dentro MBE obtendremos:

Aqui MBE tiene 3 constantes desconocidas, N, m and B

Interpretation Plot Teniendo Et

El plot de

es una linea recta que se intercepta = N and slope = B.

Si m no es conocida, entonces se procede por prueba y error hasta conseguir que la variable m sea una linea recta

Interpretation Plot

Si m = 0 ( undersaturated reservoir), entonces el plot de

es una linea recta que se intercepta = N and slope = Bno es necesario de utilizar la tecnica de prueba y error.

Steady-state models: Schilthius model El modelo Schilthius asume que: La presion en el limite externo del acuifero se mantiene en el valor inicial Pi,Y por tanto el reservorio alcanza el estado de equilibrio situation tal que la presion del reservorio se estabilizara a una presion determinada.Asi que el caudal del water influx desde el aquifer en el reservorio es igual a la produccion de fluidos (oil, gas and water) desde el reservorio.

Schilthius model

Si durante un rasonable largo periodo ( 6 meses o mas) el caudal de produccion y la reservorio presionsigue siendo sustancialmente constante, entonces asumimos de que la interaccion del reservoirio y el acuifero estan bajo condiciones de steady state. Durante la condicion de steady state, el caudal volumetrico retido o mas el caudal vaciado del reservorio sera igual al caudal del water influx.

Schilthius modelEsta relacion en terminos de la MBE sera:

Por definicion

Donde Qo and Qw son los caudales diarios de produccion en superficie en STB y SCF.

Schilthius modelOnce dWe/dt is determined from production data, it is equated to;

And solved for k. (The above relation holds because, the steady state rate flow into the reservoir, by Darcys law, is proportional to the pressure differential. )

Schilthius model

Integrando dWe/dt el comportamiento de We como funcion del tiempo y p.

We entonces podremos calcular numericamente para todas las porciones de los datos de produccion.Entonces tambien se podra utilizar para efectuar las predicciones del pozo.

Application of the Schilthius methodEl unico ejemlo en los libros de texto de Schilthius de su propio trabajo. Desde un ploteo de datos de produccion , a continuacion donde se puede identificar una porcion donde se tiene:La presion del reservorio esta estabilizada. El caudal production es sustancialmente constante. El GOR es bastanteconstante.

Application of the Schilthius method

Schilthius has identified the portion between 28 to 34 months from the start of production and collected the following data.The pressure has stabilized at 2090 psia Oil rate was substantially constant at 44100 STB/D.GOR 825 SCF/STB and Rsoi is 600 SCF/STBBt=7.520 cuft/STB and Bg=0.0063 cuft/SCF at 2090 psiaThe initial pressure was 2275 piadWp/dt=0

Application of the Schilthius methodFor the mentioned section of production plots, one calculates thedaily viodage (i.e. reservoir volume of daily production rates ofreservoir fluids) which must be equal to rate of water influx. Hence,

Since the calculated will also be equal to

Solving the influx constant yields. cuft/day/psi.

This value can be used for calculating the water influx for bothstabilized and changing reservoir pressure intervals.

Application of the Schilthius method If, in the production plot, the pressure stabilizes but withdrawal rates are not reasonably constant the water influx for the stabilized period may be found from the total oil, gas and watervoidage for the period ,

Then the influx constant is calculated as:

Application of the Schilthius methodEl cumulativo del influx es obtenido por la integracion numericaesquematicamente sera:

Sustituyendo esto en la Material Balance Equation obtedremos:

Si m = 0:

Teniendo en cuenta que con esta aproximacion se ocacionaran grandes errores en N pero no en k.

Unsteady-state modelsMetodo Van Everdingen and Hurst (VEH) :

p = pressure (psia or psig)r = radial distance (ft)t = time (days)k = permeability (md) = porosity (fraction)ct = total compressibility = cw+cf = water viscosity (cp)Area (oil zone) = rR2Area (aquifer) = (raq2 - rR2)rRraqOil zoneAquifer

Metodo Van Everdingen and HurstLa solucion cuando la presion en los limites del reservorio/acuifero es presentado en funcion de la forma adimensionaldel water influx, WeD como una funcion del tiempo adimensionless, tD y del radius, raqD

Esta solucion asume que estos cambios de intervalos entre el reservorioy la presion del acuifero. Seran:

Donde pi es la presion inicial del acuifero y pR es la presion en los limites del reservoior/acuifero con lo que supone que tambien es uniforme en todo el reservorio..Por lo tanto esta solucion se denomina en terminos de la presion constante.

Van Everdingen and Hurst methodLas variables en la solucion estan definidas a continuacion:tD = 6.33x10-3 k t/( ct rR2) = t = 6.33x10-3 k/( ct rR2) = constante de conversion del tiemporaqD = raq/Rr

B = Water influx constant (bbl/psi) = 1.119 ct rR2 h/360 = angle representing the portion of the oil zone in contact with the aquifer, full circle =360 (degrees)h = thickness of the aquifer (ft)

Water influx function, WeD

Water influx function, WeD

Water influx function, WeD

Water influx function, WeD

SuperposicionLa solucion de VEH asume que la presion del rervorio es constante, mientras que en realidad la presion del reservorio decrese con el tiempo.

Para hacer frente a esta limitaciont, representaremos que la declinacion de la presion del reservorio es continua con una serie de intervalos de decrementos de la presion y aplicando el principio de la superposicion para calcular el volumen acumulativo del water influx.

SuperposicionPara aplicar por primera vez la superposicion, el tiempo y la presion del reservorio seran dominios discretizados.. Una vez, que el dominio del tiempo se discretiza en (n+1) puntos (t0, t1, t2,.tn) donde (t0< t1, t1< t2, t2< t3.. tn-1< tn ) y t0=0, que conduce automaticamente al conjunto discreto de las correspondientes presiones promedio delreservorio ( p0, p1, p2,.pn) donde p0 es la presion inicial del reservorio

La ilustracion grafica de la presion y el tiempo discretizados y los intervalos de los decrementos de la presion partiendo desde t=0.p0=(p0-p1)/2p0p1p2p1=(p0+p1)/2-(p0+p2)/2 = (p0-p2)/2p3p2= (p1-p3)/2PressureTimet0t1t2t3

SuperposicionLet ti >tj. in the discretazied time domain.At any time (ti), the contribution of a step drop in pressure that has occurred at a previous time tj (pj) is equal to the drop times the dimensionless water influx (WeD) corresponding to the time lapse since that step drop occurred: We ( at time t=ti ) due to a step drop occurred at tj will be equl to the product B pj WeD((ti-tj)D)

The total influx We at time (t=ti) is the sum of contributions of all previous step drops that occurred at time levels j=0,1(i-1).

SuperposicionPor ejemplo, aplicando para i=1,2 y 3 se obtiene:

Systematic water influx calculation steps:1. Discretizando el domonio del tiempo y la presion (los intervalos del tiempo seran iguales a los intervalos del tiempo que aceleraran los calculos) originando una tabla del t y la p [ (n+1) points] i=0,1,..n2. Calcular la constante de conversion del tiempo. = 6.33x10-3 k/( ct rR2) and raqD = raq/rR

3. Calcula tDi los valores de cada momento y aadir a la tabla

4. Calculate time average values of pressures for each time interval

5. Determinar los valores de algunas caidas de presion, pi (i=1,2..,n) usando,

Tomar en cuenta el patron resultante (discretizacion central):

p0 = (p0 p1)/2 and p1 = (p0 p2)/2 and pi = (pi-1 pi+1)/2

Systematic water influx calculation steps: Steps from 6 to 10 is a repetitive procedure for the application of superposition. To calculate cumulative water influx at a given time ti [i.e at the end if ith decrement]

6. For (j=0,1,2i-1) , Write down all (tDi- tDj ) values in the previous table in reverse Order (i.e.from greatest to least) in a separate column to form a new table

7. Calculate and Write down WeDj values for each (tDi- tDj ) in the next column

8. Again for (j=0,1,2i-1), Write down pj values of the first table in normal order in the next column of the new table

Note in such an ordering, each pressure drop, pj is related to its, the elapsed time tj=(t-tsj) tsj = starting time for the pressure drop, and hence to its dimensionless elapsed time is (tD-tDj) = (t-tsj)

Systematic water influx calculation steps:9. Determinar el water influx adimensional debido a los decrementos de la presion:WeDx pj y se adjunta a la tabla10. Calcular el water influx adimensional desde: WeDx pj11. Usinando la constante del water influx (bbl/psi) B = 1.119 ct rR2 h /360Calcular el water influx adimensional usando:B WeDx pj

Example of water influx calculation (VEH)El historial de caidas de presion y aquifer propiedades del acuifero se tendra a continuacion.Time (day) Pressure (psig) 0 2500 365 2300 1095 2200k = 100 md = 0.2 = 1 cp ct = 7x10-6 psi-1rR = 10,000 ft raq = 50,000 fth = 50 ft = 360Calcular el water influx para un t = 1095 days.

Example. 3 punto de discretazacionp0=(p0-p1)/2p0p1p2p1= (p0-p2)/2PressureTime03651095itipi0 0 2500 25001365 2300240021095 2200 2250

Example of water influx calculation (VEH)Los resultados de la discretizacion seran tabulados como sigue: ( ya que deseamos We para t = 1095 days)t (day) p (psig) iti tDi pi pi 0 25000t0=00 p0 =2500 2500 0 365 23001t1=365 1.65 p1 = 2300 2400 100 1095 2200n=2t2=1095 4.95 p2 = 2200 2250 150

Tener en cuenta el patron pi, como se ilustra en el grafico anterior

p0=(p0-p1)/2=(2500-2300)/2=100and

p1=(p0-p2)/2=(2500-2200)/2=150

Example of water influx calculation (VEH)Usando = 6.33x10-3x100/(0.2x1x7x10-6x108) = 0.00452 day-1, raqD = 5B = 1.119x0.2x7x10-6x108x50x360/360 = 7833 (bbl/psi)

Since we want to calculate at t=1095 days (i=2 in previous table thushence j=0,1 in the new table below.)

jtDi-tDjWeDpjWeDx pj04.95-0=4.95 ?100 ?14.95-1.65=3.3 ?150 ? (tD-tDj)= * (t-tj) and WeD values needs to be obtained fromfigures of dimensionless solutions given earlier or tables such as below.

Water influx function

Example of water influx calculation (VEH)From the last colum in the previous table we read:j (tD-tDj)= * (t-tj) WeD 3.0 3.195 0(tD tD1) = 3.3 ? 3.5 3.542 4.5 4.193 1(tD tD0) = 4.95 ? 5.0 4.499

Example of water influx calculation (VEH)Linear interpolation formula for tD(m)< tD < tD(m+1) :WeD(tD)= WeDm + (tDtDm) (WeD(m+1) WeDm)/(tD(m+1)tDm)

Linear interpolation formula for raqD:WeD(rD)= WeDm + (rDrDm) (WeD(m+1) WeDm)/(rD(m+1)rDm)

Thus for the values in the previous slideWeD(tD2-tD1) = 3.195 + (3.33.0)(3.5423.195)/(3.53.0) = 3.403WeD(tD2-tD0)= 4.193 + (4.954.5)(4.4994.193)/(5.04.5) = 4.468

Example of water influx calculation (VEH) jtDi-tDjWeD(tDi-tDj)pjWeDx pj04.95-0=4.95 4.468100 446.814.95-1.65=3.3 3.403150 510.5

= 7,883[446.8 +510.5] = 7,546,002 bbl = 7.546 MM bbl

Pseudosteady-state modelFetkovich Method:pi = Initial pressure (psi)rR = radius of the oil reservoir (ft)raq = radius of the aquifer (ft)t = time (days)k = permeability (md)h = thickness (ft) = porosity (fraction)ct = total compressibility = cw+cf = angle of contact with the aquifer (deg)

PSEUDOSTEADY-STATE PROCEDURE1. Calcular la intrusion inicial del water, Wei (bbls):

2. Calcular el Productivity Index, J, para el flujo desde el acuifero hasta el reservorio sin flujo limite exterior:

PSEUDOSTEADY-STATE MODEL3. Dividir el historial de la presion en intervalos de tiempo. El tamao de algunos intervalos de tiempo sera: tn=tn-tn-1.

Definiendo las presiones a continuacion:

PSEUDOSTEADY-STATE MODEL4. Calcular la presion promedio de reservorio para algunos intervalos de tiempo :

Para t=0, desde n=0, establecer lo aiguiente:

y efectuar los pasos 6 al 8 para algunos intervalos de tiempo n=1,2,nt sucesivamente (nt es el numero de los intervalos de tiempo):

PSEUDOSTEADY-STATE MODEL6. Calcular el water influx durante el intervalo de tiempo:

7. Calcular el total water influx at the current time:

8. Calcular la presion promedio en el acuifero at the end of the time step:

EXAMPLE OF WATER INFLUX CALCULATION (FETKOVICH)

EXAMPLE OF WATER INFLUX CALCULATION (FETKOVICH)

EXAMPLE OF WATER INFLUX CALCULATION (FETKOVICH)

COMPARACION DE RESULTADOS We (MM bbls) Time VEH FETKOVICH 360 1.577 1.389 1095 7.546 7.442

COMPARACION DE RESULTADOS

VEH RESULTADOS

FETKOVICH RESULTADOS

EXEMPLO DE COMPARACION

EXAMPLE OF WATER INFLUX PARAMETERS DETERMINATIONEl volumen de water influx puede ser obtenida con la ecuacion del l balance de materia:

We = NpEp+ WpBw - N Et

donde y

Con el metodo VEH We = B pjWeDj

Donde, WeD = f(tD ,raqD) y tD = t,

De esta manera podemos encontrar dos parametros, B y raqD. El ploteo de We vs. pjWeDj con los valores correctos de y raqD y la pemdiente de la linea recta= B y la intecepcion = 0

EXAMPLE OF WATER INFLUX PARAMETERS DETERMINATION

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time constm

40.3

TimePressureBgRpTimeEoEgEo+mEgFF/(Eo+mEg)

(months)(psia)(bbl/SCF)(SCF/STB)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)(MM STB)

029200.001222000.0000.0000.0000.000

2027900.001313870200.0460.1130.0809.098114.325

3027450.001348860300.0640.1560.11115.786142.071

4026800.001402810400.0940.2230.16124.406151.477

6026300.001444830600.1190.2760.20240.022198.567

8026150.00145850800.1210.2830.20650.759246.536

10025950.0014798701000.1370.3190.23361.675264.487

12025850.0014899101200.1430.3310.24370.942292.532

raqD = 12raqD = 15raqD = 20

TimeWepWeDpWeDpWeD

205.78E+052.22E+032.31E+032.34E+03

301.23E+064.67E+034.93E+035.05E+03

402.01E+067.45E+038.03E+038.32E+03

603.65E+061.28E+041.46E+041.57E+04

805.05E+061.67E+042.02E+042.27E+04

1006.18E+061.94E+042.47E+042.92E+04

1207.08E+062.13E+042.83E+043.51E+04

Sheet2

Sheet2

577500577500577500

123250012325001232500

200750020075002007500

365000036500003650000

505000050500005050000

617500061750006175000

707500070750007075000

ReD=12

ReD=15

ReD=20

pWeD

We

y = 250 x

EXAMPLE OF WATER INFLUX PARAMETERS DETERMINATION

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time constm

40.3

TimePressureBgRpTimeEoEgEo+mEgFF/(Eo+mEg)

(months)(psia)(bbl/SCF)(SCF/STB)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)(MM STB)

029200.001222000.0000.0000.0000.000

2027900.001313870200.0460.1130.0809.098114.325

3027450.001348860300.0640.1560.11115.786142.071

4026800.001402810400.0940.2230.16124.406151.477

6026300.001444830600.1190.2760.20240.022198.567

8026150.00145850800.1210.2830.20650.759246.536

10025950.0014798701000.1370.3190.23361.675264.487

12025850.0014899101200.1430.3310.24370.942292.532

ReD = 12ReD = 15ReD = 20

TimeWepWeDpWeDpWeD

205.78E+052.22E+032.31E+032.34E+03

301.23E+064.67E+034.93E+035.05E+03

402.01E+067.45E+038.03E+038.32E+03

603.65E+061.28E+041.46E+041.57E+04

805.05E+061.67E+042.02E+042.27E+04

1006.18E+061.94E+042.47E+042.92E+04

1207.08E+062.13E+042.83E+043.51E+04

Sheet2

Sheet2

577500577500577500

123250012325001232500

200750020075002007500

365000036500003650000

505000050500005050000

617500061750006175000

707500070750007075000

raqD = 12

raqD = 15

raqD = 20

pWeD

We

y = 250 x

MATERIAL BALANCE EQUATIONF = Np[Bo+Bg(Rp-Rs)] + WpBw - WiBwF = N[Eot+mEgt] +WeF/[Eot+mEgt] = N + B pWeD/[Eot+mEgt]A plot of F/[Eot+mEgt] vs. pWeD/[Eot+mEgt] la linea recta con la intercepcion = N y la pendiente = B si m no es conocida, entonces se a trail and error procede con el procedimiento de prueba y error para diferentes valores de m hasta la obtencion de una linea rectaSi la constante conversion del tiempo, no es conocida, entonces tambien tendran que ser varidas hasta obtener la linea recta.Si m = 0, entonces:F/Eot = N + B pWeD/EotDel ploteo de F/Eot vs. pWeD/Eot es obtenida la linea recta con la intercepcion = N y la pendiente = B

MATERIAL BALANCE EXAMPLE

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time ConstRsim

48000.3

TimePressureBtBgNpRpWpWiTimeEoEgEo+mEgF

(months)(psia)(bbl/STB)(bbl/SCF)(MM STB)(SCF/STB)(MM bbl)(MM bbl)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)

029201.51660.0012220.0000.0000.00000.0000.0000.0000.000

2027901.56230.0013135.5008700.0000.000200.0460.1130.0809.098

3027451.58080.0013489.5008600.0000.000300.0640.1560.11115.786

4026801.61070.00140215.0008100.0350.000400.0940.2230.16124.406

6026301.63550.00144425.1508300.4002.600600.1190.2760.20240.022

8026151.63760.0014532.1008500.9655.100800.1210.2830.20650.759

10025951.65410.00147938.9538701.8108.6001000.1370.3190.23361.675

12025851.65970.00148945.0009102.89514.0101200.1430.3310.24370.942

sum=sum(DP*WED)x=sum(DP*WED)/(Eo+mEg)

RED=12RED=15RED=20

TimesumxsumxsumxF/(Eo+mEg)

202.22E+032.79E+042.31E+032.90E+042.34E+032.94E+04114.325

304.67E+034.21E+044.93E+034.44E+045.05E+034.54E+04142.071

407.45E+034.63E+048.03E+034.99E+048.32E+035.17E+04151.477

601.28E+046.35E+041.46E+047.23E+041.57E+047.77E+04198.567

801.67E+048.12E+042.02E+049.80E+042.27E+041.10E+05246.536

1001.94E+048.31E+042.47E+041.06E+052.92E+041.25E+05264.487

1202.13E+048.79E+042.83E+041.17E+053.51E+041.45E+05292.532

Sheet2

Sheet2

114.325114.325114.325

142.071142.071142.071

151.477151.477151.477

198.567198.567198.567

246.536246.536246.536

264.487264.487264.487

292.532292.532292.532

ReD=12

ReD=15

ReD=20

(p*WeD)/(Eo+mEg)

F/(Eo+mEg)

y = 0.002 x + 53.444

Sheet3

00

204.64

309.91

4016.1

6029.3

8040.5

10049.6

12056.9

15064.4

20070.8

25073.4

30074.6

35075

40075.2

45075.3

50075.3

04.65927

24.76829

45.04864

65.51588

86.17001

107.01111

128.03881

149.25451

1610.653

1812.2309

2013.6453

2114.8225

2215.6714

2316.453

2417.1617

2517.8081

2618.3921

2718.9042

2819.3823

2919.6845

3019.8284

3119.9312

3220.1099

3320.3821

3420.6058

3520.8195

3621.0119

3721.1892

3821.3383

3921.5068

4021.7576

4221.985

4422.162

4622.1969

4822.1944

5022.1186

5221.9786

5421.7741

5621.4969

5821.1803

6020.8339

6220.4567

6420.048

6619.617

6819.1973

7018.7801

7218.3677

7417.9594

7617.5555

7817.1559

8016.7624

8216.379

8416.0093

8615.6554

8815.3172

9014.9948

9214.688

9414.397

9614.1216

9813.862

10013.6136

10213.3672

10413.1139

10612.8489

10812.5724

11012.2843

11211.9849

11411.6728

11611.3534

11811.0023

12010.5634

12310.0798

1269.57399

1299.11968

1328.68009

1358.2688

1387.88419

1417.51931

1447.20352

1476.82436

1506.27002

1555.70943

1605.18744

1654.8407

1704.46622

1754.13017

1803.81575

1853.52406

1903.2675

1952.99523

2002.70857

2052.43975

2102.22098

2152.05357

2201.88638

2251.73315

2301.59018

2351.45846

2401.3377

2451.22799

2501.12839

2551.03713

2600.952335

2650.87311

2700.79944

2750.731316

2800.66879

2850.611817

2900.560424

2950.514596

3000.473726

3050.436687

3100.402298

3150.36996

3200.339676

3250.311443

3300.285273

3350.261171

3400.239109

3450.219139

3500.201028

3550.184428

3600.169046

3650.154639

3700.141251

3750.128838

3800.117423

3850.107016

3900.097607

3950.089223

4000.081714

4050.074854

4100.06847

4150.062413

4200.056706

4250.05135

4300.04632

4350.041661

4400.037327

4450.033349

4500.029704

4550.026395

4600.023434

4650.020828

4700.018586

4750.016669

4800.015111

4850.013875

4900.013015

4950.012518

5000.012324

Sheet3

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Time (months)

We (MM bbl)

Water Influx Rate (M bb/D)

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time constm

48000.3

TimePressureTimeEoEgEo+mEgF

(months)(psia)(bbl/STB)(bbl/SCF)(MM STB)(SCF/STB)(MM bbl)(MM bbl)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)

029201.51660.0012220.00000.0000.00000.0000.0000.0000.000

2027901.56230.0013135.5008700.0000.000200.0460.1130.0809.098

3027451.58080.0013489.5008600.0000.000300.0640.1560.11115.786

4026801.61070.00140215.0008100.0350.000400.0940.2230.16124.406

6026301.63550.00144425.1508300.4002.600600.1190.2760.20240.022

8026151.63760.0014532.1008500.9655.100800.1210.2830.20650.759

10025951.65410.00147938.9538701.8108.6001000.1370.3190.23361.675

12025851.65970.00148945.0009102.89514.0101200.1430.3310.24370.942

sum=sum(DP*WED)x=sum(DP*WED)/(Eo+mEg)

RED=12RED=15RED=20

TimesumxsumxsumxF/(Eo+mEg)

202.22E+032.79E+042.31E+032.90E+042.34E+032.94E+04114.325

304.67E+034.21E+044.93E+034.44E+045.05E+034.54E+04142.071

407.45E+034.63E+048.03E+034.99E+048.32E+035.17E+04151.477

601.28E+046.35E+041.46E+047.23E+041.57E+047.77E+04198.567

801.67E+048.12E+042.02E+049.80E+042.27E+041.10E+05246.536

1001.94E+048.31E+042.47E+041.06E+052.92E+041.25E+05264.487

1202.13E+048.79E+042.83E+041.17E+053.51E+041.45E+05292.532

Sheet2

Sheet2

114.325114.325114.325

142.071142.071142.071

151.477151.477151.477

198.567198.567198.567

246.536246.536246.536

264.487264.487264.487

292.532292.532292.532

ReD=12

ReD=15

ReD=20

(p*WeD)/(Eo+mEg)

F/(Eo+mEg)

y = 0.002 x + 53.444

Sheet3

00

204.64

309.91

4016.1

6029.3

8040.5

10049.6

12056.9

15064.4

20070.8

25073.4

30074.6

35075

40075.2

45075.3

50075.3

04.65927

24.76829

45.04864

65.51588

86.17001

107.01111

128.03881

149.25451

1610.653

1812.2309

2013.6453

2114.8225

2215.6714

2316.453

2417.1617

2517.8081

2618.3921

2718.9042

2819.3823

2919.6845

3019.8284

3119.9312

3220.1099

3320.3821

3420.6058

3520.8195

3621.0119

3721.1892

3821.3383

3921.5068

4021.7576

4221.985

4422.162

4622.1969

4822.1944

5022.1186

5221.9786

5421.7741

5621.4969

5821.1803

6020.8339

6220.4567

6420.048

6619.617

6819.1973

7018.7801

7218.3677

7417.9594

7617.5555

7817.1559

8016.7624

8216.379

8416.0093

8615.6554

8815.3172

9014.9948

9214.688

9414.397

9614.1216

9813.862

10013.6136

10213.3672

10413.1139

10612.8489

10812.5724

11012.2843

11211.9849

11411.6728

11611.3534

11811.0023

12010.5634

12310.0798

1269.57399

1299.11968

1328.68009

1358.2688

1387.88419

1417.51931

1447.20352

1476.82436

1506.27002

1555.70943

1605.18744

1654.8407

1704.46622

1754.13017

1803.81575

1853.52406

1903.2675

1952.99523

2002.70857

2052.43975

2102.22098

2152.05357

2201.88638

2251.73315

2301.59018

2351.45846

2401.3377

2451.22799

2501.12839

2551.03713

2600.952335

2650.87311

2700.79944

2750.731316

2800.66879

2850.611817

2900.560424

2950.514596

3000.473726

3050.436687

3100.402298

3150.36996

3200.339676

3250.311443

3300.285273

3350.261171

3400.239109

3450.219139

3500.201028

3550.184428

3600.169046

3650.154639

3700.141251

3750.128838

3800.117423

3850.107016

3900.097607

3950.089223

4000.081714

4050.074854

4100.06847

4150.062413

4200.056706

4250.05135

4300.04632

4350.041661

4400.037327

4450.033349

4500.029704

4550.026395

4600.023434

4650.020828

4700.018586

4750.016669

4800.015111

4850.013875

4900.013015

4950.012518

5000.012324

Sheet3

Time (months)

We (MM bbl)

Water Influx Rate (M bb/D)

MATERIAL BALANCE EXAMPLE

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time constRsim

48000.3

TimePressureBtBgNpRpWpWiTimeEoEgEo+m EgFF/(Eo+mEg)

(months)(psia)(bbl/STB)(bbl/SCF)(MM STB)(SCF/STB)(MM bbl)(MM bbl)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)(MM STB)

029201.51660.0012220.00000.0000.00000.0000.0000.0000.000

2027901.56230.0013135.5008700.0000.000200.0460.1130.0809.098114.325

3027451.58080.0013489.5008600.0000.000300.0640.1560.11115.786142.071

4026801.61070.00140215.0008100.0350.000400.0940.2230.16124.406151.477

6026301.63550.00144425.1508300.4002.600600.1190.2760.20240.022198.567

8026151.63760.0014532.1008500.9655.100800.1210.2830.20650.759246.536

10025951.65410.00147938.9538701.8108.6001000.1370.3190.23361.675264.487

12025851.65970.00148945.0009102.89514.0101200.1430.3310.24370.942292.532

sum=sum(DP*WED)x=sum(DP*WED)/(Eo+mEg)

RED=12RED=15RED=20

TimesumxsumxsumxF/(Eo+mEg)

202.22E+032.79E+042.31E+032.90E+042.34E+032.94E+04114.325

304.67E+034.21E+044.93E+034.44E+045.05E+034.54E+04142.071

407.45E+034.63E+048.03E+034.99E+048.32E+035.17E+04151.477

601.28E+046.35E+041.46E+047.23E+041.57E+047.77E+04198.567

801.67E+048.12E+042.02E+049.80E+042.27E+041.10E+05246.536

1001.94E+048.31E+042.47E+041.06E+052.92E+041.25E+05264.487

1202.13E+048.79E+042.83E+041.17E+053.51E+041.45E+05292.532

Sheet2

Sheet2

114.325114.325114.325

142.071142.071142.071

151.477151.477151.477

198.567198.567198.567

246.536246.536246.536

264.487264.487264.487

292.532292.532292.532

ReD=12

ReD=15

ReD=20

(p*WeD)/(Eo+mEg)

F/(Eo+mEg)

y = 0.002 x + 53.444

Sheet3

00

204.64

309.91

4016.1

6029.3

8040.5

10049.6

12056.9

15064.4

20070.8

25073.4

30074.6

35075

40075.2

45075.3

50075.3

04.65927

24.76829

45.04864

65.51588

86.17001

107.01111

128.03881

149.25451

1610.653

1812.2309

2013.6453

2114.8225

2215.6714

2316.453

2417.1617

2517.8081

2618.3921

2718.9042

2819.3823

2919.6845

3019.8284

3119.9312

3220.1099

3320.3821

3420.6058

3520.8195

3621.0119

3721.1892

3821.3383

3921.5068

4021.7576

4221.985

4422.162

4622.1969

4822.1944

5022.1186

5221.9786

5421.7741

5621.4969

5821.1803

6020.8339

6220.4567

6420.048

6619.617

6819.1973

7018.7801

7218.3677

7417.9594

7617.5555

7817.1559

8016.7624

8216.379

8416.0093

8615.6554

8815.3172

9014.9948

9214.688

9414.397

9614.1216

9813.862

10013.6136

10213.3672

10413.1139

10612.8489

10812.5724

11012.2843

11211.9849

11411.6728

11611.3534

11811.0023

12010.5634

12310.0798

1269.57399

1299.11968

1328.68009

1358.2688

1387.88419

1417.51931

1447.20352

1476.82436

1506.27002

1555.70943

1605.18744

1654.8407

1704.46622

1754.13017

1803.81575

1853.52406

1903.2675

1952.99523

2002.70857

2052.43975

2102.22098

2152.05357

2201.88638

2251.73315

2301.59018

2351.45846

2401.3377

2451.22799

2501.12839

2551.03713

2600.952335

2650.87311

2700.79944

2750.731316

2800.66879

2850.611817

2900.560424

2950.514596

3000.473726

3050.436687

3100.402298

3150.36996

3200.339676

3250.311443

3300.285273

3350.261171

3400.239109

3450.219139

3500.201028

3550.184428

3600.169046

3650.154639

3700.141251

3750.128838

3800.117423

3850.107016

3900.097607

3950.089223

4000.081714

4050.074854

4100.06847

4150.062413

4200.056706

4250.05135

4300.04632

4350.041661

4400.037327

4450.033349

4500.029704

4550.026395

4600.023434

4650.020828

4700.018586

4750.016669

4800.015111

4850.013875

4900.013015

4950.012518

5000.012324

Sheet3

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Time (months)

We (MM bbl)

Water Influx Rate (M bb/D)

MATERIAL BALANCE EXAMPLE

Sheet1

PETE 301 - Example showing the determination of initial oil in place and water influx parameters

Time constRsim

48000.3

TimePressureBtBgNpRpWpWiTimeEoEgEo+mEgFF/(Eo+mEg)

(months)(psia)(bbl/STB)(bbl/SCF)(MM STB)(SCF/STB)(MM bbl)(MM bbl)(months)(bbl/STB)(bbl/STB)(bbl/STB)(MM bbl)(MM STB)

029201.51660.0012220.00000.0000.00000.0000.0000.0000.000

2027901.56230.0013135.5008700.0000.000200.0460.1130.0809.098114.325

3027451.58080.0013489.5008600.0000.000300.0640.1560.11115.786142.071

4026801.61070.00140215.0008100.0350.000400.0940.2230.16124.406151.477

6026301.63550.00144425.1508300.4002.600600.1190.2760.20240.022198.567

8026151.63760.0014532.1008500.9655.100800.1210.2830.20650.759246.536

10025951.65410.00147938.9538701.8108.6001000.1370.3190.23361.675264.487

12025851.65970.00148945.0009102.89514.0101200.1430.3310.24370.942292.532

x=pWeD/(Eo+mEg)

raqD = 12raqD = 15raqD = 20

TimepWeDxpWeDxpWeDxF/(Eo+mEg)

202.22E+032.79E+042.31E+032.90E+042.34E+032.94E+04114.325

304.67E+034.21E+044.93E+034.44E+045.05E+034.54E+04142.071

407.45E+034.63E+048.03E+034.99E+048.32E+035.17E+04151.477

601.28E+046.35E+041.46E+047.23E+041.57E+047.77E+04198.567

801.67E+048.12E+042.02E+049.80E+042.27E+041.10E+05246.536

1001.94E+048.31E+042.47E+041.06E+052.92E+041.25E+05264.487

1202.13E+048.79E+042.83E+041.17E+053.51E+041.45E+05292.532

Sheet2

Sheet2

114.325114.325114.325

142.071142.071142.071

151.477151.477151.477

198.567198.567198.567

246.536246.536246.536

264.487264.487264.487

292.532292.532292.532

ReD=12

ReD=15

ReD=20

(p*WeD)/(Eo+mEg)

F/(Eo+mEg)

y = 0.002 x + 53.444

Sheet3

00

204.64

309.91

4016.1

6029.3

8040.5

10049.6

12056.9

15064.4

20070.8

25073.4

30074.6

35075

40075.2

45075.3

50075.3

04.65927

24.76829

45.04864

65.51588

86.17001

107.01111

128.03881

149.25451

1610.653

1812.2309

2013.6453

2114.8225

2215.6714

2316.453

2417.1617

2517.8081

2618.3921

2718.9042

2819.3823

2919.6845

3019.8284

3119.9312

3220.1099

3320.3821

3420.6058

3520.8195

3621.0119

3721.1892

3821.3383

3921.5068

4021.7576

4221.985

4422.162

4622.1969

4822.1944

5022.1186

5221.9786

5421.7741

5621.4969

5821.1803

6020.8339

6220.4567

6420.048

6619.617

6819.1973

7018.7801

7218.3677

7417.9594

7617.5555

7817.1559

8016.7624

8216.379

8416.0093

8615.6554

8815.3172

9014.9948

9214.688

9414.397

9614.1216

9813.862

10013.6136

10213.3672

10413.1139

10612.8489

10812.5724

11012.2843

11211.9849

11411.6728

11611.3534

11811.0023

12010.5634

12310.0798

1269.57399

1299.11968

1328.68009

1358.2688

1387.88419

1417.51931

1447.20352

1476.82436

1506.27002

1555.70943

1605.18744

1654.8407

1704.46622

1754.13017

1803.81575

1853.52406

1903.2675

1952.99523

2002.70857

2052.43975

2102.22098

2152.05357

2201.88638

2251.73315

2301.59018

2351.45846

2401.3377

2451.22799

2501.12839

2551.03713

2600.952335

2650.87311

2700.79944

2750.731316

2800.66879

2850.611817

2900.560424

2950.514596

3000.473726

3050.436687

3100.402298

3150.36996

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3450.219139

3500.201028

3550.184428

3600.169046

3650.154639

3700.141251

3750.128838

3800.117423

3850.107016

3900.097607

3950.089223

4000.081714

4050.074854

4100.06847

4150.062413

4200.056706

4250.05135

4300.04632

4350.041661

4400.037327

4450.033349

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4550.026395

4600.023434

4650.020828

4700.018586

4750.016669

4800.015111

4850.013875

4900.013015

4950.012518

5000.012324

Sheet3

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Time (months)

We (MM bbl)

Water Influx Rate (M bb/D)

MATERIAL BALANCE EXAMPLE

DETERMINATION OF WATER INJECTION REQUIREMENTNp[Bo+Bg(Rp-Rs)] + WpBw WiBw = N[Eot+mEgt] +WeIf the pressure is maintained constant over a period of time,then the pressure dependent terms are constant[Bo-BgRs)dNp/dt+Bgd(NpRp)/dt+Bw[(dWp/dt)-(dWi/dt)]=dWe/dt[Bo-BgRs)dNp/dt+BgdGp/dt+Bw[(dWp/dt)-(dWi/dt)] = dWe/dtThe water injection rate required to maintain the pressureconstant can be obtained from:BwdWi/dt = [Bo-BgRs]dNp/dt + BgdGp/dt + BwdWp/dt dWe/dtdWi/dt = Qinj = Water injection rate (STB/D)dWp/dt = Qw = Water production rate (STB/D)dWe/dt = Water influx rate (bbl/D)dNp/dt = Qo = Oil production rate (STB/D)dGp/dt = Qg = Gas production rate (SCF/D)

DETERMINATION OF WATER INJECTION REQUIREMENTBwQinj = [Bo-BgRs]Qo + BgQg + BwQw dWe/dtGOR = R = Qg/Qo Qg = R QoWOR = Qw/Qo Qw = WOR Qo

BwQinj = [Bo-BgRs]Qo + Bg R Qo + Bw WOR Qo dWe/dtBwQinj = [Bo-BgRs + Bg R + Bw WOR]Qo dWe/dtQinj = {[Bo + Bg (R-Rs ) + Bw WOR]Qo dWe/dt}/BwQinj = {[Bt + Bg (R-Rsi ) + Bw WOR]Qo dWe/dt}/BwR = Rs + (krg/kro) Boo/BggWOR = (krw/kro) Boo/BwwSw = Swi + [Bw(Wi-Wp)+We]/Vp(oz)So = Bo (N-Np) /Vp(oz)dWe/dt = B d[ pjWeDj]/dt

EXAMPLE OF WATER INJECTION REQUIREMENTOSp = 2585:Bt = 1.66 bbl/STBBg = 0.0015 bbl/SCFRsi = 800 SCF/STBBw = 1 bbl/STBParametros de Production s:Qo = 10,000 STB/DR = 1200 SCF/STBWOR = 0.5 Determinar el caudal water influx :dWe/dt = B d[ pjWeDj]/dtt =120 months:dWe/dt = B d[ pjWeDj]/dt = 10,067 bbl/D

EXAMPLE OF WATER INJECTION REQUIREMENTCalcular el caudal de injection del agua:Qinj = {[Bt+Bg (R-Rsi ) + Bw WOR]Qo dWe/dt}/BwQinj = [1.66+0.0015(1200-800)+0.5]x10,000 10,067 = 27,600 10,067 = 17,533 STB/D

Los requerimentos del caudal de injection del agua se incrementaran con el tiempo debido al incremento del WOR por el incremento de la saturation promedio del agua.

WINFLUX

TimeWedWe/dtdWe/dtQinj

204.625.80

309.8714.23

4016.0717.77

6029.1317.63

8040.3715.33

10049.3612.37

12056.6810.071006717533

13059.658.97896718633

15064.186.33633321267

20070.492.65265324947

30074.260.4545027150

50075.050.00227598

75075.040.00

100075.030.01

150075.040.00

200075.040.00

TimeWedWe/dt

204.62E+061.74E+054.65.80002.90E+04114.325

309.87E+064.27E+059.914.23334.44E+04142.071

401.61E+075.33E+0516.117.76674.99E+04151.477

602.91E+075.29E+0529.117.63337.23E+04198.567

804.04E+074.60E+0540.415.33339.80E+04246.536

1004.94E+073.71E+0549.412.36671.06E+05264.487

1205.67E+073.02E+0556.710.06671.17E+05292.532

1305.96E+072.69E+0559.68.9667

1506.42E+071.90E+0564.26.3333

2007.05E+077.96E+0470.52.6533

3007.43E+071.35E+0474.30.4500

5007.50E+074.63E+0175.00.0015

7507.50E+079.15E+0175.00.0031

10007.50E+071.98E+0275.00.0066

15007.50E+078.98E+0175.00.0030

20007.50E+072.18E+0175.00.0007

TimedWe/dtQinj

(months)(bbl/D)(STB/D)

1201006717533

130896718633

150633321267

200265324947

30045027150

WINFLUX

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DETERMINATION OF WATER INFLUX RATE

DETERMINATION OF WATER INFLUX RATE

DETERMINACION DEL CAUDAL DEL WATER INFLUX

********Understanding reservoir geology: identify communicating and noncommunicating pathways. Consult map to identify reservoir trap and impenetratable surfaces by water

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