estimacion del aof

Estimacin del AOF (Absolute Open Flow) del

Reservorio. Simulacin de

Reservorios

Docente: Ing. Daro Cruz 1

Estimacin del AOF (Absolute Open Flow) del Reservorio

The absolute open flow (AOF) potential of a well is the rate at

which the well would produce against zero sandface back

pressure. It is used as a measure of gas well performance because

it quantifies the ability of a reservoir to deliver gas to the

wellbore. Deliverability tests make possible the prediction of

flow rates against any particular back pressure, including AOF

when the back pressure is zero. This result is illustrated on the

following inflow performance relationship (IPR) plot.

1. Types of Deliverability Tests. There are a number of tests which can be conducted in order to

calculate the deliverability of a well as described below.

1.1. Conventional Back Pressure Test The conventional back pressure test is conducted by flowing a

well at different rates. Each rate is sustained until the radius of

investigation has reached the outer edge of the drainage area and

pressure stabilization has been reached. This type of test is not

practical for low permeability reservoirs because the time to

reach pressure stabilization for each rate is excessive.

1.2. Isochronal Test A fundamental reason that the conventional test is theoretically

sound is that the radius of investigation is constant for each flow

period. In order to uphold this principle, the isochronal test takes

advantage of the fact that the radius of investigation is a function

of time and not flow rate. An isochronal test is conducted by

flowing a well at several different flow rates for periods of

equal duration, normally much less than the time required for

stabilization. A shut-in, long enough for the pressure to reach

essentially static conditions, is performed between each flow



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period. In addition, an extended flow rate, long enough to reach

pressure stabilization, is required. In tight reservoirs the length

of time required to reach pressure stabilization between flow

periods could make the isochronal test impractical.

1.3. Modified Isochronal Test The modified isochronal test is an isochronal test which requires

that each shut-in between flow periods, rather than being long

enough to attain essentially static conditions, should be of the

same duration as each flow period. It also requires an extended

flow period.

1.4. Single Point Test A single point test consists only of an extended flow period. They

require an estimate of the degree of turbulent flow in the

formation. This estimate is often based on information provided by

other wells in the same formation or calculated from reservoir

and fluid properties.

2. AOF Flow Conditions.

2.1. Extended Flow. Normally an isochronal test includes one flow rate that is

extended to stabilization and a stabilized pressure and flow rate

point is determined. This point is the extended flow pressure and

flow rate for the test. Single point tests do not include the multi-

rate portion of a test and consist of only an extended rate and

pressure.

2.2. Stabilized Shut-in. Stabilized generally refers to a test in which the pressure no

longer changes significantly with time. For AOF tests, the

stabilized shut-in pressure is a pressure that reflects the average

reservoir pressure at the time. It is either measured during the test

or determined from the interpretation of the data.

2.3. Stabilized Flow. In high permeability reservoirs or wells with small drainage areas,

it may be possible to flow the well until stabilization during the

extended flow period of a deliverability test. In these cases, the

stabilized pressure and flow rate point is the extended flow point.

Many tests, however, are not flowed to stabilization because of

time constraints (especially in tight reservoirs). An extended flow

and stabilized shut-in are still performed at the end of these

deliverability tests so that the buildup data can be analyzed and

from that the stabilized rate calculated. Stabilized flow can be

determined by calculation or by creating a model of the reservoir,



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doing a forecast at a specified pressure, and finding the point

when the rate has stabilized (usually at 3 months, 6 months, or 1

year) .

3. Types of Analyses.

Two types of analysis are available, the simplified analysis or the

laminar-inertial-turbulent (LIT) analysis.

LIT analysis is more rigorous than simplified analysis and is usually

only used in tests where turbulence is dominant and the

extrapolation to the AOF is large. However, in most cases the

simplified analysis is sufficient to determine the AOF and

deliverability.

3.1. Pressure Method. For both the simplified and LIT analysis, two pressure options are

available, the pressure squared or the pseudo-pressure approach.

3.2. Pressure Squared The pressure squared approach is the more traditional method,

and is often used because it is easier to understand and

calculate. However, it is only valid for medium to low pressure

ranges but is just as accurate as the pseudo-pressure approach in

this range.

3.3. Pseudo-Pressure Using pseudo-pressure will be more accurate than the pressure

squared approach, especially when dealing with a high pressure

system, where gas viscosity (mg) and compressibility (cg) cannot be

assumed to be constant. Thus, pseudo-pressure works for all

pressure ranges, although it is more difficult to calculate and

requires more computational time.

3.4. Simplified Analysis The simplified analysis is based on the following equation:

Pressure squared:

Pseudo-pressure:

The analysis of a modified isochronal test using the simplified

method is illustrated below. For the modified isochronal test,

pws must be used instead of pR because the duration of each shut-

in period is too short to reach static conditions.



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The data is plotted on a log-log plot of Dp2 versus qst where Dp2

is defined as:

The flow and shut-in periods of equal duration provide the

information required to plot four points. A straight line, called

the transient deliverability line, is drawn through these four

points.

The duration of the last flow rate is extended until the pressure

response has stabilized. This information is used to plot another

point called the stabilized point. A line parallel to the transient

deliverability line is drawn through the stabilized point. This is

called the stabilized deliverability line. If the extended flow

period does not reach pressure stabilization, a stabilized point can

be found by calculation from a buildup test.



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The parameter n can be determined from the slope of the line as

follows:

Thus, slope is equal to 1 / n, and n is called the inverse slope.

The other parameter, C, can be determined using n and the

coordinates (qst and pR) of any point on the stabilized

deliverability line (e.g. the stabilized point) as follows:

Note that C and n are considered to be constant for a limited

range of flow rates. In theory, it is expected that this form of the

deliverability relationship will be used only for the range of flow

rates used during the test. However, in practice it is used

indiscriminately for a wide range of rates and pressures.



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4. LIT Analysis. The LIT analysis is used with dealing with high rate wells where

turbulence is a major factor. Only the pseudo-pressure approach

can be used in this situation since pressures are in a higher range

due to the turbulence effects. LIT analysis is defined by the

following equation:

Note that the pseudo-pressure squared terms (a qst and b qst2)

are equivalent to skin due to damage (sd) and skin due to

turbulence (sturb). The coefficients a and b are defined in the

example below.

The analysis of an isochronal test using the LIT method is

illustrated below.

5. Procedimiento para la estimacin del rea de la Estructura mediante el Sistema de Grillado o Mallado.

1. Objetivos. 1.1. Objetivos Generales.

Determinar el Potencial AOF del Reservorio. Determinar la productividad optima del reservorio. Determinar la distribucin del potencial del

reservorio.

Determinar la distribucin optima del reservorio. 1.2. Objetivos Especficos.

Determinar el nivel de referencia o Datum. Realizar la correccin de presiones al nivel de

referencia.

Calcular las constantes C y n del mtodo de Fetckovick para cada pozo.



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Determinar el AOF de cada pozo. Obtener C y n promedio. Obtener el AOF del Reservorio.

2. Informacin.

Para la realizacin de la presente prctica dispondremos de la

siguiente informacin:

El plano estructural del reservorio con el que se cuenta es el siguiente:

20/64 6.52 5780 6862 12.21 303 53.5 24.82 0 24/64 13.75 5420 6771 17.74 364 54.8 20.52 0 28/64 13.05 5200 6723 22.17 543 53.6 24.49 0 32/64 12 4850 6667 27.65 658 53.5 23.79 0 40/64 4.75 3880 6540 34.87 854 52 24.49 0



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YIELD

24/64 15.1 5500 7035 14 376 54.1 26.92 2.7 28/64 3.2 5372 6921 17.9 475 53 26.52 2.2 32/64 11.9 5141 6732 24.6 644 53.1 26.11 2.2 40/64 12 4625 6356 34.2 868 52.6 25.28 1.3 48/64 11.9 4022 5925 42.7 1035 52.2 24.21 2.7 52/64 11.9 3601 5639 47.4 1150 52.1 24.01 3.5

24/64 24 5627 7101 16.2 409 53.11 25.24 3.6 32/64 12 5438 7052 27.5 673 52.1 24.47 3.0 40/64 12 5155 6998 37.4 868 52 23.21 4.0 48/64 12 4751 6930 49.1 1101 51.1 22.40 3.0 52/64 14 4297 6851 60 1459 NM 24.32 NM 28/64 24 5587 7088 19.4 503 52.9 25.91 3.6

24/64 24 5811 7025 14.48 409 52.1 28.24 2.4 32/64 15 5730 6921 26.17 660 50.8 25.22 2.5 40/64 15 5527 6722 41.18 1025 51 24.89 2.5 44/64 52 5428 6630 45.48 1176 49.7 25.86 2.8



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3. Herramientas y/o Ecuaciones a Utilizar.

Para el clculo del AOF utilizaremos el mtodo propuesto por

Feitkovich, el cual nos dice que para cada pozo:

nPwfCqg 22Pr

Donde:

Qg = Caudal de gas, PCS

Pr = Presion esttica de reservorio, PSI

Pwf = Presin de fondo fluyente, PSI

C = ndice de flujo

n = ndice de turbulencia

Y C y n son obtenidos tanto de forma grfica como analtica.

Para obtener el AOF de cada pozo tenemos que tomar en cuenta

que Pwf = 0 psi, por lo tanto:

n

n

CAOF

Pwf

PwfCqg

2

22

Pr

0

Pr

Don de la lectura del AOF podemos realizarla de forma grfica,

mediante el ajuste de los puntos obtenidos en la prueba de

produccin para cada pozo, de la siguiente manera:

Log(q)

Pr2

AOF



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Y el clculo de C y n lo podemos hacer mediante el ajuste de los

puntos realizados previamente de la siguiente manera:

n

n

AOFC

Pwf

Pwf

qgC

PP

qqn

2

22

Pr

0

Pr

1log2log

1log2log

Para calcular los ndices C y n para todo el reservorio

Feitkovich propone el siguiente mtodo de C y n promedio para

el reservorio con los datos de las 4 pruebas o ms realizadas a

los pozos:

datos

qqtotal

Cq

Cq

n

n

#

_______________

)10()10(

)10()10(

66

1

55

1

datos

qqtotal

Cq

Cq

n

n

#

_______________

)10()10(

)10()10(

66

2

55

2

_

)10(

)10(

10log10log

)10(log)10(log

6

6_

56

56_

n

t

tt

qC

qqn

3.1. Correccin de las Presiones de Prueba.

Los datos registrados en cada una de las pruebas que tenemos

fueron hechos a diferentes profundidades, para poder realizar

nuestro mapa isobrico se debe llevar todos nuestros datos

hacia un nivel de referencia o DATUM, Para esto realizamos la

proyeccin de los pozos 1 2 4 que se encuentran sobre un

mismo eje y podemos realizar la reconstruccin de nuestro

anticlinal y haciendo pasar por el centro de gravedad del mismo

un recta horizontal obtenemos nuestro Datum, luego



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realizamos la conversin de las presiones encontrando un P para cada pozo con la gravedad especfica del mismo.

DATUM

Probador

DATUM



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4. SELECCIN DE INFORMACION

La grafica de volumen equivalente de gas de condensado en tanque ser utilizada para determinar el equivalente de

crudo a gas mediante su gravedad especifica.

El mapa estructural nos servir para determinar las alturas de pozos y el nivel del contacto agua gas

5. CONSTRUCCION DE LOS PLANOS ISOS

Utilizaremos 2 modelos de simulacin Iso-AOF, Iso

Productividad Optima.

Iso- AOF.- En este modelo generaremos 1 mapa isopaco de todo el campo.

Iso Productividad ptima.- De igual manera se generara 1 mapa isopaco de todo el campo.

Para la resolucin del problema se construir una Grilla Ortogonal de dimensiones 2x 2 cm a una escala de 1cm =

50000 mts.

6. PLANILLA DE CLCULO

El formato que se utilizar se deja a consideracin debido a las

variaciones existentes en la presente prctica:

7. Resultados.

Como se puede apreciar los resultados que mas nos interesan

en la siguiente practica son:

La determinacin del AOF del Reservorio. Determinar la productividad optima del Reservorio.

No obstante los clculos referidos al clculo del AOF y

cualquier clculo auxiliar que se realice debern estar en esta

seccin.

8. Conclusiones.

En esta seccin debern hacer todas las consideraciones

necesarias sobre la practica, es decir resultados, clculos

aproximaciones y cada detalle que vean conveniente.

9. Anexos.

Esta seccin deber contener todas las grficas de grillas

utilizadas para todos los sistemas de grillas o mallas.

estimacion del aof

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