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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
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 2
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,
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 3
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.
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 4
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.
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 5
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.
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 6
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.
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 7
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
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 8
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
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 9
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
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 10
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
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 11
realizamos la conversin de las presiones encontrando un P para cada pozo con la gravedad especfica del mismo.
DATUM
Probador
DATUM
Estimacin del AOF (Absolute Open Flow) del
Reservorio. Simulacin de
Reservorios
Docente: Ing. Daro Cruz 12
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.