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 performance because 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.
There are a number of tests which can be conducted in order to calculate the deliverability of a well as described below. 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 stabilization has been reached. reached. This type of test is not practical for low permeability reservoirs because the time to reach pressure stabilization for each rate is excessive. 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 this principle, the isochronal isochronal test takes advantage of the fact that the radius of investigation is a function of time and not flow flow rate. An isochronal 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 for the pressure to reach reach essentially static conditions, is performed between each flow Docente: Ing. Darío Cruz
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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. 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. 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.
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 multirate portion of a test and consist of only an extended rate and pressure. 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. 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, Docente: Ing. Darío Cruz
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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) .
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. For both the simplified and LIT analysis, two pressure options are available, the pressure squared or the pseudo-pressure approach. 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. 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. The simplified analysis is based on the following equation:
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 shutin period is too short to reach static conditions. Docente: Ing. Darío Cruz
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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.
Docente: Ing. Darío Cruz
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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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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.
Determinar el Potencial AOF del Reservorio. Determinar la productividad optima del reservorio. Determinar la distribución del potencial del reservorio. Determinar la distribución optima del reservorio. Determinar el nivel de referencia o Datum. Realizar la corrección de presiones al nivel de referencia. Calcular las constantes C y n del método de Fetckovick para cada pozo.
Docente: Ing. Darío Cruz
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Determinar el AOF de cada pozo. Obtener “C” y “n” promedio. Obtener el AOF del Reservorio.
Para la realización de la presente práctica dispondremos de la siguiente información:
El plano estructural del reservorio con el que se cuenta es el siguiente:
6.52 5780 6862 12.21 20/64 13.75 5420 6771 17.74 24/64 13.05 5200 6723 22.17 28/64 12 4850 6667 27.65 32/64 4.75 3880 6540 34.87 40/64
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53.5
24.82
0
364
54.8
20.52
0
543
53.6
24.49
0
658
53.5
23.79
0
854
52
24.49
0
7
15.1 5500 7035 24/64 3.2 5372 6921 28/64 11.9 5141 6732 32/64 12 4625 6356 40/64 11.9 4022 5925 48/64 11.9 3601 5639 52/64
24 5627 7101 24/64 12 5438 7052 32/64 12 5155 6998 40/64 12 4751 6930 48/64 14 4297 6851 52/64 24 5587 7088 28/64
YIELD
14
376
54.1
26.92
2.7
17.9
475
53
26.52
2.2
24.6
644
53.1
26.11
2.2
34.2
868
52.6
25.28
1.3
42.7
1035
52.2
24.21
2.7
47.4
1150
52.1
24.01
3.5
16.2
409
53.11
25.24
3.6
27.5
673
52.1
24.47
3.0
37.4
868
52
23.21
4.0
49.1
1101
51.1
22.40
3.0
60
1459
NM
24.32
NM
19.4
503
52.9
25.91
3.6
24 5811 7025 14.48 24/64 15 5730 6921 26.17 32/64 15 5527 6722 41.18 40/64 52 5428 6630 45.48 44/64
409
52.1
28.24
2.4
660
50.8
25.22
2.5
1025
51
24.89
2.5
1176
49.7
25.86
2.8
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Para el cálculo del AOF utilizaremos el método propuesto por Feitkovich, el cual nos dice que para cada pozo:
qg C Pr 2 Pwf 2
n
Donde: Qg = Caudal de gas, PCS Pr = Presion estática de reservorio, PSI Pwf = Presión de fondo fluyente, PSI C = Índice de flujo n = Índice de turbulencia Y “C” y “n” son obtenidos tanto de forma gráfica como analítica. Para obtener el AOF de cada pozo tenemos que tomar en cuenta que Pwf = 0 psi, por lo tanto: qg C Pr 2 Pwf 2
n
Pwf 0 AOF C Pr 2
n
Don de la lectura del AOF podemos realizarla de forma gráfica, mediante el ajuste de los puntos obtenidos en la prueba de producción para cada pozo, de la siguiente manera:
Pr2
AOF
Docente: Ing. Darío Cruz
Log(q) 9
Y el cálculo de C y n lo podemos hacer mediante el ajuste de los puntos realizados previamente de la siguiente manera: logq 2 log q1
n
log P 2 log P 1
C
qg
Pr Pwf
2 n
2
Pwf 0 C
AOF
Pr
2 n
Para calcular los índices C y n para todo el reservorio Feitkovich propone el siguiente método de C y n promedio para el reservorio con los datos de las 4 pruebas o más realizadas a los pozos: q1 (105 ) C (105 ) n
q2 (105 ) C (105 ) n
q1 (106 ) C (106 ) n
q2 (106 ) C (106 ) n
__________ _____
__________ _____
qtotal
q
qtotal
# datos 6
_
n
_
C
q # datos
5
log qt (10 ) log qt (10 ) log106
5
log10
6
qt (10 ) _
6 n
(10 )
Los datos registrados en cada una de las pruebas que tenemos fueron hechos a diferentes profundidades, para poder realizar nuestro mapa isobárico se debe llevar todos nuestros datos hacia un nivel de referencia o , Para esto realizamos la proyección de los pozos 1 – 2 – 4 que se encuentran sobre un mismo eje y podemos realizar la reconstrucción de nuestro anticlinal y haciendo pasar por el centro de gravedad del mismo un recta horizontal obtenemos nuestro Datum, luego Docente: Ing. Darío Cruz
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realizamos la conversión de las presiones encontrando un P para cada pozo con la gravedad específica del mismo.
Probador
DATUM
DATUM
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La grafica de volumen equivalente de gas de condensado en tanque será utilizada para determinar el equivalente de crudo a gas mediante su gravedad especifica. El mapa estructural nos servirá para determinar las alturas de pozos y el nivel del contacto agua –gas
Utilizaremos 2 modelos Productividad Optima.
de
simulación
Iso-AOF,
Iso
–
Iso- AOF.- En este modelo generaremos 1 mapa isopaco de todo el campo. Iso – Productividad Óptima.- De igual manera se generara 1 mapa isopaco de todo el campo. Para la resolución del problema se construirá una Grilla Ortogonal de dimensiones 2x 2 cm a una escala de 1cm = 50000 mts.
El formato que se utilizará se deja a consideración debido a las variaciones existentes en la presente práctica:
Como se puede apreciar los resultados que mas nos interesan en la siguiente practica son:
La determinación del AOF del Reservorio. Determinar la productividad optima del Reservorio.
No obstante los cálculos referidos al cálculo del AOF y cualquier cálculo auxiliar que se realice deberán estar en esta sección.
En esta sección deberán hacer todas las consideraciones necesarias sobre la practica, es decir resultados, cálculos aproximaciones y cada detalle que vean conveniente.
Esta sección deberá contener todas las gráficas de grillas utilizadas para todos los sistemas de grillas o mallas. Docente: Ing. Darío Cruz
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