Conceptos basicos de simulacion matematica de reservorios
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SIMULACION MATEMATICA RESERVORIOSSimulación de Reservorios
Un modelo es un conjunto de datos que describen un reservorio
Profundidad, dimensiones, porosidad, espesor, permeabilidad
Densidad de fluidos, viscosidad, solubilidad gas, factores de
volumen
Presión de reservorio, presión capilar, permeabilidades
relativas
Un simulador es un programa que calcula la distribución de presión
y saturación de un reservorio, como función de tiempo.
SIMULADOR VERSUS MODELO DE RESERVORIO
*
Simulators and Models
Through the years, many engineers have referred to simulators and
models as though they were the same, which is not true, and can
cause confusion. A simulator is a program, generally written in
fortran, that is typically leased from one of the major vendors,
such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data
used to describe a reservoir, its fluids, wells, etc.
During this course we will be building a model using data provided
by the instructor. ECLIPSE 100 is the simulator (or program) we
will be using to do this work.
Seferino Yesquen
Simulación de reservorios.- Uso de modelos matemáticos para simular
el comportamiento de un reservorio real
INPUT
Calidad de un estudio de simulación = f ( datos ingreso, modelo,
simulador )
Ec. de continuidad ( E B M ).
Ec. de flujo de fluidos ( Darcy ).
Ec. de estado. = f (p)
Simulador
OUTPUT
*
Ecuacion de la difusividad, es la combinacion de las principales
ecuaciones que describen el proceso fisico del movimiento de fluido
dentro del reservorio, convina:
La EBM (continuidad) se basa en la ley de conservación de la
materia, que establece que la masa de un sistema cerrado permanece
sirmpre constante. La EBM establece que la diferencia entre la
cantidad de fluidos iniciales en el yac. Y la cantidad de fluidos
remanentes es igual a la cantidad de fluidos producidos.
Para la aplicación del BM se toma en cuenta algunas consideraciones
importantes:
Volumen poroso es constante, no existe compactacion ni
subcidencia.
El PVT es representativo del yac.
Proceso isotermico
Cw y Cf son despreiables
Se considera equilibrio termodinamico entre entre el gas y el
petroleo a presion y temperatura de yac.
(Ecuacion de flujo) La unidad mas comun de la permeabilidad es el
Darcy, el cual esta definido como el flujo Q en cm3/s resultante
cuando la caida de presion es de 1 atm, aplicada a un lecho de 1cm2
de are transversal A de 1 cm de largo y para un fluido de
viscosidad 1Cp
Ecuacion de estado (compresibilidad), describe la relacion
volumen-presion o presion – densidad para los fluidos
presentes.
Para cada momento, estas tres ecuaciones son combinadas en una
unica ecuacion diferencial parcial, luego escritas como ec.
Difrenciales finitas, es decir que el yacimiento es visto como una
sucesion de bloques y la produccion es dividida en espacios de
tiempo, osea discretizar el problema en tiempo y espacio.
Seferino Yesquen
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Espacio : División del reservorio en pequeñas
distancias;
z
x
y
Distancia
Es necesario DISCRETIZAR las variables espacio y tiempo.
Discretización Tiempo : División. de historia de producción en
intervalos de tiempo
Tiempo
Discretización de las ecuaciones de flujo
Primero la coordenada en X deberá ser dividido en un numero
discreto de bloques. Considerando un sistema poroso horizontal en
una dimensión, se tiene un sistema de N grid blocks, cada uno de
longitud Dx:
Esto es llamado un grid de block centrado, y las propiedades
promedios de reservorio se refieren al punto medio del
bloque.
1
N
i-1
i
Aproximación por Serie de Taylor
*
Método de Modelaje con diferencias finitas
Se resuelven las ecuaciones par cada celda (grid block) por métodos
numéricos para obtener los cambios de PRESION y SATURACION con el
TIEMPO
La exactitud de los datos de entrada
Impacta la exactitud de los cálculos del simulador
La ecuación de Difusividad (1 Fase, flujo 1D)
*
1.-
Matrices
In order to solve the mass balance equation for each grid cell, all
cells have to be solved at the same time. The reason for this is
that in order to determine the flow of fluids into and out of a
cell, you need to know what is going on in the surrounding cells.
In other words, there has to be consistency between cells. To solve
several equations at the same time, it is convenient to use
matrices.
Seferino Yesquen
Consideraciones
Metodología de modelado
Recursos:
Cantidad y Calidad
Los resultados deberán estar asociados a una “banda de
incertidumbre”
*
Ejemplos de Metas de Estudios en Campos Nuevos
Definir limites internos y externos del reservorio.
Definir net pay, volumen & reservas
Determinar numero optimo de locaciones y configuración de
pozos
Optimizar el timing y tamaño de las facilidades de producción
Estimar el potencial de recuperación.
Anticipar la producción futura de fluidos y cambio
operacionales.
Determinar los caudales críticos para conning de agua gas.
CLARIDAD DEL PROPOSITO
Ejemplos de Metas de Estudios en Campos Maduros
Monitorear el movimiento de los contactos de fluidos
Evaluar y seguir la productividad de los pozos
Evaluar el comportamiento histórico. Determinar tendencias y
anomalías.
Determinar la fuente de la producción de agua y gas. Identificar
pozos potenciales para workover.
Monitorear barrido del reservorio. Localizar petróleo by paseado.
Perforación infill
Estimar beneficios de procesos de recuperación secundaria y
EOR:
Determinar conectividad entre reservorios múltiples.
Cuantificar migración a través de los limites del contrato.
*
Transformación de Datos
Caracterización Geológica
La descripción Geológica deberá identificar los factores claves que
afectan el flujo de fluidos en el reservorio.
*
Etapa 2: Caracterización del reservorio
La caracterización de los fluidos define las propiedades físicas de
las mezclas de los fluidos en el reservorio y como pueden variar
con cambios de P, T y V.
Clasificar el tipo de fluido
Determinar las propiedades de los fluidos.
Describir los mecanismos de producción del reservorio.
Caracterización de los fluidos
Etapa 2: Caracterización del reservorio
El modelo Petro físico define donde están localizados los volúmenes
de petróleo, gas y agua, así como es el comportamiento de estos
fluidos en la presencia de diferentes tipos de rocas.
Mojabilidad de la roca
SELECCIÓN DEL MODELO
Determine La Dimensionalidad
Use modelos 1D para flujos lineales o radiales en una
dirección.
Use modelos 2D para flujos en dos direcciones: Cross sections
*
CONSTRUCCION DEL MODELO
Convirtiendo el Modelo de la Tierra en un Modelo de
Simulación.
Control de Calidad de errores y problemas del modelo
geológico.
Scalar el modelo
Hacer un Output del modelo en formato del simulador
*
Equilibrar el modelo
AJUSTAR LA HISTORIA
Calibrar el Modelo
Seferino Yesquen
Datos Requeridos
A fin de realizar balance de materia en cada grid block, el
simulador necesita saber:
La presión y saturación inicial de cada grid block
La transmisibilidad para el flujo en las direcciones X, Y Z
La producción o inyección de cada grid block
*
Data Requirements
In order to perform a mass balance on each cell, the simulator
needs to be able to determine the initial mass of oil, water and
gas that exists in each grid block and also be able to determine
how much fluid flows in or out of each block.
The initial mass of each fluid is determined from the dimensions,
net thickness and porosity of each block, the initial saturation of
each fluid within the block, and the fluid density. The fluid
densities are determined from PVT data required for each fluid
present in the reservoir. The initial saturations are determine
from the depth of each block relative to the fluid contacts,
relative permeability endpoints, and capillary pressure data.
The flow of fluids in a simulator can be described in general
as:
q = T l DF
Here you have a flow rate equal to a
transmissibility*mobility*driving force.
The driving force in our case is the potential drop either between
two cells or a cell and the well. The initial pressure of each
block is determined from the initial pressure at datum, the depth
of each block, and initial reservoir fluid gradients. The gradients
are determined from the PVT data specified for each fluid initially
present in the reservoir.
K
A
L
Volumen de roca = DX*DY*DZ
El punto medio de la celda puede ser calculado
Punto medio = Prof. Tope + DZ/2
Volumen de roca y profundidad de los puntos medios
Dx
Dy
Dz
Bulk Volume and Midpoint Depth
The dimensions and top depth of each grid cell are required by the
simulator. The Areal dimension of each cell is taken from the
simulation grid. The vertical dimension of each cell is actually
the gross thickness assigned from gross thickness maps. The top
depth of each grid cell can be assigned from structure maps for
each model layer, however, where applicable, most simulators will
allow the user to specify the top depth of the reservoir for the
first model layer and the simulator will determine the depth of
each grid block from the top of the reservoir and gross thickness
values.
From these data, the simulator is able to determine the bulk volume
of each cell and the midpoint depth of each cell. The cell is
actually represented vertically by this mid-cell depth to determine
the initial pressure of the block and the angle and distance of
flow from one cell to another. Therefore, if this value is
incorrect, its effect with regard to these calculations needs to be
considered.
Seferino Yesquen
Valores de porosidad, relacion Net-to-gross y espesor neto son
asignados a cada celda de los mapas.
EL volumen poral es calculado :
VOLUMEN PORAL: DX*DY*DZ*NTG*PORO
VOLUMEN PORAL
Volumen Poral
Pore Volumes
The porosity and net thickness or net to gross are specified by the
user for each grid cell. These values are taken from maps created
for each model layer and are used to determine the initial pore
volume and, subsequently, initial volumes of oil, water, and gas in
each cell. As a result, the net thickness includes all sand that
contains fluid expected to add pressure support, regardless of the
type of fluid that initially exists in the sand.
It is actually the pore volume that is needed by the simulator.
After the pore volume for each cell has been determined, the
porosity becomes unimportant.
The net thickness or net to gross values will also be used to
determine the net sand thickness used in flow calculations from one
cell to another.
Seferino Yesquen
La permeabilidad para cada celda es especificada ya sea de mapas o
de correlaciones
La transmisibilidad para cada cara de flujo puede ser
calculada.
Transmisibilidad = K A / L
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order
to determine the flow of fluids between cells. By default, most
simulators use what is referred to as a five point finite
difference scheme. The five points refer to a cell and the four
cells surrounding it, in the horizontal plane. In other words,
there is no diagonal flow considered by the simulator. Some
simulators have what is referred to as a nine point finite
difference scheme which, in its most rigorous form, does consider
diagonal flow in the horizontal plane. In a five point finite
difference scheme, flow is allowed between a cell, the four cells
surrounding it in the horizontal plane, and the cells above and
below it. Therefore, transmissibilities are required for each of
the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and
the well must be determined to calculate flow in and out of each
well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified
using a correlation. In most cases the permeability in the x and y
direction are specified to be the same, though most simulators will
allow directional permeabilities. The permeability in the vertical
direction is usually specified as the horizontal permeability times
some factor. These values are used together with the net thickness
and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are
discussed in Chapter 6 along with different formats for specifying
this data.
It is actually the transmissibility that is important for each flow
face, for each cell. Once all transmissibilities are determined,
the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
K
A
L
Parámetros de Equilibración
El nivel de referencia, presión a este nivel, y los contactos de
fluidos son especificados
De estos datos, la presión de petróleo, agua y gas son tabuladas
como función de la profundidad.
Estas tablas usan las gradientes de los fluidos tomadas de los
datos PVT
*
Equilibration Parameters
For most problems, the reservoir is initialized assuming that the
reservoir is in equilibrium. Many problems can arise from poor
initialization of pressures and saturations. It is therefore
important that the initial pressures, saturations, and capillary
pressures are consistent with each other.
Initial Pressures
The initial pressure for each grid cell is determined from the
midpoint depth of the block, a datum depth, the initial pressure at
datum, and the initial fluid gradients present in the reservoir. We
have already seen how the midpoint depth of each block is
determined. The initial pressure at datum is specified to the
simulator along with the initial oil-water and gas-oil contacts.
These parameters are generally referred to as Equilibration or
Initialization parameters. The simulator uses this data to
determine the initial pressure, for each phase, for each
cell.
In ECLIPSE, tables of oil pressure, water pressure, and gas
pressure are created as a function of depth. The range of depths is
determined from the midpoint depths of each cell and the fluid
contacts specified by the user. The pressure at each depth is
calculated using the pressure at datum and the appropriate fluid
gradients determined from the PVT data. The initial pressure for
each cell is then determined from a table look-up process
OWC
P
i
h
Seferino Yesquen
Para celdas que no caen dentro de la zona de transición, las
saturación inicial de agua y gas son determinadas de los endpoints
de las curvas de permeabilidades relativas.
La saturación de petróleo es siempre determinada de 1-Sw-Sg
Fuera de la zona de transicion
Saturaciones Iniciales: So, Sw, Sg
*
Initial Oil, Water, and Gas Saturations
The initial oil, water, and gas saturations are used to determine
the initial volume of fluids in each cell. To rigorously determine
these volumes we need to recognize that part of a cell may be in
the transition zone and the cell may be cut by a fluid
contact.
For those volumes of the cell that do not lie in the transition
zone, the initial water and gas saturation are determined from the
relative permeability endpoints. This is usually true for all
simulators. The lowest water saturation value found in the table is
usually assigned to those volumes above the oil-water contact. For
volumes below the oil-water contact, in some simulators, the value
of water saturation is automatically set to a value of 1.0,
however, in ECLIPSE, the value is set to the highest water
saturation found in the relative permeability table. Similarly for
gas, the values of gas saturation for any volume below the gas-oil
contact is set to the lowest value found in the relative
permeability table. This value is usually 0.0. The value of gas
saturation above the gas-oil contact is set to the highest values
found in the table, usually 1-Swc. For those volumes of a cell that
are in a transition zone, the saturation is determined from the
capillary pressure table. The resulting water and gas saturations
are then a pore volume average of the volumes in the transition
zone and outside the transition zone. The oil saturation is always
calculated as 1-Sw-Sg.
Initialization Runs
It is important for the user to check the initial volumes of oil,
water, and gas calculated by the simulator. This is a first step,
basic check of the reservoir data. In particular, the initial oil
volume should be checked and compared to other estimates of the
initial oil in place.
Gas
Oil
Seferino Yesquen
En las zonas de transición, los valores iniciales de Sw y Sg son
determinados de una tabla de presión capilar versus Sw ó Sg.
Las presiones capilares son calculadas como la diferencia entre las
presiones de las fases.
Saturaciones Iniciales, So, Sw, Sg
En la zona de transición
*
Capillary Pressures
In the simulator, capillary pressures are determined for each grid
cell from the phase pressures. The oil-water capillary pressure is
calculated as a difference between the oil and water phase
pressures. Similarly, the gas-oil capillary pressure is a
difference between the oil and gas phase pressures.
Capillary pressures are used to determine the initial fluid
saturations for each cell, in the transition zone. A table of water
saturation versus capillary pressure is specified by the user, to
the simulator. The simulator knows the capillary pressure for each
cell and simply determines the water saturation from the
table.
Capillary pressure measurements taken in the laboratory are usually
not used to specify the initial water saturation distribution in
the reservoir. Instead, initial values of water saturation are
derived from logs and specified to the simulator. This data is
referred to as Pseudo Capillary Pressure data.
Oil Water Contact
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order
to determine the flow of fluids between cells. By default, most
simulators use what is referred to as a five point finite
difference scheme. The five points refer to a cell and the four
cells surrounding it, in the horizontal plane. In other words,
there is no diagonal flow considered by the simulator. Some
simulators have what is referred to as a nine point finite
difference scheme which, in its most rigorous form, does consider
diagonal flow in the horizontal plane. In a five point finite
difference scheme, flow is allowed between a cell, the four cells
surrounding it in the horizontal plane, and the cells above and
below it. Therefore, transmissibilities are required for each of
the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and
the well must be determined to calculate flow in and out of each
well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified
using a correlation. In most cases the permeability in the x and y
direction are specified to be the same, though most simulators will
allow directional permeabilities. The permeability in the vertical
direction is usually specified as the horizontal permeability times
some factor. These values are used together with the net thickness
and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are
discussed in Chapter 6 along with different formats for specifying
this data.
It is actually the transmissibility that is important for each flow
face, for each cell. Once all transmissibilities are determined,
the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
Permeability and Transmissibilities
A transmissibility must be calculated for each flow face in order
to determine the flow of fluids between cells. By default, most
simulators use what is referred to as a five point finite
difference scheme. The five points refer to a cell and the four
cells surrounding it, in the horizontal plane. In other words,
there is no diagonal flow considered by the simulator. Some
simulators have what is referred to as a nine point finite
difference scheme which, in its most rigorous form, does consider
diagonal flow in the horizontal plane. In a five point finite
difference scheme, flow is allowed between a cell, the four cells
surrounding it in the horizontal plane, and the cells above and
below it. Therefore, transmissibilities are required for each of
the six faces of flow, for each cell.
Similarly, a transmissibility for fluid flow between each cell and
the well must be determined to calculate flow in and out of each
well. These transmissibilities are calculated in general as:
Values for permeability are assigned either from maps or specified
using a correlation. In most cases the permeability in the x and y
direction are specified to be the same, though most simulators will
allow directional permeabilities. The permeability in the vertical
direction is usually specified as the horizontal permeability times
some factor. These values are used together with the net thickness
and perforated thickness to calculate transmissibilities.
There are a variety of transmissibility calculations. These are
discussed in Chapter 6 along with different formats for specifying
this data.
It is actually the transmissibility that is important for each flow
face, for each cell. Once all transmissibilities are determined,
the permeability becomes unimportant.
.00707Kh
ln( )+
S
r
e
r
w
VALIDACION DEL MODELO
Para VALIDAR adecuadamente el Modelo de Reservorios debemos
mantener en la mente siempre :
El ajuste de Historia no deberá nunca ser logrado a expensas de
modificar parámetros que son físicamente y/o geológicamente
errados.
*
Que es ajuste de Historia?
*
Por que ajustar la Historia ?
*
Datos de producción
Distribución de saturación (pozos, de 4D ), …
*
Que parámetros son cambiados para lograr un ajuste de
historia?
Permeabilidad (distribución espacial)
Porosidad (volumen poral)
Fallas (transmisibilidad, ubicación)
Otros ????
*
Consideraciones Importantes para hacer predicciones
Los casos de predicciones nunca deben exceder las capacidades del
modelo de simulación.
Las predicciones necesitan ser consistentes con las practicas de
campo.
Cas siempre la simulación trae consigo una solución no única con
incertidumbres inherentes de:
Falta de validación. Ej Reservorios con datos escasos de geología e
ingeniería.
*
R1
I1
VAN1
R2
I2
VAN2
R3
I3
VAN3
Simulators and Models
Through the years, many engineers have referred to simulators and
models as though they were the same, which is not true, and can
cause confusion. A simulator is a program, generally written in
fortran, that is typically leased from one of the major vendors,
such as GEOQUEST RESERVOIR TECHNOLOGIES. A model is a set of data
used to describe a reservoir, its fluids, wells, etc.