Thermal Simulation with Multisegment Wells

Prévia do material em texto

Copyright 2001, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the SPE Reservoir Simulation Symposium held in
Houston, Texas, 11–14 February 2001.
This paper was selected for presentation by an SPE Program Committee following review of
information contained in an abstract submitted by the author(s). Contents of the paper, as
presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material, as presented, does not necessarily reflect any
position of the Society of Petroleum Engineers, its officers, or members. Papers presented at
SPE meetings are subject to publication review by Editorial Committees of the Society of
Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper
for commercial purposes without the written consent of the Society of Petroleum Engineers is
prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300
words; illustrations may not be copied. The abstract must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.
Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract
The extension of a previously reported well model to
compositional and thermal applications is discussed. This
multisegment, multi-branching wellbore model has been fully
coupled to a commercial reservoir simulator which can operate
in black-oil, compositional or thermal modes. In this paper,
the discussion will focus on thermal, heavy oil applications
where simulation requires a better representation of the
wellbore geometry and the physics of fluid flow and heat
transfer.
Introduction
Gravity drainage processes with possible steam (SAGD) or
gas vapour (VAPEX) assistance and other recovery
technologies often require the use of long horizontal wells
with flow in an inner tubing and outer annulus. For example,
a discussion of the design of a commercial Canadian SAGD
heavy oil project is given by Edmunds and Suggett1.
Carpenter and Dazet2 review the use of horizontal wells in a
steam drive project in the Midway Sunset field in Kern
County, California. An overview of recent advances in
steamflood technology that includes a good discussion of
horizontal well applications, and the impact of numerical
simulation on this technology is given by Hong3.
Thermal studies which simulate horizontal and vertical
wells have been discussed by many authors. We briefly
review some of the work on thermal fields in western Canada
and California, USA.
Horizontal infill well performance in a mature Midway-
Sunset cyclic-steam project was simulated and analyzed by
Chona et al.4 and Al-Hadrami et al.5,6. Other engineering
analyses using thermal horizontal cyclic well simulations in
Midway Sunset include Hazlett et al.7, Rajtar and Hazlett8 and
Deo and Schamel9. In this region, the oil can be 14° API and
6000 cp at 32°. C. Chiou et al.10 discuss utilising simulation
to develop strategies for the South Belridge field in California.
A typical oil API for this field is 13° and viscosity is 2000 cp
at 32° C.
Somewhat heavier oils are found in Canada. A simulation
study was carried out of the Burnt Lake Oil Sands lease which
is part of the Cold Lake oil sands deposit, by Kisman and
Yeung11. Here the oil is 11-12° API and 7000 cp at 30° C.
They simulated the SAGD process of a 1000 metre long
horizontal well pair. There has also been some success in
using a single horizontal well with a SAGD process, as
discussed by Oballa and Buchanan12. They used two
representative oils, one similar to a viscous oil found at the
UTF project13 of 1,000,000 cp at 12° C (8° API), and a more
mobile oil with a viscosity of 6000 cp at 12° C which is
similar to a Cold Lake oil. The UTF project is situated in the
Athabasca tar sands deposit.
The above reviewed studies have, for the most part, used
the conventional wellbore line source/sink model available in
any thermal simulator.
Simulation technology for horizontal wells has improved
dramatically since the late 1980’s. At this time Stone et al.14
described a horizontal well model that featured a mechanistic
multi-phase fluid flow model in the wellbore, and allowed
flow simultaneously in an inner tubing and outer annulus.
This was designed to handle simulations in the near wellbore
region of a dual-well SAGD process and, because of the more
detailed flow regime map, could not handle larger-scale
simulations for stability reasons. Also during this time period,
Nghiem et al.15 carried out the Seventh SPE Comparative
Solution Project concerning the modelling of horizontal wells
in reservoir simulation. A variety of methods was used by the
participants to model the inflow into the horizontal well
model. These included the use of an inflow performance
relationship with a separate well model or direct coupling by
modelling the well as part of the grid. Similarly, there were
various wellbore hydraulics models from a constant-pressure
line-sink to friction pressure drop relations or simple
functional fits of published holdup correlations. All of these
SPE 66373
Thermal Simulation with Multisegment Wells
T. W. Stone, Schlumberger GeoQuest, J. Bennett, Schlumberger GeoQuest, D. H.-S. Law, Alberta Research Council,
J. A. Holmes, Schlumberger GeoQuest
SPE Members
2 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
horizontal well models were designed to run robustly and
stably in large-scale field simulations. However, some were
limited in the ability to calculate a multi-phase pressure drop,
others in not allowing the wellbore model geometry to
correspond to the engineering design of the well rather than to
the simulation grid. Some of the methods allowed multi-phase
pressure drops using explicit updates or other approximations.
Recently, Tan et al.16 have described a fully coupled
discretized thermal wellbore model with the ability to simulate
flow in casing/annulus wellbore cells. Estimates of the
relative flow rates are made based on phase saturations and
straight-line relative permeability curves. These estimates are
passed to a subroutine that calculates flow rates from the
correlated Beggs and Brill17 measurements. Wellbore cells are
connected to reservoir cells.
A multisegment well model which can simulate flow in
advanced wells was discussed by Holmes et al.18,19. This
model, implemented in a commercial black oil simulator, is
able to determine the local flowing conditions (the flow rate of
each fluid and the pressure) throughout the well. It allows for
pressure losses along the wellbore and across any flow control
devices. In addition to being fully implicitly coupled, with
crossflow modelling and the standard group control facilities,
horizontal, multi-lateral wells and ‘smart’ wells containing
flow control devices can also be modelled. The trajectory is
not constrained by the simulation grid. For example, the
wellbore may run outside the grid or across layers. Properties
and geometry can be updated at any time in the simulation.
In this paper, we first describe the implementation and
enhancements to the implicit multisegment well model
discussed in Ref. 18 that allow this model to run in
compositional and thermal modes. In these modes, the EOS or
thermal K-value treatment of the fluid PVT is extended to the
wellbore flow. Phase volumes are computed in each segment
which are then used to calculate the multi-phase pressure drop.
In thermal mode, an enhancement allows heat transfer
coefficients to be defined which permit heat loss to the
reservoir, to another segment or to the overburden. Another
enhancement allows individual segments to inject or produce
fluids which permits the direct modelling of gas lift, down-
hole water pumps or circulating wells, availablein any mode.
It is important to properly initialise compositional and
especially thermal wellbore simulations. A method for
predicting the initial state within the well is also shown below.
We then present four case studies. Each case study has
been set up from published engineering analyses of fields in
western Canada and California. The well model used in these
studies is considerably more detailed than in the original
published simulation work. Not only are the wellbore
hydraulics more accurately modelled with multi-phase flow
models, but also the geometry of the wells is specified in more
detail. Wellbore geometry includes the ability to run the well
outside the simulation grid, allowing the modelling of heat
loss from a steam injection well to the formation, between the
surface and the simulation grid. Also, an undulating well
trajectory can be specified and is demonstrated in one of the
studies. Fluid flow down an inner tubing and back along an
outer completed annulus is demonstrated in three of the
studies where heat transfer occurs between the inner tubing
and outer annulus as well as heat transfer from the annulus to
formation. Two of these studies contain a segment at the heel
of a horizontal annulus that removes fluids to an external sink,
allowing part of the circulating fluids to return to the surface
while the remainder are injected, produced or stored in the
wellbore. Where possible, differences are shown between the
multisegment model and a standard line source/sink model
that demonstrate the effects of modelling the improved
wellbore physics.
Description of the Multisegment Well Model
The multisegment well model reported by Holmes et al.18 was
originally implemented in a black oil simulator. It uses four
main variables: PFFG gwT ,,, . These are, respectively, a
total fluid flow rate through the segment, weighted fractional
flows of water and gas, and pressure in the segment.
This model has now been implemented in a
compositionally based commercial simulator. Multisegment
well model variables were chosen to represent the segment
pressure P , total molar flow rate in the segment TG ,
component moles per segment fluid volume cM and internal
energy per segment bulk volume E .
A simple drift-flux model18 has also been implemented for
black oil and compositional simulation, but not thermal
simulation. This allows the phases to flow with unequal flow
rates. If a drift-flux flow model is chosen in some or all of the
segments, the total molar flow rate variable in those segments
is replaced with total volume flow rate.
A schematic of an example multi-lateral multisegment well
is shown in Figure 1. Each segment consists of a ‘node’ and a
‘flowpath’ to its parent segment’s node. The node lies at the
far end of the segment, i.e. the end furthest from the wellhead.
At branch points, two or more segments may connect to the
same node. Flow from the reservoir grid cells may also enter
the segment at its node. In thermal simulations, energy can be
transferred to a segment by conduction, from the formation or
from neighbouring segments. Each segment has a length,
diameter, roughness, area and volume. The volume is used for
wellbore storage calculations, while the other attributes are
properties of the flowpath and are used in the pressure loss
calculation. In thermal simulations the segments have a wall
volume, heat capacity, area and conductivity.
In black oil and compositional mode there are 2+cN
variables and equations for each segment node where cN is
the number of components in the simulation. In thermal mode
an extra energy equation is needed. The first cN equations
are material balance equations for each component,
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 3
0=+--
D
D
= åå
ÎÎ
cn
nj
cj
ni
ci
cn
cn QqQt
m
R …………(1)
cnmD is the molar gain in the amount of component c in the
segment n over the time step tD . ciQ represents the molar
flow rate through each inlet junction i to segment n . cnQ is
the flow rate through the outlet junction of segment n .
In equation (1), cjq is the flow rate from any reservoir grid
blocks j connecting with segment n which in turn is
obtained from an inflow performance relationship as described
in Ref. 18. For production from the formation, the component
mobilities within the connecting grid block are used. For
injecting flows, a mobility relation as described in Ref. 19 is
evaluated using the segment’s main variables so that the fluid
mixture flowing into the formation reflects the contents of the
segment. This inflow performance relationship includes
hydrostatic depth corrections between the centre of the grid
block and the depth of the completion, and between the
segment’s node depth and the depth of the completion. In the
work described in this paper, the depth correction between the
centre of the grid block and the depth of the completion differs
slightly from that described in Ref. 18. Here, the head is
calculated from an average of the mobile fluid densities in the
grid block, weighted according to the fluid saturations in the
grid block, instead of the grid block’s relative permeabilities
which were used in the previous work. These depth
corrections are implicit. They allow the depth of the segment
node to be different from the depth of the grid block, which is
useful for modelling undulating horizontal wells or wells
whose trajectory does not align with the grid’s orthogonal
directions.
In thermal simulation, energy is conserved in the segments
according to
0=++--
D
D
= åå
ÎÎ
EsEn
nj
Ej
ni
Ei
n
En QQqQt
E
R .…(2)
nED is the gain in energy stored in the segment fluids and
wall during the time step tD . A cross-sectional area is set
which, when multiplied by the segment length, gives the
volume of the segment wall in which energy is stored. The
amount of stored energy in the segment bulk volume and the
rate of heat conduction from a segment to its neighbour are
determined by input heat capacities and thermal
conductivities. EiQ represents the energy flow rate through
each inlet junction i to segment n including convective and
conductive heat flow. EnQ is the energy flow rate through the
outlet junction of segment n or through a specified external
sink. Ejq is the inflow rate from any reservoir grid blocks j .
This inflow includes energy convected via an inflow
performance relationship as well as energy conducted through
a specified heat transfer coefficient. EsQ accounts for energy
gain/loss by heat transfer, specified with a heat transfer
coefficient, to an external source/sink with a known
temperature. For example, because the multisegment well is
not constrained to lie within the simulation grid, this term can
account for conductive heat loss to the overburden from a
steam injection well. EsQ also represents heat transfer from
one segment to another via a heat transfer coefficient. In this
case, the connecting segment may be neither an inlet segment
nor the outlet segment. For example, in simulations involving
an inner tubing and outer annulus, conductive heat transfer can
be modelled from each inner tubing segment to its companion
outer annulus segment.
In order that the sum of all phase volumes equals the
segment volume, a volume balance equation is solved.
The final equation for each segment, except the topmost
segment, calculates a pressure drop as a function of flow rate
through its outlet junction and is described in Ref. 18. This
pressure loss includes a hydrostatic, friction and acceleration
pressure drop across the segment. The multisegment well
model offers a choice of three methods for calculating the
pressure drop:
1. A homogeneous flow model, in which all phases flow
with the same velocity.
2. A simple ‘drift flux’ vertical and inclined flow modelwhich allows the phases to flow with different
velocities.
3. Interpolating a pre-calculated pressure drop table.
Here, pressure loss data as a function of outlet
pressure, flow rate, water fraction and gas fraction are
supplied in the form of a Vertical Flow Performance
(VFP) table. This model enables the use of more
sophisticated multiphase flow models such as
published hold-up correlations, for example Beggs
and Brill17. These correlations can be used to
construct the table in a separate software program.
VFP tables are also useful for modelling pressure
drops across specific devices such as chokes, for
which there are no correlations currently built into the
well model.
A pressure drop scaling factor is available that allows the
user to tune the pressure drop calculation. This multiplier can
be set for each segment to be a constant or to be a function of
water-oil ratio and/or gas-oil ratio.
The top segment is the segment that corresponds to the
well’s bottom hole reference depth. Pressure in this segment
is the same as the well’s bottom hole pressure (BHP).
Material, energy and volume balance equations are solved in
this segment as described above. In place of the pressure drop
equation, the equation used in the top segment is the well’s
control mode equation. All of the well and group control
modes available with the standard well model in black-oil,
compositional and thermal modes are available to the
multisegment well model. In addition, the multisegment well
model is fully compatible with the other available features
4 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
such as group control options, pressure maintenance,
economic limits (including completion limits), etc.
Initialisation of the Multisegment Well Model
To initialise the set of compositional molar densities, cM ,
and energy density E , we extend a simple idea originally
used by Modine and Coats20. A wellbore reservoir volume
balance was employed in their work to determine the wellbore
phase saturations. Individual phase rates were calculated from
the inflow performance relationship for each completion and
the total volume flow rates for all nodes were accumulated
throughout the wellbore. Then a tri-diagonal matrix equation
was set up to solve for the corresponding phase saturations.
An initial pressure is needed for each layer but they did not
discuss the formulation of the wellbore pressure gradient.
We use the same idea as follows. An initial pressure
solution is estimated using an average wellbore density and a
given BHP. Then the total volume flow rates for all segments
are determined starting from the furthest nodes in all branches.
For each component, the molar injection/production from each
completion and, if applicable, from the surface injection
stream is then used together with the total volume flow rate in
all segments to set up a tri-diagonal matrix to solve for the
moles of this component per total fluid volume. This
initialisation, which conserves reservoir fluid volumes,
neglects compressibility and mass transfer effects within the
wellbore, and hence is an approximation to the exact mass
conservation.
An energy prediction for thermal mode follows the same
idea. The volume flow rates together with the energy
injection/production from each completion and surface
injection stream form a matrix equation which is solved for
energy densities. Account is taken of the energy stored in the
walls. Completion energy injection and production includes
both convective and conductive heat transfer.
Enhancements: External Source/Sink
It is possible to import water or gas into a segment from a
source that is external to the reservoir grid. The import rate
may be defined either as a constant value or as a function of
the segment’s pressure. The imported fluid is added to fluid
flowing through the segment. There are a number of possible
applications for this facility. Gas import may be used to
model the effects of lift gas injection, to examine the kick-off
process for example. Gas lift may even be used in a thermal
SAGD heavy oil project as reported by Edmunds1. Water
import may be used to take account of the water injected to
power a down-hole hydraulic pump.
There is also an option to remove fluid from a segment to
an external sink, at a rate that is a function of the segment’s
pressure. This facility is primarily intended for use with the
thermal option to model recirculating wells.
Enhancements: Heat Transfer Coefficients
Heat transfer can take place along the well and across the well,
from the segment to the reservoir grid, to another segment or
to a specified fixed external temperature.
The heat transfer rate, htQ , to/from the segment is
( ) hexicisseght RTTLQ /,,-×= ………………………….(3)
where
L is the thermal contact length,
segT is the temperature in the segment
exicisT ,, is the temperature of a target segment or completion
grid block or external fixed temperature,
hR is the specific thermal resistance
Thermal resistance can be thought of as an inverse heat
transfer coefficient per unit length, for example with metric
units 
1-
÷
ø
ö
ç
è
æ
°×× CDm
KJ
. This thermal resistance to heat
transfer from the segment to the formation can be determined
as presented by Prats21. As shown in Figure 2, it may include
resistance due to scale deposits on the pipe wall, insulation,
annulus gas, casing wall, cement and altered formation.
Along the well, heat transfer by conduction through the
walls is included in the energy flow term EiQ in equation 2.
Heat transfer is handled implicitly in the numerical scheme.
Case Studies
Four case studies were designed with two objectives. Firstly,
the design of three of the four studies closely followed
published engineering simulation studies of fields in western
Canada and California, USA. As many of the reported
parameters as possible were accounted for including wellbore
design, placement, rock parameters such as absolute and
relative permeabilities and injection rates. The fourth study
uses parameters reported in a thermal SPE Comparative
Solution Project22. Secondly, to highlight the capability of the
multisegment well model reported in this paper, we then added
parameters in wellbore design, heat loss and trajectory that
may not have been used in the original work but were typical
of the thermal operation on which the original simulation
study was based. All additional parameters were found either
in the original study or in other published accounts and are
referenced. The purpose of adhering closely to the actual
process and simulation conditions was to demonstrate the
ability of the thermal multisegment well model to handle the
wellbore physics and geometry. A second purpose was to
demonstrate stability and robustness under these conditions.
Table 1 contains reservoir properties for the four studies.
Well design parameters are listed in Table 2. Table 3 contains
well operation rates and limits and Table 4 contains some
simulation parameters.
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 5
Case Study 1
Sheppard et al.23 review the operations of Husky Oil at the
Pike’s Peak heavy oil field in Saskatchewan, Canada. This
field is part of the Lloydminster deposit and features a 12° API
oil, GOR of 15 m3/m3 and a gas-free viscosity of 25000 cp at
18° C. We have based our first case study on properties of this
field.
Two 400 m horizontal undulating wells have been
simulated with a 7 m vertical separation. Net pay thickness is
20 m. A schematic of a section of the upper injector and lower
producer is shown in Figure 3. Figure 4a shows the
undulating trajectory. This study models the start of a SAGD
operation, where these two horizontal wells are initially
circulating hot steam for 60 days in order to heat the region of
reservoirnear the wells for the purpose of establishing hot
communication. Both wells are open during this time so that
some of the circulating steam may enter the reservoir and
reservoir fluids may be produced. Subsequently, after 60
days, circulation is stopped, the upper horizontal well becomes
an injector, the lower a producer.
Both wells were modelled with inner tubing and outer
annulus segments for fluid and energy flow. During the
startup period, 65% quality steam at 250° C was injected into
the inner tubing of both wells and circulated back along the
annulus. An external sink was defined at the heel of the
annulus of both wells where fluids were removed to a
specified external pressure.
Heat transfer was modelled between the inner tubing and
outer annulus as well as from the annulus to formation. An
annulus to formation heat transfer coefficient was obtained
from Prats21 who calculates this coefficient for heat loss from
a steam injection well to undisturbed formation. For purposes
of this study, heat transfer coefficients from inner tubing to
outer annulus were estimated to be an order of magnitude
larger than those to the formation, because of the lower
thermal resistance.
We obtained Lloydminster oil-water and oil-gas relative
permeability curves and endpoints from Wang and Chen24
who also did a simulation study of a field in this region. The
P-T solution gas K-value function was taken to be that of
methane25. The heavy component was non-volatile.
The problem is symmetric along the axis of the wells. To
simulate half of a multisegment well, we have used half the
cross-sectional flow areas for the tubing/casing and the full
hydraulic diameters for each. The retention of the original
diameters was in order to correctly calculate the multi-phase
Reynold’s number in the pressure drop calculation, while the
flow areas and volumes were halved to account for the
symmetry. The thermal resistance was doubled. Injection
rates as noted in Ref. 23 were halved. The size of the first grid
cell in the direction orthogonal to the well axis and well PI
were also halved to account for the symmetry.
Figures 4a and 4b show temperature contours along the
axis of the well at the end of the 60 day circulation period and
at 365 days. During the initial 60 days, there was insufficient
injectivity for any notable steam penetration into the formation
– all of the heat present in the reservoir was conducted from
the wells.
Undulation of the wells causes some areas of the formation
to heat more readily than others. There is a hotter zone that
can be seen in Figure 4 at 365 days around the middle of the
upper injection well. This zone is in the region of a depression
in the trajectory of this injector. It results from a local
crossflow that is causing the steam to inject from adjoining
segments and produce at a single segment in the middle,
depressed region. A local circulation cell is established. Part
of the steam injected in this region is immediately produced
due to the local crossflow cell, part travels downward to be
produced in the lower producer while the rest flows upwards
to enhance the steam chest. There is also a smaller circulation
cell near the toe. Both of these cells are stable in time. The
circulation rate slowly decreases as the steam chamber builds
in these regions of the well and the cells can eventually die
out. Figure 5 shows temperature contours in the plane
orthogonal to the well at the same times as in Figure 4.
Figure 6 is a plot at 365 days of the hydrostatic, frictional
and accelerational pressure drops in the upper injection well.
Hydrostatic and frictional heads are presented along the outer
annulus while the accelerational head is shown through the
entire length. The acceleration pressure drop, which models a
change in fluid inertia, is important only in the last inner
tubing segment before the annular segments begin.
Acceleration pressure drop is caused by a change in velocity
of the fluids at the toe of the well where the cross section to
flow changes. The friction pressure drop is highest in
magnitude at the point where some multi-phase production is
occurring in the middle of the annulus as discussed in the
above paragraph. Hydrostatic contributions to the pressure
drop are also shown. These are a result of the undulating
trajectory. The largest contribution to the hydrostatic head
occurs at the heel of the annulus, where stagnant water has
pooled (liquid holdup fraction = 0.98).
Case Study 2
We have followed Kisman et al.11 who carried out a two-
dimensional simulation study of the Burnt Lake oil sands lease
situated in the Cold Lake Alberta oil sands deposit. Oil is 12°
API, dead oil viscosity is 80,000 cp at 12° C and the GOR is
7.5 m3/m3. Net pay thickness is 30 m.
Their 2-D grid has been extended to 3-D in our study. We
have retained the same x-y grid sizes and dimensions as in the
original simulation and have added the extra dimension
because this study concerns the simulation of a single-well
SAGD operation which is more three dimensional in nature.
The single well in our simulation study features an inner
tubing and outer annulus. 90% quality steam was injected into
the inner tubing at a temperature of 295° C. All fluids were
removed from the heel of the annulus to a specified external
pressure. Since the well is open, upon leaving the toe of the
tubing the injected steam can either return down the outer
annulus and out of the well to the external sink, or inject into
the formation. Fluids from the formation can be produced at
6 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
any completion along the well. The well was simulated over a
ten year time period.
Symmetry was again employed as in the first study and
heat transfer coefficients were evaluated similarly. The above
paragraphs on these topics under Case Study 1 are applicable
here as well.
A schematic of this study is presented in Figure 7. We did
not include an undulating trajectory. The well is 800 m in
length. As can be noted in Table 2, the ID and OD of the
outer annulus are less than in the first study. The smaller
diameters were chosen since an elevated pressure drop in the
outer annulus is necessary to promote injection into the
reservoir.
Relative permeability curves and endpoints were also
obtained from Reference 11. The intermediate volatility oil
discussed in that reference was used in this study including K-
value parameters and other oil properties. Measured volatility
of the light component was less than that of methane and
seems to resemble ethane or propane25.
Oil saturations for each vertical layer and the use of
permeability barriers were also taken from Ref. 11. Although
different relative permeability curves were used for each layer
in that reference, only those for layer 2 were presented and
these were used throughout the grid in this study.
Figures 8a and 8b show temperature contours at two times
along the axis of the well demonstrating growth of the hot
zone near the toe. Steam and hot water are injected into the
formation here and fluids are produced further back towards
the heel of the annulus. Figure 9 shows injection and
production rates along the outer annulus at selected times.
Production is favored at the heel because of the higher
pressure drop down the annulus. This causes a more favorable
drawdown at the heel. Injection can be seen moving back
from the toe to the heel in the same figure.
Case Study 3
This case study concerns a modification of one of the
problems used for the Fourth SPE Comparative Solution
Project: Comparison of Steam Injection Simulators22. We
have employed the same two-dimensional radial cross-
sectional grid together with an oil consisting of two volatile
components and one nonvolatile component as described in
that paper. Singlewell cyclic steam injection is modelled.
A schematic of the well used in this simulation is shown in
Figure 10.
The injection well in our study extends from the surface in
order to model the reduction of steam quality due to heat loss
in the overburden. Pressure in the first segment of the
multisegment well model is therefore a tubing head pressure.
Segments that model flow in the tubing are defined from the
surface downwards to the midpoint of the lowest grid block
and annular segments are then used to model flow up to a
packer situated at the top of the pay zone.
Heat transfer coefficients were employed as discussed by
Prats21. Above the packer, heat loss occurred from tubing
through a gas filled annulus, annulus wall and cement to
formation. Below the packer, heat loss occurred from the
annulus to disturbed formation and then to undisturbed
formation. Heat transfer coefficients from tubing to annulus in
the lower completed part of the well were estimated as
discussed above under Case Study 1.
Cycles of the same duration, injection/production rates and
other parameters from Reference 22 were used. The producer
is represented by a standard (non multisegment) well model
with a BHP reference depth at the top of the formation.
Figure 11 is a plot of the steam quality along the injector at
selected times. Steam quality is lost down the injector because
of energy loss due to conduction heat transfer in the
overburden. It remains roughly constant throughout the three
cycles because the wellbore temperature and pressure stay the
same.
Figure 12 shows differences between production with and
without the multisegment well model for the injector. The
simulation without the multisegment well model was corrected
for the loss of steam quality in the injector predicted by the
multisegment well model study, as shown in Figure 11. Using
this correction in the standard well model case makes it agree
it closely with the multisegment well model case.
Case Study 4
Our final case study simulates the cyclic recovery of a
California Midway-Sunset oil from a short radius horizontal
well. Various published studies of Midway-Sunset fields were
merged to define this simulation.
Figures 13a and 13b contain schematics for this study.
A short radius horizontal well as described by Carpenter
and Dazet2 was modelled. They discussed drilling and
completion design of horizontal wells in a Midway-Sunset
steam drive. Of the three wells mentioned in that paper, we
use parameters for the second. This is a well placed just above
an oil-water contact with tubing extending from the surface
through a gas-filled annulus (with a packer at the casing point)
to a kick-off-point (KOP), a turning radius and then to a
horizontal completed liner. The slotted length is 113 m,
turning radius is 13 m, KOP is at a depth of 528 m and
diameter of the liner is .09 m. There is no flow through the
annulus.
The gridding for our simulation follows that of Chona et
al.4 who analysed the performance of a horizontal infill well in
a mature cyclic-steam project in Midway-Sunset. We have
used their grid dimensions and sizes. Oil viscosities, PVT and
relative permermeability curves including temperature-
dependent endpoints were taken from Al-Hadrami et al.5 who
simulated the same field. Although several vertical wells were
interspersed with infill horizontal wells in References 4 and 5,
we have simply placed a single short radius horizontal well
along a plane of symmetry. In addition to the design
parameters of this well as discussed in the above paragraph,
we have added an 8° dip in the horizontal section. In
Reference 5, the top of the simulated reservoir was a mature
steam-chest which we have included in our study. Initial
temperatures, oil, water and gas saturations as presented in
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 7
that reference were used together with a non-equilibrium
initialisation to fix the initial conditions. We have taken a
representative cycle to be 15 days injection, 3 days soak and
90 days production. The simulation was run out to 3 years
(10 cycles).
The multisegment well in this study cuts across grid lines.
It initially starts 12 m above the oil-water contact but
continues into the transition zone at the toe. While angling
slightly downwards with an 8° dip, it cuts across grid layers
while maintaining a linear direction (as discussed above, the
simulator corrects for segment nodes that are at a different
depth than grid nodes). One of the purposes of this study is to
illustrate a thermal multisegment well trajectory that does not
follow the grid, another is to simulate a less than optimal well
placement.
Figure 14 shows the change in steam quality along the well
at the end of several injection cycles. In this figure, the
contributions to heat loss from the overburden and reservoir
are shown. During the early stages of the first cycle, the
injection steam quality is reduced from 70% at the surface to
zero at a point approximately half way down the completed
liner. By the end of the first injection cycle, quality at the toe
has risen to 24%, as can be seen in the figure. This is a result
of energy (heat) loss from the wellbore in the overburden and
reservoir. As the first cycle progresses, pressure in the
injection well lowers somewhat as steam injectivity increases
in the reservoir. As the pressure in the well lowers, the steam
temperature lowers and heat loss decreases. In cycle 2
through to the last cycle, injection pressure stays
approximately the same, which in turn allows the temperature
and heat loss to remain constant. In this part of the run, there
is only a 3% loss of steam quality from the surface to the toe
of the well.
Figure 15 shows the injection rates along the well at
selected cycles. At the beginning of the simulation, injection
occurs more uniformly from the middle towards the toe.
During the second and third cycles, injectivity has notably
improved at the toe. Injection during the final 10th cycle is
approximately the same as during the third. In the first cycle,
although the drawdown at the toe is less than in the middle,
the PI to water is higher there because the toe is located in the
water-to-oil transition zone. Once steam has gained a foothold
in a part of the formation around the toe, injection tends to
concentrate at that point for two reasons. Firstly, heating the
oil here causes the viscosity to drop thereby increasing the
total fluid mobility. Secondly, higher water saturations
increase the water mobility and hence also increase the total
fluid mobility. The simulator uses an implicit fluid mobility
for injection wells.
Figure 16 presents water and oil production rates along the
well as a function of time. There is negligible water and oil
production during the first production cycle. In the early
cycles, oil production is more uniform along the length of the
well with some oil production at the heel because of the higher
oil PI. As the cycles progress, higher water production rates at
the toe and a higher rate of heating around the toe due to steam
injection cause oil production to improve notably here.
Although there is only a very small water injection at the heel,
oil production also improves somewhat in this region because
of the gradual improvement in oil PI due to conduction heating
of the formation. Water production is initially highest at the
toe because the toe is located in the transition zone and this
does not change in time.
Figure 17 displays differences in oil production between
the standard well model and multisegment well model
simulations. During all production cycles, the standard well
model produced much more water from the toe of the well and
less oil from other areas, in particular the heel of the liner.
The multisegment well model was able to producemore
uniformly along the length of the well, as seen in Figure 16
and discussed above. Conduction heating improves the oil PI
all along the liner. At the end of the 10 cycles, the oil PI at the
heel is an order of magnitude higher than the simulation
without the multisegment well due to heating of the formation.
As a consequence, after 10 cycles the predicted oil production
by the multisegment well was more than 2.5 that with the
standard well model. Oil production from the toe region is
approximately the same in both simulations.
Stability and Robustness
Figure 18 shows the time step sizes for all four studies.
The most difficult case to simulate was the first study after
the initial 60 day startup phase. No simulation problems were
experienced during this initial period. After the changeover in
the wells from circulation to injector and producer, the time
step sizes were slow to improve, not reaching a 1 day size for
20 days. Once the steam chest had begun to develop and
expand, the simulation proceeded more robustly, as can be
seen in Figure 18.
On the other hand, Case Study 2 proceeded robustly right
from the beginning. A considerable degree of crossflow exists
in this single well simulation study. Injection is occurring
from nearer the toe of the outer annulus. Production is
simultaneously occurring nearer the heel. The crossover point
moves from the toe towards the heel in time. However, none
of these appeared to degrade robustness.
Case Study 3, the vertical cyclic simulation, demonstrated
average stability and robustness for a cyclic run of this type.
The small volumes of the innermost radial grid blocks and the
high production rates combined with the heat loss were the
primary reason for any reductions in time step size. Study 4,
the cyclic run whose well trajectory crossed vertical layers,
was very robust.
Conclusions
1. We have described the implementation of a previously
reported multisegment well model into a
compositional simulator. Several enhancements were
discussed which are important for the simulation of
thermal processes.
2. Four case studies were constructed to highlight
features of the thermal multisegment wells. Each was
8 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
designed to realistically simulate thermal operations
using horizontal or vertical wells. In each of these
studies, we have hopefully demonstrated an improved
understanding of the reservoir engineering by using an
improved description of the well geometry, design and
fluid/energy flow with the multisegment well model.
Acknowledgements
We would like to thank Schlumberger GeoQuest for
permission to publish this paper.
References
1. Edmunds, N.R. and Suggett, J.C.: “Design of a
Commercial SAGD Heavy Oil Project”, SPE 30277
presented at the international Heavy Oil Symposium,
Calgary, Alberta, Canada, 19-21 June 1995.
2. Carpenter, D.E., and Dazet, S.C.: “Horizontal Wells in a
Steamdrive in the Midway Sunset Field”, SPE/DOE
24127 presented at the SPE/DOE Eighth Symposium on
Enhanced Oil Recovery, Tulsa, Oklahoma, April 23-24,
1992.
3. Hong, K.C.: “Recent Advances in Steamflood
Technology”, SPE 54078 presented at the 1999
International Thermal Operations and Heavy Oil
Symposium held in Bakersfield, California, 17-19 March
1999.
4. Chona, R.A., Love, C.L. and Rajtar, J.M.: “Evaluation of
a Horizontal Infill Well in a Mature Cyclic-Steam
Project”, SPE 37087 presented at the 1996 SPE
International Conference on Horizontal Well Technology,
Calgary, Canada, 18-20 November, 1996.
5. Al-Hadrami, H., Rajtar, J.M., Chona, R.A., and Hazlett,
W.G.: “Simulation Study of Development Strategies for a
Gravity-Assisted, Cyclic-Steam Project”, SPE 38289
presented at the 1997 SPE Western Regional Meeting
held in Long Beach, California, 25-27 June, 1997.
6. Al-Hadrami, H., Rajtar, J.M., Hazlett, W.G.:
“Optimization of Horizontal Well Performance in a
Mature Cyclic-Steam Project”, SPE 39081 presented at
the Fifth Latin American and Caribbean SPE Conference,
Rio de Janeiro, Brazil, 30 Aug – 3 Sept, 1997.
7. Hazlett, W.G., Love, C.L., Chona, R.A., and Rajtar, J.M.:
“Simulation of Development Strategies for a Mature
Midway-Sunset Cyclic-Steam Project”, SPE 37552
presented at the 1997 SPE International Thermal
Operations and Heavy Oil Symposium, Bakersfield,
California, 10-12 February, 1997.
8. Rajtar, J.M. and Hazlett, W.G.: “Cyclic-Steam Injection
Initiation Project in Heavy Oil Reservoir – A Simulation
Study”, SPE 53692 presented at the 1999 SPE Latin
American and Caribbean Petroleum Engineering
Conference held in Caracas, Venezuela, 21-23 April,
1999.
9. Deo, Milind D., Forster, Craig and Schamel, Steven:
“Strategies for Steam Flood Optimization in a High-Water
Saturation Reservoir in the Midway-Sunset Field”, SPE
54075 presented at the 1999 SPE International Thermal
Operations and Heavy Oil Symposium held in
Bakersfield, California, 17-19 March, 1999.
10. Chiou, C.S., Badger, S.D., Carlsen, M.M., Pereira, K.S.:
“A Focus Development for Heavy Oil Reservoir: The
Last Frontier at the South Belridge Field”, SPE 54625
presented at the 1999 SPE Western Regional Meeting
held in Anchorage, Alaska, 26-28 May, 1999.
11. Kisman, K.E. and Yeung, K.C.: “Numerical Study of the
SAGD Process in the Burnt Lake Oil Sands Lease”, SPE
30276 presented at the International Heavy Oil
Symposium held in Calgary, Alberta, Canada, 19-21 June,
1995.
12. Oballa, Viera and Buchanan, W. Lloyd: “Single
Horizontal Well in Thermal Recovery Processes”, SPE
37115 presented at the 1996 SPE International
Conference on Horizontal Well Technology held in
Calgary, Canada, 18-20 November, 1996.
13. Edmunds, N.R., Kovalsky, J.A., Gittins, S.D., and
Pennacchioli, E.D.: “Review of the Phase A Steam
Assisted Gravity Drainage Test at the AOSTRA UTF”,
SPE 21529 presented at the First International Thermal
Operations Symposium, Bakersfield, February 7-8, 1991..
14. Stone, T.W., Edmunds, N.R. and Kristoff, B.J.: “A
Comprehensive Wellbore/Reservoir Simulator”, SPE
18419 presented at the 10th SPE Symposium on Reservoir
Simulation, Houston, Feb. 1989.
15. Nghiem, Long, Collins, David A. and Sharma, Ravi:
“Seventh SPE Comparative Solution Project: Modelling
of Horizontal Wells in Reservoir Simulation”, SPE 21221
presented at the 11th SPE Symposium on Reservoir
Simulation held in Anaheim, California, February 17-20,
1991.
16. Tan, T.B., Butterworth, E. and Yang, P.: “Application of a
Thermal Simulator With Fully Coupled Discretized
Wellbore Simulation to SAGD”, Paper 2000-15 presented
at the Canadian Institute of Mining, Metallurgy &
Petroleum Society’s Canadian International Petroleum
Conference 2000, June 4-8, 2000.
17. Beggs, H.D., Brill, J.P., Palmer, C.M., Payne, G.A.:
“Evaluation of Inclined-Pipe, Two-Phase Liquid Holdup
and Pressure-Loss Correlation Using Experimental Data”,
SPE 6874, Journal of Petroleum Technology, p. 1198,
1979.
18. Holmes, J.A., Barkve, T., Lund, O.: “Application of a
Multisegment Well Model to Simulate Flow in Advanced
Wells”, SPE 50646 presented at the 1998 SPE European
Petroleum Conference, The Hague, The Netherlands, 20-
22 October, 1998.
19. Holmes, J.A.: “Enhancements to the Strongly Coupled,
Fully Implicit Well Model: Wellbore Crossflow Modeling
and Collective Well Control”, SPE 12259 presented at the
SPE Reservoir Simulation Symposium held in San
Francisco, CA, November 15-18, 1983.
20. Modine, A.D., Coats, K.H.: “A Superposition Method for
Representing Wellbore Crossflow in Reservoir
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 9
Simulation”, SPE 20746 presented at the 65th Annual
Technical Conference and Exhibition of the Society of
Petroleum Engineers, New Orleans, LA, Sept 23-26,
1990.
21. Prats, Michael: “Thermal Recovery”, SPE Monograph
Series, Society of Petroleum Engineers,1986, Dallas.
22. Aziz, K., Ramesh, A.B., Woo, P.T.: “Fourth SPE
Comparative Solution Project: Comparison of Steam
Injection Simulators”, Journal of Petroleum Technology,
1576-1584, December, 1987.
23. Sheppard, G.L., Wong, F.Y., and Love, D.: “Husky’s
Success at the Pikes Peak Thermal Project”, Manuscript
No. 210, Unitar Conference, 1998, Beijing, China.
24. Wang, Yarlong and Chen, Carl C.: “Improved Production
and Sand (Cold) Production in Conventional and Heavy
Oil Reservoirs – A Field Case and Simulation”, SPE
57290 presented at the 1999 SPE Asia Pacific Improved
Oil Recovery Conference held in Kuala Lumpur,
Malaysia, October 25-26, 1999.
25. Edmister, Wayne C., and Lee, Byung Ik: “Applied
Hydrocarbon Thermodynamics, Volume 1”, 1983, Gulf
Publishing Company, Houston, Texas.
Table 1 – Reservoir Properties for Case Studies
Case Depth
(m)
Max Dip
(m)
Poros
(%)
Perm
(d)
Oil
Sat
(%)
Init
Press
(bar)
1 500 0 34 5 89 33.5
2 396 0 22-33 1.5-
2.5
40-
80
31
3 457 0 33 0.5-
2.0
55 5.5
4 300 44 30 .3 80 1.4
Table 2 – Well Design
Case ID
Tubing
(m)
OD
Tubing
(m)
ID
Casing
(m)
OD
Casing
(m)
Compl
Length
(m)
1 .076 .089 .219 .241 400
2 .090 .102 .125 .138 800
3 .076 .089 .219 .241 24
4 .089 .114 NA NA 94
Table 3 – Well Operation
Case Water
Inj Rate
(m3/D)
CWE
Max
Inj BHP
(bar)
Liquid
Prod Rate
(m3/D)
Min
Prod
BHP
(bar)
Circ
Rate
(m3/D)
1 1200 50 1200 30 120
2 200 70 NA NA NA
3 160 70 160 1.2 NA
4 103 48 320 1.0 NA
Table 4 – Simulation Parameters
Case Gridding Time
Simulated
(yr)
Max Time
Step Size
(D)
1 20´12´15 1 20
2 30´20´15 10 20
3 13´1´4 3 90
4 11´24´21 3 20
Figure 1: Schematic diagram illustrating the segment structure for
an example multilateral well.
10 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
Figure 2: Resistance to heat transfer between a bulk flow in a
segment and unaltered formation (after Prats23).
Figure 3: Schematic of the simulation in Case Study 1 – a dual-
well SAGD study. Flow directions are shown for operation after
the 60 day startup period.
Figure 4a: Case Study 1: Temperature contours along the well
axis at 60 days (end of circulation period)
Figure 4b: Case Study 1: Temperature contours along the well
axis at 365 days.
Figure 5: Case Study 1: Temperature contours orthogonal to the
well axis at 60 days (end of circulation period) and 365 days.
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 11
Figure 6: Case Study 1: Pressure drop along the annulus at 365
days.
Figure 7: Schematic of the simulation in Case Study 2 – a single-
well SAGD study.
Figure 8a: Case Study 2: Temperature contours along the well
axis at 350 days illustrating growth of the hot zone near the toe.
Figure 8b: Case Study 2: Temperature contours along the well
axis at 1460 days illustrating growth of the hot zone near the toe.
Figure 9: Case Study 2: Production and Injection along the
annulus at selected times.
Figure 10: Schematic of the simulation in Case Study 3 – single
vertical well cyclic steam injection.
12 T.W. STONE, J. BENNETT, D. H.-S. LAW, J.A. HOLMES SPE 66373
Figure 11: Case Study 3 – Steam quality along the injector at
selected times.
Figure 12: Case Study 3 – Production rates with and without the
multisegment well model.
Figure 13a: Schematic of the wellbore in Case Study 4 – single
short radius horizontal well cyclic injection and production (after
Carpenter and Dazet2).
Figure 13b: Schematic of the simulation grid in Case Study 4 –
single short radius horizontal well cyclic injection and production.
(For clarity, some vertical grid refinement near the well has not
been shown.)
Figure 14: Case Study 4 – Steam quality in the well as a function
of time.
Figure 15: Case Study 4 – Injection rates along the well at
selected cycles.
SPE 66373 THERMAL SIMULATION WITH MULTISEGMENT WELLS 13
Figure 16: Case Study 4 – Water and Oil production rates along
the well as a function of time.
Figure 17: Case 4 oil production rate with and without a multi-
segment well.
Figure 18: Stability and Robustness - Timestepping for the four
case studies.