Note: Descriptions are shown in the official language in which they were submitted.
CA 02741930 2011-05-27
METHODS, SYSTEMS, APPARATUSES, AND COMPUTER-READABLE
MEDIUMS FOR INTEGRATED PRODUCTION OPTIMIZATION
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims priority, pursuant to 35 U.S.C. 119(e), to
the filing date
of U.S. Patent Application Serial No. 61/350540, entitled "Integrated
Production
Optimization," filed on June 2, 2010, with Attorney Docket No. 94.0271, which
is hereby
incorporated by reference in its entirety.
BACKGROUND
[0002] Oil and gas field operators may strive to maximize hydrocarbon
production rates
and ultimate field recovery in the face of unknowns and associated business
and technical
risks. This challenge may be compounded by a number of factors, which may
include
one or more of the following:
1. Complex, integrated system: Oil and gas fields may be large-scale systems
that include one or more interconnected elements (e.g., reservoir, wells,
network,
facilities), the management of which may span a number of disciplines and time-
scales
(for example, fast equipment operations, longer time scale production and
reservoir
management);
2. Time-varying: Assets may be characterized by pressures, temperatures and
flow rates that may vary with time; these variations can be expressed
mathematically in
terms of relationships such as partial differential equations (PDEs);
furthermore,
variations may also be introduced by human manipulation, such as changing
valve and
equipment settings, as well as drilling of new wells;
2 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
3. Real-time measurements: in modem fields a large number of different
types of real-time measurements may be acquired, such as pressure and
temperature, flow
rate, pump mechanical and electrical attributes, tank levels, etc.;
4. Software systems: various software systems may bring measurements
together with mathematical models that represent the various subsystems; these
software
systems may extend across a range of spatio-temporal scales and measurement
types, for
example, to model pressure transients, flow through pipelines and equipment
(e.g.,
SCHLUMBERGER's PIPESIM software), pumps and other fluid lifting systems in
weilbores, etc;
5. Predict and control: oil and gas operators may mathematically simulate
and predict field subsystems to obtain short- and long-term forecasts, which
may become
the basis for making field management decisions.
[0003] The oil and gas industry uses methods for combining different types of
measurements with mathematical models in order to manage oil and gas fields.
One
notable advance is so-called Integrated Reservoir Management or '*seismic-to-
simulation" workflows, which may start with processing full-coverage seismic
data and
well logs, and proceed to modeling a reservoir system subsurface, including
representing
uncertainties in the reservoir model (e.g., see El Ouair, Y., Lygren, M.,
Osdal, B., Husby,
0. and Springer, M., "Integrated Reservoir Management Approach: From Time-
Lapse
Acquisition to Reservoir Model Update at the Norne Field", paper IPTC 10894,
2005).
Such workflows may enable prediction or forecasting of future behavior, and
may
thereby assist with oilfield reservoir decision-making, such as where and when
to place
new wells, and how to drain hydrocarbons from various layers. See for example,
3 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
"Seismic-to-simulation" workflows, including geostatistical, (stochastic)
modeling
methods to handle uncertainties (e.g., see Deutsch, C.V, 2002. Geostatistical
Reservoir
Modeling, Oxford Univ. Press, 384 pp.). Such workflows have evolved into
methods that
optimize oil and gas reservoirs referred to as Integrated Reservoir
Optimization (IRO)
(see for example, U.S. Patent Nos. 7,739,089 to Gurpinar et. al; 7,478,024 to
Gurpinar;
and 6,980,940 to Gurpinar).
[0004] Integrated production optimization methods and systems aimed at merging
models for wells and production networks with real-time production data
(pressures,
temperatures and flow rates), can be used to predict or forecast future
behavior and
decide the best steps for managing field production. For example, such methods
and
systems may be used to set well pump rates and alter flow rates through
surface flow
lines.
[0005] One notable advance in this domain is Integrated Asset Modeling (IAM)
(e.g., as
described in Moitra, S.K., Chand, S., Barua, S., Adenusi, D., Agrawal, V., A
Field-Wide
Integrated Production Model and Asset Management System for the Mumbai High
Field.
Paper OTC-18678-PP, 2007), which is an integrated software modeling method
that
combines the reservoir model with production system and facilities models in
order to
jointly manage the combined reservoir and production systems. However, even
with
JAM, the production domain has not developed methods to characterize levels of
uncertainty in the main production variables such as pressure, flow rate and
temperature,
and to use these uncertainties to manage technical and business risk.
[0006] Generally, compared to seismic-to-simulation workflows, there is a lack
of
stochastic modeling, as well as methods to perform data reconciliationError!
Hyperlink
4 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
reference not valid. (i.e., taking into account the possible redundancy and
different
levels of uncertainty in the different measurements and models, in order to
resolve or
reconcile differences among production system sensor data and mathematical
modeling
results).
[0007] Conventional methods, systems, and apparatuses for modeling oil and gas
reservoirs are not ideal in all respects. Thus, there is a need for a general
framework for
integrated production optimization of oil and gas fields, as described in the
present
disclosure.
SUMMARY
[0008] According to an embodiment of the present disclosure, a method of
modeling a
production system may include providing a non-linear deterministic model
representing
the production system, the model including one or more inputs and one or more
outputs.
The method may further include associating a prior probability density
function (PDF)
with one or more of a first input of the one or more inputs and a first output
of the one or
more outputs, wherein the one or more of the first input and the first output
are not
measured and not deterministically known. Further, the method may include
linearizing
the non-linear deterministic model, and obtaining a measurement of one or more
of a
second input of the one or more inputs and/or a second output of the one or
more outputs.
In addition, the method may include determining, using a joint mean and
covariance, a
joint uncertainty related to one or more of the one or more inputs and one or
more
outputs; and determining, using the joint mean and covariance and the
measurement, a
conditional mean and covariance for the one or more of the first input and
first output.
Another embodiment of the present disclosure may include a system for modeling
a
Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
production system, wherein the system may include a memory, and a processor
operatively connected to the memory and having functionality to execute
instructions for
performing the foregoing method.
[0009] Yet another embodiment of the present disclosure may include a computer
readable storage medium storing instructions for modeling a production system,
wherein
the instructions when executed may cause a processor to perform the foregoing
method.
BRIEF DESCRIPTION OF THE DRAWINGS
[00010] The detailed description is described with reference to the
accompanying
figures. The same numbers are used throughout the drawings to reference like
features
and components.
[00011] Figure 1 is a schematic illustration of an Integrated Production
Optimization
(IPRO) system according to an embodiment of the present disclosure.
[00012] Figure 2a is a schematic illustration of a single branch network
according to
an embodiment of the present disclosure.
[00013] Figure 2b is a schematic illustration of a software model for a subsea
network according to an embodiment of the present disclosure.
[00014] Figure 3a is a chart 300 that shows exemplary pressure and temperature
solutions computed using software according to an embodiment of the present
disclosure.
[00015] Figure 3b is a table 301 showing the values for exemplary input
parameters
according to an embodiment of the present disclosure.
6 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00016] Figure 3c is a table 302 showing software-computed pressure and
temperature values at three specific points along a flow path, along with a
liquid flow rate
at standard conditions according to an embodiment of the present disclosure.
[00017] Figure 3d is a table 303 showing the input parameters from the table
301
shown in Figure 3b, expressed with a representative level of parameter
uncertainty
according to an embodiment of the present disclosure.
[00018] Figure 3e is a table 304 showing the estimated pressure and
temperature
valves and liquid flow rate as described in Figure 3c, along with levels of
uncertainty.
[00019] Figure 3f is a table showing a priori (before a rate measurement is
incorporated) and a posteriori (after a rate measurement is incorporated)
values and
uncertainties for a plurality of parameters according to an embodiment of the
present
disclosure.
[00020] Figure 3g is a table showing a posteriori estimates for mid-branch
rate,
pressure and temperature, given uncertain measurements of upstream and
downstream
pressures and temperatures according to an embodiment of the present
disclosure.
[00021] Figure 4 is a schematic illustration of a choke and flow line with
three
pressure and temperature measurements according to an embodiment of the
present
disclosure.
[00022] Figure 5 is a chart that shows pressure differences used in data
reconciliation that may also be used to identify drift in a sensor measurement
according
to an embodiment of the present disclosure.
[00023] Figure 6 is a schematic illustration of a computational architecture
to detect
sensor drift according to an embodiment of the present disclosure.
7 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00024] Figure 7 is a flowchart for modeling a production system according to
an
embodiment of the present disclosure
[00025] Figure 8 is a schematic illustration of a computer system according to
an
embodiment of the present disclosure.
DETAILED DESCRIPTION
[00026] An embodiment of the present disclosure includes methods, systems,
apparatuses, and computer-readable mediums related to "Integrated Production
Optimization" (IPRO), wherein the various modules may be inter-connected to
provide
high-level functionality required by oil and gas assets.
[00027] Figure 1 shows an exemplary embodiment of an IPRO system 100. The
IPRO system 100 includes a MODEL module 101 which may include one or more
mathematical models to predict the response of the reservoir, wellbore,
network and
facilities. The MODEL module 101 may be a steady state model, as shown in Fig.
1, or
alternatively may be a transient model, as known in the art. In an embodiment,
the
MODEL module 101 includes functions provided by SCHLUMBERGER's PIPESIM
software (referred to herein as "PIPESIM software"). In various exemplary
embodiments
described herein, the PIPESIM software is used. However, it should be
understood that
in other embodiments according to the present disclosure, other modeling
software may
provide the data for MODEL module 101.
[00028] The models provided for use with MODEL module 101 may be combined
and integrated using Integrated Asset Management (IAM) descriptions. In an
embodiment, the IAM descriptions are provided by SCHLUMBERGER's AVOCET
software product. However, other IAM software may also be used. The MODEL
module
8 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
101 may enable a user to represent uncertainty related to key system variables
such as
pressure, temperature and flow rate.
[00029] PRODUCTION MEASUREMENTS module 102 may provide various
types of real-time and occasional measurements. For example, PRODUCTION
MEASUREMENTS module 102 may include one or more of the following
measurements: (1) readings from pressure and temperature sensors permanently
placed in
the wells, trees, manifold, flow lines and facilities (as may be provided by
P,T module
102a); (2) readings from injected fluid flow rate meters such as water and gas
rate (as
may be provided by Total Qinj module 102b); (3) measurements of fluid
properties such
as composition from fluid samples (as may be provided by Fluid Measurements
module
102c); (4) production well tests providing water, oil and gas flow rates, for
example, from
scheduled separator well tests or multiphase flow meters (as may be provided
by
Production Well Tests module 102d); and (5) other measurements such as
acoustic sand
detectors using microphones clamped to production piping (as may be provided
by Sand
Acoustic module 102e). The foregoing measurements are merely exemplary, and in
other
embodiments, PRODUCTION MEASUREMENTS module 102 may include other
measurements.
[00030] A CALIBRATION module 103 may history-match or otherwise validate
the mathematical models of the MODEL module 101 using new measurement data in
order to calibrate the mathematical models and to ensure that the data and
models are
self-consistent using various levels of measurement redundancy as known in the
field of
data reconciliation.
9 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00031] A PWT SCHEDULE module 104 may use knowledge of the level of flow
rate uncertainty to optimize the scheduling of one or more production well
tests (e.g.,
which well to test, how long to test) using oil/water/gas separation and
metering
equipment located in one or more surface facilities.
[00032] PTA module 105 may process data when a well experiences a sudden
change in flow rate, for example, it may have been shut-in (i.e., flow rate
stopped) for
some reason. Data processing may include extracting the pressure measurements
during
the shut-in interval (e.g., transient data) for use in estimating the
reservoir pressure (Pr)
and wellbore skin, (i.e. information about producer well productivity index or
injector
well injectivity index). This data can be used to help refine well and/or
reservoir models
provided by MODEL module 101. This data may also be used to examine
derivatives of
late transient data on a log scale, and obtain information about spatial
variations in fluid
mobility at some distance from the wellbore associated with gas/oil/water
fluid contacts
and barriers or compartments.
[00033] An INJ-PRD CONNX module 106 may describe the degree of inter-
connectedness between injection wells that inject fluids into a reservoir and
producer
wells that extract fluids from a reservoir. For example, the INJ-PRD CONNX
module
106 may describe material balance with interference (MBI)Error! Hyperlink
reference
not valid.. This knowledge can be combined with other reservoir knowledge from
PTA
module 105 to refine a reservoir model provided in MODEL module 101. MBI
functionality may be provided using software, such as SCHLUMBERGER's DECIDE!
MBI software.
Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00034] An ESTIMATION module 107 may extract calibrated models and
uncertainty descriptions in the MODEL module 101, and use them together with
recent
measurement data to estimate system quantities with uncertainties. For
example, if only
combined rates are measured, such as total Qinj in the PRODUCTION
MEASUREMENT module 102, the models provided by MODEL module 101 can be
used to determine how much of the total is associated with each contributing
well (i.e.,
the so called continuous injection allocation problem), along with
uncertainty. Similarly,
real-time data such as pressure and temperature can be combined with the
models
provided by MODEL module 101 to provide continuous estimates of oil, water and
gas
production flow rates (so called continuous production allocation), along with
uncertainty. Knowledge of injection flow rates and production flow rates from
wells can
be used to compute voidage replacement ratios (VRR). Finally, the models
provided by
the MODEL module 101 can be used to estimate pressure and temperature profiles
along
the length of pipes, flow lines and risers with uncertainties, for later use
in flow
assurance.
[00035] A SIMULATION module 108 may extract calibrated models and uncertainty
descriptions provided by MODEL module 101, and may use them to simulate or
make
short-term future predictions of system behavior, along with uncertainty. This
allows so-
called "what if' experiments to predict the response to various production
decisions or
actions and test for an optimal decision. This computation might use only the
subset of
the models provided by MODEL module 101 that are required to obtain a
solution. For
example, this SIMULATION module 108 may determine how to set valves in the
network, and thus may require modeling only the network, not the reservoir,
wells and
11 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
facilities (so called "fit for purpose" modeling). This ability in module 108
allows
methods that optimize the production system or gas lift system (PO and GLO
respectively), resulting in the best settings for field controls, such as gas
lift rates, chokes
and valves, to vary production and injection flow rates, as well as chemical
injection
rates, and other general equipment settings.
[00036] A GEOMECHANICAL MODELING module 109 may provide
geomechanical modeling of the earth formation around the wellbores. In an
embodiment,
the GEOMECHANCIAL MODELING module 109 may use knowledge of 3-dimensional
oriented earth stress and the geometry of the wellbore in 3D to compute the
rock strength
and combinations of well flowing pressure (Pwf) and reservoir pressure (Pr)
under which
a well is safe to operate (planar area 109a) versus likely to fail and form
high levels of
sand inside the production wellbore (planar area 109b).
[00037] A PVT PHASE DIAGRAM module 110 may be used to compute the
pressure-volume-temperature response for wellbore fluids (e.g., PVT Phase
Diagram)
using, for example, a "flash" computation.
[00038] Once the system 100 is implemented and data are input into the system
100
(e.g. via PRODUCTION MEASUREMENTS module 102) and processed, a
SURVEILLANCE module 111 may be provided in order to provide a high-level view
of
the production system health surveillance by summarizing the health of a
contributing
module. SURVEILLANCE module 111 may include one or more of the exemplary
modules described below.
[00039] In an exemplary embodiments of a SURVEILLANCE module 111, a SAND
surveillance module may be provided to process continuous acoustic sand
microphone
12 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
data to alert when levels are high or increasing, and may overlay the current
well flowing
pressure Pwf (as may be provided by PRODUCTION MEASUREMENTS module 102)
and reservoir pressure Pr (as may be provided by PTA module 105) and
bottomhole
flowing pressure Pwf in injector wells (as may be provided by PRODUCTION
MEASUREMENTS module 102) from each well on top of the Geomechanical Modeling
crossplot (as may be provided by module 109) to assure that the wellbore is
not close to
failing.
[00040] A FLOW ASSURANCE module may be provided in the exemplary
surveillance module 111 to overlay the P,T profiles along the pipes, flow
lines and risers
(as may be provided by ESTIMATION module 107) on top of the PVT phase diagram
(as
may be provided by PVT PHASE DIAGRAM module 110) to assure that the system 100
is not close to forming unwanted solids.
[00041] Further, a WATER GAS INJECTION module may monitor water and gas
injection rate estimates (as may be provided by ESTIMATION module 107) and
pressure-temperatures (as may be provided by PRODUCTION MEASUREMENTS
module 102) along with reservoir pressure Pr estimated in the injector wells
(as may be
provided by PTA module 105) using for example Hall plots or other injection
key
performance indicators to ensure that the injection process is behaving well.
[00042] An exemplary SURVEILLANCE module 111 may also include a P
SUPPORT, VOIDAGE module that monitors reservoir pressure Pr (as may be
provided
by PTA module 105) and voidage replacement ratio VRR (as may be provided by
ESTIMATION module 107) to assure that pressure is behaving as desired across a
13 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
reservoir with respect to undesirable drop below bubblepoint pressure and
possible
formation subsidence.
[00043] SKIN surveillance module may be provided in an exemplary
SURVEILLANCE module 111 to monitor estimates of wel.lbore skin factor (as may
be
provided by PTA module 105) to insure that it is not changing too fast or
increasing
above a certain threshold beyond which the well may need to be stimulated to
restore
production or injection levels.
[00044] A RATES, BREAKTHROUGH, HIWCUT module may monitor the
estimated injection and production rates (as may be provided ESTIMATION module
107)
as well as their time variations, derivatives and trends to spot anomalous
conditions or
limits of warning, such as, the arrival or breakthrough of water into an oil
production
well, or a high level of water cut on an oil production well that could
trigger the start of
artificial lift such as gas lifting.
[00045] Finally, an UNWANTED FLUID ADVANCE module may be provided as
part of an exemplary SURVEILLANCE module 111 to monitor a location of
estimated
fluid contacts away from a well (module 105) or from the distribution of oil-
water-gas
saturations using simulator (module 108) to provide early warning if unwanted
fluids,
such as water or gas, are approaching an oil production well.
[00046] In an exemplary embodiment, the MODEL module 101 may include
TRANSIENT SIMULATOR module 112, which may provide transient simulation
capability. TRANSIENT SIMULATOR module 112 may provide support for transient
operations such as one or more of the following: (a) starting up or shutting
down a well,
with associated issues of fluid cooling and formation in the pipes, flow lines
and risers of
14 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
unwanted solids such as wax, asphaltenes and hydrates; (b) pre-heating of shut-
in lines in
cold seawater environments to prevent problems when restoring oil production
through
the otherwise cool lines; (c) circulating and flushing of lines and injection
of chemicals to
inhibit formation of wax, asphaltenes and hydrates; and (d) changing well
valving
configurations to mix warmer oil with cooler oil to insure the mixture is hot
enough to
avoid solid formation. For example, transient simulator software, such as OLGA
software distributed by SPT GROUP, or KONGSBERG's LEDAFLOW software may be
used to implement some or all of the transient simulator module 112.
[00047] In summary, the system 100 shown in Figure 1 may provide functionality
sufficient to span a wide range of oil and gas production and reservoir
engineering
activities, including, for example, one or more of the following list of work
activities that
may be encountered: Model calibration and history matching; Data
reconciliation; Meter
verification; Production system health surveillance; Sanding surveillance;
Flow
assurance; Gas lift optimization; Production optimization; Pressure transient
analysis;
Estimation of water injection rates; Production well test management; Water
and gas
breakthrough surveillance; High WCUT surveillance (triggers gas lift); Well
productivity/injectivity (skin damage); Water injection surveillance; Gas
injection
surveillance; Injector-producer connectivity; Pressure support surveillance;
Continuous
back-allocation; and Proactive surveillance of unwanted fluids.
[00048] As discussed in the following paragraphs with respect to various
embodiments described herein, the system 100 may include software that
performs
methods for using uncertainty to history match and/or calibrate a production
model. For
15 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
example, an embodiment of the present disclosure may provide one or more of
the
following:
(1) explicitly track and account for uncertainties in model variables of
importance;
(2) address data reconciliation in the context of variable uncertainty;
(3) reduce the level of human effort required to continuously calibrate
production
models;
(4) enable scheduling production well tests based on levels of production
system
uncertainty; and
(5) enable new learnings from pressure transient analysis (e.g. estimated
reservoir
pressure, wellbore skin, variations in mobility away from the wellbore) into
the system
models.
[000491 SINGLE BRANCH NETWORK MODEL. With continued reference to
Figure 1, MODEL module 101 may include a software system with one or more
steady-
state or transient mathematical models to predict the response of the
reservoir, wells,
network and facilities. Together with uncertainty modeling capability, this
may provide
a foundation for related activities, such as simulating model outputs with
uncertainty
(e.g., as may be provided by SIMULATION module 108), model calibration history-
matching and data reconciliation (e.g., as may be provided by CALIBRATION
module
103), estimation of key system variables including continuous back-allocation
(e.g., as
may be provided by ESTIMATION module 107), scheduling of production well tests
(PWT Schedule module 104), meter verification (e.g., as may be provided by
CALIBRATION module 103) and transient operations (e.g., as may be provided by
TRANSIENT module 112).
16 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00050] In the present embodiment, details of the foregoing modules are
further
described and illustrated with representative calculations using examples that
involve a
single branch network having only a choke, flow line, and riser. With respect
to more
complex networks, the model shown in Figure 1 may not fully illustrate the
modules
described above. As an example, continuous back-allocation, as may be provided
by
ESTIMATION module 107, may use wellbore inflow curves, and may require a
coupled
or combined well-network model. However, for purposes of simplicity and
transparency
of the example computations, the exemplary IPRO system 100 shown in Figure 1
includes a simple single branch network model. These examples illustrate the
computations and show how a representative deterministic commercial off-the-
shelf
software modeling system (such as PIPESIM software) may be adapted to perform
uncertainty modeling and the associated tasks such as those described above
with respect
to the various modules included in the exemplary IPRO system 100. It should be
understood that in practice, principles related to the exemplary embodiments
described
herein may also be used to model more complex scenarios, such as combined well-
network systems with inflow curves.
[00051] Figure 2a shows exemplary single branch network 200. Specifically,
single
branch network 200 includes a subsea network extending from a well through a
subsea
flow line and a subsea riser up to the topsides equipment. A number of
deterministic
steady-state and transient modeling software systems may be used to model this
network
200. For example, PIPESIM software, PETROLEUM EXPERT's PROSPER software
(referred to herein as "PROSPER"), and SPT GROUP'S OLGA software (referred to
herein as "OLGA"), among other software known in the art, may be used to
represent
17 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
network 200. These modeling software systems may be described as
"deterministic,"
because for a given set of model input values the models compute a single set
of output
values. Inputs may include certain boundary conditions, such as downstream
pressure
and upstream pressure and temperature, as well as internal system parameters
such as
fluid properties (e.g., phase specific gravity, API, composition) and
mechanical properties
(e.g., pipe diameter, wall insulation and roughness). Outputs may include
other boundary
conditions, such as flow rate and downstream temperature. This may be
contrasted with
stochastic or probabilistic models, where inputs and/or outputs may be
probabilistic,
wherein, for example, each variable may be represented by a probability
density function
instead of a single number.
[00052] Figure 2b shows a PIPESIM software model 250 for a portion of the
example subsea network 200. Specifically, the PIPESIM software model 250
extends
from a point just downstream of the wellhead and upstream of the subsea
wellhead
choke, through a subsea flow line and riser extending to the topsides. Some
exemplary
model details are indicated in Figure 2.
[00053] PIPESIM software may provide a steady-state thermal-hydraulic
simulator
model that accepts certain inputs u and computes certain outputs v. The
nonlinear
simulator provided by PIPESIM software may be represented symbolically in this
disclosure by the function F in Equation 1 below:
v = F(u) (Equation 1)
[00054] The input parameter set u of Equation 1 may include certain boundary
conditions (e.g., downstream pressure, upstream pressure and temperature, as
well as
various fluid and piping properties).
18 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00055] Figure 3a is a chart 300 that shows an exemplary pressure and
temperature
solution computed using the PIPESIM software. Figure 3b is a chart 301 that
illustrates
the values for some of the key PIPESIM software input parameters u for the
current
single branch example (P indicates pressure, T indicates temperature, SG
indicates fluid
specific gravity, GOR denotes gas-oil ratio, API denotes fluid API gravity and
ID denotes
pipe inside diameter; source denotes upstream and sink denotes downstream).
Figure 3c
is a chart 302 that illustrates the PIPESIM software computed pressure and
temperature
values at three specific points along the flow path, along with the liquid
flow rate at
standard conditions.
[00056] Referring to Figure 3a, the chart 300 shows pressure and temperature
as a
function of position along a flow path starting at the source just upstream of
the choke.
Most of the pressure decline may be hydrostatic pressure drop along the riser
starting at
the end of the 3610' long flow line, whereas temperature decline due to
thermal loss may
occur steadily along the insulated flow line and riser.
[00057] The nonlinear function F in Equation I maps the multi-dimensional
input
vector u into the multi-dimensional output vector v. In the example provided
in the
remainder of the present disclosure, input vector u is represented by a 15-
dimensional
vector that includes the variables in chart 301, and the output vector v is
represented by a
7-dimensional vector that includes the variables in chart 302.
[00058] MODEL module 101 - Uncertainty Characterization. As described
above, the steady-state thermo-hydraulic model F in Equation 1 may be a
deterministic
nonlinear simulator. Although F may be deterministic, the model inputs a might
not be
19 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
precisely known. For example, the model inputs u might not be precisely known
because of one or more of the following:
= the actual fluid in the production system may not be identical to the fluid
sample(s) analyzed in the laboratory;
= the detailed geometry and characteristics of the flow line and riser may not
be completely known or have changed with time due to erosion, corrosion, build
up of
scale, wax, hydrates, or other solids, etc.;
= the pressure and temperature boundary conditions may be measured using
in-situ instruments that have small but non-negligible measurement errors.
[00059] Figure 3d includes a chart 303 that shows the input parameters from
chart
301, but now expressed with a representative level of parameter uncertainty.
The actual
values provided in this example are merely exemplary. In practice, other
parameter
uncertainty values may be chosen.
[00060] Prior Uncertainty. Chart 303 shows a level of uncertainty in some of
the
main PIPESIM software model input parameters u prior to taking any
measurements of
the system (so-called a priori level of uncertainty in the model inputs).
Although the
PIPESIM software model F is deterministic, the computed PIPESIM software
outputs v
= F(u) must now be considered as also being uncertain due to the uncertainty
associated
with the input parameters u. The a priori level of uncertainty in the PIPESIM
software
outputs v can be assessed in several ways. For example, Monte Carlo sampling
may be
used. One approximate technique is to linearize the PIPESIM software model F
around
the nominal parameter values u in chart 301 (these specific values of u may be
represented as m,, in Equations 2a-2c below):
20 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
mõ = F(m (Eq 2a)
mõ+8v=F(mu+(5u)=F(mu)+ VF-8u+... (Eg2b)
V-VF8u (Eg2c)
[00061] Equation 2b above expresses the nonlinear function F in a Taylor
series
expansion about the nominal input values mu, where the series is truncated
after two
terms and VF denotes the gradient of the function F. In this example, because
F in
Equation 1 maps 15-dimensional inputs u into 7-dimensional outputs v, the
gradient VF
can be represented as a 7x]5 matrix, where the (j , k) entry of the matrix is
given by (a
F(u)r /a uk). This matrix may be calculated in a straightforward way using
perturbational
PIPESIM software computations that does not require manual intervention and
may be
performed in an automated fashion using, for example, the OpenLink
programmatic link
to PIPESIM, or by analytically differentiating the internal PIPESIM software
equations.
Assuming that the locally linearized representation in Equation 2 is valid,
variations in
the input parameters 8u can be related to variations in the PIPESIM software
outputs 8v.
As an example, the input perturbations 8u will be described as a random vector
with a
Gaussian probability distribution having mean m,, and covariance matrix A. The
linear
relation in Equation 2c implies that the PIPESIM software output vector v is
also
Gaussian, with mean mõ = F(mu) and corresponding covariance satisfying the
following
Equation 3 below (where ' denotes matrix transpose):
AV=VFA,, VF' (Eq3)
[00062] To illustrate with the current example, the 7x15 gradient matrix VF
was
computed by perturbing PIPESIM software. The 15 diagonal elements of the
covariance
matrix A, were defined by squaring the fifteen standard deviations indicated
in chart 303
21 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
shown in Figure 3d. Computing the PIPESIM software output error covariance in
Equation 3 provides the a priori estimate of the model output v along with
levels of
output uncertainty.
[00063] Figure 3e is a chart 304 showing that prior to making measurements of
the
flow network, the prior estimates of pressures, temperatures and flow rates
have
considerable levels of uncertainty due to imprecise knowledge of the internal
parameters,
such as fluid properties and flow line attributes in the PIPESIM software
model.
[00064] CALIBRATION module 103 - Posterior Uncertainty - Updating the
Model / Data Reconciliation. In an embodiment relating to "CALIBRATION module
103 - Posterior Uncertainty - Updating the Model / Data Reconciliation,"
suppose
measurement sensors are installed along a flow network. For example, pressure
and
temperature gauges may take measurements at various points along a flow path.
Multi-
phase flow rate may be obtained by instruments in a flow line, or using
separator well
testing. When flow rate, pressure and temperature measurements are obtained,
they may
provide information that serves to reduce the uncertainty previously
described. As
illustrated in CALIBRATION module 103 shown in Figure 1, new measurement data
can
be used to update or calibrate the mathematical models in CALIBRATION module
103.
Further, different types of measurements such as pressure, temperature and
flow rate may
provide redundant information about a network. Because they measure different
but
related attributes, they may be cross-validated using a mathematical model
such as a
thermo-hydraulic fluid flow simulator such as that provided by PIPESIM
software.
[00065] To illustrate, suppose that in the example presented earlier, a
measurement
of the liquid flow rate at standard conditions (with uncertainty) is made for
the single
22 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
branch network 200 shown in Figure 2a. This would be the case, for example, if
a well is
put on production well test and the rate is determined from test separator
accumulated
volume or averaged instantaneous rates. Generally, the longer the stable test
is carried
out, the smaller the level of uncertainty on the flow rate measurement. The
well test
liquid rate measurement may be considered as new information about the network
200,
and system identification methods may be used to refine the knowledge about
the internal
PIPESIM software system parameters u.
[00066] Consider a modified version of Equation 1 above, where now the PIPESIM
software model is thought of as having the same 15 input parameters u and a
single
output q representing the branch liquid flow rate. This PIPESIM software model
may be
represented by the following Equation 4 below:
q = Fq(u) (Equation 4)
[00067] As earlier, with reference to parameters 303 in Figure 3d, prior to
the flow
rate measurement, the input parameters u may be considered to satisfy a
Gaussian
probability density function with a priori mean mu and covariance A, As
earlier, the
nonlinear PIPESIM software model Fq may be expanded in a 2-term Taylor series
approximation to arrive at Equations 5a-5c below:
mq = Fq(mu) (Eq 5a)
mq+(5q=Fq(mu+(5u)=Fq(mu)+ DgB"+ (Eg5b)
,5q = Vq 15" (Eq 5c)
[00068] Suppose now that a liquid flow rate measurement is made of Q sbbl/day
which is uncertain and has a standard deviation of 6q. Because the model Fq in
Equation
4 relates u and q, the flow rate q is statistically correlated to the PIPESIM
software model
23 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
inputs u. Because of this, we can use an uncertain measurement of q to learn
something
about (i.e., refine the estimates of) the inputs u. Note, however, that from
the point of
view of statistical degrees of freedom, such a computation uses a single
uncertain flow
rate measurement to learn something about 15 input parameters. A well-behaved
algorithm should not radically alter the estimates for u, but instead is
expected to gently
"nudge" the parameter vector. We may see a change in the expected value or
mean of u
and a small reduction in the covariance for some of the elements in u,
specifically those
elements with higher sensitivity and good signal-to-noise ratio.
[00069] To illustrate an exemplary approach, we begin by creating a 16-
dimensional vector [q; u]. Equation 5c can now be used to approximate the a
priori joint
probability distribution for this vector, which is Gaussian with 16x1 mean
given by the
Equations 6a-6b below:
[m=J - [FTt~nu}J
(Eq 6a)
and a 16x16 covariance matrix given by:
1y A Y-1 _ VgtluVq+ VgA.u
[ A AX Aa q -~ (Eq 6b)
[00070] In the above Equations 6a-6b, we define new terminology on the left
side,
where the y subscript denotes the measured quantity (in this case q) and the x
subscript
denotes the estimated quantity (in this case u).
[00071] We may then make use of Bayes rule, as represented in Equation 7
below:
(Eq 7)
24 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00072] The conditional a posteriori mean and covariance for the 15-
dimensional
input parameters x=u after the measurement y=q=Q is taken into account are
given by
(e.g., as described in Mendel, J. M., Lessons in Digital Estimation Theory,
Prentice-Hall,
1987, 306 pp.), as represented by Equations 8a-8b below:
E{x y} = rnx + AxyAy' (y - rm,,) (Eq 8a)
Cov(xly) = A;; - A_,,Ay1 A (Eq 8b)
[00073] Suppose, for purposes of illustration, that the actual flow rate
measured
value is 5100 +- 5 sbbl/day. Chart 305, which is shown in Figure 3f, lists the
a priori
(before) and a posteriori (after the rate measurement is incorporated) values
for the 15
input parameters in u, including updated uncertainty from Equation 8b above
(values are
shown to 3 decimal places to illustrate comparisons only). As expected, using
a single
uncertain measurement to refine 15 parameters results in a slight change to
only two of
the parameters, watercut (WCUT) and gas-oil ratio (GOR). In each case, the
changes to
the mean values were slight (0.05% and 0.5%) and the uncertainty levels
decreased --
slightly for watercut and more significantly for GOR. Because Bayesian
updating is
iterative, the a posteriori values in chart 305 may be used as the a priori
values for the
next iteration.
[00074] As a reminder, this exemplary embodiment may include updating the
PIPESIM software model inputs u using a well test flow rate measurement. In
other
embodiments, well test allocation tied to a model (e.g., ESTIMATION module
107) may
use wellbore inflow performance relations (IPR) curves, which would require a
coupled
or combined well-network model. In practice, the same methodology can be used
to
include well inflow performance curves for analyzing production well test
results.
25 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
Finally, it should be noted that in oil and gas fields one or more branches
may be
combined or commingled at a manifold and the combined fluid stream may be
passed
into the separator to measure combined oil, water and gas rates. By using the
same
methodology as above, but for multiple commingled branches, the total combined
rate
measurements can be used to refine the parameters in the contributing
branches.
[00075] ESTIMATION module 107 - Estimating Rates and Pressures with
Uncertainties. During the course of production, real-time sensors may provide
continuous streams of real-time pressure and temperature data at one or more
locations
along the fluid flow path between the toe of a well and one or more
facilities.
ESTIMATION module 107 shown in Figure 1 may use such data in the context of an
appropriate model in order to estimate dynamic network variables such as
pressure and
temperature at locations where sensors are not installed, or to use one type
of
measurement (e.g., pressure and temperature) to estimate another type of
measurement
(e.g., liquid flow rate).
[00076] To illustrate, suppose in the current example that two pressure-
temperature
gauges are placed in a single branch at the locations indicated in chart 302 -
one gauge
located just downstream of (i.e., after) a choke, and another gauge located
just upstream
of (i.e., prior to) a separator. From the uncertain pressure-temperature
measurements
obtained at these two locations, a user may want to estimate (1) the pressure-
temperature
at a point mid-way between the sensors (e.g., at a location 3,867 feet along
the flow
stream near the sea bottom, as indicated (i.e., mid-stream) in chart 302), for
example, for
flow assurance reasons, as well as (2) the liquid flow rate in the branch.
26 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00077] Refer back to the PIPESIM software model 100 shown in Equation 1,
where
the inputs u are 15-dimensional (e.g., parameters in chart 305) and the
outputs v are 7-
dimensional (e.g., variables in chart 304). Note that some of the variables in
v may be
measured, while the unmeasured variables may be estimated. For this reason,
the vector
v may be partitioned into two parts, adopting the earlier notation where y
denotes the
measured quantity and x denotes the estimated quantity:
Pup
T up
Pdn
Tdo
P,nid
Tmid (Eq 9)
[00078] Suppose, for sake of illustration, that the actual measurements y with
uncertainty are represented by Equation 10 below:
Pup 102L0=0.1
Tu _ 149.0-0.1
Pd,, 54.6 0.1
Tdn 127.0=0.1 (Eq 10)
[00079] Because the PIPESIM software model can relate y and x, the upstream
and
downstream pressures and temperatures y may be statistically correlated to the
flow rate
and mid-point pressure and temperature x. For this reason, we can make use of
a
measurement of y (with uncertainty) in Equation 10 to learn something about
(i.e., refine
the estimate of) the variables in x.
[00080] As described earlier, consider the vector v to be Gaussian with a
priori mean
given by the entries in chart 304. This may be represented by the following
Equation 1 la
below:
27 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
1023.05
150.49
53.01
125.913
5014.7"3
926.55
15.33 (Eq 11a)
[00081] From Equation 3 and the measurement uncertainties in Equation 10, the
a
priori covariance of v may be represented by Equation 1 lb below:
AL, Ay A V'k"vF+ (0.1)'I4 0
Ax.Y A, 0 0 (Eq 11 b)
[00082] Here, 14 denotes the 4x4 identity matrix, and the pressure and rate
measurement noises are (without loss of generality; a more general scenario
can be
handled using non-zero off-diagonal terms in the matrix) assumed to be
statistically
independent and identically distributed (same size of statistical uncertainty;
Equation 10).
Proceeding in a similar manner as described with respect to Equation 7 and
Equation 8
above, a posteriori estimates for a branch flow rate and mid-point pressure
and
temperature can be computed using Bayes Rule. Exemplary results are shown in
chart
306, where the standard deviations are given by the square root of the
diagonal entries of
the a posteriori covariance matrix computed using Equation 8b above.
[00083] Note the significant reduction in uncertainties in the a posteriori
values in
the right column of chart 306 shown in Figure 3g compared to the a priori
values in chart
304 shown in Figure 3e. For example, the uncertainty in liquid flow rate
dropped from
=869 sbbl/day (prior in chart 304) to 5] sbbl/day by incorporating the
upstream and
downstream pressure and temperature measurements. Similarly, uncertainty of
the mid-
branch pressure dropped from 38 psi (prior in chart 304) to -1.5 psi, and mid-
branch
28 Applicant's Docket No_: 94.0271
CA 02741930 2011-05-27
temperature uncertainty dropped from 2.4 degF to 0.1 degF. Translating these
uncertainties into practice, if the estimated mid-branch pressure and
temperature are used
for flow assurance, the (T, P) data can be plotted as an overlay on the P vs.
T phase
diagram for the flow line fluid (illustrated as module 110 in system 100 in
Figure 1, and
obtained, for example, from a PVT flash computation). With uncertainties
available, the
overlay can be considered an elliptical area rather than a single point, with
a one-standard
deviation ellipse height in the P direction of 1.49 psi and an ellipse width
in the T
direction of --0.12 degF. The ellipse location on the cross-plot can be
compared to the
locations of phase transition curves to infer the possibility (and associated
risk) of
incipient formation of solids such as hydrates, wax or asphaltenes.
[00084] PWT SCHEDULE module 104 - Production Well Test Scheduling. In an
embodiment of the PWT SCHEDULE module 104, Production Well Tests may be
scheduled. Specifically, the sequence of wells to be tested and the duration
of each test
may be defined. Recall that once a well test is performed, a new uncertain
measurement
of flow rate may be available for the selected branch, and the result may be
used in
CALIBRATION module 103 to update or calibrate the underlying well and network
flow
models. This may provide better understanding at the overall system level
about how
much of the total field production is coming from each well and branch (see
the section
above titled "CALIBRATION module 103 - Posterior Uncertainty - Updating the
Model
/ Data Reconciliation").
[00085] New branch flow rate measurements are typically made using a multi-
phase
flow meter or a test separator, and the test may be carried out for a
specified time
interval. Generally, the longer the stable test time interval, the better the
quality of the
29 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
resulting flow rate measurement in terms of lower standard deviation. In some
situations
where the number of flow meters and test separators is smaller than the total
number of
wells/branches to be tested, a "Production Well Test Scheduling" activity is
an
optimization problem - i.e., how best to allocate limited flow rate
measurement
equipment resource to meet testing measurement objectives.
[00086] An approach to Well Test Scheduling may include performing off-line
numerical "what if' evaluations using the current uncertain model for the
production
wells and network. By characterizing the well test error for each well or
branch and
knowledge of the way the error will decrease as the test duration increases
(e.g. inverse of
square root of time if measurement noise is statistically independent), then
it is possible
to evaluate ahead of time how each hypothetical allocation of limited well
test
measurement resource can reduce system uncertainty, and depending on the
foregoing,
select the well or branch for subsequent testing that maximally reduces the a
posteriori
model uncertainty.
[00087] CALIBRATION module 103 - Meter Verification - Sensor Drift. As
mentioned earlier, an embodiment of CALIBRATION module 103 may include the
ability to carry out ``meter verification" and "data reconciliation." For
example, this may
include taking into account the possible redundancy and levels of uncertainty
in the
different measurements and models in order to resolve or reconcile differences
among
production system sensor data and mathematical modeling results. In an
exemplary
embodiment relating to meter verification and sensor drift, concepts of meter
verification
and data reconciliation may involve using available thermo-hydraulic
mathematical
system models found in MODEL module 101 to cross-validate different types of
30 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
measurements, such as, e.g., pressure, temperature, and flow rate to assure
that they are
self-consistent. This might be done, for example, by considering two pressure
measurements taken at successive points along a branch, and relating the
pressure
difference with the measured flow rate using a thermo-hydraulic model. The
earlier
embodiment related to "Updating the Model / Data Reconciliation" assumed that
the
measurement sensors are performing correctly and the uncertainty in each
sensor
measurement is due to zero-mean additive sensor noise. In some embodiments, a
sensor
may be experiencing drift, i.e., the sensor measurement might not be
represented as the
true variable value plus zero-mean additive sensor noise, but rather the
sensor may be
affected by a non-zero-mean additive bias or offset that may grow with time
corresponding to sensor drift.
[00088] Consider a simple single branch, as illustrated in Figure 4, which
includes a
choke and flow line with three pressure-temperature measurements. Figure 5
illustrates
exemplary pressure differences that may be used in data reconciliation.
[00089] Pressure difference A12 represents the pressure difference or drop
across the
choke, and a simple thermo-hydraulic choke model may be used to reconcile or
cross-
check the branch flow rate Q with the pressure drop A12. Pressure difference
d7,3
represents the pressure drop across the flow line, and a simple thermo-
hydraulic flow line
model may be used to cross-check the branch flow rate Q with the pressure drop
d23. In
the earlier embodiment related to "Updating the Model / Data Reconciliation,"
differences between the pressure drop and flow rate measurements were assumed
to be
entirely due to model calibration issues, and linearized Bayesian updating was
described
as a means to refine the model parameters to force a better fit between the
measurements
31 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
and the models. In an exemplary embodiment relating to meter verification and
sensor
drift, we allow that some of the difference may be due to meter drift and
proceed
accordingly.
[00090] Suppose, as illustrated in Figure 5, that the pressure gauge providing
measurement P2 is drifting with time, thereby causing 412 to be reported as
smaller than
its true value, and also causing A23 to be reported as larger than its true
value. If the
earlier embodiment relating to "Updating the Model / Data Reconciliation" is
used in this
case, the model parameters for the choke and flow line will both change as
time advances
in order to force agreement between the choke and flow line models and the
measured
pressures and flow rate. In this case, the choke and flow line models may
include the
offsets due to gauge drift, which may not be desirable.
[00091] As an alternative, the exemplary methodology related to "Updating the
Model / Data Reconciliation" can be modified to explicitly consider the
possibility of
sensor/meter drift and to statistically test for it. In an exemplary
embodiment relating to
relating to meter verification and sensor drift, this include evaluating time
series residuals
(y - my) (e.g., Equation 8a). With sensor drift, the residuals may be time-
correlated
(non-white), and in turn may be detected by testing the residuals for
statistical whiteness.
Specifically, if meter drift is detected, as described herein, it can be
modeled separately
from the choke and flow line and the estimated degree of drift can be
introduced into
short-term sensor corrections, and longer-term it can be used to flag the
sensor for
possible replacement during a future workover. Also, if dual pressure-
temperature
gauges are installed at the same location (not unusual with inaccessible
subsea
developments to offer additional robustness) meter drift detection can help to
identify
32 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
which sensor should be trusted more when two sensors at the same location are
drifting
apart.
[00092] Let P2, Crue(t) denote the true time-varying pressure P2 in Figure 4.
If the
measurement of P2 has unknown linear (i.e., other parametric drift rates can
be assumed
such as quadratic or exponential - in this embodiment, a linear model is
chosen for sake
of illustration without loss of generality) drift of rate a starting at time
to, it can be
represented as follows in Equation 12 below:
P2(t) = P2, true(t) + a (t - to) (Eq 12)
[00093] Consider the computational architecture shown in Figure 6 which may be
carried out over an extended interval of data over which the sensor may be
experiencing
drift. In this computation, the inputs consist of time series of the three
pressures and one
flow rate measured on the branch shown in Figure 4. The pressure drops A12 and
423 may
be computed as time series. Also, the flow rate measurement time series Q(t)
may be
used to calibrate a single (fixed parameter) choke model and flow line model,
which may
in turn be used to estimate (^ notation) the pressure drops A12 and A23, which
are
subtracted from the measured drops to form drop differences 812(t) and 823(t).
These may
be subtracted to form the final time series A (t).
[00094] For the drift detection problem, consider the following two
hypotheses:
(1) HI(a): the hypothesis that the sensor P2 is drifting with rate a
(2) Ho: the null hypothesis that the sensor P2 is not drifting
[00095] Under the null hypothesis Ho of no sensor drift, the fixed calibrated
choke
and flow line models should do a good job of representing the two pressure
drop time
series, in which case the drop differences 812(t) and 823(t) will be
statistically
33 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
characterized as zero-mean white (no time correlation) time series, as will
the final output
time series A (t).
[00096] Under hypothesis HI(a) of a drifting sensor (i.e., Equation 12), the
fixed
calibrated choke and flow line models may be unable to represent the linearly
increasing
drift signals in the two pressure drop time series. In this case the pressure
drop
differences 812(t) and 623(t) may be statistically characterized as two
linearly increasing
signals (one of rate a and the other of rate -a) plus small levels of zero-
mean white
measurement noise. The final output time series d (t) may be computed as a
difference
of two opposing ramp signals, and may be statistically characterized as a
linearly
increasing signal (with rate 2a) plus small levels of zero-mean white
measurement noise.
Statistical methods such as Generalized Likelihood Ratio Testing (GLRT) may be
used to
(1) determine the maximum likelihood estimate a,VL for the rate a, and (2) use
this
estimate to test hypothesis HI (avfL) versus Ho.
[00097] TRANSIENT SIMULATOR module 112 - Transient Operations.
Earlier portions of the present disclosure have described the use of steady-
state well and
network models (e.g. as may be provided by PIPESIM software) to represent the
wellbore and flow line pressure, temperature and flow rate behavior. These
variables
may be functions of position within the network and time. The steady-state
models may
identify solutions that are functions of position only (i.e. the pressure,
temperature and
flow rate solutions are time-invariant for the given fixed boundary
conditions). These
models may be adequate, for example, to detect network flow restrictions
(bottlenecks),
to evaluate well inflow and lift performance under steady conditions, etc.
34 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
[00098] However, oil and gas operators may require transient well and network
modeling to handle situations where conditions are not time-invariant. This
need may
arise in particular with well and network fluids that are susceptible to
forming solids
under certain temperature and pressure conditions (e.g., wax, hydrates and
asphaltenes;
avoiding solid formation may be referred to as "flow assurance"). This can be
a
particular problem with sea-bottom flow lines sitting in cold sea water, which
may be a
few degrees above freezing. In this case, transient modeling capability may be
needed,
particularly during transient operations, such as one or more of the
following:
(1) Start-up: During well start-up, hot reservoir fluid may flow up a producer
well and into the cold subsea flow lines and riser. Rapid cooling of the
reservoir fluids
can result in significant formation of solids unless the subsea flow lines
have been pre-
heated prior to startup. For such situations, measurements and transient
modeling may be
needed to plan and assess start-up operations;
(2) Shut-in: If production is temporarily halted in a subsea environment,
passage
of hot reservoir fluids through the subsea flow lines and riser may cease and
an entire
system may begin to cool down. If proactive steps are not taken quickly (e.g.
flushing
the lines, circulating another fluid, or pre-injecting chemicals into the
lines) fluids may
cool to a critical point where solids may form. In this situation as well,
measurements
and transient modeling may be needed to plan and assess shut-in operations.
[00099] Software modeling codes exist to handle transient modeling, and these
codes may reside in MODEL module 101 (alongside or replacing the steady-state
modeling codes). The methodologies described earlier in the present disclosure
may be
35 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
applicable to transient modeling as well steady-state modeling, although the
computational demands may grow with due to the time-dependent nature of the
solution.
In particular, Bayesian updating of model uncertainties that account for
uncertainty in the
measurements may still be applicable. However, other methods may need to be
used to
handle the Bayesian updating with a time-varying underlying system. These
methods
may include Kalman filtering and Extended (linearized) Kalman filtering, as
described in
Na2vdal, G., Johnsen, L.M., Aanonsen, S.L. Vefring, E.H., Reservoir Monitoring
and
Continuous Model Updating Using Ensemble Kalman Filter, SPE Journal, Vol. 10,
No.
1, 2005, and in the presence of strong nonlinearities, Ensemble Kalman
filtering.
[000100] As described herein, embodiments of the present disclosure may
include a
framework for integrated production optimization of oil and gas fields.
Specifically,
exemplary embodiments may include a system architecture that brings together
(1)
modeling capability with (2) field sensor measurements, including measurement
uncertainties. Furthermore, embodiments of the present disclosure may include
using
real-time sensor data together with uncertainty descriptions to update and
calibrate
models, estimate and predict key system variables, use measurement-model
redundancies
to cross-verify that different kinds of measurements are self-consistent, and
determine if a
sensor is drifting. As mentioned herein, these embodiments may be applicable
to both
steady-state and transient oil and gas systems and work processes.
[000101] Figure 7 illustrates an exemplary method of modeling a production
system
according to an embodiment of the present disclosure. Figure 7 begins at block
710,
which may include providing a non-linear deterministic model representing the
production system, the model comprising one or more inputs and one or more
outputs.
36 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
Block 720, may include associating a prior probability density function (PDF)
with one
or more of a first input of the one or more inputs and a first output of the
one or more
outputs, wherein the one or more of the first input and the first output are
not measured
and not deterministically known. Block 730 may include linearizing the non-
linear
deterministic model. At block 740, a measurement of one or more of a second
input of
the one or more inputs and/or a second output of the one or more outputs may
be
obtained. Block 750 may include determining, using a joint mean and
covariance, a
joint uncertainty related to one or more of the one or more inputs and one or
more
outputs. Block 760 may include determining, using the joint mean and
covariance and the
measurement, a conditional mean and covariance for the one or more of the
first input
and first output.
[000102] Figure 8 illustrates a computer system 800 into which implementations
of
various technologies described herein may be implemented. The computing system
800
(system computer) may include one or more system computers 830, which may be
implemented as any conventional personal computer or server. However, those
skilled in
the art will appreciate that implementations of various techniques described
herein may
be practiced in other computer system configurations, including hypertext
transfer
protocol (HTTP) servers, hand-held devices, multiprocessor systems,
microprocessor-
based or programmable consumer electronics, network PCs, minicomputers,
mainframe
computers, and the like.
[000103] The system computer 830 may be in communication with disk storage
devices 829, 831, and 833, which may be external hard disk storage devices. It
is
contemplated that disk storage devices 829, 831, and 833 are conventional hard
disk
37 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
drives, and as such, will be implemented by way of a local area network or by
remote
access. Of course, while disk storage devices 829, 831, and 833 are
illustrated as
separate devices, a single disk storage device may be used to store any and
all of the
program instructions, measurement data, and results as desired.
[000104] In one implementation, exploration and production data may be stored
in
disk storage device 831. The system computer 830 may retrieve the appropriate
data
from the disk storage device 831 according to program instructions that
correspond to
implementations of various techniques described herein. The program
instructions may
be written in a computer programming language, such as C++, Java and the like.
The
program instructions may be stored in a computer-readable medium, such as
program
disk storage device 833. Such computer-readable media may include computer
storage
media and communication media. Computer storage media may include volatile and
non-volatile, and removable and non-removable media implemented in any method
or
technology for storage of information, such as computer-readable instructions,
data
structures, program modules or other data. Computer storage media may further
include
RAM, ROM, erasable programmable read-only memory (EPROM), electrically
erasable
programmable read-only memory (EEPROM), flash memory or other solid state
memory
technology, CD-ROM, digital versatile disks (DVD), or other optical storage,
magnetic
cassettes, magnetic tape, magnetic disk storage or other magnetic storage
devices, or any
other medium which can be used to store the desired information and which can
be
accessed by the system computer 830. Communication media may embody computer
readable instructions, data structures or other program modules. By way of
example, and
not limitation, communication media may include wired media such as a wired
network
38 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
or direct-wired connection, and wireless media such as acoustic, RF, infrared
and other
wireless media. Combinations of any of the above may also be included within
the scope
of computer readable media.
[000105] In one implementation, the system computer 830 may present output
primarily onto graphics display 827, or alternatively via printer 828. The
system
computer 830 may store the results of the methods described above on disk
storage, for
later use and further analysis. The keyboard 826 and the pointing device
(e.g., a mouse,
trackball, or the like) 825 may be provided with the system computer 830 to
enable
interactive operation.
[000106] The system computer 830 may be located at a data center remote from
where data may be stored. The system computer 830 may be in communication with
various databases having different types of data. These types of data, after
conventional
formatting and other initial processing, may be stored by the system computer
830 as
digital data in the disk storage 831 for subsequent retrieval and processing
in the manner
described above. In one implementation, these data may be sent to the system
computer
830 directly from the databases. In another implementation, the system
computer 830
may process data already stored in the disk storage 831. When processing data
stored in
the disk storage 831, the system computer 830 may be described as part of a
remote data
processing center. The system computer 830 may be configured to process data
as part of
the in-field data processing system, the remote data processing system or a
combination
thereof. While Figure 8 illustrates the disk storage 831 as directly connected
to the
system computer 830, it is also contemplated that the disk storage device 831
may be
accessible through a local area network or by remote access. Furthermore,
while disk
39 Applicant's Docket No.: 94.0271
CA 02741930 2011-05-27
storage devices 829, 831 are illustrated as separate devices for storing input
data and
analysis results, the disk storage devices 829, 831 may be implemented within
a single
disk drive (either together with or separately from program disk storage
device 833), or in
any other conventional manner as will be fully understood by one of skill in
the art
having reference to this specification.
[000107] While the foregoing is directed to implementations of various
technologies
described herein, other and further implementations may be devised without
departing
from the basic scope thereof, which may be determined by the claims that
follow.
Although the subject matter has been described in language specific to
structural features
and/or methodological acts, it is to be understood that the subject matter
defined in the
appended claims is not necessarily limited to the specific features or acts
described
above. Rather, the specific features and acts described above are disclosed as
example
forms of implementing the claims.
40 Applicant's Docket No.: 94.0271
