U.S. patent application number 15/550497 was filed with the patent office on 2019-09-19 for directional drilling with automatic uncertainty mitigation.
The applicant listed for this patent is Halliburton Energy Services, Inc.. Invention is credited to Jason D. Dykstra, Yuzhen Xue.
Application Number | 20190284908 15/550497 |
Document ID | / |
Family ID | 62492017 |
Filed Date | 2019-09-19 |
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United States Patent
Application |
20190284908 |
Kind Code |
A1 |
Dykstra; Jason D. ; et
al. |
September 19, 2019 |
DIRECTIONAL DRILLING WITH AUTOMATIC UNCERTAINTY MITIGATION
Abstract
A disclosed drilling system includes a drill string assembly
having subsystem inputs that control ROP and other performance
parameters; and a processing system that provides automated
uncertainty mitigation of a model for controlling the subsystem
inputs. The drilling string assembly may include a BHA subsystem
and a drill string that connects the BHA to a drilling rig
subsystem and a fluid circulation subsystem. The processing system
operates by: obtaining a drilling system model having interaction
states representing how each subsystem input impacts the subsystem;
characterizing an uncertainty for each interaction state;
evaluating an influence of each interaction state's uncertainty on
the performance parameters; calculating a net benefit for
mitigating said model uncertainties; automatically mitigating said
one or more model uncertainties when the net benefit exceeds a
threshold, thereby improving the model of the drilling system; and
controlling the subsystem inputs based on the model.
Inventors: |
Dykstra; Jason D.; (Spring,
TX) ; Xue; Yuzhen; (Humble, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Halliburton Energy Services, Inc. |
Houston |
TX |
US |
|
|
Family ID: |
62492017 |
Appl. No.: |
15/550497 |
Filed: |
December 9, 2016 |
PCT Filed: |
December 9, 2016 |
PCT NO: |
PCT/US2016/065790 |
371 Date: |
August 11, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B 44/00 20130101;
E21B 41/0092 20130101; E21B 41/00 20130101; E21B 44/02 20130101;
E21B 7/06 20130101 |
International
Class: |
E21B 41/00 20060101
E21B041/00; E21B 7/06 20060101 E21B007/06; E21B 44/02 20060101
E21B044/02 |
Claims
1. A drilling method that comprises: obtaining a model of a
drilling system having subsystem inputs that control one or more
performance parameters of the drilling system, said model having
interaction states that each represent one of said subsystem
input's impact on a subsystem of the drilling system; estimating a
probability distribution of a model uncertainty for each
interaction state; evaluating an influence of each interaction
state's model uncertainty on each of said performance parameters;
calculating a net benefit for mitigating one or more of said model
uncertainties; automatically mitigating said one or more model
uncertainties when the net benefit exceeds a threshold, thereby
improving the model of the drilling system; and controlling the
drilling system based on the model.
2. The method of claim 1, wherein the model further accounts for
subsystem input uncertainties and performance parameter measurement
uncertainties.
3. The method of claim 2, wherein the model is expressible as
x'.sub.ij=(a.sub.ij+.DELTA..sub.ij)x.sub.ij+b.sub.iju.sub.j+v.sub.ij
y.sub.i=.SIGMA..sub.jy.sub.ij+w.sub.i=.SIGMA..sub.jc.sub.ijx.sub.ij+w.sub-
.i where j is the subsystem input index, u.sub.j is the subsystem
input, i is the performance parameter index, y.sub.i is the
performance parameter, x.sub.ij is the interaction state, v.sub.ij
is the subsystem input uncertainty, .DELTA..sub.ij is the
interaction model uncertainty, w.sub.i is the performance parameter
measurement uncertainty, and model coefficients are a.sub.ij,
b.sub.ij, and c.sub.ij.
4. The method according to claim 1, wherein said performance
parameters comprise one or more of: rate of penetration (ROP);
circulation efficiency, bottomhole pressure, drilling path error,
and bit wear.
5. The method according to claim 1, wherein the subsystem inputs
include one or more of: hook load, topdrive torque, rotation rate
(RPM), pump rate, pump pressure, choke opening, tool face
orientation, and fluid viscosity.
6. The method according to claim 1, wherein said net benefit
accounts for performance parameter degradation during a mitigation
process and duration of the mitigation process.
7. The method of claim 6, wherein said net benefit further accounts
for achievable performance parameter improvements.
8. The method of claim 7, wherein the achievable performance
parameter improvements are determined based on maintaining a margin
of stability.
9. The method according to claim 1, wherein the threshold is
zero.
10. A drilling system that comprises: a drilling assembly having
subsystem inputs that control one or more performance parameters of
the drilling system, the drilling assembly including: a bottomhole
assembly (BHA) subsystem with a steerable drill bit; and a drill
string that connects the BHA subsystem to a drilling rig subsystem
and a fluid circulation subsystem; and a processing system that
provides automated uncertainty mitigation of a model for
controlling the drilling assembly by: obtaining a model of the
drilling system, said model having interaction states that each
represent an impact of one of said subsystem inputs on one of: the
BHA subsystem, the drilling rig subsystem, and the fluid
circulation subsystem; estimating a probability distribution of a
model uncertainty for each interaction state; evaluating an
influence of each interaction state's model uncertainty on each of
said performance parameters; calculating a net benefit for
mitigating one or more of said model uncertainties; automatically
mitigating said one or more model uncertainties when the net
benefit exceeds a threshold, thereby improving the model of the
drilling system; and controlling the subsystem inputs based on the
model.
11. The system of claim 10, wherein the model further accounts for
subsystem input uncertainties and performance parameter measurement
uncertainties.
12. The system of claim 11, wherein the model is expressible as
x'.sub.ij=(a.sub.ij+.DELTA..sub.ij)x.sub.ij+b.sub.iju.sub.j+v.sub.ij
y.sub.i=.SIGMA..sub.jy.sub.ij+w.sub.i=.SIGMA..sub.jc.sub.ijx.sub.ij+w.sub-
.i where j is the subsystem input index, u.sub.j is the subsystem
input, i is the performance parameter index, y.sub.i is the
performance parameter, x.sub.ij is the interaction state, v.sub.ij
is the subsystem input uncertainty, .DELTA..sub.ij is the
interaction model uncertainty, w.sub.i is the performance parameter
measurement uncertainty, and model coefficients are a.sub.ij,
b.sub.ij, and c.sub.ij.
13. The system according to claim 10, wherein said performance
parameters comprise one or more of: rate of penetration (ROP);
circulation efficiency, bottomhole pressure, drilling path error,
and bit wear.
14. The system according to claim 10, wherein the subsystem inputs
include one or more of: hook load, topdrive torque, rotation rate
(RPM), pump rate, pump pressure, choke opening, tool face
orientation, and fluid viscosity.
15. The system according to claim 10, wherein said net benefit
accounts for performance parameter degradation during a mitigation
process and duration of the mitigation process.
16. The system of claim 15, wherein said net benefit further
accounts for achievable performance parameter improvements.
17. The system of claim 16, wherein the achievable performance
parameter improvements are determined based on maintaining a margin
of stability.
18. The system according to claim 10, wherein the threshold is
zero.
Description
BACKGROUND
[0001] Directional drilling is the process of steering a drill
string, and hence the borehole. It can be achieved with a variety
of drill string steering mechanisms, e.g., whipstocks, mud motors
with bent-housings, jetting bits, adjustable gauge stabilizers, and
rotary steering systems (RSS). Each of these mechanisms employs
side force, bit tilt angle, or some combination thereof, to steer
the drill string's forward and rotary motion. They may be used to
avoid obstacles and reach desired targets, both of which may take
various forms. For example a target may be specified in terms of an
entry point to a formation, together with a desired entry vector.
Both the entry point and vector may be specified as ranges or
accompanied by acceptable tolerances. Some boreholes may even be
associated with a series of such entry points and vectors.
[0002] Drillers generally employ careful trajectory planning not
only to ensure that targets are reached and obstacles avoided, but
also to limit curvature and tortuosity of the borehole. Such limits
are needed to prevent the drill string and other tubulars from
getting stuck, to avoid excessive friction, and to minimize casing
wear.
[0003] Trajectory planning is generally subject to information
uncertainty from a number of sources. For example, the drill string
assembly continuously encounters formations whose precise
properties are often not known in advance, but which affect the
operation of the bit, or more precisely, affect the operating
parameter ranges that induce bit whirl, stick-slip, vibration, and
other undesirable behaviors, as well as affecting the relationship
between those parameters and the rate of penetration ("ROP") or
other measures of drilling performance. The drilling system model
used to predict such behaviors might be mismatched with the
physical drill string assembly. The formation heterogeneity may
also be uncertain, as well as the precise positions of the
formation boundaries and any detected formation anomalies. The
operating parameters themselves may not be precisely known (e.g.,
rotations per minute (RPM), torque, hook load, weight on bit (WOB),
downhole pressure, drilling fluid flow rate), whether due to
inaccuracies in the control mechanisms or sensor noise. The
steering mechanism may suffer from bit walk or other steering
inaccuracies.
[0004] When faced with such uncertainties, drillers are often
forced to adopt a conservative approach or suffer the consequences.
Fortunately, many of the uncertainties can be reduced and many
drillers may choose to do so to achieve better drilling performance
while maintaining the same safety margin. However, such uncertainty
reduction comes at a cost that may be unjustifiable in view of the
achievable performance gains, making it difficult for drillers to
determine when and how to undertake uncertainty mitigation.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] Accordingly, there are disclosed herein directional drilling
systems and methods employing stochastic path optimization of the
operating parameters for drilling. In the drawings:
[0006] FIG. 1 is a schematic diagram of an illustrative well
drilling environment.
[0007] FIG. 2 is a function-block diagram of a logging while
drilling (LWD) system.
[0008] FIGS. 3A-3D schematically illustrate various forms of
drilling operation uncertainty.
[0009] FIG. 4 is a flow diagram of an illustrative directional
drilling method.
[0010] It should be understood, however, that the specific
embodiments given in the drawings and detailed description thereto
do not limit the disclosure. On the contrary, they provide the
foundation for one of ordinary skill to discern the alternative
forms, equivalents, and modifications that are encompassed together
with one or more of the given embodiments in the scope of the
appended claims.
DETAILED DESCRIPTION
[0011] To provide context and facilitate understanding of the
present disclosure, FIG. 1 shows an illustrative drilling
environment, in which a drilling rig subsystem having a platform
102 supporting a derrick 104 with a traveling block 106 and motors
for raising and lowering a drill string 108. A top-drive motor 110
supports and turns the drill string 108 as it is lowered into the
borehole 112. The drill string's rotation, alone or in combination
with the operation of a downhole motor, drives the drill bit 114 to
extend the borehole. The drill bit 114 is one component of a
bottomhole assembly (BHA) subsystem 116 that may further include a
rotary steering system (RSS) 118 and stabilizer 120 (or some other
form of steering assembly) along with drill collars and logging
instruments. A fluid circulation subsystem employs a pump 122 to
circulate drilling fluid through a feed pipe to the top drive 110,
downhole through the interior of drill string 8, through orifices
in the drill bit 114, back to the surface via the annulus around
the drill string 108, and into a retention pit 124. The drilling
fluid transports cuttings from the borehole 112 into the retention
pit 124 and aids in maintaining the integrity of the borehole. An
upper portion of the borehole 112 is stabilized with a casing
string 113 and the lower portion being drilled is open (uncased)
borehole.
[0012] The drill collars in the BHA subsystem 116 are typically
thick-walled steel pipe sections that provide weight and rigidity
for the drilling process. The thick walls are also convenient sites
for installing logging instruments that measure downhole
conditions, various drilling parameters, and characteristics of the
formations penetrated by the borehole. Among the drilling
parameters typically monitored downhole are measurements of weight
on bit (WOB), downhole pressure, and vibration or acceleration.
Further downhole measurements may include torque and bending
moments at the bit and at other selected locations along the
BHA.
[0013] The BHA subsystem 116 typically further includes a
navigation tool having instruments for measuring tool orientation
(e.g., multi-component magnetometers and accelerometers) and a
control sub with a telemetry transmitter and receiver. The control
sub coordinates the operation of the various logging instruments,
steering mechanisms, and drilling motors, in accordance with
commands received from the surface, and provides a stream of
telemetry data to the surface as needed to communicate relevant
measurements and status information. A corresponding telemetry
receiver and transmitter module is located on or near the drilling
platform 102 to complete the telemetry link. The most popular
telemetry technique modulates the flow of drilling fluid to create
pressure pulses that propagate along the drill string ("mud-pulse
telemetry or MPT"), but other known telemetry techniques are
suitable. Much of the data obtained by the control sub may be
stored in memory for later retrieval, e.g., when the BHA 116
physically returns to the surface.
[0014] A surface interface 126 serves as a hub for communicating
via the telemetry link and for communicating with the various
sensors and control mechanisms on the platform 102 of the drilling
rig subsystem. A data processing system (shown in FIG. 1 as a
tablet computer 128) communicates with the surface interface 126
via a wired or wireless link 130, collecting and processing
measurement data to generate logs and other visual representations
of the acquired data and the derived models to facilitate analysis
by a user. In at least some embodiments, the user may further
employ the data processing system to send commands downhole to
control the steering mechanism and/or to adjust the surface
operating parameters. Representative surface operating parameters
include: hook load, torque, rotations per minute (RPM), and rate of
penetration (ROP).
[0015] The data processing system may take many suitable forms,
including one or more of: an embedded processor, a desktop
computer, a laptop computer, a central processing facility, and a
virtual computer in the cloud. In each case, software on a
non-transitory information storage medium may configure the
processing system to carry out the desired processing, modeling,
and display generation.
[0016] To assist the driller with steering the borehole along a
desired trajectory, the BHA 116 may acquire various types of
measurement data including multi-component measurements of the
earth's magnetic field and gravitational field at each of a series
of survey points (or "stations") along the length of the borehole.
The survey points are typically those positions where the
navigation tool is at rest, e.g., where drilling has been halted to
add lengths of drill pipe to the drill string. The gravitational
and magnetic field measurements reveal the slope ("inclination")
and compass direction ("azimuth") of the borehole at each survey
point. When combined with the length of the borehole between survey
points (as measurable from the length added to the drill string),
these measurements enable the location of each survey point to be
determined using known techniques such as, e.g., the tangential
method, the balanced tangential method, the equal angle method, the
cylindrical radius of curvature method, or the minimum radius of
curvature method, to model intermediate trajectories between survey
points. When combined together, these intermediate trajectories
form an overall borehole trajectory that may be, for example,
compared with a desired trajectory or used to estimate relative
positions of any desired targets and known obstacles.
[0017] Also among the various types of measurement data that may be
acquired by the BHA 116 are caliper measurements, i.e.,
measurements of the borehole's diameter, optionally including the
borehole's cross-sectional shape and orientation, as a function of
position along the borehole. Such measurements may be combined with
the trajectory information to model fluid flows, hole cleaning,
frictional forces on the drill string, and stuck pipe
probabilities.
[0018] FIG. 2 is a function-block diagram of an illustrative
directional drilling system. One or more downhole tool controllers
202 collect measurements from a set of downhole sensors 204,
preferably but not necessarily including navigational sensors,
drilling parameter sensors, and formation parameter sensors, to be
digitized and stored, with optional downhole processing to compress
the data, improve the signal to noise ratio, and/or to derive
parameters of interest from the measurements.
[0019] A telemetry system 208 conveys at least some of the
measurements or derived parameters to a processing system 210 at
the surface, the uphole system 210 collecting, recording, and
processing measurements from sensors 212 on and around the rig in
addition to the telemetry information from downhole. Processing
system 210 generates a display on interactive user interface 214 of
the relevant information, e.g., measurement logs, borehole
trajectory, and recommended drilling parameters to optimize a
trajectory subject to target tolerances, limits on tortuosity, and
information uncertainty. The processing system 210 may further
accept user inputs and commands and operate in response to such
inputs to, e.g., control the operating parameters of the surface
rig and transmit commands via telemetry system 208 to the tool
controllers 202. Such commands may alter the settings of the
steering mechanism 206.
[0020] The software that executes on processing systems 128 and/or
210, addresses the information uncertainty that is typically
encountered in the drilling process. Prior to the borehole's
completion there are many unknowns, including the environmental
uncertainties (e.g., formation properties and boundary locations)
and operational uncertainties (e.g., optimal values of operating
parameters). If taking an approach that neglects the issue of
uncertainty (e.g., the model is presumed accurate, and a fixed
schedule is presumed for all events), drillers may use unsuitable
operating parameters and/or follow trajectories having undue risk
for high tortuosity, stuck pipe, poor formation contact, and
rework.
[0021] As discussed in greater detail below, the software estimates
the level of uncertainty in a drilling system and identifies the
source(s). Moreover, the software determines the net value of
reducing uncertainty from those sources, and automatically manages
the process of uncertainty mitigation. Uncertainty exists in all
control systems, whether in the form of sensor noise, model
inaccuracies, changes to the physical system, communication delays,
or other forms. Control systems are preferably designed to be
robust and handle at least some level of uncertainty, though the
greater the amount of uncertainty, the more negatively such
accommodation affects performance. As field personnel are not
expected to have control system design experience, the software is
preferably configured to automatically manage the uncertainty by:
estimating how much uncertainty exists, determining the sources and
the sizes of their contributions, examining the net value of
reducing those contributions, and then suitably mitigating those
contributions.
[0022] FIG. 3A illustrates a first type of uncertainty in the form
of a behavior map as a function of RPM and WOB. Marked on the axes
are the maximum design WOB 302 and the maximum design RPM 304,
defining a WOB parameter range 306 and RPM parameter range 308.
Within this range, the processing system has modeled the drilling
operation to determine the likelihood of undesirable stick-slip
behavior. Due to uncertainties in properties of the formation rock
and in how well the drill string model matches the actual drill
string, the regions are associated with probabilities derived from
a probability distribution .rho..sub.0. Region 310 represents the
"good" region, where probability of stick-slip behavior is very
low, e.g., less than 10%. Regions 312, 314, and 316 represent
regions of increasing probability, with region 316 being the
highest probability, e.g., higher than 90%. These regions are
expected to vary for different formation properties, different
inclinations, different degrees of bit wear, and with different
degrees of model mismatch as additional information is obtained and
the model is refined.
[0023] FIG. 3B illustrates a second type of uncertainty known as
"bit walk". FIG. 3B shows a straight "ideal" borehole 320 that the
driller seeks to extend along a straight trajectory from end point
322. Even under such idealized circumstances, the actual trajectory
324 may wander off track due to imbalances in the bit-rock
interaction forces. The rate at which this occurs exhibits a degree
of uncertainty that is often represented by a Gaussian probability
distribution .rho..sub.1, which can be defined in terms of a mean
and variance, which may vary with the operating parameters. The
mean and variance can be derived by statistical methods, e.g.
hypothesis test.
[0024] FIG. 3C illustrates a third type of uncertainty. A borehole
330 has been drilled to a point 331 within a formation bed 332
adjacent to a reservoir 334. The driller seeks to extend the
borehole along a trajectory below and parallel to the reservoir
boundary. However, because the borehole 330 has not yet reached the
boundary, the precise boundary position remains uncertain. If the
borehole turns too soon (because the driller believes the boundary
is at position 336, while it is actually at position 338), the
borehole may miss the reservoir until corrective action can be
taken. The boundary position uncertainty may be represented by a
Gaussian probability distribution .rho..sub.2 with a variance that
may vary based on how close point 331 is to the boundary.
[0025] FIG. 3D illustrates other types of uncertainty. Operating
parameter uncertainties 340, represented as having a probability
distribution .rho..sub.3, arise from causes such as measurement
noise. Inaccuracies in the navigational sensors cause uncertainty
in the precise location and shape of the borehole trajectory 342,
represented here as having a probability distribution .rho..sub.4.
The degree and distribution of heterogeneity in the formation may
also be treated as probabilistic distribution .rho..sub.5.
[0026] Automated drilling systems may optimize different
performance parameters, e.g., ROP, circulation efficiency, downhole
pressure, and drilling direction. In some embodiments, an automated
drilling system is an integrated combination of multiple control
subsystems for different aspects of the drilling system. For
example, it may include a surface drilling control subsystem, fluid
circulation control subsystem, and BHA control subsystem. The
surface drilling control subsystem may control the surface inputs
(e.g., torque and hook load). The fluid circulation control
subsystem may control the fluid properties (e.g., density,
viscosity, and flow rate). The BHA control subsystem may control
geometry (e.g., tool face orientation and bend angle) and bit-rock
interaction (e.g., fluid force and flow distribution).
[0027] Although these control sub-systems are often treated
separately, they are closely coupled. For example, ROP is affected
by the surface inputs, the fluid properties, and the bit-rock
interactions. The fluid circulation efficiency is affected by the
ROP, the fluid properties, and drilling direction (e.g., the
inclination angle). Downhole pressure is affected by the ROP, RPM,
and the fluid properties. The drilling direction is affected by the
ROP, the BHA geometry and the bit-rock interaction.
[0028] This close coupling makes it difficult for the control
subsystems to maintain their effectiveness in the presence the
various forms of uncertainty. For example, in a formation where the
bit behavior exhibits a high variance, the subsystem coupling may
introduce random dynamics with a broad frequency spectrum that
overlaps with that of the reference signals used for feedback
control. Such overlap reduces the control subsystem's tracking
capability and degrades its effectiveness. Although robust control
techniques (e.g. an H.sub..infin. controller) can be adopted to
solve the control problem under uncertainties, the coupled
uncertainties may require an overly conservative solution that
compromises the drilling efficiency.
[0029] Accordingly, the software that executes on processing
systems 128 and/or 210 implements an adaptive method for analyzing
system sensitivity to uncertainty and providing suitable
uncertainty mitigation. The software determines the sensitivity of
an overall performance index (e.g., some combination of ROP,
circulation efficiency, bottomhole pressure, and drilling path
error) with respect to each subsystem. The software then uses the
sensitivity analysis results to determine the severity of each
uncertainty contribution. Suitably severe contributions are
identified and reduced to improve the overall system performance in
an efficient manner.
[0030] FIG. 4 is a flowchart of an illustrative method that may be
implemented by the software. The method begins in block 402, with
the processing system retrieving the available historical and real
time drilling data, including logs of the system's input parameters
(e.g., hook load, topdrive torque, pump rate, pump pressure, choke
opening, BHA tool face orientation, etc.), the reference signal
measurements (e.g., ROP, RPM, bit behavior, etc.), and measured
formation properties. The processing system may also retrieve
expected data (e.g., formation models and drilling system models to
provide estimated responses to programmable inputs). General
empirical data on the drilling system design and behavior may also
be gathered and employed to customize the drilling system model and
aid in analyzing sources of uncertainty.
[0031] In block 404 the software-configured processing system
identifies a comprehensive model for the drilling system. The model
may be based on empirical data, real-time drilling data, or derived
from first principles. The processing system then decomposes the
comprehensive model into a group of interacting subsystem models.
Alternatively the subsystem models are identified directly from the
data and provided to the software. Each of the subsystem models
expresses one of the performance parameters in terms of some subset
of the inputs and an internal state.
[0032] The comprehensive drilling model can be expressed as:
X'=F(X,U)
Y=G(X) (1)
where X' is a vector of subsequent internal states, which is a
function of the current state vector X and the system inputs U. Y
is a vector of the system outputs, which are a function of the
current state vector X. Y may include ROP, circulation efficiency,
downhole pressure, and drilling direction. While the functions are
generally nonlinear, the drilling process changes slowly in the
short term, enabling the model to be linearized for control
purposes:
X'=AX+BU
Y=CX (2)
where A, B, and C are matrices. The linearized equation can be
broken down in terms of subsystem interaction states:
x'.sub.ij=a.sub.ijx.sub.ij+b.sub.iju.sub.j
y.sub.i=.sub.jy.sub.ij=.sub.jc.sub.ijx.sub.ij (3)
where x.sub.ij is the interaction state reflecting the impact of
input u.sub.j on subsystem i, which yields subsystem output y.sub.i
as the combination of contributions from the interaction states for
that subsystem. For example, the interaction dynamics between the
mud circulation system and the surface drilling system are captured
by the interaction states (representing, e.g., position and speed)
that reflect the impact of inputs for the mud circulation system
(e.g., the pump pressure, flow rate and choke opening).
[0033] When uncertainties are considered, the linearized subsystem
equations become
x'.sub.ij=(a.sub.ij+.DELTA..sub.ij)x.sub.ij+b.sub.iju.sub.j+v.sub.ij
y.sub.i=.SIGMA..sub.jy.sub.ij+w.sub.i=.SIGMA..sub.jc.sub.ijx.sub.ij+w.su-
b.i (4)
where .DELTA..sub.ij is the interaction model uncertainty due to,
e.g. the model inaccuracy and incomplete information, v.sub.ij
denotes the uncertainties that impact the interaction states, for
example the uncertainties associated with the rock surface profile
or a formation anomaly, and w.sub.i denotes the measurement
uncertainties which are from the sensing noise or estimation error
(when the outputs cannot be directly measured).
[0034] In blocks 406 and 408, the processing system characterizes
the uncertainties associated with the model, the interaction
states, and the output measurements. The characterization yields a
probability distribution function for each of the uncertainties,
which may be derived from historical data, set based on empirical
evidence, or obtained by system characterization.
[0035] In block 410, the software causes the processing system to
analyze the system sensitivity to uncertainty, i.e., to quantify
the impact of the uncertainties associated with each sub-system to
the overall system's performance. Various suitable methods exist
for this analysis. In at least some embodiments, the software
implements a Monte Carlo simulation to analyze the system's
sensitivity to disturbance and uncertainties in the absence of
explicit inputs (i.e., u.sub.j is taken as being equal to zero).
Using the probability distributions derived in blocks 406 and 408,
the software randomly samples .DELTA..sub.ij, v.sub.ij, w.sub.i,
and initial states x.sub.ij. For each set of samples, the software
determines a subsequent state x.sub.ij' (again, assuming a zero
input), and the corresponding interaction state outputs y.sub.ij
calculated from that subsequent state. The probability
distributions for interaction state outputs y.sub.ij and subsystem
outputs y.sub.i are then characterized, e.g., using histograms.
[0036] Based on equation (4), the output distribution of y.sub.i
will be a convolution of the distributions for y.sub.ij and
w.sub.i. Because the subsystem outputs must be maintained within an
operational envelope, excessive degrees of uncertainty may limit
operating parameters to a suboptimal range of values. The
performance loss of the system as compared with that achievable
with optimized operating parameter values may be used to evaluate
the benefits of uncertainty mitigation. Those subsystems having
interaction state output distributions with high variances are the
primary contributors to the variance in the subsystem output
distribution and may be prioritized for mitigation. The Monte
Carlo-based sensitivity analysis can also be applied to the
(nonlinear) comprehensive drilling model incorporating
uncertainty:
X'=[F+.DELTA.](X,U,V)
Y=G(X,W) (5)
[0037] Alternatively, or in addition, the software may incorporate
the feedback control function into the sensitivity analysis. From
equation (4) the open-loop transfer function in the Laplace domain
is:
G ij = b ij c ij s - a ij ( 6 ) ##EQU00001##
Augmenting equation (4) with the feedback equation
u.sub.j=k.sub.ij (y.sub.i-r.sub.i) (7)
(where r.sub.i is the desired value for output y.sub.i, and
k.sub.ij is the feedback error gain for input u.sub.j) yields a
closed loop transfer function of
H ij = k ij ( G ij + .DELTA. ij ) 1 + k ij ( G ij + .DELTA. ij ) .
( 8 ) ##EQU00002##
This closed loop transfer function remains stable so long as there
is no complex right-hand plane (RHP) value of the Laplace variable
s for which the denominator is zero. This criterion can be restated
in terms of ensuring that the contour around the right half of the
complex plane (which represents all values of s having a
non-negative real part), when mapped through the function
k.sub.ij(G.sub.ij+.DELTA..sub.ij), does not enclose -1+0j. This
mapped contour, known as the Nyquist plot, is a function of
k.sub.ij and G.sub.ij for a given value of model uncertainty
.DELTA..sub.ij. Assuming the contour does not enclose -1+0j, the
margin of stability is the shortest distance between this contour
and -1+0j, or
m=min.parallel.-1-k.sub.ij(G.sub.ij+.DELTA..sub.ij).parallel.
(9)
[0038] When there is no model uncertainty, the Nyquist plot
correspond to interaction state x.sub.ij can be accurately
determined and the margin of stability readily calculated. When the
model uncertainty .DELTA..sub.ij is present, its range blurs the
contour of the original Nyquist plot into band of possible
contours. For a given error gain k.sub.ij, the range of the
uncertainty .DELTA..sub.ij determines the system's margin of
stability. If the range of uncertainty is large enough to eliminate
the stability margin, the error gain k.sub.ij must be reduced if
stability is to be guaranteed, yet such reductions translate into a
performance loss. Alternatively, mitigation may be performed to
reduce the range of uncertainty and perhaps enable an increase in
the error gain.
[0039] In block 412 the software configures the processing system
to determine the net benefit of reducing the various uncertainties.
As part of this block, the processing system accounts for the
effort required to reduce the various uncertainties. Such
uncertainty reduction may take various forms, each of which may
have a (temporary) adverse impact on the drilling performance, as
measured by ROP, circulation efficiency, downhole pressure,
drilling direction, bit wear or other performance parameters. For
example, to reduce the interaction model uncertainties
.DELTA..sub.ij, a system identification process may be executed to
re-characterize the drilling model, e.g., by applying systematic
perturbations to the various inputs and observing the responses of
the subsystems and changes to the overall system behavior. The
perturbations may need to cover a significant portion of the
operating ranges for the inputs at a range of frequencies to
adequately reduce the interaction model uncertainties,
significantly reducing the time spent near the optimum operating
point during the process.
[0040] As another example, the input uncertainties v.sub.ij that
may be associated with the rock surface profile or formation
anomalies may be mitigated by collecting and analyzing logging
while drilling (LWD) data for the formation. Often such data
collection involves a pause in drilling and/or a regulation of
fluid flow to enable effective mud-pulse telemetry (MPT). As still
another example, the measurement uncertainties w.sub.i may be
mitigated with the installation of additional or improved sensors,
which typically requires a temporary cessation of drilling
operations.
[0041] The processing system further estimates the improvement in
drilling performance that the contemplated uncertainty mitigation
would be expected to produce, e.g., by enabling the use of a more
aggressive feedback error gain, or by enabling the use of more
optimal operating parameter values. An adjustable time frame may be
employed for evaluating this improvement, on the grounds that the
improvement is temporary due to the expected gradual increase of
uncertainties during operations. For example, uncertainties such as
frictional effects with the wellbore will change as the mud
properties change and as the wellbore profile changes. Therefore
the benefit phase for improvement in such uncertainties may be
limited to the next several hundred feet of drilling, instead of
the remaining well path. The net benefit may be expressed as:
N=.sub.t+T.sub.1.sup.t-T.sup.1.sup.+T.sup.2.parallel.improvement.paralle-
l.dt-.sub.t.sup.t-T.sup.1.parallel.loss.parallel.dt+benefit-cost
(10)
where t is the current time, T.sub.1 is the time required for
mitigation ("mitigation phase"), T.sub.2 is the adjustable time
frame for evaluating the improvement ("benefit phase"),
.parallel.improvement.parallel. is the square root of a weighted
sum of squares of changes to the performance parameters (e.g., ROP,
bit wear rate, path error, risk of non-productive time) after the
uncertainty mitigation relative to pre-mitigation performance,
.parallel.loss.parallel. is the square root of the same weighted
sum for changes to the performance parameters during the
uncertainty mitigation, benefit is the sum of non-time based
benefits achieved by the mitigation (e.g., diagnostics value), and
cost is the sum of non-time based costs required for the mitigation
(e.g., new sensors, non-productive time to be incurred). The
improvement and loss may be calculated using a subset of the
performance parameters, or higher weights may be assigned to those
parameters considered more critical.
[0042] The net benefit function may be evaluated using a model
(which could be either deterministic or probabilistic model) of the
uncertainty mitigation technique on the operational inputs and the
estimated uncertainty reduction with the drilling process over the
benefit phase. For example, to reduce the uncertainty in the
rock/bit model by using system identification over a specified
operational space (perhaps by mapping of the torque input to ROP
with a specified discretization for steady state input), the amount
of time to achieve this can be determined. Where multiple
mitigation techniques may be applied jointly, the software
calculates the net benefit for each combination and identifies the
combination yielding the maximum net benefit.
[0043] In block 414, the software-configured processing system
determines whether the net benefit exceeds a threshold (e.g.,
zero), and if not, the processing system employs the existing model
in block 416 for continued drilling. For example, dynamics of
bit-rock interactions may be the largest sources of model
uncertainties, yet mitigation might often require ROP reductions
that are too substantial for the mitigation to be justified.
Accordingly, the existing uncertainty ranges are used to set the
control gains k, as needed to provide the desired margin for
stability. Where the system is subject to high uncertainties, the
control gain would be low, and where the uncertainties are low, the
control gain can be more aggressive without losing the
stability.
[0044] Otherwise, where mitigation is justified, the processing
system in block 418 recommends or initiates mitigation of the
uncertainties that provide the maximum net benefit. The software
may include experiment design techniques for system identification,
enabling the processing system to automate the uncertainty
mitigation. The system (or subsystem) model is re-calibrated,
multiple sensor measurements (including repeated measurements or
redundant sensors) are fused, and/or equipment is
replaced/upgraded, thereby reducing the selected uncertainties. In
block 420, the drilling proceeds with reduced uncertainties,
providing a greater margin of stability or enabling the use of more
aggressive control gains to maintain the same margin of stability
while enhancing drilling system performance.
[0045] As drilling proceeds with block 416 or 420, the
software-configured processing system collects additional data in
block 424 to augment the data from block 402. The processing system
repeats blocks 404-424 with the gradually increasing data set to
provide automated uncertainty mitigation for the drilling process.
This systematic approach to automated uncertainty analysis and
mitigation is suitable for field use with operators to optimize
performance with little or no experience in drilling control
systems.
[0046] Accordingly, the embodiments disclosed herein include:
[0047] Embodiment A: A drilling method that comprises: obtaining a
model of a drilling system having subsystem inputs that control one
or more performance parameters of the drilling system, said model
having interaction states that each represent one of said subsystem
input's impact on a subsystem of the drilling system; estimating a
probability distribution of a model uncertainty for each
interaction state; evaluating an influence of each interaction
state's model uncertainty on each of said performance parameters;
calculating a net benefit for mitigating one or more of said model
uncertainties; automatically mitigating said one or more model
uncertainties when the net benefit exceeds a threshold, thereby
improving the model of the drilling system; and controlling the
drilling system based on the model.
[0048] Embodiment B: A drilling system that comprises: a drilling
assembly having subsystem inputs that control one or more
performance parameters of the drilling system; and a processing
system that provide automated uncertainty mitigation of a model for
controlling the drilling assembly. The drilling assembly includes:
a bottomhole assembly (BHA) subsystem with a steerable drill bit;
and a drill string that connects the BHA subsystem to a drilling
rig subsystem and a fluid circulation subsystem. The processing
system provides uncertainty mitigation by: obtaining a model of the
drilling system, said model having interaction states that each
represent an impact of one of said subsystem inputs on one of: the
BHA subsystem, the drilling rig subsystem, and the fluid
circulation subsystem; estimating a probability distribution of a
model uncertainty for each interaction state; evaluating an
influence of each interaction state's model uncertainty on each of
said performance parameters; calculating a net benefit for
mitigating one or more of said model uncertainties; automatically
mitigating said one or more model uncertainties when the net
benefit exceeds a threshold, thereby improving the model of the
drilling system; and controlling the subsystem inputs based on the
model.
[0049] Each of the foregoing embodiments may further include any of
the following additional elements alone or in any suitable
combination: 1. The model further accounts for subsystem input
uncertainties and performance parameter measurement uncertainties.
2. The model is expressible as
x'.sub.ij=(a.sub.ij+.DELTA..sub.ij)x.sub.ij+b.sub.iju.sub.j+v.sub.ij
y.sub.i=.SIGMA..sub.jy.sub.ij+w.sub.i=.SIGMA..sub.jc.sub.ijx.sub.ij+w.su-
b.i
where j is the subsystem input index, u.sub.j is the subsystem
input, i is the performance parameter index, y.sub.i is the
performance parameter, x.sub.ij is the interaction state, v.sub.ij
is the subsystem input uncertainty, .DELTA..sub.ij is the
interaction model uncertainty, w.sub.i is the performance parameter
measurement uncertainty, and model coefficients are a.sub.ij,
b.sub.ij, and c.sub.ij. 3. Said performance parameters comprise one
or more of: rate of penetration (ROP); circulation efficiency,
bottomhole pressure, drilling path error, and bit wear. 4. The
subsystem inputs include one or more of: hook load, topdrive
torque, rotation rate (RPM), pump rate, pump pressure, choke
opening, tool face orientation, and fluid viscosity. 5. Said net
benefit accounts for performance parameter degradation during a
mitigation process and duration of the mitigation process. 6. Said
net benefit further accounts for achievable performance parameter
improvements. 7. The achievable performance parameter improvements
are determined based on maintaining a margin of stability. 8. The
threshold is zero.
[0050] Numerous other modifications, equivalents, and alternatives,
will become apparent to those skilled in the art once the above
disclosure is fully appreciated. It is intended that the following
claims be interpreted to embrace all such modifications,
equivalents, and alternatives where applicable.
* * * * *