FIELD OF INVENTION
This invention relates to controlling a bottom hole assembly in a wellbore
and generally to management (e.g., automated) of. wellbore operation for the
production of hydrocarbons from subsurface formations.
s BACKGROUND TECHNICAL INFORMATION
Drilling for hydrocarbons, such as oil and gas, typically involves the
operation of drillkg equipment at underground depths that can reach down to
thousands of feet below the surface. Such remote distances' of downhole d,rilling
equipment, combined with unpredictable downhole operating conditions and
lo vibrational drilling disturbances, creates numerous challenges in accurately
controlling the trajectory of a wellbore. Compounding these problems is often
the existence of neighboring wellbores, sometimes within close proximity of
each other, that restricts the tolerance for drilling error. Drilling operations
typically collect measurements from downhole sensors, located at- or near a
l j bottom hole assembly (BHA), to detect various conditions related to the drilling,
such as position and angle of the wellbore trajectory, characteristics of the rock
formation, pressure, temperature, acoustics, radiation, etc. Such sensor
measurement data is typically tr.a nsm. itted to the surface, where human operators
analyze the data to adjust the downhole drilling equipment. However, sensor
20 measurements can be inaccurate, delayed, or infrequent, -limiting the
effectiveness of using such measurements. often, a human operator is left to use
best-guess estimates of the wellbore trajectory in controlling the drilling
operation.
BRIEF DESCRIPTION OF DRAWINGS
25 FIG. 1 illustrates an example of an implementation of at least a portion
of a wellbore system in the context of a downhole operation;
FIG. 2 illustrates an example three-dimensional state space
representation of a piecewise-linear control law;
FIG. 3 illustrates a flow diagram of an example of a process of
implementing a MPC technique by generating and providing relational
information to a downhole BHA control;
FIGS. 4A and 4B illustrate examples of determining different sets of
operating conditions that are used to generate relational information provided to a
BHA;
FIG. 5 is .a flow chart of an example process for generating and
providing relational information to a BHA for performing model-based
predictive control;
FIG. 6 is a flow chart of an example process for accessing relational
information at a BHA and determining a control input to apply for a detected
operating condition;
FIG. 7 is a flow chart of an example of further processing to update a
model of BHA dynamics and update relational information provided to the
15 BHA;
I FIG. 8 is a flow chart of an example of further details of detecting that
1 a relational information update event has occurred, based on sensor
measurements from the BHA; and
FIG. 9 is a block diagram of an example of a control system on which
20 some examples may operate.
DESCRIPTION OF INVENTION w.r.t. DRAWINGS
This disclosure describes, generally, automated control of wellbore
drilling operations by making model-based predictive control (MPC) decisions
for the BHA. In particular, techniques are described in which a secondary
2s system generates relational information that relates BHA control inputs to
different operating conditions, and provides the relational information to the
BHA to implement MPC operations. The secondary system may be above the
surface (e.g., as part of an above-surface controller) or may be below the
surface (e.g., as a downhole module together with or separate from the BHA).
30 The relational information may be stored locally at the BHA or, in some
'examples, may be stored apart from, and remotely aicessible by, the BHA.
E ~Qpring gr-illi&g tl-@ ac@@es relational information to determine
control inputs for different operating conditions. In some examples, the
relational information may include an input-output function, such as a lookup
table.
The relational information may be generated by the secondary system
j based' on a model-based predictive control (MPC). The MPC is based on a
model of BHA dynamics, which is determined based on sensor measurements
and may be used to estimate predictions of wellbore trajectory. In some
examples, it may be desirable to control the BHA such that an objective
function is satisfied, which may include a combination of one. or more
lo predicted costs of drilling over a future horizon of time. The secondary system
may generate the relational information by pre-computing BHA control inputs
that satisfy an objective function for different sets of operating conditions.
The secondary system may monitor the performance of the drilling
operation, and determine whether to update the model of BHA dynamics. For
15 example, the model of BHA dynamics may diverge from the true wellbore
environment for various reasons, including changes in downhole conditions or
modeIing inaccuracies and uncertainties. If the secondary system determines
that the model of BHA dynamics diverges significantly from sensor
measurements, thin the secondary system may update the model of BHA
20 dynamics and generate corresponding updated relational information, which it
then provides to the BHA.
In a general implementation, a computer-implemented method of
controlling a bottom hole assembly (BHA) includes determining a model of
BHA dynamics based on sensor measurements from the BHA; determining,
25 based on the model' of BHA dynamics, an objective function comprising a
predicted future deviation from a planned wellbore path; determining a
control input to the BHA .that satisfies the objective function for a set of
operating conditions of the BHA; generating, at a secondary system, relational
information that relates the control input to the set of operating conditions; and
30 transmitting the relational information from the secondary system to the BHA.
Other general implementations include corresponding computer
I
systems, apparatus, and computer programs recorded on one or more computer
-+ P- O DE L iH&ra&3~~@&-,e d;@&iffigu&8 tb $&om the actions of the methods. A
system of one or more computers can be configured to perform operations to
perform the actions. One or more computer programs can be configured to
perform particular operations or actions by virtue of including' instructions
that, when executed by data processing apparatus, cause the apparatus to
s perform the actions.
A first aspect combinable with any of the general' implementations
further includes storing, at a memory location of the BHA, the relational
information that relates the control input to the set of operating conditions;
detecting an operating condition of the BHA; determining a candidate set of
lo operating conditions including the detected operating condition; accessing the
relational information from the memory location of the BHA; and
determining, based on accessing the relational information, a control input to
the BHA that is related to the candidate set of operating conditions including
the detected operating condition.
15 In a second aspect combinable with any of the previous aspects,
determining, based on accessing the relational information, a control input to
the BHA is performed without performing computations to solve the objective
function for a control input that satisfies the objective function.
In a third aspect combinable with any of the previous aspects,
20' generating, at a secondary system, relational information that relates the
control input to the set of operating conditions includes generating a relational
database that relates the control input to the set of operating conditions. .
In a fourth aspect combinable with any of the previous aspects,
generating, at a secondary system, relational information that relates the
25, control input to the set of operating conditions further includes determining a
first control input to the BHA that satisfies the objective function for a first set
of operating conditions of the BHA; determining a second control input to the
BHA that satisfies the objective function for a second set of operating
conditions of the BHA; determining that the first control input to the BHA and
30 the second control input to the BHA are identical to each other; combining
the first set of operating conditions and the second set of operating conditions
into a combined set of operating conditions; and relating, in the relational
-H- p 0~~ ~ e1.3 z,- g 17
34
information, the combined set of operating conditions to asingle control input
that corresponds to both the first and second control inputs.
A fifth aspect combinable with anyof the previous aspects Mher
includes detecting, at the secondary system and based .on sensor measurements
. .
5 from the BHA, that a relational information update event has. occurred; and
updating the relational information at the BHA based on detecting that a
relational information update event has occurred.
In a sixth aspect combinable with any of the previous aspects, updating
the relational information at the BHA includes determining an updated model
10 of BHA dynamics based on updated sensor measurements from the BHA;
determining an updated objective function based on the updated model .of
BHA dynamics; determining an updated control input to the BHA that satisfies
the updated objective function for the set of operating conditions of the BHA;
generating, at the secondary system, updated relational'information that relates
15 the updated control input to the set of operating conditions; and transmitting
the updated relational information from the secondary system to the BHA.
. .
In a seventh aspect combinable with any of the previous aspects,
I transmitting the updated relational information from the secondary system to
the BHA includes determining a difference between the updated relational
20 information and the relational information; and transmitting the difference
between the updated relational information and the relational information from
the secondary system to the BHA. f
In an eighth aspect combinable with any of the previous. aspects,
detecting that a relational information update event has occurred includes
25 , determining a threshold bound for a drilling parameter; and determining that at
Ieast one of a-rate of change of the drilling parameter or an absolute value of
the diilling does not satisfythe threshold bound.
In a ninth aspect combinable with .any of the previous aspects,
determining a threshold bound hrther includes determining the threshold
30 bound based on at least one of a desired control performance, a
communication bandwidth between the secondary system and the BHA, or a
L
, processing capability of the secondary system. zpa DELBz- zGIG
-= 54
A tenth aspect combinable with any of the previous aspects further
includes implementing a constraint on the control input to the BHA while
updating the relational information at the BHA.
In an eleventh aspect combinable with any of the previous aspects,
5 transmitting the relational information from the secondary system to the BHA
includes transmitting the relational information and the model of BHA
dynamics from an above-surface location of the secondary system to the BHA.
In a twelfth aspect combinable with any of the previous aspects,
transmitting the relational information from the secondary system to the BHA
lo includes transmitting the relational information and the model of BHA
dynamics from a below-surface location of the secondary system to the BHA.
In a thirteenth aspect combinable with any of the previous aspects,
determining an objective function includes determining a weighting factor
based on at least one .of the model of BHA dynamics or the sensor
15 measurements from the BHA; and determining a weighted combination of the
predicted future deviation from the planned wellbore path and a predicted
future cost of applying a control input to the BHA, weighted by the weighting
factor.
In a fourteenth aspect combinable kith any of.the previous aspects,
20 determining a control input to the BHA that s'atisfies the objective function for
a set of operating conditions includes determining a control input to the BHA
that minimizes a weighted combination of the predicted future deviation from
the planned wellbore path and a predicted future cost of applying the control
input to the BHA over a subsequent period of time during which the model of
23 BHA dynamics satisfies the set of operating conditions.
I
~. In a fifteenth aspect combinable with any of the previous aspects, the
predicted future cost of applying a control input to the BHA includes at least
one of a predicted energy consumption for the BHA, a predicted torque on the
BHA, a predicted fluid flow to the BHA, a predicted angular position of the
30 BHA, or a predicted financial cost.
A sixteenth aspect combinable with any of the previous aspects further
includes determining a candidate control input to the BHA; determining a
- -
1 P f3 ifC L. E$edi&t&l ~ ~ & ~ ~ r ~ e &b&td&r dy &,e candidate control'input to the BHA
and the model of BHA dynamics; and determining the predicted future
deviation from the planned wellbore path based on a deviation between the
predicted wellbore trajectory and the planned wellbore path.
. In a seventeenth aspect combinable with any of the previous aspects,
5 determining a control input to the BHA includes determining at least one of a
first bend angle control, a second 'bend angle control, a first packer control, or
a second packer control.
Various implementations of a control system for wellbore drilling
according to the present disclosure may include none, one or some of the
lo following features. For example, the system may improve the efficiency and
cost of drilling operations. In particular, techniques described herein may
enable a low-latency, low-power and/or less computationally intensive
downhole implementation of model-based predictive control by a BHA. In
some examples, by shifting some of the computational burden of model-based
15 predictive control to a secondary'system, the BHA may be allowed to perform
simpler operations, such as accessing data from a local database (e.g.,
performing lookups in a lookup table), which may be performed in less time
and with fewer downhole resources.
In some examples, techniques described herein may be applied to
20 directional drilling systems to enable reductions in downhole power and
computing resources while satisfying a desired objective function. Relational
information, such as a lookup table, stored in the BHA may provide a fast and
efficient way to apply model-based predictive control inputs without
necessarily performing computations to optimize the desired objectiv. e.
25 function.
A model of BHA dynamics may be used to generate predictions of
future wellbore trajectory, and the secondary. system may determine BHA
'control inputs that proactively adapt to predicted conditions in the wellbore;
The model of BHA dynamics may be updated as new sensor measurements are
30
' received and as new control inputs are determined, and may enable close
tracking of the true wellbore conditions. The secondary system may use these
a i 6
predictions, as well as planned wellbore path information andlor other
-r Ba BEhHS i3-65- zal& I f 54
information, to anticipate future changes in the wellbore and. proactively adapt
the control inputs in the relational information that is provided to the BHA.
The details. of one or more implementations are set forth in the
accompanying drawings and the description below. Other features, objects,
5 and advantages will be apparent .from the description and drawings, and from
the claims.
FIG. 1 .illustrates a portion of one implementation of a deviated
wellbore system 100 according to the present disclosure. Although shown as a
deviated system (e.g., with a directional, horizontal, or radiussed wellbore),
.IO the system can include a relatively vertical wellbore only (e.g., including
normal drilling variations) as well as other types of wellbores (e.g., laterals,
1 pattern wellbores, and otherwise). Moreover, although shown on a terranean
~. 1 . surface, the system 100 may be located in a sub-sea or water-based
environment. Generally, the deviated wellbore .system 100 accesses one or
15 more subterranean formations, and' provides easier and more efficient'
production of hydrocarbons located in such subte.manean. formations. Further,
the deviated wellbore system 100 may allow for easier and more efficient
fracturing or stimulation operations: As illustrated in FIG. 1, the deviated'
wellbore system 100 includes a drilling assembly 104 deployed on a terranean
20 surface 102. The drilling assembly 104 may be used to form a vertical
wellbore portion 108 extending from the terranean surface "1 02 and through
one or more geological formationsyin the Earth. One or more .subterranean
.fo~ationss,u ch as productive formation 126, are located under the terranean
surface 102. As will be explained in more detail below, one or more wellbore
25 casings, such as a surface casing 1 12 and intermediate casing 1 14, may be
installed in at Ieast a portion of the vertical wellbore portion 108.
In some implementations, the drilling assembly 104 may be
deployed on a , body of water .rather than the terranean surface 102. For
instance, in some implementations, the terranean surface 102 may be an ocean,
30 gulf, sea, or any other body of water under which hydrocarbon-bearing
formaCions may be found. In short, reference to the terranean surface 102
includes both land' and 'water surfaces and contemplates forming and/or
developing one or more deviated wellbore systems 100 from either or both
locations.
~enerally,t he drilling assembly 104 may be any appropriate
assembly or drilling rig used to form wellbores or wellbores in the Earth. The
5 drilling assembly 104 may use traditional techniques to form such wellbores,
such as the vertical wellbore portion 108,. or may use nontraditional of novel
i techniques. In some implementations, the drilling assembly 104 may use
rotary drilling equipment to form such wellbores. Rotary drilling equipment is
known and may consist of a drill string 106 and a bottom hole assembly
lo (BHA) 11 8. In some implementations, the drilling assembly 104 may consist
of a rotary drilling rig. Rotating equipment on such a rotary drilling rig may
consist of components that serve to rotate a drill bit, which in turn forms a
wellbore, such as the vertical wellbore portion 108, deeper and deeper into the
ground. Rotating equipment consists of a number of components (not all
15 shown here), which contribute to transferring power from a prime mover to the
drill bit itself. The prime mover supplies power to a rotary table, or top direct
drive system, which in turn supplies rotational power to the drill string 106.
The drill string 106 is typically attached to the drill bit within the bottom hole
assembly 118. A swivel, .which is attached to hoisting equipment, carries
20 much, if not all of,' the weight of the drill string 106,'but may allow it to rotate
' freely.
The drill string 106 typically consists of sections of heavy steel
pipe, which are threaded so that they can interlock together. Below the drill
pipe are one or more drill collars, which are heavier, thicker, and stronger than
25 the drill pipe. The threaded drill collars help to add weight to the drill string
106 above the drill bit to ensure that there is enough downward pressure on the
drill bit to allow the bit to drill through the one or more geological formations.
The number and nature of the drill collars on any particular rotary rig may be
altered depending on the downhole conditions experienced while drilling.
3 o The drill bit is typically located within or attached to the bottom
hole assembly 11 8, which is located at a downhole end of the &ill string 106.
+
The drill bit is primarily responsible for making contact with the material' (e.g ,
-
I P a E t @rEck)hBiu&B 03 QMre &8o~&@formations and drilling through such
material. According to the present disclosure, a drill bit type may be chosen
depending on the type of geological formation encountered while drilling. For
example, different geological formations encountered during drilling may
require the use of different drill bits to achieve maximum drilling efficiency.
j Drill bits may be changed because of such differences in the formations or
because the drill bits experience wear. Although such detail is not critical to
the present disclosure, there are generally four types of drill bits, each suited
for particular conditions. The four most common types of drill bits consist of:
delayed or dragged bits, steel to rotary bits, polycrystalline diamond compact
10 bits, and diamond bits. Regardless of the particular drill bits selected,
continuous removal of the "cuttings" is essential to rotary drilling.
The circulating system of a rotary drilling operation, such as the
drilling assembly 104, may be an additional component of the drilling
assembly 104. Generally, the circulating system has a number of main
15 objectives, including cooling and lubricating the drill bit, removing the
cuttings from the drill bit and the wellbore, and coating the walls of the
wellbore with a mud type cake. The circulating system consists of drilling
! fluid, which is circulated down through the wellbore throughout the drilling
process. Typically, the components of the circulating system include drilling
20 fluid pumps, compressors, related plumbing. fixtures, and specialty injectors
for the addition of additives to the drilling fluid. In some implementations,
such as, for example, during a horizontal or directional drilling process,
downhole motors may, be used 'in conjunction with or in the bottom hole
assembly 118. Such a downhole motor may be a mud motor with a turbine
25 arrangement, or a progressive cavity arrangement, such as a Moineau motor.
These motors receive the drilling fluid through the drill string 106 and rotate to
drive the drill bit or change directions in the drilling operation.
In many rotary drilling operations, the drilling fluid is pumped
down the drill string 106 and out through ports or jets in the drill bit. The fluid
30 then flows up toward .the surface 102 within an annular space (e.g., an
annulus) between the wellbore portion 108 and the drill string 106, carrying
b
cuttings in suspension to the surface. The drilling fluid, much like the drill bit,
- -
P P O DE L Hzays& -h&feg aeHdd&@ on&& iymgfe ological conditions found under '
subterranean surface 102. For example, certain geological conditions found 1
and some subterranean formations may require that a liquid, such as water, be 1
used as the drilling fluid. In such situations, in excess of 100,000 gallons of I
water may be required to complete a drilling operation. If water by itself is
not suitable to carry the drill cuttings out of the bore hole or is not of sufficient
density t o control the pressures -in the well, clay additives (bentonite) or
polymer-based additives, may be added to the water to form drilling fluid (e.g.,
drilling mud). As noted above, there may be concerns regarding the use of
such additives in underground formations which may be adjacent to or near
subterranean formations holding fresh water. ' .
In some implementations, the drilling assembly 104 and the
bottom hole assembly 118 may operate with air or foam as the drilling fluid.
For instance, in an air rotary 'drilling process, compressed air lifts the cuttings
generated by the drill bit vertically upward through the annulus to the
15 terranean surface 102. Large compressors may provide air that is then forced
down the drill string 106 and eventually escapes through the small ports or jets
in the drill bit. Cuttings removed to the terranean surface 102 are then
collected.
As noted above, the choice of drilling fluid may depend on the
20 type of geolo.gica1 formations encountered during .the drilling operations.
Further, this decision may be impacted by the type of drilling, such as vertical
, drilling, horizontal drilling, or directional drilling.. In some cases; for example,
. .
certain geological formations may be more amenable to air drilling when
drilled vertically as compared to drilled directionally or ho;izontally.
25 As illustrated in FIG. 1, the bottom hole assembly 118,
including the drill bit, drills or creates the vertical wellbore portion 108, which
extends from the terranean surface 102 towards the target subterranean
. . formation 124 and the productive formation 126. In some implementations,
the target subterranean formation 124 may be a geological formation amenable
30 to air drilling. In addition, in some implementations, the productive'formation
126 may be a geological formation that is less amenable to air drilling
processes. As illustrated in FIG. 1, the productive formation 126 is directly
- -
I P B D E b HaBja&d to@Ed- d&rI 6 e targeet: 6Aation 124. Alternatively, in some
implementations, there may be one or more intermediate subterranean
formations (e.g., different rock or mineral formations) between the target
subterranean formation 124 and the productive formation 126.
In some implementations of the deviated wellbore system 100,
the vertical wellbore portion 108 may be cased with one or more,casings. As
illustrated, the vertical wellbore portion 108 includes a conductor casing 11 0,
Which extends frdm the terranean surface 102 shortly into the Earth. A portion
of the vertical wellbore portion 108 enclosed by the conductor casing 1 10 may
be a large ]diameter wellbore. For instance, this portion of the vertical
lo wellbore portion 108 may be a 17-1/2" wellbore with a 13-318" conductor
casing 1 10. Additionally,, in some implementations, the vertical wellbore
portion 108 may-be offset from ve. r.t ical (e.g., a slant wellbore). Even further,
in some implementations, the vertical wellbore portion 108 may be a stepped
I wellbore, such that a portion is drilled vertically downward and then curved to
15 a substantially horizontal wellbore portion. The substantially horizontal
! wellbore portion may then be turned downward to a second substantially
I vertical portion, which is then turned to a second substantially horizontal
wellbore portion. Additional substantially vertical and. horizontal wellbore
portions may-be added according- to, for example, the type of terranean surface
20 102, the depth of one or more target subterranean formations, the depth of one
or more productive subterranean formations, and/or other criteria.
Downhole of the conductor casing 110 may bk the surface
casing 112. .The surface casing ,112 may enclose a slightly smaller wellbore
and. protect the vertical wellbore portion 108 from intrusion of, for example,
25 freshwater aquifers located near the terranean surface 102. The vertical
wellbore portion 108 may than extend vertically downward toward a kickoff
point 120, which may be between 500 and 1,000 feet above the target
subterranean formation 124. This portion .of the vertical wellbore portion 108
may be enclosed by the intermediate casing 114. The diameter of the vertical
30 . - wellbore partion 108 at any point within its length, as well as the casing size
: of any of the aforementioned casings, may be an appropriate size depending
,
on the drilling process.
Upon reaching the kickoff point 120, drilling tools such as
logging and measurement. equipment may be deployed into the wellbore
portion 108. At that point, a determination of the. exact location of the bottom.
hole assembly 11 8 may be made and transmitted to the terranean surface 102.
5 Further; upon reaching the kickoff point 120, the bottom hole assembly 118
. .
may be changed or adjusted such that appropriate directional drilling tools
may be inserted into the vertical wellbore portion 108.
-As illustrated in FIG. 1, a curved wellbore portion 128 and a
horizontal. wellbore portion 130 have been formed within. one or more
lo geological formations. Typically, the curved wellbore portion 128 may be
drilled starting fiom the downhole end of the vertical wellbore portion '1 08 and
deviated fiom ,the vertical wellbore portion 108 toward 'a predetermined
azimuth gaining from between 9 and 18 degrees of angle per 1 OO'feet drilled.
~ l t ~ r n a t i v edlif~fe,r ent predetermined azimuth may be used to drill the curved
15 wellbore portion 128. In drilling the curved wellbore portion 128, the bottom
hole assembly 1 1 8 often uses measurement-while-drilling ("MwD',')
equipment to more precisely determine the location of the drill bit within the
one or more geological formations, such as the target subterranean formation
124. Generally, MWD equipment may be utilized to directionally steer the
20 drill bit as it forms the curved wellb6re portion 128, as. well as the horizontal
wellbore portion 130.
t Alternatively to or in addition. to MWD data being compiled
during drilling of the wellbore portions shown in FIG. 1, certain high-fidelity
measurements (e.g., surveys) may be taken during the drilling of the wellbore
25 portions. For example, surveys may be taken periodically in time (e.g., at
particular time durations of drilling, periodically in wellbore length (e.g., at
particular distances drilled, such as every 30 feet or otherwise), or as needed or
desired (e.g., when there is a concern about the path of the wellbore).
Typically, during a survey, a completed measurement of the inclination and
30, aiimuth of a location in a well '(typically the total depth at the time of
measurement) is made. in order to know, with- reasonable accuracy, that a
correct or particular wellbore path' is being followed (e.g., according to a
BE ~'~&ll&rTjp:1 &)5 ~&&4@sit&dnia@S helpful to know in case a relief well
must be drilled. High-fidelity measurements may include inclination from
vertical and the azimuth (or compass heading) of the wellbore if the direction
of .the path is critical. These high-fidelity measurements may be made at
discrete points in the well, and the approximate path of the wellbore computed
s from the discrete points. The high-fidelity measurements may be made with
any suitable high-fidelity sensor. Examples include, for instance, simple
pendulum-like devices to complex electronic accelerometers and gyroscopes.
For example, in simple pendulum measurements, the position of a freely
hanging pendulum relative to a measurement grid (attached to the housing of a
lo measurement tool and assumed to represent the path of the wellbore) is
captured on photographic film. The film is developed and examined when the
tool is removed from the wellbore, either on wireline or the next time pipe is
tripped out of the hole.
The horizontal wellbore portion 130 may typically extend for
1s hundreds, if not thousands, of feet within the target subterranean formation
124. Although FIG. 1 illustrates the horizontal wellbore portion 130 as exactly
perpendicular to the vertical wellbore portion 108, it is understood that
directionally drilled wellbores, such as the horizontal wellbore portion 130,
have some variation in their paths. Thus, the horizontal wellbore portion 130
20 may include a "zigzag" path yet remain in the target subterranean formation
124. Typically, the horizontal wellbore portion 130 is drilled to a
predetermined end point 122, which; as noted above, may be up to thousands
of feet from the kickoff point 120. As noted above, in some implementations,
the curved wellbore portion 128 and the horizontal wellbore portion 130 may
25 be formed utilizing an air drilling process that uses air or foam as the drilling
fluid.
The wellbore system 100 also includes a controller 132 that is
communicative.with the BHA 118. The controller 132 may be located at the
wellsite. (e.g., at or near drilling assembly 104, either above-surface or
30 underground) or may be remote from the wellsite (e.g., at a remote location
and communicative with components of the wellsite using one or more
communication mechanisms). The controller 132 may also be communicative
- -
E P d D E L s g i t h I &er f%f&~dsP& e%ced iid&aBa@es, and networks. Generally, the
controller 132 may include a processor based computer or ,computers (e.g.,
desktop, laptop, server, mobile device, cell phone, or otherwise) that includes
memory (e.g., magnetic, optical, ~ . A ~ / R ~ ~ , ~ e m o vreambotlee o,r local), a
network interface (e.g., softwarehardware based interface), and one or more
inputloutput peripherals (e.g., display devices,. keyboard, mouse, to. u. ch screen,
and others).
The controller 132 may at least parthlly 'control, manage, and
execute operations associated with the -drilling operation of .the 'BHA. Ln
some aspects, the controller. 132 may control and adjust' one or more of the
illustrated' components of wellbore system 100 dynamically, such as, in realtime
during drilling operations; at the wellbore system 100. The real-time
control may be adjusted based on sensor measurement data or based on
changing predictions -of the wellbore trajectory, even without any sensor
measurements.
15
'
, The controller 132 may perform such 'control operations based
on a model of BHA dynamics. The model of BHA dynamics. may simulate
, .
various .physical phenomena in the drilling operation, such as vibrational ~ disturbances and sensor noise. The controller 132 may use the model of BHA
1 dynamics to determine relational information that relates BHA control inputs
20 to different sets of operating conditions for which the BHA control inputs
satisfy an objective function, and to periodically transmit andlor update the
relational information to the. BHA, based on changing downhole conditions. .
In general, a model of BHA dynamics may rely on an
underlying state variable that evolves with time, representing changing
25 conditions in the drilling operation. The state variable in the model of BHA
dynamics may be an estimate of the true state of the BHA, from which
estimates of wellbore trajectory can be derived. The time evolution of the
BHA dynamics .may be represented by a discrete-time state-space model, an
example of which may'be formulated as:
where the matrices A, B, and C are system matrices that represent the
underlying dynamics of BHA drilling and measurement. The system matrices
A, B, and Care determined by the underlying physics and mechanisms employed
in the drilling process. In practice, these matrices are estimated and modeled
5 based on experience. The state x(k) is a vector that represents successive states
of the BHA system, the input u(k) is a vector that represents BHA control
inputs, and the output y(k) is a vector that represents the observed (measured)
trajectory of wellbore.
In some aspects, the vector w(k) represents process noise and
10 the vector, v@), represents measurement noise. The process noise w accounts
for factors such as the effects of rock-bit interactions and vibrations, while the
measurement noise v accounts for noise in the measurement sensors. The
noise processes w(k) and v(k) may not be exactly known, although reasonable
guesses can be made for these processes, and these guesses can be modified
15 based on experience. The noise vectors w@) and v(k) are typically modeled by
Gaussian processes, but non-Gaussian noise can also be modeled by
modifying the state x and matrix A to include not only the dynamics described
by the states variables, but also the dynamics of stochastic noise, as described
further below.
20 In the examples discussed below, the BHA control input vector
u(k) includes 6 control variables, representing first and second bend angles of
the BHA, a depth of the BHA, activation of first and second packers (e.g:, by
inflation of the packers, mechanical compression of the packers, etc.), and a
separation of the packers. The output vector y(k) includes 12 observed
25 measurement values, including 6 measurement values from a near
inclinometer and magnetometer package and another 6 measurements from a
far inclinometer and magnetometer package (hereinafter, "inclmag"). The
state vector x(k) is a vector of dimension 12+nd, which includes 12 states that
represent the actual azimuth and inclination values, as would be observed
.3o (measured) by the near and far inclmag packages. The value nd is the order of
a disturbance model which filters the un-modeled disturbances, and adds to the
4
12 states representing the system dynamics.
- , , , I$ : 54
The state transition matrix A is therefore; in this example, a (12
+ nd) by (12 + nd) dimensional state transition matrix that represents the
underlying physics, the matrix B is a (12 + nd) by 6 dimensional matrix that
governs the relation between the control variables and the state of the system,
and the matrix C is a 12 by (12 + nd) matrix that governs the relation between
the observations, y, and the state of the system, x. The matri-ces A, By and C
may be determined using any suitable estimation or modeling technique, such
as a lumped-miss system model. There can be more states, if a'more complex
dynamic model is used to describe the system.
Due to the random noise and potential inaccuracies in modeling
the system matrices A, B, and C, the state'x of the model of BHA dynamics in
Equation 1 is, in general, not exactly known, but rather inferred. In these
scenarios, Equation 1 may,be used to determine inferences, or estimates, of the
state x and measurements y, rather than their true values. In particular, the
model of Equation 1 may be used to generate predictions of future values of
state x and observations y. Such predictions may take into account actual
measurements to refine the model dynamics in Equation 1.
For example, the following equation may be used to obtain an
estimate 2 of the next state of the BHA system, in the absence of any current
20 measurements:
R(k + 1) = AR (. k) + Bu(k) 9(k) = CR (k) 4 (2)
If current measurements y are available, then predictions may
be generated by using Kalman filtering update equations:
In ~ ~ u a t i o3n, y@) represents the actual observation (e.g.,
provided by high-fidelity sensor measurements, MWD sensor measurements,
or any other suitable sensor. measurements). The factor K (e.g., a time-varying
'factor), also known as the ~ a l m a nob servation gain, represents a correction
1p D E + j f ~ c t o ~ t g a c ~ ~ t - fq~pro&r$qm eg&e actual trajectory and the estimated
trajectory, y(k) - 9(k). In general, a larger value of K implies that more
weight is given to the measured observation y(k) in determining the estimate
of the next state f (k + 1). Typically, K depends on the amount of vibration
I
and reaction force that is affecting the drill bit. The value of K may be chosen
5 according to any suitable criterion (e:g., minimize mean-squared error of state
estimate, or any other suitable criterion), to achieve a desired tradeoff between
relative importance of measured observations and underlying model dynamics.
The model of BHA dynamics in Equation 1 may be updated
dynamically as new information is received by the controller (e.g., the controller
lo 132 in FIG: 1). For example, matrices A and B may be affected by know . '
control inputs (e.g., BHA control, trajectory, etc.) in addition to being affected by
any measurements (e.g., logging measurements, high-fidelity measurements,
etc.). Therefore, the model of BHA dynamics may be updated as the control
inputs andlor drilling environment change.
1.5 A model-based predictive controller may use the model of BHA
dynamics in Equation 1 to generate predictions of future wellbore trajectory,
and based on these predictions, determine BHA input controls that satisfy a
desired objective function. The objective function may be a combination of
one or more objectives, weighted by weighting factors. As examples, the
20 objectives may relate to reducing deviation from a planned wellbore path,
reducing input energy consumption for the BHA, reducing torque on the BHA,
or any other suitable objective related to the drilling opetation.
As an illustrative .example, the objective function may
minimize, over a future horizon of time, a weighted combination of two
25 objectives: (1) a deviation from a planned wellbore path, and (2) a future cost
of applying a control input to the BHA, subject to a set of constraints. The
future cost of applying a control input may relate to, as examples, input energy
consumption for the BHA, torque on the BHA, fluid flow to the BHA, angular
position of the BHA, financial cost associated with drilling (e.g., a financial
30 cost per distance or per time) or any other suitable cost parameter related to the
drilling operation. An example objective function is shown below:
If converted to the state-spice formulation; the objective
fiuiction becomes:
x(k + 1) = Ax(k) + BU(k)
subject to
~ ( k=) C x(k)
umin 5 u(k) < umax
ymin 5 y(k) 5 ymax
where ySP is the planned wellbore path (and xSP the
corresponding sequence of states), t denotes the current time instant, and T is
lo the prediction horizon (which may be finite to obtain a dynamic solution, or
may be infinite to obtain a steady-state solution). The first term in the
objective function in Equation 4 is a quadratic term that corresponds to the
objective of minimizing a squared deviation from the planned wellbore path,
, weighted by' a weighting matrix QF) (which may be time-varying). The
l j second term in Equation 5 is a quadratic term that corresponds to an objective
. .
of minimizing a squared change in the input controls, which represents input
energy consumption, weighted by a weighting matrix S(k) (which may be
time-varying). In the second term, it is assumed that the downhole.power
consumption is proportional to change rates of input controls (e.g., bend
20 angles and activation of packers). The change in input controls is the
difference between the input controls in successive time steps, Au(k) =
u(k) - u(k - 1). The function G(.) is an input-output representation based
on the' model of BHA dynamics in Equation 1. In particular, the function G(.)
may use either ' ~ ~ u a t i o2n (e.g., 'for updates without measuriments) or
2 $3 6 muad ado^ 3 @.&,Xi@ @&a@s w~t@nie@@ementst)o yield next-step predictions
of the measurement y based on a desired BHA input control u. An example of
a state-space based input-output formulation is given in Equation 4.
There may be one or more constraints on the input (umLnandor
umaxa)n dor the output (ymLnandloyr max), andor any suitable combination
5 of input constraints and output constraints, of the objective function, as shown
in Equation 5. Such constraints may represent real-life drilling constraints,
such as maximum bend angles, minimum fluid flow, maximum rate of
penetration, etc. One or more or none of the constraints in Equation 5 may be
considered in the solution of the objective function in Equation 4.
10 In the current time step t, after solving the objective function in
Equation 4 to generate a desired control signal sequence u@), k = t, t + 1, ... ,
(t + T), only the first control signal u(t) is applied to the BHA. At the next
time instant t+l, the objective function in Equation 4 is solved again to
generate the next sequence of controls, u@), k = t + 1, ... , (t + 1 + T), of
15 which the first control u(t+l) is applied to the BHA. These iterations
continue, looking ahead T steps into the future to yield the best current-step
control u that should be applied to the BHA to satisfy the objective function in
Equation 4.
As a downhole BHA control technique, the computations to generate
20 control inputs u(k) that satisfy the objective function in Equation 4 can require
a significant amount of resources. If the downhole resources are limited (e.g.,
in terms of processing speed, power supply, etc.) and the BHA operates in
high-temperature-high-pressure drilling environments, then a large capital cost
may be expended to implement a model-based predictive control as described
25 above. Exacerbating this problem, in some examples, fast dynamics of BHA
operations can result in control algorithm sampling rates of at least 1 Hz for
tool face control and 10 Hz for vibration control. In many scenarios, a fast
processor is typically used to compute BHA control inputs for a model-based
predictive control (e.g., as a solution to Equation 4). This can impose
30 significant burdens on the downhole computing equipment.
In some examples, the computational burden of solving the objective
9
function in Equation 4 (and, in same examples, the constraints in Equation 5)
-- c r x - - E - - - - -
ZP f$ DE g g a y &-per~'rmed$@&~or ih %h05,%~ a secondary system apart from the
BHA. For example, the secondary system may be the controller 132 in FIG. 1,
or may be any suitable system (above or below the surface) that is local or
remote'to the wellsite.
The secondary system may pre-compute control inputs that satisfy an
5 ' objective function, generate relational information (e.g., a lookup table) that
provides the control inputs in a more easily-accessible manner, and provide the
relational information to the BHA. Such techniques may enable a more
affordable and feasible solution to implement MPC to control downhole BHA
that may have limited resources.
10 In general, any suitable objective function, not necessarily
quadratic as in Equation 4, may be used to control the BHA. However, in
some examples, a quadratic cost may be a good model of actual costs that are
considered by upper layer controllers or optimizers in managing the drilling
operations. Also, the set of constraints need not necessarily be convex, as in
15 Equation 5. However, in some examples, convex constraints may be desirable.
In particular, models of BHA dynamics that are used by model-predictive
control are typically based on linearization of a first-principle BHA model.
The physical constraints that are applied to the BHA are typically derived from
various mechanical properties of the BHA and rock formation properties,
20 which are also typically linearized. These various constraints, including both
model constraints and physical constraints, may be well-modeled by c.onvex
constraints (e.g., as in Equation 5). +
In the case of quadratic objective functions and convex constraint sets
(e.g., in Equations 4 and 5), the control input that satisfies the objective
25 function has a linear form. Therefore, in the example above, the secondary
system may solve the objective function and constraints to generate control
inputs that have the form:
u(k) = Fx(k) + uo (6)
where ti0 is an offset vector term and F represents a feedback
~ 3 o . term, which depends on the operating point inswhich the system state. x@)
-
-X P ~BE cEer?< istas, _sT-heoB_sHA- rG-~onatroZl-injp uti n. Equation 6 is a piecewise linear finction,
H P ; 34
such that over a particular range of values of state x@) (representing a
particular set of operating conditions for the BHA), Equation 6 is a linear
function with constant slope matrixF. The slope matrixF may change to
another constant. value in a different range of values for state x(k) representing
5 another set of operating conditions. In this example, the slope matrixF
uniquely defines the relationship between the state x and'the control u
(assuming a known offset uo). If a secondary system solves the constrained
objective function in Equations 4 and 5 to obtain the values of slope matrixF
corresponding to different regions of x, then it may simply provide the BHA
10 with the values of matrig, from which the BHA may determine the control
input u by the multiplicative operation in Equation 6 (e.g., by using one or . ,
more processors within the BHA to perform the multiplicative calculations).
If the state-space realization of the model is properly chosen, the
system state x(k) can represent a physical drilling parameter, for example, a
15 rate of penetration (ROP), a radius of curvature, etc. In such scenarios, the
control law in Equation 6 enables the BHA control decision u(k) to be based
on an operating condition of the drilling, via the value of state x(k). Also, in
the example of quadratic-cost and convex-constraints in Equations 4 and 5, a set
of operating conditions for the BHA can be determined that correspond to each
20 constant value of input control gain matrixF. Therefore, if the BHA
determines that a system state x belongs to a particular set of operating
conditions, then it may easily determine the control input u(k) by' determining
the slope matrixF that corresponds to the set of operating conditions (e.g., via
a lookup table) and multiplying the matrixF and the system state x.
2 5 In the quadratic-cost-convex-constraint example above, each set of
operating conditions corresponds to an "active" constraint set of Equation 5
(e.g., the input u equal to one of the bounds umLnoru max or the output y equal
to one of the output bounds ymLnor ymax). The secondary system may
precompute BHA control inputs (e.g., using t'he linear control law in Equation
30 6) in advance by considering each constraint (e.g., in Equation 5) and solving
for the control input that satisfies that constraint. The relational information
(e.g., look-up table or other input-output function) for the control input is then
fPO 7 BEr--& - - = = E ne te4d- b $B zafh7en~=i g=~ Rth setA e8 tha?&rrespond to the active constraint, and
'
the control law for that constraint. In some examples, this may be repeated for
all the other constraints in Equation 5 to generate, for all possible states,
control inputs that satisfy the objective h c t i o n in Equation 4 and the
constraints in Equation 5.
5 The relational information may then be transmitted from the secondary
system to the BHA. In some examples, the model of BHA dynamics may also
be transmitted the BHA. .Such information may be transmitted using any
suitable comrnunicati'on technique via a suitable number of communication
modules communicating over a communication medium (e.g., wired or
lo ' wireless). In some examples, the communication techniques may ' include
various forms of data processing such data compression, channel coding,
filtering, andlor other suitable data processing techniques. Upon receiving the
relational information, and in some examples, receiving the model of BHA
dynamics, the BHA may store the information in local memory. Intuitively,
15 each entry in the relational information corresponds to a particular operating
condition during drilling. The BHA can detect an operating condition in the
wellbore and determine an appropriate control input by accessing the lookup
table. The BHA may detect a past or current operating condition (e.g., based
on sensor measurements) or may detect a predicted operating condition (e.g.,
20 based on wellbore planning information or model-based predictions).
For example, if wellbore planning information or a model-based
prediction indicates a sharp turn ahead in the wellbore trajectory, then a
constraint on maximum bend angle may be active, in order to satisfy the
objective function in Equation 4. That is, the bend angle may be maintained at
25 its maximum value over the entire planning or prediction horizon. This
information may be gleaned by the BHA by simply accessing the relational
information to determine the input control corresponds to the detected
operating condition (e.g., by determining a gain matrixF and applying the gain
F in the control law in Equation 6). This lookup operation may, in the
30 example of Equations 4 and 5, have the same effect as if an MPC optimization
problem were solved to obtain the control input that satisfies the objective
function for the detected operating condition. This may enable more efficient
- -
I P O BE L ~ S i l l i i ~ S ~ e P t@f kflg& &ingIGn;p&&on time and power in the BHA. In
I or if cost of storage is restrictive, the relational information may be stored
I apart from the BHA and accessed by the BHA.
I FIG. 2 illustrates an example 3-dimensional state space representation of
I 5 a piecewise-linear control law. In this example, there are two states, xl and x2,
and 252 sets of operating conditions, or regions, in the state space. Each
region is represented by a 3-dimensional hyperplane with constant slope, and
the values along each hyperplane represent the control input corresponding to
different values of state (XI, x2). The number of regions in the state space may
lo depend on several factors. For example, one factor that affects the number of
sets of operating conditions is the number of states. A larger number of states
typically results in more regions, .because each state may have its own
constraints according to the model (e.g., the model in Equations 1-5).
Fortunately, a typical BHA model includes 4 inputs and 12 outputs with
15 relatively simple dynamics. The number of states is also typically limited, for
example it may be 12 + nd where nd depends on the complexity of the
disturbance model. Another factor that determines the number of sets of
operating conditions is the number of physical constraints (e.g., inequality
constraints in Equation 5). More physical constraints tend to create more
20 regions in the state space. The impact of the number of physical constraints is
typically exponential in the resulting number of regions. For example, a
constraint of maximum bend angle, 8 5 8, results in two regions,
corresponding to an active constraint, 8 = 8,,,, or an inactive constraint
8 < em,,. This example partitions the feasible region of states (or 4 inputs,
25 due to the dynamics) into two halves. In some examples, for a BHA MPC
problem, the physical constraints are primarily imposed by mechanical
properties. Another factor that impacts the number of regions in the state
space is the prediction horizon of the MPC. A longer prediction horizon
creates more control variables u@),u( k+l), ... to solve for, and therefore a
30 more complex state space in which a solution to the objective function is to be
found, resulting in a larger number of regions generated by constraints. In
particular, this factor may contribute more significantly to the complexity of
--
1 F a D E L Hae l &$&&&np i as &&xi& 3 fg&$namics of the BHA. '
FIG. 3 illustrates a flow diagram of an example of a process of
implementing a MPC technique by generating and providing relational
information to a downhole BHA control. In this example, the secondary
system (e.g., controller 132 in FIG. 1) is above-surface, but may generally be
s located at any suitable .lo.cation, such as below the surface. In the example of
FIG. 3, relational information, such as a lookup table, is generated by lookup
table generation module 302. The generation of the lookup table may depend
on a model of BHA dynamics provided by model .update module 304. The
lookup table'generation module 302 may calculate different possibilities of
10 active constraint sets. Then, the lookup table generation module 302 may
translate each region to quantitative equalities/inequalities for the state x. The
I lookup table generation module 302 may then compute a control input (e.g.,
using the control law in Equation 6) within each region, including a feedback
gain F and an offset uo, to generate a lookup table 306. The lookup table
15 generation module 302 may then provide the lookup table 306 to a lookup
table module 308 in the BHA, which may store the lookup table 306 in a local
memory store. In some examples,, the model associated with the lookup table
may also be passed downhole to the BHA.
During drilling operations, the lookup table module 308 may access the
20 stored lookup table to determine BHA control inputs 310 based on detected
operating conditions in the wellbore, and provide the BHA control inputs 3 10
, to the BHA 3 12. The operating conditions in the wellbore may be determined
based on state estimates 314 received from an observer module 316. The
observer module 3 16 may determine the state estimates 3 14 based on a model
25 of BHA dynamics 3 18 provided by the lookup table generation module 302 at
the secondary system. In this example, the observer module 3 16 also uses
sensor measurements 320 to determine the state estimates 314 used by the
lookup module 308. As a specific example, the observer module 3 16 may use
a Kalman filtering formulation (e.g., as in Equation 3) to determine an
3.0 estimate f ( k + 1) of the true state x(k + 1) based on observations and
applied controls, since the true state may not be exactly known due to noise in
9
the downhole environment.
During drilling operations, a model monitoring module 322 in the
secondary system may monitor sensor measurements 320 and the control
signals 3 10 to determine whether the model of BHA dynamics 3 18 accurately
tracks the true wellbore conditions. This may be determined by monitoring for
j a relational information update event, and updating the relational information at
the BHA based on detecting that a relational information update event has
occurred. If the model monitoring module 322 determines that a relational
information update event has occurred, and that the model of BHA dynamics
318 has significantly diverged from the actual wellbore conditions (e.g., as
lo measured by the sensors), then the model update module 304 may generate an
updated model of BHA dynamics, based on tracking information provided by
the model monitoring module 322. During this model update, the control input
to the BHA may be restrained or adapted to be less aggressive.
The relational information update event may be configured to be any
15 suitable event that represents a divergence between the model of BHA
dynamics and the true conditions in the wellbore. As an example, the model
monitoring module 322 may determine residual values rmode, of the model
based on sensor measurements and/or predictions, and compare the residual
values against a design residual value rd,,,,,. The design residual value rdesign
20 may be determined during an initial design of the model or at a time of a
model update. The residual value rm,-,del may be based on a model of change of
a model parameter (e.g., a rate of change, an integral of a drilling parameter, a
functional transform of a drilling parameter, etc.), or additionally or alternatively,
may be determined based on an absolute value, or other suitable characteristic, of
25 a model parameter, or may be directly determined based on measured output
observations (e.g., a difference or other deviation between measured and
estimated outputs, such as y(k) - 9(k) in Equation 3). If the residual values
diverge from the design residual values by a significant amount, then the model
monitoring module 322 may determine that a relational information update
30 event has occurred and the model should be updated. In some examples, the
model monitoring module 322 may compute a ratio q of aggregate residual
7
values to the design residual values, over a suitable horizon of time:
-1 8a ~ 51 9~- 6 5 - z ~a1g ~17 1 r s4
If the ratio q exceeds some threshold bound, such as an upper limit
qma, then it may be considered that the model of BHA dynamics has
dramatically diverged from true wellbore conditions. The limit q, may be
5 determined by considering one or more drilling parameters,. such as the desired
control performance, the bandwidth of downlink, the computing power in the
secondary system, etc. A smaller value of the threshold bound vmrtvu sually
leads to more frequent update of the model, while a larger value of the
threshold bound qmav results in a coarser control that may reduce control
! lo performance. After model update by the model update module 304, the 1 procedure of computation and generation of an updated lookup table is
performed again by the lookup table generation module 302, and the updated
lookup table, along with the updated model, is re-sent to the downhole BHA.
FIGS. 4A and 4B illustrate examples of determining different sets of
l j operating conditions that are used to generate relational information (e.g., lookup
table 306 in FIG. 3) provided to a BHA to implement MPC control. In these
examples, there are two states, xl and x2. FIG. 4A is a sketch of an example of a
. state space that includes different sets of operating conditions, represented by
partitioned regions. In this example, the state space 400 is partitioned into kve
20 different regions, 402,404, 406; 408, and 410. Each region corresponds to a
particular set of operating coliditions (shown in the lookup table 412 in FIG. 4B) *
for which a fixed BHA control input satisfies an objective function and
inputloutput constraints (e.g., as in Equations 4 and 5).
For example, region 402 corresponds to the set of operating conditions
23 defined by states XI and x2 in the region x, I 1, x2 2 -1, x2 - x1 2 1. For all
states (operating conditions) in this region, the BHA control input that satisfies a
given objective function and constraints (e.g., given by Equations 4 and 5) is
.u = x, - x2. In terms of the control law formulation of Equation 6, the BHA
control input u corresponds to slope matrix F = [I -11 and offset uo = 0.
-30 Therefore, in the lookup table provided to the BHA, the entry for region 402 may
-9p -T G BELEiTnd ica1te3 ei-th0er 5th-e cpon6tr1ol 6in p1ut 7u :.=5 xl4 - x2, or may indicate just the slope
matrix F and the offset uo (or any other suitable representation of the control
input u).
In some examples, an extra step of combining different entries having
the same control inputs may be performed , as illustrated by the 4th and 5th
entries in the lookup table 412 of FIG. 4B, corresponding to regions 408 and
410 in FIG. 4A. For example, the secondary system may determine that the
control input for region 408, u = Zx, - x2 - lis identical to the control input
for region 410. In such scenarios, the set of operating conditions
corresponding to region 408 may be joined with the set of operating conditions
lo corresponding to region 410 to yield a single combined set of operating
conditions. The relational information (e.g., the lookup table 412 in FIG. 4B)
may then relate the combined set of operating conditions to a single control
input (e.g., u= 2x, - x2 - 1 in this example) that satisfies the objective
function for those operating conditions. In some examples, this may enable a
15 more compact representation of the relational information, and thus reduce
storage requirements in the BHA for storing the relational information.
FIG. 5- is a flow chart of an example process 500 for generating
and providing relational. information to a BHA for performing model-based
predictive control. One or mo,re steps of the .example process 500 of FIG. 5
20 may be performed by a secondary system (e.g., controller 132 in'FIG. 1). Ln
this example, the controller determines a model of BHA dynamics (e.g., the .
model in Equations. 1-3) based on sensor measurements from the BHA (502).
The controller then, determines, based on the model of BHA dynamics, an
. .
bbjective function including a predicted future deviation from a planned
25 wellbore path (504). The controller determines a control input to the BHA that
satisfies the objective function f0r.a set of operating conditions of -the BHA
(506). The controller then generates relational information (e.g., the lookup
table 412 in FIG. 4B) that relates the'control input to the set of operating
conditions (508). i he controller then transmits the relational information from
30 the secondary system to the BHA (5 10).
FIG. 6 is a 'flow chart of an example process 600 for accessing
relational information and determining a control input to apply for a detected
DE L Hcjber&i-s cdct-itio-d ' %- i-k%-r rdbg &$@of the example process of FIG. 6 may
.
- . be performed by the BHA (e.g., BHA 118 in FIG. 1). In some examples, the
process 600 may, be performed subsequent to step 5 10 in- FIG. 5, after the
BHA received relational information from the secondary system. In this
example, the BHA stores, at a memory location of the BHA, the relational
5 information that relates the control input to the set of operating. conditions
(602). The BHA then detects an operating conditiondf the BHA (604). For
example, the operating condition may be a part or current operating condition
determined from sensors measurements,. or- may be a predicted operating
condition based on model-based predictions. The. BHA then determines. a
lo candidate set of operating conditions including the detected operating
condition (606). The BHA accesses the stored relational information from the
memory location of the BHA (608) and determines, based'on accessing the
relational information and without solving the objective function, a control
input to the BHA that is related to the candidate set of operating conditions
I j including the detected operating condition (6 10). .
FIG. 7 is a flow chart of an example of further processing to update a
model of BHA dynamics and update relatiqnal information provided to the
BHA. The example process 700 may be performed by a secondary system
(e.g., the controller 132 in FIG. 1) and may be performed, for example, at a
20 time subsequent t o step 5 10 in FIG. 5. In this example,the controller detects
that a relational information update event has occurred, based on sensor
'measurements from the BHA (702). The relat. ion.a l information update event
may be defined according to any suitable criterion, an example of which is
provided in FIG. 8 below. The controller then updates the relational
25 information at the BHA based on detecting that a relational information update
event has occurred (704).
FIG. 8 is a flow chart of an example of fbther details of detecting that
a relational information update event has occurred, based on sensor
measurements from the BHA (e.g., step 702 in FIG. 7). In this example, the
30 controller determines a threshold bound for a drilling parameter (800). The
drilling may be related to a design objective, a predicted wellbore
,
trajectory, or a sensor measurement. ~ x m ~ loef dsr illing parameters include
zPQ
a- de&r&- &&r& ;b@f%&an&7 &dmunication bandwidth betwekn the
secondary system and the BHA, or a processing capability of the secondary
system. The controller then determines that at least one of a rate of change of
. .
the drilling parameter or an absolute value of the drilling parameter does not
satisfy the threshold bound (802).
5 . FIG. 9 is a block diagram of an exarhple of a computer -system 900.
For example, referring to, FIG; 1, one or more parts of the controller 132 could
be an example of the system 900 described here, such as a computer system
used by any of the users who access resources of the wellbore system 100.
The system 900 includes a processor 910, a memory 920, a storage device
lo 930, and an input/output device 940. Each of the components 910, 920, 930,
and 940 can be- interconnected, for example, using a system bus 950. The
processor 9 10 is capable of processing instructions for execution within 'the
system 900. In some implementations, the processor 910 is a single-threaded
processor. In some implement~tions, the processor 910 is a multi-threaded
1s processor. In some implementations, the processor 910 is a quantum
,. computer. The processor 910 is capable of processing instructions stored in
+ , the memory 920 or on the storage device 930. The processor 910 may execute
operations such as generating control inputs that satisfy an objective function,
generating relational information, sending the relational information to the
20 BHA, applying control, inputs indicated by the relational information, etc.
(e.g., FIGS. 5-8).
The memory 920 stores information within the system 900. In some
implementations, the memory 920 is a computer-readable medium. In some
implementations, the memory 920 is a volatile memory unit. In some
25 implementations, the memory 920 is a non-volatile memory unit.
The stdrage device 930 is capable of providing mass storage for
the system 900. In some implementafions, the storage device 930 is a
computer-readable medium. In various different implementations, the storage
device 930 can include, for example, a .hard disk device, an optical disk
30 device, a solid-date drive, a flash drive, magnetic tape, or some other large
capacity storage device. In some implementations, the storage device 930 may
4
be a cloud storage device, e.g., a logical storage device including multiple
- -
I P O DE b B&ysiL&i?i staage- &@&bdis&i%tk6& a network and acdessed using a
network. In some examples, the storage device may store long-term data, such
as rock formation data or ROP design capabilities. The inputloutput device
940 provides inputloutput operations for the system 900. In some
implementations, the inputloutput device 940 can include one or more of a
5 network interface devices, e.g., an Ethernet card, a serial communication
device, e.g., an RS-232 port; andor a wireless interface device, e.g., an 802.1 1
card, a 3G wireless modem, a 4G wireless modem, or a canier pigeon
interface. A network interface device allows the system 900 to. communicate,
for example, transmit and receive instructions to and from the controller 132 in
lo FIG. 1. In some implementations, the inputloutput device can include driver
devices configured to receive input data and send output data to other
inputloutput devices, e.g., keyboard, printer and display devices 960. In some
implementations, mobile computing devices, mobile communication devices,
and other devices can be used.
15 A server (e.g., a server forming a portion of the controller 132
or the wellbore system 100 shown in FIG. 1) can be realized by instructions
that upon execution cause one or more processing devices to carry out the
processes and functions described above, for example, such as generating
control inputs that satisfy an objective function, generating relational
20 information, sending the relational information to the BHA, and applying
control inputs indicated by the relational .information, etc. (e.g., FIGS. 5-8).
Such instructions can include, for example, interpreted instructions such as
script instructions, or executable code, or other instructions stored in a
computer readable medium. Different components of a wellbore system 100
25 can be distributively implemented over a network, such as a server farm, or a
set of widely distributed servers or can be implemented in a single virtual
device that includes multiple distributed devices that operate in coordination
with one another. For example, one of the devices can control the other
devices, or the devices may operate under a set of coordinated rules or
30 protocols, or the devices may be coordinated in another fashion. The
coordinated operation of the multiple distributed devices pre.s ents the
appearance of operating as a single device.
The features described can be implemented in digital electronic
circuitry, or in computer hardware, firmware, software, or in combinations of
them. The apparatus can be implemented in a computer program product
tangibly embodied in an information carrier, e.g., in a machine-readable
5 storage device, for execution by a programmable processor; and method steps
can be performed by a programmable processor executing a program of
instructions to perform functions of the described implementations by
operating on input data and generating output. The described features can be
implemented advantageously in one or more computer programs that are
lo executable on a programmable system including at least one programmable
processor coupled to receive data and instructions from, and to transmit data
and instructions to, a data storage system, at least one input device, and at least
one output device. A computer program is a set of instructions that can be
used, directly or indirectly, in a computer to perform a certain activity or bring
15 about a certain result. A computer program can be written in any form of
programming language, including compiled or interpreted languages, and it
can be deployed in any form, including as a stand-alone program or as a
module, component, subroutine, or other unit suitable for use in a computing
environment.
20 Suitable processors for the execution of a program of
instructions include, by way of example, both general and special purpose
microprocessors, and the sole processor or one of multiple processors of any
kind of computer. Generally, a processor will receive instructions and data
from a read-only memory or a ;andom access memory or both. Elements of a'
25 computer can include a processor for executing instructions and one or more
memories for storing instructions and data. Generally, a computer can also
include, or be. operatively coupled to communicate with, one or more mass
storage devices for storing data files; such devices include magnetic disks,
such as internal hard disks and removable disks; magneto-optical disks; and
30 optical disks. Storage devices suitable, for tangibly embodying computer
program instructions and data include all forms of non-volatile memory,
including by way of example semiconductor memory devices, such as
-+ -P O b E L F % Z ? R ~ T~ @ R ~ d , G & & f l aF&mk && devices; magnetic disks such as
internal hard disks and removable disks; magneto-optical disks; and CD-ROM
and DVD-ROM disks. The processor and the memory can be supplemented
by, or incorporated in, ASICs (application-specific integrated circuits).
To provide for interaction with a user, the features can be
implemented on a computer having a display device such as a CRT (cathode
ray tube) or LCD (liquid crystal display) monitor for displaying information to
the user and a keyboard and a pointing device such as a mouse or a trackball
by which the user can provide input to the computer.
The features can be implemented in a computer system that
includes a back-end component, such'as a data server, or that includes a
middleware component, such as an application server or an Internet server, or
that includes a front-end component, such as a client computer having a
graphical user interface or an Internet browser, or any combination of them.
The components of the system can be connected by any form or medium of
digital data communication such as a communication network. Examples of
communication networks include, e.g., a LAN, a WAN, and the computers and
networks forming the Internet.
The computer system can include clients and servers. A client
and server are generally remote fiom each other and typically interact through
20 a network, such as the described one. The relationship of client and server
arises by virtue of computer programs running on the respective computers
and having a client-server relationship to each other. +
In .addition, the logic flows depicted in the figures do not
require the particular order shown, or sequential order, to achieve desirable
25 results. In addition, other steps may be provided, or steps may be eliminated,
from the described flows, and other components may be added to, or removed
from, the described systems. Accordingly, other implementations are within
the scope of the following claims.
A number o f . implementations have been described.
30 Nevertheless, it will be understood that various modifications may be made.
For example, additional aspects of processes 500 and 600 may include more
I
steps or fewer steps than those illustrated in FIGS. 7 and 8. Further, the steps/

WE CLAIM:
1. A computer-implemented method of controlling a bottom hole
assembly (BHA), the method comprising:
determining a model of BHA dynamics based on sensor measurements
s from the BHA;
determining, based on the model of BHA dynamics, an objective
function comprising a predicted future deviation from a planned wellbore
path;
determining a control input to the BHA that satisfies the objective
lo function for a set of operating conditions of the BHA;
generating, at a secondary system, relational information that relates
the control input to the set of operating conditions; and
transmitting the relational information from the secondary system to
the BHA.
15 2. A computer-implemented method as claimed in claim 1, further
comprising:
storing, at a memory location of the BHA, the relational information
that relates the control input to the set of operating conditions;
detecting an operating condition of the BHA;
20 determining a candidate set of operating conditions comprising the
detected operating condition; *
accessing the relational information from the memory location of the
BHA; and
determining, based on accessing the relational information, a control
2s input to the BHA that is related to the candidate set of operating conditions
comprising the detected operating condition.
3. A computer-implemented method as claimed in claim 2,
wherein determining, based on accessing the relational information, a control
input to the BHA is performed without performing computations to solve the
30 objective function for a control input that satisfies the objective function.
4. A computer-implemented method as claimed in claim 1,
wherein generating, at a secondary system, relational information that relates
the control input to the set of operating conditions comprises: generating a
relational database that relates the control input to the set of operating
5 conditions.
5. A computer-implemented method as claimed in claim 1,
wherein generating, at a secondary system, relational information that relates
the control input to the set of operating conditions further comprises:
determining a first control input to the BHA that satisfies the objective
lo function for a first set of operating conditions of the BHA;
determining a second control input to the BHA that satisfies the
objective function for a second set of operating conditions of the BHA;
determining that the first control input to the BHA and the second
control input to the BHA are identical to each other;
15 combining the first set of operating conditions and the second set of
operating conditions into a combined set of operating conditions; and
relating, in the relational information, the combined set of operating
conditions to a single control input that corresponds to both the first and
second control inputs.
20 6. A computer-implemented method as claimed in claim 1, further
comprising: 4
detecting, at the secondary system and based on sensor measurements
from the BHA, that a relational information update event has occurred; and
25 updating the relational information at the BHA based on detecting that
a relational information update event has occurred.
7. A computer-implemented method as claimed in claim 6,
wherein updating the relational information at the BHA comprises:
determining an updated model of BHA dynamics based on updated
sensor measurements from the BHA;
5. determining an updated objective function based on the updated model
of BHA dynamics;
. .
determining an updated control input to the BHA that satisfies the
updated objective function for the set.of operating conditions of the BHA;
generating, at the secondary system, updated relational information
10' that relates the updated control input to the.set of operatingconditions; and
transmitting the updated relational information from the secondary
system to the BHAl
8. A computer-implemented method as claimed in claim 7,
wherein transmitting the updated relational -information from the secondary
15 system to the BHA comprises:
determining a difference between the updated relational information
and the relational information; and
transmitting the difference between the updated relational information
and the relational information from the secondary system to the BHA.
20 9. A computer-implemented. method as claimed in claim 6,
1 - wherein detecting that a relational information' update event 'has occurred
comprises:
determining a threshold bound for a drilling parameter; and
. .
, determining that at least one of. a rate of change of the drilling
25 parameter or an absolute value of the drilling parameter does not satisfy the
threshold'bound.
10 ' A .computer-implemented method as claimed in claim 9,
wherein determining a threshold bound further comprises determining the
threshold bound based on at least one of a desired control performance, a . '
30 cornrnunicatiori bandwidth between, the secondary system and the BHA, or a
11. A computer-implemented method as claimed in claim 6, further
comprising implementing a constraint on the control input to the BHA while
updating the relational information at the BHA.
12. A computer-implemented method as claimed in claim 1,
5 wherein transmitting the relational information from the secondary system to
the BHA comprises transmitting the relational information and the model of
BHA dynamics fiom an above-surface location of the secondary system to the
BHA.
13. A computer-implemented method as claimed in claim 1,
lo wherein transmitting the relational information from the secondary system to
the BHA comprises transmitting the relational information and the model of
BHA dynamics from a below-surface location of the secondary system to the
BHA.
I 14. A computer-implemented method as claimed in claim 1,
I. l j wherein determining an objective function comprises:
I determining a weighting factor based on at least one of the model of
I BHA dynamics or the sensor measurements from the BHA;,an d
I determining a weighted combination of the predicted future deviation
I
! from the planned wellbore path and a predicted future cost of applying a
, .
20 control input to the BHA, weighted by the weighting factor.
15. A computer-implemented method as claimed in claim 1,
wherein determining a control input to the BHA that satisfies the objective
function for a set of operating conditions comprises determining a control
input to the BHA that minimizes a weighted 'combination of the predicted
25 future deviation from the planned wellbore path and a predicted future cost of
applying the control input to the BHA over a subsequent period of time during
which the model of BHA dynamics satisfies the set of operating conditions.
16. A computer-implemented , method as claimed in claim 15,
wherein the predicted future cost ofapplying a control input to the BHA
comprises at least one of a predicted energy consumption forthe BHA, a
predicted torque on the BHA, a predicted fluid flow to the BHA, a predicted
angular position of the BHA, or a predicted financial cost.
17. A computer-implemented method as claimed in claim 1, further
comprising:
determining a candidate control input to the BHA;
determining a predicted wellbore trajectory, based on the candidate
lo control input to the BHA and the model of BHA dynamics; and
determining the predicted future deviation fiom the pianned wellbore
path based on a deviation between the predicted wellbore trajectory and the
planned wellbore path.
18. A computer-implemented method . as claimed in claim 1,
15 wherein determining a control input to the BHA comprises determining at least
one of a first bend anglecontrol, a second bend angle control, a first packer . - .
control, or a second packer control.
19. A system compfising:
a first component located at or near a terranean surface;
a bottom hole assembly (BHA) at least partially disposed within a
wellbore at or near a subterranean zone, the BHA associated with at least one
5 sensor; and
a controller communicably coupled to the first component and the
BHA, the controller operable to perform operations comprising:
determining a model of BHA dynamics based on sensor
measurements from the BHA;
10 determining, based on the model of BHA dynamics; an
objective function comprising a predicted future deviation from a planned
wellbore path;
determining a control input to the BHA that satisfies the
objective function for a set of operating conditions of the BHA;
15 generating, at a secondary system, relational information that
relates the control input to the set of operating conditions;' and
transmitting the relational information from the secondary
system to the BHA.
20. A non-transitory computer-readable storage medium encoded
with at least one computer program comprising instructions that, when
executed, operate to cause at least one processor to perform operations for
controlling drilling of a bottom hole assembly (BHA) in a borehole, the
5 operations comprising:
determining a model.of BHA dynamics based on sensor measurements
from the BHA;
determining, based on the model of BHA dynamics, an objective
hnction comprising a predicted future deviation from a planned wellbore
lo path;
determining a control input to the BHA that satisfies the objective
function for a set of operating conditions of the BHA;
generating, at a secondary system, relational information that relates
the control input to the set of operating conditions; and
15 transmitting the relational information from the secondary system to
the BHA.