Pressure Control for Offshore Managed Pressure Drilling (MPD): Analysis, Design, and Experimental Validation
Abstract
Deepwater offshore drilling operations are among the most complex activities. For
example in regions such as the Gulf of Mexico, wells are drilled in water depths
of up to 3 kilometers, drilling depths can exceed 6 kilometers, and geologic formation
pressures can exceed 1400 bar. In offshore wells safe drilling and completion
operations can be difficult due to narrow margins between pore pressure and fracture
pressures. Moreover multiple zones of uncertain pore pressures and fracture
pressures in reservoir formation makes drilling operation even more challenging.
To avoid fracturing, collapse of the well, or influx of fluids from the reservoir surrounding
the well, it is crucial to control the pressure in the open part of the well
within a certain operating window. One method to regulate bottom-hole pressure
is Managed Pressure Drilling (MPD). In Constant Bottom-hole Pressure (CBHP)
MPD, the annulus is sealed and the drilling fluid exits through a controlled choke,
allowing for faster and more precise control of the annular pressure. In automatic
MPD systems, the choke is controlled by an automatic control system which manages
the annular well pressure to be within specified upper (fracture pressure) and
lower (pore pressure) bounds.
In the North Sea environment, a large number of subsea wells are drilled from
floating rigs. In this case, there would be the extra challenging factor of severe
vertical motion (heave) of the rig in harsh weather, typically more than 3m up
and down with a 10 - 20 seconds period. When drilling from a floating rig, the
rig moves vertically with the waves. While drilling with weight on bit (WOB), a
heave compensation system is in operation that isolates the drill string from the
heave motion of the rig. As drilling proceeds, the drill string needs to be extended
with new sections, referred to as pipe connection. Thus, every couple of hours or
so, drilling is stopped to add a new segment of about 27 meters to the drill string.
During connections, the pump is stopped and the drill-string is disconnected from
the heave compensation mechanism and put into slips rigidly connected to the rig.
The drill string then moves vertically with the heave motion of the floating rig, and
acts like a piston on the drilling fluid in the well. The heave motion in this case
can result in severe pressure fluctuations (surge and swab pressures) in the bottom
of the well. Pressure changes have been observed to be beyond the standard limits
for pressure regulation accuracy in MPD.
The goal of this thesis is mainly to develop control design methodologies for
regulating bottom-hole pressure (BHP) in offshore drilling operations. In essence
extending control over BHP to the pipe connections scenario when the rig pumps
are off and the drilling string is moving vertically. Two different lines of research are presented, which will be discussed in the sequel. This thesis comprises two parts.
First part gives an introduction to MPD, and discusses briefly variants of MPD.
Next common equipment and technology components in MPD are discussed. Then
different estimation and control techniques proposed in the literature are reviewed
thoroughly. Variety of estimation and control techniques have been applied in different
scenarios in drilling operations. The majority of the control methods are
based on PID and Model Predictive Control (MPC). While estimation techniques
are mostly based on Kalman filters and Lyapunov techniques. Then an introduction
to the connection scenario and down-hole pressure fluctuations (surge and swab)
caused by the heave motion of floating drilling rig is given. Methods for modeling
and prediction of surge and swab pressures are reviewed and different techniques
proposed for compensating their effect in MPD and Under-Balanced Drilling operations
(UBD) are discussed. An introduction to MPD-Heave lab at NTNU and a
comparison with industrial scale MPD systems are given. Contributions are stated
in detail.
In the second part selected conference and journal papers are presented. In the
first paper a simplified nonlinear dynamic model based on mass and momentum
balances for managed pressure drilling (MPD) is presented. The sources of uncertainty
in drilling operations is discussed and two parameters for calibrating the
hydraulic model against uncertainties in the viscosity of mud, temperature distribution
in the well, frictional pressure losses, the geometry of the well, and bulk
modulus are considered. The key uncertain model parameters and the bottom-hole
pressure are simultaneously estimated using joint unscented Kalman filter based on
only available top-side pump and choke pressure measurements. The performance
of the algorithm is tested for the case of normal drilling operations and connection
operations, in which there is no flow through the drill-string and borehole
pressure reduces significantly. The results of simulations show accurate estimation
of the bottom-hole pressure and uncertain parameters during both transient and
steady-state drilling operations.
In the second paper a model describing the flow and pressure fluctuations in the
bore-hole due to drill-string movement has been presented. It consists of a pair of
coupled nonlinear partial differential equations modelling the distributed pressure
and flow in the well, and a simple oscillator for the disturbance. Considering only
top-side flow and pressure as measurements, it is shown that the model can be
represented by a linear time invariant finite-dimensional system with output delay.
This result is achieved by linearization and de-coupling using Riemann invariants.
An infinite-dimensional observer is designed that estimates the disturbance, and
the estimate is used in a controller that rejects the effect of the disturbance on
the down-hole pressure. A model reduction technique based on the Laguerre series
representation of the transfer function is used to derive a simple, rational, transfer
function for the controller. The performance of the full-order and reduced-order
controllers are compared in simulations, which show satisfactory attenuation of
the heave disturbance for both controllers. In the third paper the results of the
previous paper are extended by incorporating friction partially into the model and
considering the heave disturbance to be a superposition of multiple sine waves.
In the fourth paper, the output regulation problem for an offshore deep-water
managed pressure drilling system subject to periodic disturbances is addressed.
The disturbance is caused by the heave motion of the floating drilling rig during
pipe connections and the objective is to maintain a constant pressure at the bottom
of the well. The controller for the heave disturbance attenuation consists of three
cascaded parts: First, a nonlinear inversion element is applied to invert nonlinearity
of choke. Second, an adaptive compensator is designed based on internal model,
and certainty equivalence principles for asymptotic rejection of time-varying heave
disturbance. Third, an output feedback controller is synthesized using LMIs for
providing stability and improving transient performance of closed-loop system.
Robust stability of closed-loop time-varying system is analyzed using edge theorem.
Simulation results of the combined adaptive output regulator are presented, which
show satisfactory set-point tracking and attenuation of the heave disturbance.
In the fifth paper, a modified L1 adaptive controller is applied to handling heave
disturbances in MPD. It presents a modification to L1 adaptive control that allows
for disturbances entering at the plant output. By incorporating the disturbance
at the output into the reference model, it is shown that the L1 adaptive control
structure can be left unchanged while the original transient performance bounds
are preserved. It is further shown that rejection of the output disturbance can be
taken care of entirely in the filter design step of L1 adaptive control using the
internal model principle. A systematic filter design procedure based on LMIs is
provided, that requires only one tuning parameter to be adjusted by the designer.
While satisfying asymptotic robust regulation constraints, it guarantees a desired
level of performance measured in terms of peak value of output signal subject to
a peak value constraint on the control signal. The control design is applied for
disturbance attenuation and set-point tracking in the so-called heave problem in
oil well drilling, and successfully tested in a medium size experimental test facility
containing a 900m long well. The results demonstrate that the proposed regulator
efficiently regulates the down-hole pressure to the desired set-point, with significant
attenuation of unmatched periodic disturbances.
Finally in the last chapter, the conclusions and future work directions are offered.