A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. In this paper, we describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we present the results from an experiment on a nonlinear ball and beam system. 1Underactuated systems and the matching conditionOver the past five years several researchers have proposed nonlinear control laws for which the closed loop system assumes some special form, see the controlled Lagrangian method of [8, 9, 10] the generalized matching conditions of [11,12,13], the interconnection and damping assignment passivity based control of [7], the λ-method of [6,5], and the references therein. In this paper we describe the implementation of the λ-method of [6] on a ball and beam system. For the readers convenience we start with the statement of the main theorem on λ-method matching control laws (Theorem 1). We also present an indicial derivation of the main equations. We then prove a new theorem showing that the family 1

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This paper presents modelling, system identification, simulation, and experimental results for passivity-based robust control of piezo-actuated flexible beam. The flexible beam configuration considered is a cantilever aluminum beam with a piezoelectric transducer used as the actuator and tip-accelerometer as the sensor. The actuator and sensor are non-collocated. The Lagrangian formulation is used to obtain mathematical model of the flexible link dynamics with piezo actuator. For control design purposes, a finite dimensional approximate model is derived using assumed modes approach. It is shown that the approximate model compares very well with the experimentally identified model. Since the system is inherently not passive, passification techniques are used to render the system robustly passive which enables the use of passivity-based feedback control design. The controller design is validated both in simulation as well as in experiments. The simulation and experimental results demonstrate the effectiveness of controller in suppressing the tip vibrations of the link. The controller design is shown to be robust to both parametric uncertainties and unmodeled dynamics.

We present a method for modeling drilling induced fractures dynamic growth through a porous medium in the near wellbore region. Understanding the early time fracture growth behavior, and related near wellbore stress state, can provide an effective tool to improve the treatment selection through parameters such as particle size distribution and ideal drilling fluid rheology. Also, it will help with field diagnostics for various lost circulation treatments and lost return events. ExxonMobil Upstream Research Company and SIMULIA® co-developed fully-coupled hydraulic fracturing modeling capabilities. The method is based on Cohesive Zone Modeling (CZM) elements, with pore pressure degrees of freedom, which were recently implemented into SIMULIA® Abaqus finite element package. The model was benchmarked with known solutions to analytical fracture growth regimes and validated with a laboratory scale experimental setup of hydraulic fracturing. The model allows for fluid leak-off from the wellbore and fracture faces into the porous medium, as well as an arbitrary injection schedule. Additionally, the physics of dynamic fracture growth and a variety of material properties and constitutive models for both the solid and liquid, are also captured in the model. The time-dependent fracture growth and interaction between the stress concentration region near the fracture tip and the wellbore result in a non-linear behavior of the near-wellbore stress state during early time fracture propagation, which was not possible to capture with static models. The model generation, execution, and post-processing are part of an automated workflow which requires minimal user time. This analysis allows for recommendation of optimum fracture width for maximum increase in wellbore integrity in the target formation. This is done by selecting the fracture width at the mouth, at which a necessary increase in the near-wellbore tangential stresses has been achieved as to prevent initialization of further fractures.

The Erha field is a deepwater subsea oil development located in OML 133 off the coast of Nigeria. Erha North is a satellite of the Erha Field and is characterized by multiple unconsolidated sand intervals separated by shale sections. Due to the potential for reservoir compaction and early water breakthrough in these multi-layered Erha North reservoirs, high rate water injection is an important element of primary production through pressure support and is considered critical to project economics and reserves capture. This paper presents a case history of a successful field application of an innovative water injector completion technique addressing the issue of long-term injection conformance. Standalone screens with flow-control devices (i.e., downhole chokes) and openhole packers were utilized on the two most challenging water injectors in the Erha field. The completion objectives were:(a) target multiple intervals to reduce well count and cost,(b) sustain target injection rates and allocations, and(c) install sand control to prevent wellbore fill. Traditional water injector completion techniques, such as frac packs or openhole standalone screens, were judged to be incapable of meeting all the completion objectives. Unfractured completions, such as openhole standalone screens, have been reported to lose injectivity over time due to plugging and require fracturing to sustain injection rates (Sharma 2000). Fracturing may result in poor injection conformance and has the potential for broaching cap shale. Application of stacked completions or intelligent well systems would have added significant cost and complexity. Detailed completion simulations and fracture modeling were conducted to design the completions to their unique geologic settings. It is expected that this completion technique will maintain the desired injection allocations to the multiple target intervals over the well life in the matrix and fracture injection regimes. Upfront planning, communication, and alignment between reservoir, subsurface, and drilling functions enabled a successful real-time completion design and resulted in an operational success with less than 5% completion non-productive time (NPT). Performance of the injectors is being monitored by downhole pressure and temperature gauges. Introduction Water injection has been a successful secondary recovery technique in the oil industry for many years. In the past 10 to 15 years, however, projects have been developed where high-rate water injection is a primary recovery method because completion reliability and economic constraints require early voidage replacement and pressure support. As water injection becomes integral to the economic justification for capital intensive (i.e., offshore, subsea) projects, considerable attention to the design and performance of the water injectors is required. Regardless of rock cementation, there are very few documented cases of long-term, high-rate water injection without some form of continual or periodic stimulation. In well cemented rock formations, successful high-rate water injection programs rely on continual formation fracturing. Highly compressible, uncemented sands such as those found in many deepwater reservoirs, including those in the Erha North Field, do not easily fracture. High-rate water injection into such sands has been very difficult for some operators even when these sands have multi-Darcy permeability. In Yemen, one operator has experienced a "check valve phenomena" when attempting to inject water into an uncemented formation. Formation water was produced at a productivity index of 400 bwpd/psi, but later attempts to reinject that same water resulted in an injectivity index of less than 10 bwpd/psi (Wilkie 1996).