This paper describes the combination of a Perkins–Kern–Nordgren (PKN) type model for hydraulic fracture propagation with a method for calculation of proppant transport and settling in order to simulate the dynamic growth, stress induced closure, and final geometry of vertically oriented two-dimensional fractures. A mathematical model is developed to describe the fracture growth, fluid flow, and proppant movement along with proppant settling and bank formation. A particle tracking method which uses the concept of pseudoparticles to represent the proppant phase is used for the computation of solids distribution within the fracture and the proppant bank growth. A technique for periodically combining the elements of the computational grid allows for reduced simulation time. Using the computational model, contraction of fracture dimensions after the end of pumping can be simulated in order to determine the final shape of the propped fracture. A sensitivity analysis was conducted to study the effects of pumping rate, inlet proppant concentration, and proppant particle size on the final fracture condition. To evaluate the efficacy of different treatment designs, the resulting geometry of the propped fracture dimensions and the achieved conductivities were compared. Based on the simulation results obtained, specific recommendations on how to avoid premature tip screen-out and achieve desired fracture conductivity are presented.

Hydraulic fracturing is a technique for enhancing the extraction of oil and gas from deep underground sources. Two important goals during this process are to achieve a final fracture with a predefined geometry and to have a proper distribution of proppant material within the fracture to keep the fracture walls open and allow oil and gas to flow to the surface. The hydraulic fracturing system contains limited real-time measurements of the actual fracture conditions largely due to the remote subterranean location where the fracture propagates. The fracturing process is characterized by multiphase transport, proppant settling, and coupling of fluid and fracture growth mechanics, all occurring within a time-varying spatial domain. These features present a challenge for the implementation of online feedback control of the fracture growth and proppant placement, and there are very few accounts of attempting this goal in the open literature. To address these issues, the current work proposes a control strategy that allows for closed-loop model-based control of the hydraulic fracturing process. Previous work introduced a dynamic fracture model capable of describing the fracture propagation, fluid and particle transport, proppant bank formation, and fracture closure processes necessary to determine the fracture state evolution and predict the fracture's final performance. The QDMC (quadratic-dynamic matrix control) form of model-based control is studied. A particle filter provides a means for effective state estimation due to limited real-time measurements. Controlling the fracture geometry and proppant distribution within a hydraulic fracture is a novel application for real-time model-based control. Results of a numerical study are provided to demonstrate the performance of the closed-loop system.

Stick/slip-induced vibration has been recognized as a cause for bit wear, premature tool failure, and poor drilling performance, which represents a contribution of approximately 30% of drilling vibration dysfunction. Dynamic modeling of stick/slip phenomena in drillstrings shows that the vibrational waves travel back and forth along the drillstring between the bit and top drive, which typically leads to 15% fluctuation in surface torque. It is also found that stick/slip is much more likely to occur with certain drilling fluid types and in deviated holes with large dogleg severity. One method of stick/slip mitigation is through control of the top drive. In existing applications, the vibrational wave at a fundamental frequency is absorbed by tuning a proportional-integral (PI) controller. Stick/slip-induced vibrations do not exist at a single frequency, and the simple PI controller cannot mitigate stick/slip occurrence at all vibration frequencies. Vibrations at frequencies other than the frequency chosen for mitigation can be amplified using existing tuning methods. In tests in which the method was applied, there were cases in which the vibration shifts to the second mode when the first torsional mode is mitigated. Therefore, the challenge is to target more than one vibration frequency. A new control system has been designed to observe stick/slip frequencies and then to dampen the stick/slip across a wide frequency range, while regulating the rotational speed of the drillstring at the desired set point. All control algorithms are implemented on a standard programmable logic controller (PLC). To eliminate the need to modify the existing top variable-frequency drives (VFD), this paper also proposes several methods to seamlessly implement the proposed controller. Existing configurations and stick/slip mitigation tests based on PI controller-gained tuning have been achieved on a test rig. Field tests demonstrating the new control method have been performed, and the results are presented and analyzed in this paper.

Directional drilling technique can provide flexibility in rig location selection as well as increase drilling and production efficiencies through extended reach to isolated reservoirs. However, as well complexity increases, analyzing the mechanical performance of the associated drillstring and its components becomes more difficult. A standard Finite element method (FEM) can accurately analyze directional drilling statics and dynamics by discretizing the structure into a series of straight beam elements. However, this method has a drawback of high computational cost. To increase the computational efficiency, this paper introduces the application of curved beam FEM to model directional drillstring. The minimum curvature method is applied to obtain directional well profiles in which the adjacent survey points are connected by circular arcs. Based upon this assumption, the curved beam is used to model the curved drillstring to minimize the discretization error and to increase the computational efficiency. Static and dynamic analyses are carried out to verify the proposed method. As compared to the straight beam approximation method, fewer elements are needed to obtain a given accuracy, leading to more efficient simulations. The utility of the proposed model is also demonstrated through analyzing realistic drilling scenarios.

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