This paper investigates the effects of a down-hole anti-stall tool (AST) in deviated wells on the drilling performance of a rotary drilling system. Deviated wells typically induce frictional contact between the drill-string and the borehole, which affects the drill-string dynamics. In order to study the influence of such frictional effects on the effectiveness of the AST in improving the rate-of-penetration and drilling efficiency, a model-based approach is proposed. A dynamic model with coupled axial and torsional dynamics of a drilling system including the down-hole tool in an inclined well is constructed. Furthermore, the frictional contact between the drill-string and the borehole is modelled by a set-valued spatial Coulomb friction law affecting both the axial and torsional dynamics. These dynamics are described by state-dependent delay differential inclusions. Numerical analysis of this model shows that the rate-ofpenetration and drilling efficiency increases by inclusion of the AST, both in the case with and without spatial Coulomb friction. Furthermore, a parametric design study of the AST in different inclined drilling scenarios is performed. This study reveals a design for the AST,

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Summary In this paper, we investigate the effect of a downhole passive regulator [anti-stall tool (AST)] on the dynamics of rotary drilling systems in interbedded formations. Drilling in interbedded formations can significantly affect the vibrational signature of these systems and the associated drilling performance. Hence, models to assess the impact of drilling in such formations are needed. Here, we construct a dynamic model of the drillstring system which incorporates the bit/rock interface laws for the transitional phase of bit motion between rock layers with distinct mechanical properties. In the model, the axial and torsional dynamics of the drillstring systems are coupled by these interface laws and cast in the form of discontinuous (state-dependent) delay differential equations. Next, we include the AST in the dynamic model to enable the assessment of the influence of this downhole tool on drilling performance, in particular in terms of rate-of-penetration (ROP) and drilling efficiency. Furthermore, we also investigate the mechanical specific energy (MSE) and steady-state power losses at the bit (due to frictional torque) for different operational conditions and rock layer thicknesses. The analysis reveals that an increased drilling efficiency and lower MSE are obtained by incorporating the downhole tool in the drillstring, resulting in a higher ROP and a lower frictional contact between the bit and rock in interbedded formations.

Thermo-acoustic instabilities are a well-known problem in combustions systems. In general, the type of these modes can be divided in two categories: (i) modes with an acoustic origin and (ii) modes with an intrinsic thermo-acoustic (ITA) origin. It is an challenging task to observe the ITA modes experimentally. Therefore, a setup with a burner in an acoustic embedding with close to anechoic up- and downstream terminations is required. In previous research we introduced such a setup and conducted an experimental bifurcation analysis on the dominant pure ITA mode. In this bifurcation analysis, we observed that for increasing upstream velocity the flames loose stability through a supercritical Hopf bifurcation and subsequently exhibit limit cycle, quasi-periodic and period-2 limit cycle oscillations. The quasi-periodic oscillations were characterized by low frequency amplitude and frequency modulation. In this research we present a phenomenological model consisting of two coupled oscillators that is able to reproduce all the different experimentally observed regimes. This model consists of a nonlinear Van der Pol oscillator and a linear mass-spring-damper oscillator, which are nonlinearly coupled to each other. Furthermore, we executed a parameter identification of the model and concluded that the model is able to describe the experimental data quantitatively well.