Discontinuous Method Research Articles

Study Explores Fracture-Driven Interaction Mitigation Strategies for Field Development

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 4055561, “Numerical Investigation of Fracture-Driven-Interaction Mitigation Strategies and Field Development Optimization,” by Ruiting Wu, SPE, Xiaolong Liu, and Lili Xu, Chevron, et al. The paper has not been peer reviewed. _ Numerical modeling of fracture-driven interactions (FDI) using a coupled hydraulic-fracturing-propagation, reservoir-flow, and geomechanics tool has been conducted. The numerical study showed that, for the basins studied, FDI and some mitigation strategies have minimal effect on long-term parent-well productions. Parent depletion (volume and areal extent), well spacing, and child-fracture asymmetry, however, greatly affect child-well production as the result of FDI. Introduction Interwell FDI, also known as frac hits, has garnered recent attention given that more than 60% of new wells drilled in US unconventional reservoirs are infill drilling. Whereas uncontrollable parameters, such as natural fractures and matrix permeability, do contribute to the effect of FDI on well production, the authors’ primary focus lies on controllable factors. Field observations have shown that tighter well spacing and smaller completion sizes tend to result in fewer negative effects on both parent- and child-well production. Additionally, fracture-fluid injection rates, the number of clusters, and cluster spacing all influence FDI effects. Simulation Tool and Workflow A coupled hydraulic-fracture, reservoir, and wellbore simulator was used to simulate the fracturing and production stage of the parent and child wells and related fracture-driven well interaction. The simulator simultaneously solves the equations of fluid flow, proppant transport, water/solute transport, fracture mechanics, and poroelasticity in the well, fracture, and matrix domains. Fracture propagation is calculated using the multilayer-tip-elements algorithm. Fracture elements are represented by uniformly sized rectangles. Fracture-to-fracture stress shadow is calculated with the 3D displacement discontinuity method, and the poroelastic stress responses during fracture propagation and depletion are calculated with a finite-volume method. The tool is designed to simulate the entire life cycle of the FDI interaction. The modeling workflow also includes calibration with field observations of fracture geometry, the pressure response at the parent well during fracturing of the child well, the water cut change at the parent well as the result of FDI, and production performance. Field Case Study: Permian Basin The primary objective of this study is to identify the key parameters that contribute to FDI and mitigate the negative effects of FDI. Two field case studies were conducted in two basins, the Permian Basin and the DJ Basin. In both field studies, a history match of parent and child well performance was first conducted. Then, a sensitivity study was performed on various key parameters to understand their effects on the production performance at both parent and child wells. Both field case studies are focused on the lateral FDI. The first case study is included in this synopsis.

Numerical Modeling of Hydraulic Fracturing Interference in Multi-Layer Shale Oil Wells

Multi-layer horizontal well development and hydraulic fracturing are key techniques for enhancing production from shale oil reservoirs. During well development, the fracturing performance and well-pad production are affected by depletion-induced stress changes. Previous studies generally focused on the stress and fracturing interference within the horizontal layers, and the infilled multi-layer development was not thoroughly investigated. This study introduces a modeling workflow based on finite element and displacement discontinuity methods that accounts for dynamic porous media flow, geomechanics, and hydraulic fracturing modeling. It quantitatively characterizes the in situ stress alteration in various layers caused by the historical production of parent wells and quantifies the hydraulic fracturing interference in infill wells. In situ stress changes and reorientation and the non-planar propagation of hydraulic fractures were simulated. Thus, the workflow characterizes infill-well fracturing interferences in shale oil reservoirs developed by multi-layer horizontal wells. Non-planar fracturing in infill wells is affected by the parent-well history production, infilling layers, and cluster number. They also affect principal stress reorientations and reversal of the fracturing paths. Interwell interference can be decreased by optimizing the infilling layer, infill-well fracturing timing, and cluster numbers. This study extends the numerical investigation of interwell fracturing interference to multi-layer development.

Modeling proppant transport and settlement in 3D fracture networks in geothermal reservoirs

In this paper, we develop an efficient proppant transport model using the Eulerian-Eulerian approach for simulating proppant transport in fractures and 3D fracture networks in geothermal reservoirs. The proposed model accounts for proppant settling, pack/bed formation, bridging/screenout, proppant concentration effect, fracture wall effect, and the transition from Poiseuille flow (fracture channel) to Darcy flow (proppant pack). Notably, the heat transfer process and its impact on proppant transport are also considered—a facet often overlooked in previous proppant transport models. A three-dimensional displacement discontinuity method (3D DDM) that incorporates the stress shadow effect is employed to generate the fracture geometry. The governing equations for slurry flow, proppant transport, and heat transfer are discretized and solved using the finite volume method (FVM). The model is verified against analytical solutions and published experimental data, demonstrating good agreement with these references. To demonstrate the proposed model, we applied it to both low-temperature (depleted hydrocarbon wells) and high-temperature (dry hot rocks) enhanced geothermal systems (EGS). The simulation results highlight the significant influence of reservoir temperature on proppant transport and settlement in a reservoir environment. Heating of the slurry by higher temperature reservoir rocks reduces fluid viscosity and accelerates proppant settling, thereby shortening the transport distance and reducing the coverage area of the proppant. Both ultra-light and micro-proppant are effective in mitigating proppant settlement in enhanced geothermal systems. However, proppant is susceptible to bridging at fracture intersections, where the fracture widths are narrower due to more pronounced stress shadow effects in these areas. Consequently, the use of micro-proppant could offer substantial benefits over ultra-light proppant in enhancing proppant coverage area in enhanced geothermal systems.

Binary neutron star mergers using a discontinuous Galerkin-finite difference hybrid method

Abstract We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-Characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.

Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems

We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter is bounded by data only for fixed polynomial order, mesh, and time. In the absence of dissipation, coupling of the overlapping domains is destabilizing by allowing positive eigenvalues in the system to be integrated in time. This coupling can be stabilized in one space dimension by using the upwind numerical flux. To help provide additional dissipation, we introduce a novel penalty method that applies dissipation at arbitrary points within the overlap region and depends only on the difference between the solutions. We present numerical experiments in one space dimension to illustrate the implementation of the well-posed penalty formulation, and show spectral convergence of the approximations when sufficient dissipation is applied.

Comparative analysis between continuous and discontinuous methods for the assessment of a cultural heritage structure

AbstractIn an era marked by the urgent need to ensure the safety of existing buildings according to current standards, evaluating the stability of masonry structures against hazard events has become a significant challenge. Despite the versatility and durability of masonry, structural assessments are hampered by factors such as limited information on material properties, irregular geometries, and ageing. To address this issue, numerous modelling techniques have been developed, supported by extensive scientific literature. However, significant factors related to the case study replication, such as the geometric complexity, the mechanical behaviour of masonry, the loading applications, contribute to the challenges associated with modelling procedures, including computational time, discretization procedures, and step incrementation. This paper critically discusses the most innovative modelling approaches. Specifically, it aims to compare the efficiency of the Distinct Element (discontinuous) Methods and the Finite Element (continuous) Method, both applied to the numerical simulation of a case study structure severely damaged by the 2016 Central Italy earthquake under lateral loading conditions. The continuous method is analysed using Midas FEA NX©, while the discontinuous methods are studied using 3DEC© and LMGC90© software, each with different contact conditions. Finally, the investigation highlights the main advantages and disadvantages of each method. In particular, the discontinuous method demonstrates reliability in accurately replicating failure patterns, whereas the continuous method allows for a faster model setup, making it suitable for preliminary studies on structural dynamics.

Modelling of courtyard acoustics using the nodal discontinuous Galerkin finite element method to validate a newly developed PML

Evaluating the acoustics of courtyards has gained increasing attention from a sustainable urban design perspective, which requires numerical predictions tools for estimation of noise pollution and assessment of the influence of acoustic conditions. Accurate modeling of the acoustics of a courtyard is scarce because of the variety of factors to include: meteorological effects, building material properties, and geometry of the inner façades. We consider the nodal Discontinuous Galerkin finite element method framework in a 3D static and uniform medium and use it to model the sound propagation in a courtyard. A new and efficient Perfectly Matched Layer formulation is implemented at the open boundary of the courtyard model to absorb outgoing acoustic waves and this way limiting the size of the computational domain. The numerical results are validated against experimental measurements carried out in a scaled model of a courtyard with an elementary design to implement an accurate corresponding numerical model. The experiments were conducted in an anechoic chamber where the meteorological effects are controlled, and the courtyard facades are modelled as flat surfaces with known material properties.

Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation

Abstract In [L. Bourhrara, A new numerical method for solving the Boltzmann transport equation using the PN method and the discontinuous finite elements on unstructured and curved meshes, J. Comput. Phys. 397 2019, Article ID 108801], a numerical scheme based on a combined spherical harmonics and discontinuous Galerkin finite element method for the resolution of the Boltzmann transport equation is proposed. One of its features is that a streamline weight is added to the test function to obtain the variational formulation. In the present paper, restricting our attention to the advective part of the Boltzmann equation, we prove the convergence and provide error estimates of this numerical scheme. To this end, the original variational formulation is restated in a broken functional space. The use of broken functional spaces enables to build a conforming approximation, that is the finite element space is a subspace of the broken functional space. The setting of a conforming approximation simplifies the numerical analysis, in particular the error estimates, for which a Céa’s type lemma and standard interpolation estimates are sufficient for our analysis. For our numerical scheme, based on ℙ k {\mathbb{P}^{k}} discontinuous Galerkin finite elements (in space) on a mesh of size h and a spherical harmonics approximation of order N (in the angular variable), the convergence rate is of order 𝒪 ⁢ ( N - t + h k ) {\mathcal{O}(N^{-t}+h^{k})} for a smooth solution which admits partial derivatives of order k + 1 {k+1} and t with respect to the spatial and angular variables, respectively. For k = 0 {k=0} (piecewise constant finite elements) we also obtain a convergence result of order 𝒪 ⁢ ( N - t + h 1 2 ) {\mathcal{O}(N^{-t}+h^{\frac{1}{2}})} . Numerical experiments in one, two and three dimensions are provided, showing a better convergence behavior for the L 2 {L^{2}} -norm, typically of one more order, 𝒪 ⁢ ( N - t + h k + 1 ) {\mathcal{O}(N^{-t}+h^{k+1})} .

A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough for the sound waves to decay. The computational cost is lowered by strategically truncating the computational domain with an efficient boundary treatment. One commonly used boundary treatment is the perfectly matched layer (PML), which dampens outgoing waves without polluting the computed solution in the inner domain. The purpose of this study is to propose and assess a new perfectly matched layer formulation for the 3D acoustic wave equation, using the nodal discontinuous Galerkin finite element method. The formulation is based on an efficient PML formulation that can be decoupled to further increase the computational efficiency and guarantee stability without sacrificing accuracy. This decoupled PML formulation is demonstrated to be long-time stable, and an optimization procedure for the damping functions is proposed to enhance the performance of the formulation.

Discontinuous Galerkin finite element method for the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes

Context. The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to handle numerically, they often fail to accurately describe the radiation field inside complex geometries. For these cases, it is necessary to directly solve the radiative transfer equation numerically. Aims. We investigate the accuracy of the discontinuous Galerkin finite element method (DGFEM hereafter) applied to the frequency-dependent two-dimensional radiative transfer problem, and coupled with the radiative equilibrium equation. We next used this method in the context of axis-symmetric circumstellar envelopes. Methods. The DGFEM is a variant of finite element methods. It employs discontinuous elements and flux integrals along their boundaries, ensuring local flux conservation. However, as opposed to the classical finite element methods, the solution is discontinuous across element edges. We implemented this approach in a code and tested its accuracy by comparing our results with the benchmarks from the literature. Results. For all the tested cases, the temperatures profiles agree within one percent. Additionally, the emerging spectral energy distributions (SEDs) and images, obtained by ray-tracing techniques from the DGFEM emissivity, agree on average within 5% and 10%, respectively. Conclusions. We show that the DGFEM can accurately describe the continuum radiative transfer problem inside axis-symmetric circumstellar envelopes. Consecutively the emerging SEDs and images are also well reproduced. The DGFEM provides an alternative method (other than Monte-Carlo methods for instance) for solving the radiative transfer equation, and it could be used in cases that are more difficult to handle with the other methods.

Distributed Consensus Tracking of Incommensurate Heterogeneous Fractional-Order Multi-Agent Systems Based on Vector Lyapunov Function Method

This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method.

Propagation prediction of asymmetrically originated fractures by use of displacement discontinuity method

In existing fracture propagation simulation studies, the fracture propagation simulation is based on the assumption that the fracture originates symmetrically with respect to the wellbore. However, the drilling treatments can induce stress reorientation near the wellbore, resulting in asymmetrically originated fractures, which is different from the assumption of existing studies. In such cases, it can be difficult to predict the fracture geometries. In this work, the authors propose a fracture propagation model to simulate the propagation of asymmetrically originated fractures with the displacement discontinuity method. With the aid of the proposed model, the authors investigate the impact of the redistribution of stress field on the propagation of asymmetrically originated fractures and conduct a comprehensive study to investigate the effects of various geological and fluid parameters on the propagation of asymmetrically originated fractures. The results show that the redistribution of the stress field renders the newly generated fracture segments to deviate from the initial originations so that although the initial fracture origination is asymmetric, the asymmetrically originated fractures rapidly propagate along an approximately symmetrical path and propagate parallel to the direction of maximum principal stress as it goes away from the wellbore. The closer the two wings of the fracture are to the symmetric origin, the faster it is for the change of propagation direction to the direction of the maximum principal stress. A large principal stress difference tends to cause asymmetrically originated fractures to quickly deviate from the initial originations and propagate parallel to the direction of maximum principal stress. As the fluid power law index decreases, the fluid viscosity is significantly reduced due to the effect of shear thinning, causing the asymmetrically originated fractures to propagate parallel to the direction of maximum principal stress. The fluid leak-off coefficient only influences the fracture length and width, whereas its influence on the propagation trajectory can be slight.

Effect of age-related premium readjustment on health insurance cancellation in Brazil: Regression discontinuity approach.

Age is one of the most relevant observable risk attributes in determining the value of health insurance premiums. Empirical evidence indicates that the cost of health insurance is the leading cause of contract switching, which can compromise access to healthcare services and potentially result in treatment discontinuities. Using data from a Health Maintenance Organization in the Southern region of Brazil, we examined the effect of health plan price readjustment resulting from changes in the beneficiary's age group on disenrollment or switches to a more limited coverage plan. The estimates were obtained using the method of regression discontinuity. The main findings indicate that for age group transitions at 59years old, the price readjustment effect led to an increase in contract cancellations and switching to cheaper plans. These findings highlight that an important consequence of the difference in premium sensitivity among age groups is that the exit of individuals from the health insurance sector is selective in age. The results of this paper can support policymaking to improve access to health insurance.

A RANDOMIZED CARRIER-BASED DISCONTINUOUS PULSE WIDTH MODULATION STRATEGY FOR NEUTRAL POINT CLAMPED THREE-LEVEL INVERTER

This article introduces a novel approach called randomized carrier-based discontinuous pulse width modulation (RCDPWM) to address the challenge of mitigating both low-order and high-order harmonics concentrated at the switching frequency and its integer multiples in the output voltage and current of a three-level inverter. The proposed strategy reduces switching losses and a wide dispersion of voltage and current harmonics with significantly smaller amplitudes by integrating features from discontinuous and randomized PWM methods. This characteristic proves beneficial for enhancing efficiency and electromagnetic compatibility. The RCDPWM strategy involves three schemes: two simple schemes (one random parameter), randomized pulse position modulation (RPP-DPWM) and randomized carrier frequency modulation (RCF-DPWM), and a dual scheme combining the two previous ones (RPPRCF-DPWM). Power spectral density (PSD) is used to assess the effectiveness of the proposed strategy in quantitatively analyzing the harmonic dispersion degree. The results demonstrate that the proposed RCDPWM strategy significantly expands harmonic clusters around the switching frequency, reducing its intensity. The spectrum analysis revealed that the RPPRCF-DPWM scheme is the most effective in spreading the output voltage and current spectrum compared to simple schemes (RPP-DPWM and RCF-DPWM).

The Impact of Air Pollution Information on Individuals' Exercise Behavior: Empirical Study Using Wearable and Mobile Devices Data.

Physical exercise and exposure to air pollution have counteracting effects on individuals' health outcomes. Knowledge on individuals' real-time exercise behavior response to different pollution information sources remains inadequate. This study aims to examine the extent to which individuals avoid polluted air during exercise activities in response to different air pollution information sources. We used data on individuals' exercise behaviors captured by wearable and mobile devices in 83 Chinese cities over a 2-year time span. In our data set, 35.99% (5896/16,379) of individuals were female and 64% (10,483/16,379) were male, and their ages predominantly ranged from 18 to 50 years. We further augmented the exercise behavior data with air pollution information that included city-hourly level measures of the Air Quality Index and particulate matter 2.5 concentration (in µg/m3), and weather data that include city-hourly level measures of air temperature (ºC), dew point (ºC), wind speed (m/s), and wind direction (degrees). We used a linear panel fixed effect model to estimate individuals' exercise-aversion behaviors (ie, running exercise distance at individual-hour, city-hour, or city-day levels) and conducted robustness checks using the endogenous treatment effect model and regression discontinuity method. We examined if alternative air pollution information sources could moderate (ie, substitute or complement) the role of mainstream air pollution indicators. Our results show that individuals exhibit a reduction of running exercise behaviors by about 0.50 km (or 7.5%; P<.001) during instances of moderate to severe air pollution, and there is no evidence of reduced distances in instances of light air pollution. Furthermore, individuals' exercise-aversion behaviors in response to mainstream air pollution information are heightened by different alternative information sources, such as social connections and social media user-generated content about air pollution. Our results highlight the complementary role of different alternative information sources of air pollution in inducing individuals' aversion behaviors and the importance of using different information channels to increase public awareness beyond official air pollution alerts.

Finite element modelling of linear rolling contact problems

The present work is devoted to the finite element modelling of linear hyperbolic rolling contact problems. The main equations encountered in rolling contact mechanics are reviewed in the first part of the paper, with particular emphasis on applications from automotive and vehicle engineering. In contrast to the common hyperbolic systems found in the literature, such equations include integral and boundary terms, as well as time-varying transport velocities, that require special treatment. In this context, existence and uniqueness properties are discussed within the theoretical framework offered by the semigroup theory. The second part of the paper is then dedicated to recovering approximated solutions to the considered problems, by combining discontinuous Galerkin finite element methods (DGMs) with explicit Runge–Kutta (RK) schemes of the first and second order for time discretisation. Under opportune assumptions on the smoothness of the sought solutions, and owing to certain generalised Courant–Friedrichs–Lewy (CFL) conditions, quasi-optimal error bounds are derived for the complete discrete schemes. The proposed algorithms are then tested on simple scalar equations in one space dimension. Numerical experiments seem to suggest the theoretical error estimates to be sharp.

Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation‐based approach

AbstractThe contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral‐shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr‐Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic‐like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases.

Discontinuous PWM-based common-mode voltage suppression method for three-phase inverter

Discontinuous PWM-based common-mode voltage suppression method for three-phase inverter

Investigations of sequential excavation and reinforcement in tunnels based on the extended three-dimensional discontinuous deformation analysis method

The unloading effect of excavation is the key factor leading to rock mass instability, and bolt support is the key means of controlling the stability. However, the original three-dimensional discontinuous deformation analysis method (3D DDA) can only simulate rock mass instability and bolt support after the tunnel is excavated, which makes it difficult to study the effect of tunnel excavation and bolt support on rock mass stability. Therefore, an algorithm to confirm the excavated blocks and reinforced blocks based on the volume judgment method (VJM) was proposed in this paper. Sequential excavation and reinforcement in tunnels can be simulated by introducing the time variables of block excavation and bolt deployment into the 3D DDA method. By embedding these two algorithms in the 3D DDA method, an extended 3D DDA method for sequential excavation and reinforcement in tunnels was developed, named the 3D DDA_ES method. Based on the 3D DDA_ES method, the collapse that occurred during the construction of the Huangjiazhuang Tunnel was simulated, and the displacement of key blocks and the axial force of the bolts were analyzed. According to the simulation results, the axial force on the bolts is strongly related to the position of the key blocks, and the axial force on the bolts at the tunnel roof is much greater than that at the tunnel arch shoulder. In this regard, these bolts with axial forces less than 1 kN are removed during the simulation, and the key blocks remain stable with a maximum displacement of 12 cm. The research results can provide a theoretical basis for tunnel construction and reinforcement parameter optimization for similar projects.

Efficient entropy-stable discontinuous spectral-element methods using tensor-product summation-by-parts operators on triangles and tetrahedra

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations employ a recently introduced family of sparse tensor-product summation-by-parts (SBP) operators in collapsed coordinates within an entropy-conservative modal formulation, which is rendered entropy stable when a dissipative numerical flux is used at element interfaces. The proposed algorithms exploit the structure of such SBP operators alongside that of the Proriol–Koornwinder–Dubiner polynomial basis used to represent the numerical solution on the reference triangle or tetrahedron, and a weight-adjusted approximation is employed in order to efficiently invert the local mass matrix for curvilinear elements. Using such techniques, we obtain an improvement in time complexity from O(p2d) to O(pd+1) relative to existing entropy-stable formulations using multidimensional SBP operators not possessing such a tensor-product structure, where p is the polynomial degree of the approximation and d is the number of spatial dimensions. The number of required entropy-conservative two-point flux evaluations between pairs of quadrature nodes is accordingly reduced by a factor ranging from 1.56 at p=2 to 4.57 at p=10 for triangles, and from 1.88 at p=2 to 10.99 at p=10 for tetrahedra. Through numerical experiments involving smooth solutions to the compressible Euler equations on isoparametric triangular and tetrahedral grids, the proposed methods using tensor-product SBP operators are shown to exhibit similar levels of accuracy for a given mesh and polynomial degree to those using multidimensional operators based on symmetric quadrature rules, with both approaches achieving order p+1 convergence with respect to the element size in the presence of interface dissipation as well as exponential convergence with respect to the polynomial degree. Furthermore, both operator families are shown to give rise to entropy-stable schemes which exhibit excellent robustness for test problems characteristic of under-resolved turbulence simulations. Such results suggest that the algorithmic advantages resulting from the use of tensor-product operators are obtained without compromising accuracy or robustness, enabling the efficient extension of the benefits of entropy stability to higher polynomial degrees than previously considered for triangular and tetrahedral elements.