Physical Equations Research Articles

Artificial Lift: 25 Years of Change Tracked in the Pages of JPT

Nodding donkeys. Thirsty birds. Rocking horses. All are playful nicknames for the oil and gas icon known as a pumpjack. To the uninformed, the pumpjack is a thing-a-ma-jig that has something to do with oil, probably “fracking” because that’s what drilling rigs do, right? But as an industry-educated and well-informed reader of JPT, you know this is inaccurate. By whatever name you call it, you know that the pumpjack is the visible manifestation of an invisible physics equation, a mechanism buried deep underground that lifts reservoir fluids to the surface. You also know it is one type of artificial lift available in a stable of systems with equally curious and technical names like progressive cavity, plunger, jet, gas lift, and electrical submersible pump (ESP). While there is no global repository of artificial lift statistics, industry observers estimate that 90 to 95% of the world’s producing wells use artificial lift, as noted in a 2013 JPT story on the challenges and opportunities for artificial lift. Artificial lift, as applied in oil and gas production, has existed for over 100 years. A 2014 JPT story laid out a brief history of the practice, sharing how the walking beam principle dates back to at least 476 CE when used in Egypt, and evidence of the use of sucker rods to lift fluids has been excavated from the homes of wealthier families in the early days of the Roman Empire. Even as we leap forward to the modern-day application of artificial lift systems, many techniques and technologies resemble their original designs. How these systems are applied has changed, especially in the past decade-plus with the emergence of shale. As highlighted in a JPT story on the past 25 years of technology advances, the industry underwent a robust era of technology development in its rush to crack the shale development riddle. Since 1999, the industry also delivered a 36% increase in global supplies, as noted in this JPT story celebrating this industry’s biggest innovations. 1999 represents an interesting turning point in the industry’s technological journey. Also, it is the last time JPT editors took the opportunity to celebrate the publication as it turned 50 years old that year. What follows are a few highlights from JPT’s coverage of advances and changes made in artificial lift applications and practices over the past quarter century.

High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes.

A type system for formal verification of cyber-physical systems C/C++ software

The subject: This study focuses on improving the quality of Cyber-Physical System (CPS) software by eliminating incorrect usage of units of measurement and orientation in C/C++ programs. Incorrect usage often leads to critical errors that conventional systems cannot effectively prevent. Manual examination of code using dimensional and orientation analysis can detect these errors in physical equations, but these methods become impractical when dealing with complex physical computations. Objectives: As suggested by Siano, the proposed approach uses physical quantities and prefixes defined by the International System of Units and orientation operations on physical objects. The elaborated system incorporates dimensional and orientation analysis and metaprogramming techniques. The methods used are dimensional & orientational analysis and metaprogramming. The following results were obtained: ensuring consistency of the units, incorporating orientation operations into the programming model for accurately handling physical object rotations and alignments, and using Siano’s work to precisely manipulate object orientation, thereby reducing the likelihood of orientation-related errors. Checking physical dimensions and orientations during the compilation stage identifies potential software defects before code execution, thereby reducing debugging time and lowering the cost of addressing issues later in development. The elaborated system represents a crucial step towards safer and more dependable Cyber-Physical System applications. This approach allows us to identify approximately 90% of incorrect usage of program variables; additionally, it detects over 50% of erroneous operations during compilation and execution of large-scale programs in real-world conditions. Conclusions. Scientific novelty: it proposed and developed a specialized C++-type library for formal compile-time software verification of Cyber-Physical Systems software. The proposed C++-type library leverages dimensional and orientational analysis to enhance software quality, reliability, and real-time formal verification. Although the proposed method for formal verification is not tailor-made for cyber-physical objects and systems, given its primary focus on software-level concerns, it does exhibit adaptability for verifying general-purpose software that incorporates various physical parameters. This versatility extends to diverse domains such as educational, gaming, and simulation software.

Physics guided heat source for quantitative prediction of IN718 laser additive manufacturing processes

Challenge 3 of the 2022 NIST additive manufacturing benchmark (AM Bench) experiments asked modelers to submit predictions for solid cooling rate, liquid cooling rate, time above melt, and melt pool geometry for single and multiple track laser powder bed fusion process using moving lasers. An in-house developed Additive Manufacturing Computational Fluid Dynamics code (AM-CFD) combined with a cylindrical heat source is implemented to accurately predict these experiments. Heuristic heat source calibration is proposed relating volumetric energy density (ψ) based on experiments available in the literature. The parameters of the heat source of the computational model are initially calibrated based on a Higher Order Proper Generalized Decomposition- (HOPGD) based surrogate model. The prediction using the calibrated heat source agrees quantitatively with NIST measurements for different process conditions (laser spot diameter, laser power, and scan speed). A scaling law based on keyhole formation is also utilized in calibrating the parameters of the cylindrical heat source and predicting the challenge experiments. In addition, an improvement on the heat source model is proposed to relate the Volumetric Energy Density (VEDσ) to the melt pool aspect ratio. The model shows further improvement in the prediction of the experimental measurements for the melt pool, including cases at higher VEDσ. Overall, it is concluded that the appropriate selection of laser heat source parameterization scheme along with the heat source model is crucial in the accurate prediction of melt pool geometry and thermal measurements while bypassing the expensive computational simulations that consider increased physics equations.

Physics-informed ConvNet: Learning physical field from a shallow neural network

We introduce a novel methodology for solving nonlinear partial differential equation (PDE) on regular or irregular domains using physics-informed ConvNet, which we call the PICN. The network structure consists of three parts: 1) a convolutional neural network for physical field generation, 2) a pre-trained convolutional layer corresponding to the finite-difference filters to estimate differential fields of the generated physical field, and 3) an interpolation network for loss analysis in irregular geometry domains. From a CNN perspective, the physical field is generated by a deconvolution layer and a convolution layer. Unlike the standard Physics-informed Neural Network (PINN) approach, the convolutions corresponding to the finite-difference filters estimate the spatial gradients forming the physical operator and then construct the PDE residual in a PINN-like loss function. The total loss function involving boundary conditions and the physical constraints in irregular geometry domains can be calculated from an efficient linear interpolation network. The theoretical analysis of PICN convergence is performed on a simplified case for solving a one-dimensional physical field, and several examples of nonlinear PDE of solutions with multifrequency characteristics are executed. The theory and examples confirm the effective learning capability of PICN for the physical field solution with high-frequency components, compared to the standard PINN. A series of numerical cases are performed to validate the current PICN, including the solving (and estimation) of nonlinear physical operator equations and recovering physical information from noisy observations. First, the ability of PICN to solve nonlinear PDE has been verified by executing three nonlinear problems including ODE with sine nonlinearity, PDE involving nonlinear sine-square operators, and Schrödinger equation. The proposed PICN has been assessed by solving some nonlinear PDE on irregular domains such as star-shaped domain, bird-like domain, and starfish domain. Moreover, PICN is applied to identify the thermal diffusivity parameters in an anisotropic heat transfer problem from noisy data, and a denoising display of the temperature field from strong noisy data with standard deviations ranging from 0.1 to 0.4. The numerical results demonstrate the high accuracy approximation and fast convergence performance of PICN. The potential advantage in approximating complex physical field with multi-frequency components indicates that PICN may become an alternative efficient neural network solver in physics-informed machine learning. This paper is adapted from the work originally posted on arXiv.com by the same authors (arXiv:2201.10967, Jan 26, 2022). The data and code accompanying this paper are publicly available at https://github.com/zengzhi2015/PICN.

Deep hybrid modeling of a HEK293 process: Combining long short-term memory networks with first principles equations.

The combination of physical equations with deep learning is becoming a promising methodology for bioprocess digitalization. In this paper, we investigate for the first time the combination of long short-term memory (LSTM) networks with first principles equations in a hybrid workflow to describe human embryonic kidney 293 (HEK293) culture dynamics. Experimental data of 27 extracellular state variables in 20 fed-batch HEK293 cultures were collected in a parallel high throughput 250 mL cultivation system in an industrial process development setting. The adaptive moment estimation method with stochastic regularization and cross-validation were employed for deep learning. A total of 784 hybrid models with varying deep neural network architectures, depths, layers sizes and node activation functions were compared. In most scenarios, hybrid LSTM models outperformed classical hybrid Feedforward Neural Network (FFNN) models in terms of training and testing error. Hybrid LSTM models revealed to be less sensitive to data resampling than FFNN hybrid models. As disadvantages, Hybrid LSTM models are in general more complex (higher number of parameters) and have a higher computation cost than FFNN hybrid models. The hybrid model with the highest prediction accuracy consisted in a LSTM network with seven internal states connected in series with dynamic material balance equations. This hybrid model correctly predicted the dynamics of the 27 state variables (R2 = 0.93 in the test data set), including biomass, key substrates, amino acids and metabolic by-products for around 10 cultivation days.

Quantum Gravitational Acceleration

In this study, we present the quantum gravitational acceleration. By having something in common All modern theoretical physics equations. Therefore, we can connect the theory of relativity General Einstein with quantum physics, we discuss the physics of black holes from one side and theory Information We show that it is natural to introduce the concept of black hole entropy as a metric Information about the inner parts of a black hole that cannot be accessed by Monitor outside. All equations have physical variables and variables, which express the values of certain, and these values are preserved that preserve all equations and information in theoretical physics modernity.

Impact of uncertainty in the physics-informed neural network on pressure prediction for water hammer in pressurized pipelines

In pressurized pipeline systems, accurate prediction of water hammer pressure is crucial for ensuring safe system operation. When the boundary conditions are unknown and measured data is sparse, both traditional methods fully based on physical equations and data-driven neural network methods have difficulty in accurately predicting water hammer pressure. The physics-informed neural network (PINN) overcomes these challenges by simultaneously incorporating measured data and physical equations during the network training process. However, PINN has uncertainties and their impact on the accuracy of pressure prediction is not yet clear. In this study, the valve closing water hammer in a reservoir-pipeline-valve system is taken as the research object, we investigate the influence of the uncertainty of physics and data in the PINN on prediction accuracy by using water hammer equations with various friction models and training data with various noise levels. The results show that using the water hammer equation with the Brunone model, the PINN model has higher prediction accuracy. Furthermore, data noise levels less than 10% have a relatively small impact on pressure prediction accuracy, indicating that the PINN model has good robustness in terms of data noise levels.

Snapping of a viscoelastic cylindrical panel under loading with small volume compressed gas

The paper considers the dynamics of the process of a flat rectangular elastic panel having an initial deflection equal to the critical deflection of the static problem of panel stability. The panel is loaded with compressed gas enclosed in a small volume container. Using this value, the load acting on the panel during the snapping process will depend on the deflection of the panel as a result of the adiabatic expansion of the compressed gas. The main goal of the work is to investigate the stability region of a cylindrical panel when loaded with compressed gas. The problem is solved using a developed methodology based on the method of separating variable equations of mathematical physics. Based on calculations, it was found that when the panel is loaded with compressed gas enclosed in a small-volume container, a stabilizing effect appears, i.e. a certain deflection interval appears where the panel does not lose stability. The presence of external pressure makes it possible to expand this area, i.e. the external environment increases the “stabilizing” effect. Also, taking into account the viscoelastic properties of the material expands this area to 10%.

Diverse optical wave structures to the time-fractional phi-four equation in nuclear physics through two powerful methods

Diverse optical wave structures to the time-fractional phi-four equation in nuclear physics through two powerful methods

Application of higher-order FV-WENO scheme to the interaction between shock wave and bubble

The high-order finite volume-WENO (Weighted Essentially Non-Oscillatory) scheme combines the finite volume method with the WENO method, allowing for high-order accuracy and accurate simulation of complex physical phenomena. It has advantages in handling shock waves and bubble interactions. The idea of this method is to discretize the physical equations into a set of conservation equations and use the WENO method to calculate the numerical fluxes on each finite volume cell. This approach is effective in dealing with problems such as shock wave propagation, bubble deformation, and evolution. In fluid dynamics simulation and research, the high-order FV-WENO scheme has significant application prospects. It can provide accurate numerical solutions and simulate complex physical phenomena, making it widely applicable in scientific research and engineering. In this study, we simulated the interactions between shock waves and single or double bubbles, obtaining the complete process of bubble collapse with clear bubble interfaces and strong program stability.

Numerical simulation and investigation of soliton solutions and chaotic behavior to a stochastic nonlinear Schrödinger model with a random potential.

The stochastic nonlinear Schrödinger model (SNLSM) in (1+1)-dimension with random potential is examined in this paper. The analysis of the evolution of nonlinear dispersive waves in a totally disordered medium depends heavily on the model under investigation. This study has three main objectives. Firstly, for the SNLSM, derive stochastic precise solutions by using the modified Sardar sub-equation technique. This technique is efficient and intuitive for solving such models, as shown by the generated solutions, which can be described as trigonometric, hyperbolic, bright, single and dark. Secondly, for obtaining numerical solutions to the SNLSM, the algorithms described here offer an accurate and efficient technique. Lastly, investigate the phase plane analysis of the perturbed and unperturbed dynamical system and the time series analysis of the governing model. The results show that the numerical and analytical techniques can be extended to solve other nonlinear partial differential equations in physics and engineering. The results of this study have a significant impact on how well we comprehend how solitons behave in physical systems. Additionally, they may serve as a foundation for the development of improved numerical techniques for handling challenging nonlinear partial differential equations.

Simulation and experimental results of plasma opening switch operation with inductive and electron beam diode loads in different plasma regimes

This paper reports the experimental results of a plasma opening switch (POS) that operates at hydrogen and carbon plasma regimes confirmed based on the conduction bipolar limit of the plasma species and the availability of plasma species during the conduction based on the density profiles. The generator is the compact capacitor bank developed using the synchronization of four field distortion spark gap switches. The plasma source is coaxial cable plasma guns characterized using the Faraday cup plasma diagnostic. The experimental results are compared with the time domain simulation code in which the POS is represented as the dynamic resistance governed by the physical equations of the bipolar model. The experiments and simulations are compared for inductive load and dynamic load of accelerating gap of 5 mm between the anode and cathode at the load end. From the results, POS can be operated based on the availability of plasma species with proper synchronized triggering between the plasma gun firing and generator firing that can operate at low and high values of currents.

Equations of physics that have most important impact on electromechanical engineering

Equations of physics that have most important impact on electromechanical engineering

Review: Fractal Geometry in Precipitation

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves.

Analytic pulse technique for computational electromagnetics

Numerical modeling of electromagnetic waves is an important tool for understanding the interaction of light and matter, and lies at the core of computational electromagnetics. Traditional approaches to injecting and evolving electromagnetic waves, however, can be prohibitively expensive and complex for emerging problems of interest and can restrict the comparisons that can be made between simulation and theory. As an alternative, we demonstrate that electromagnetic waves can be incorporated analytically by decomposing the physics equations into analytic and computational parts. In particle-in-cell simulation of laser–plasma interaction, for example, treating the laser pulse analytically enables direct examination of the validity of approximate solutions to Maxwell's equations including Laguerre–Gaussian beams, allows lower-dimensional simulations to capture 3-D–like focusing, and facilitates the modeling of novel space–time structured laser pulses such as the flying focus. The flexibility and new routes to computational savings introduced by this analytic pulse technique are expected to enable new simulation directions and significantly reduce computational cost in existing areas.

Study of Jupiter’s interior: Comparison of 2, 3, 4, 5, and 6 layer models

With the goal of matching spacecraft measurements from Juno and Galileo missions, we construct ensembles of 2, 3, 4, 5, and 6 layer models for Jupiter’s interior. All except our two layer models can match the planet’s gravity field as measured by the Juno spacecraft. We find, however, that some model types are more plausible than others. In the best three layer models, for example, the transition from molecular to metallic hydrogen needs to be at ∼500 GPa while theory and experiments place this transition at ∼100 GPa. Four layer models with a single sharp boundary between core and mantle would be short-lived due to rapid convective core erosion. For this reason, we favor our five layer models that include a dilute core surrounded by a stably stratified core transition layer. Six layer models with a small compact core are also possible but with an upper limit of 3 Earth masses for such a compact core. All models assume a 1 bar temperature of 166.1 K, employ physical equations of state, and are constructed with the nonperturbative Concentric Maclaurin Spheroid (CMS) method. We analyze the convergence of this method and describe technical steps that are needed to make this technique so efficient that ensembles of models can be generated.

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended ‐dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti‐cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended ‐dimensional nonlinear CKE with generalized anti‐cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1‐soliton, singular 1‐soliton, and bright 1‐soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended ‐dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields.

The Study of Internal Gravity Waves in the Earth’s Atmosphere by Radio Occultations: A Review

Internal gravity waves (IGWs) in the middle atmosphere are the main source of mesoscale fluctuations of wind and temperature. The parameterization of IGWs and study of their climatology is necessary for the development of global atmospheric circulation models. In this review, we focus on the application of Radio Occultation (RO) observations for the retrieval of IGW parameters. (1) The simplest approach employs the retrieved temperature profiles. It is based on the fact that IGWs are highly anisotropic structures and can be accurately retrieved by RO. The basic assumption is that all the temperature fluctuations are caused by IGWs. The smoothed background temperature profile defines the the Brunt–Väisälä frequency, which, together with the temperature fluctuations, defines the IGW specific potential energy. Many studies have derived the distribution and climatology of potential energy, which is one of the most important characteristics of IGWs. (2) More detailed analysis of the temperature profiles is based on the derivation of the temperature fluctuation spectra. For saturated IGWs, the spectra must obey the power law with an exponent of −3. Such spectra are obtained by using Wave Optical (WO) processing. (3) More advanced analysis employs space–frequency analysis. It is based on phase-sensitive techniques like cross S- or wavelet transforms in order to identify propagating IGWs. (4) Another direction is the IGW parameter estimate from separate temperature profiles applying the stability condition in terms of the Richardson number. In this framework, a necessary condition is formulated that defines whether or not the temperature fluctuations can be related to IGW events. The temperature profile retrieval involves integral transforms and filtering that constitute the observation filter. (5) A simpler filter is implemented by the analysis of the RO amplitude fluctuation spectra, based on the diffraction theory in the framework of the phase screen and weak fluctuation approximations. The two spectral parameters, the external scale and the structural characteristic, define the specific potential energy. This approach allows the derivation of the spacial and seasonal distributions of IGW activity. We conclude that the success of IGW study by RO is stimulated by a large number of RO observations and advanced techniques based on Fourier and space–time analysis, physical equations describing IGWs, and diffraction theory.

Monte Carlo simulation of photopolymerizable ceramic suspension curing profile in vat photopolymerization

Vat photopolymerization holds promise for intricate ceramic structures through additive manufacturing. However, the scattering of ceramic pastes during printing can result in inaccuracies and defects. To address this, we propose utilizing a Monte Carlo method to account for scattering in absorbing media, predicting the curing profile of photopolymerizable ceramic suspensions. This method considers factors like the reflective air-slurry interface and the impact of particle size distributions on the curing profiles, which have been relatively overlooked in prior research. Employing physical equations, we developed a Matlab simulation program, facilitating the study of various process parameters on curing performance. The simulations accurately predict solidification width and depth for slurries with distinct volume fractions and powder particle sizes. The calculated correlation coefficient score was 0.9530 regarding curing depth in all six cases, significantly supporting the proposed method. Overall, this study underscores the potential of the Monte Carlo method in enhancing the precision of vat photopolymerization 3D printing for ceramics.