Balance Equation Method Research Articles

Development of Machine Learning-Based Production Forecasting for Offshore Gas Fields Using a Dynamic Material Balance Equation

Offshore oil and gas fields pose significant challenges due to their lower accessibility compared to onshore fields. To enhance operational efficiency in these deep-sea environments, it is essential to design optimal fluid production conditions that ensure equipment durability and flow safety. This study aims to develop a smart operational solution that integrates data from three offshore gas fields with a dynamic material balance equation (DMBE) method. By combining the material balance equation and inflow performance relation (IPR), we establish a reservoir flow analysis model linked to an AI-trained production pipe and subsea pipeline flow analysis model. We simulate time-dependent changes in reservoir production capacity using DMBE and IPR. Additionally, we utilize SLB’s PIPESIM software to create a vertical flow performance (VFP) table under various conditions. Machine learning techniques train this VFP table to analyze pipeline flow characteristics and parameter correlations, ultimately developing a model to predict bottomhole pressure (BHP) for specific production conditions. Our research employs three methods to select the deep learning model, ultimately opting for a multilayer perceptron (MLP) combined with regression. The trained model’s predictions show an average error rate of within 1.5% when compared with existing commercial simulators, demonstrating high accuracy. This research is expected to enable efficient production management and risk forecasting for each well, thus increasing revenue, minimizing operational costs, and contributing to stable plant operations and predictive maintenance of equipment.

Balance equations for physics-informed machine learning

Using traditional machine learning (ML) methods may produce results that are inconsistent with the laws of physics. In contrast, physics-based models of complex physical, biological, or engineering systems incorporate the laws of physics as constraints on ML methods by introducing loss terms, ensuring that the results are consistent with these laws. However, accurately deriving the nonlinear and high order differential equations to enforce various complex physical laws is non-trivial. There is a lack of comprehensive guidance on the formulation of residual loss terms. To address this challenge, this paper proposes a new framework based on the balance equations, which aims to advance the development of PIML across multiple domains by providing a systematic approach to constructing residual loss terms that maintain the physical integrity of PDE solutions. The proposed balance equation method offers a unified treatment of all the fundamental equations of classical physics used in models of mechanical, electrical, and chemical systems and guides the derivation of differential equations for embedding physical laws in ML models. We show that all of these equations can be derived from a single equation known as the generic balance equation, in conjunction with specific constitutive relations that bind the balance equation to a particular domain. We also provide a few simple worked examples how to use our balance equation method in practice for PIML. Our approach suggests that a single framework can be followed to incorporate physics into ML models. This level of generalization may provide the basis for more efficient methods of developing physics-based ML for complex systems.

Theoretical perfection and application of entransy analysis method on absorption systems

In thermal energy utilization scenarios, absorption systems have been widely and effectively utilized as heat exchange devices. However, existing thermal research methods on absorption systems for these scenarios have limitations. Therefore, the entransy parameter, which is applicable for analyzing the heat exchange process is chosen to study. The entransy balance relationship of the absorption system is theoretically analyzed, and the entransy analysis method is further perfected to break through the limitations. First, the entransy imbalance of the reversible absorption cycle is proved, and the reason for this imbalance is clarified that two heat-work conversion processes at different temperatures occur inside the cycle. Then, the working fluid's entransy change during the conversion process is theoretically derived and defined, and a new parameter: conversion entransy is defined based on it. Moreover, the comprehensive entransy balance equation and comprehensive entransy analysis method of absorption systems are further proposed. Finally, a specific case study is carried out, and this method is compared with the existing exergy analysis method and entransy analysis method without considering the conversion entransy respectively. By using this method, the optimal process form of the absorption heat exchanger can be directly obtained without numerical simulation calculations, demonstrating significant advantages.

Air change rates and infection risk in school environments: Monitoring naturally ventilated classrooms in a northern Italian urban context

The importance of building ventilation in avoiding long-distance airborne transmission has been highlighted with the advent of the COVID-19 pandemics. Among others, school environments, in particular classrooms, present criticalities in the implementation of ventilation strategies and their impact on indoor air quality and risk of contagion. In this work, three naturally ventilated school buildings located in northern Italy have undergone monitoring at the end of the heating season. Environmental parameters, such as CO2 concentration and indoor/outdoor air temperature, have been recorded together with the window opening configurations to develop a two-fold analysis: i) the estimation of real air change rates through the transient mass balance equation method, and ii) the individual infection risk via the Wells-Riley equation. A strong statistical correlation has been found between the air change rates and the windows opening configuration by means of a window-to-volume ratio between the total opening area and the volume of the classroom, which has been used to estimate the individual infection risk. Results show that the European Standard recommendation for air renewal could be achieved by a window opening area of at least 1.5 m2, in the most prevailing Italian classrooms. Furthermore, scenarios in which the infector agent is a teacher show higher individual infection risk than those in which the infector is a student. In addition, the outcomes serve school staff as a reference to ensure adequate ventilation in classrooms and keep the risk of infection under control based on the number of the students and the volume of the classroom.

Associating occupants' interaction with windows with air change rate --One case study

Air change rate (ACR) significantly influences the indoor thermal environment and indoor air quality. Moreover, as a matter of fact, ACR varies with time during natural ventilation. However, to date only a few studies have accounted for the dynamic ACR for the actual in-use buildings. To address this issue, a field measurement of outdoor/indoor environments and the window state was conducted in a dormitory in Beijing in spring, summer, and autumn. Transient Mass Balance Equation (TMBE) method associated with the extended Kalman filter (Hereinafter referred to as Kalman filter method) was adopted to obtain the dynamic results of the ACR. Then the correlations of outdoor/indoor environments with the ACR and the probability of window opening were investigated. The results confirm the validity of Kalman filter method for tracking the dynamic nature of natural ventilation in residential units, and further demonstrate that occupants' interaction with windows does not simply refer to opening/closing windows, but also refer to adjusting the extent of the window being open in response to occupants' ventilation needs. Therefore, in addition to the probability of window opening, ventilation needs, i.e., the dynamic ACR, as the underlying trigger for window opening behavior, should be used as an indispensable part of describing occupants' interaction with windows. This study provides a complete framework to describe occupants’ interactions with windows by combining the dynamic ACR and the probability of window opening.

HgCdTe-based quantum cascade lasers operating in the GaAs phonon Reststrahlen band predicted by the balance equation method.

The lack of radiation sources in the frequency range of 7-10 THz is associated with strong absorption of the THz waves on optical phonons within the GaAs Reststrahlen band. To avoid such absorption, we propose to use HgCdTe as an alternative material for THz quantum cascade lasers thanks to a lower phonon energy than in III-V semiconductors. In this work, HgCdTe-based quantum cascade lasers operating in the GaAs phonon Reststrahlen band with a target frequency of 8.3 THz have been theoretically investigated using the balance equation method. The optimized active region designs, which are based on three and two quantum wells, exhibit the peak gain exceeding 100 cm-1 at 150 K. We have analyzed the temperature dependence of the peak gain and predicted the maximum operating temperatures of 170 K and 225 K for three- and two-well designs, respectively. At temperatures exceeding 120 K, the better temperature performance has been obtained for the two-well design, which is associated with a larger spatial overlap of weakly localized lasing wavefunctions, as well as, a higher population inversion. We believe that the findings of this work can open a pathway towards the development of THz quantum cascade lasers featuring a high level of optical gain due to the low electron effective mass in HgCdTe.

Multi-phase particle-in-cell coupled with population balance equation (MP-PIC-PBE) method for multiscale computational fluid dynamics simulation

The ‘multiphase particle-in-cell coupled with population balance equation’ (MP-PIC-PBE) method is introduced for simulating multi-scale multiphase particulate flows. This method couples the meso‑scale fluid dynamics simulated by the MP-PIC method with the simulation of the micro-scale particle size distribution. The homogeneous population balance equation is calculated for each discrete particle tracked in a Lagrangian frame, after the MP-PIC numerical procedure is followed at each time instance. This approach allows the particulate phase to accommodate the particulate stresses using spatial gradients and allows the Lagrangian description to predict particle properties by the PBE. For the antisolvent crystallization of Lovastatin in a biradial mixer, the proposed method is compared to an existing method that simulates the spatiotemporal evolution of the particle distribution by combining a multi-environment probability density function with the spatially varying PBE. The MP-PIC-PBE method has lower computational cost and provides more detailed information, such as particle age and location.

Mid-infrared optical absorption in InAs/AlSb/GaSb based quantum well system

Abstract The dependence of the optical absorption coefficient on the width of the AlSb caplayer is investigated in InAs/AlSb/GaSb based quantum well system (QWs). The optical absorption coefficient is calculated by employing the balance equation method to solve the Boltzmann equation. Two peaks in the optical absorption coefficient are observed due to the intraband transitions. The AlSb caplayer is inserted between the InAs layer and the GaSb layer to reduce the generation–recombination (g–r) noise induced by the interband transitions. The optical absorption coefficients induced by the interband transitions are significantly reduced when the width of the AlSb caplayer reaches up to 2 nm . The optical absorption peaks lie in the mid-infrared region and decrease slightly with the increase of the temperature even up to room temperature. Our theoretical results suggest that the InAs/AlSb/GaSb based QWs can be used as room temperature mid-infrared detectors with low noise.

Assessing the effects of plant density and plastic film mulch on maize evaporation and transpiration using dual crop coefficient approach

Plastic film mulching, in combination with high plant density, is a common practice for rain-fed maize production, especially in Northeastern China. To explore effects of plant density and plastic film mulching on the evapotranspiration of maize during its different growth periods, a two-year split-plot field experiment with non-mulching (M0) and plastic film mulching (M1) and three plant densities (60,000 (D1), 75,000 (D2), and 90,000 plants ha−1 (D3)) was conducted at a site of Shenyang located in the Northeast China in 2016 and 2017. Based on the field experimental data of spring maize, water balance equation and dual crop coefficient method were adopted to explore effects of plant density and plastic film mulch on evapotranspiration of maize at different growing stages. The results showed that compared with non-mulching treatment, the plastic film mulching increased maize transpiration by about 20.0%–32.0% and 3.5%–15.4% and reduced soil evaporation by 51.8%–63.0% and 21.5%–39.5% in 2016 and 2017, respectively. Overall, the mulching treatment significantly reduced maize water consumption by about 12.4% and 6.2% in 2016 and 2017, respectively. The mulching treatment also increased the basic maize crop coefficient by 0.03–0.07 and reduced the average evaporation coefficient by 0.14, compared with non-mulching treatment. In addition, compared with non-mulching, plastic film mulching increased ratio of transpiration by 19%–32% and 5%–12% in 2016 and 2017, respectively. For effects of plant density on maize evapotranspiration, higher plant density resulted in more evapotranspiration during the whole growth season of maize except for its initial growth stage. The average evapotranspiration of D1–D3 treatments from two growing seasons of maize were 469.2, 509.6 and 534.1 mm, respectively. For evaporation and transpiration, the maize transpiration increased with the increase of planting density, and the maize evaporation increased with the increase of planting density under plastic film mulching conditions but decreased with non-mulching treatment.

ANALISIS PERMINTAAN DAN PENAWARAN MAKANAN KHAS LANGKITANG DI PANTAI PADANG

Padang Beach has a typical culinary tour like Langkitang. Typical food is one of the factors supporting a region's famous. This study aims to analyze the demand and supply of typical food langkitang in Padang Beach. In particular it aims to analyze the market balance that is influenced by the price of the goods itself, the price of the substitute, the consumer's income, the number of buyers, the cost of production, and the number of producers in the market. The type of research conducted in this study is the type of descriptive quantitative research by survey method. The population of this study are visitors who buy typical food Langkitang and typical food vendors Langkitang which has a stall in the area of ​​Padang Beach. The sampling technique used is purposive sampling, the buyer is 10 people based on the number of samples from the merchant as many as 10 people, with the assumption that 1 trader 1 buyer. Data collection techniques used were observation, interview, documentation, and questionnaire. The data obtained will be analyzed and interpreted in accordance with the objectives and research hypotheses that have been proposed. The analysis was conducted using simultaneous equation model and market balance equation method. Based on the results of this study can be emphasized that the demand and supply of typical food Langkitang in Padang Beach has reached the point of market balance, which is at the equilibrium price of Rp. 4,600, - the proportion with the balance quantity of 32 servings. This means that the equilibrium price will determine the quantity of balance between demand and supply of typical food of Langkitang in Padang Beach. Break event point is on sale of 21 servings of Langkitang with revenue of Rp. 105.000, -.

Terahertz photoconductivity in InAs/GaSb based quantum well system

Great attention has been paid to the terahertz (THz) technology due to its potential applications, in which THz radiation source and detector with excellent performances at the room temperature are most desired. The semi-classical Boltzmann equation is employed to study the response of electrons and holes to the electromagnetic radiation field in InAs/GaSb based type Ⅱ quantum well system (QWS). The balance equation method is used to solve the Boltzmann equation, and the influences of the structure of the QWS on the photoconductivity is studied in detail to reveal the mechanism of the photoconductivity in the QWS. The photoconductivity is influenced by the carrier density, the subband energy of the carriers and the coupling of the wavefunctions which can be modulated conveniently by the structure of the QWS. In this study, our attention focuses on the influence of the structure of the QWS on the conductivity. When the width of the InAs layer and the GaSb layer are both 8 nm, a sharp peak in photoconductivity is observed at about 0.2 THz due to the electron transition in different layers. The strength of the peak decreases slightly with the increase of the temperature, and a red shift is observed. However, the photoconductivity is not sensitive to the temperature and has good performances at relatively high temperatures up to the room temperature, which indicates that the InAs/GaSb based type-Ⅱ QWS can be used as a THz photoelectric device at room temperature.

PEMETAAN DATA RECHARGE AIR TANAH DI KABUPATEN SLEMAN BERDASARKAN DATA CURAH HUJAN

Water is a basic need for humans and other living things. Various sources of water on this earth has formed a system of close interaction with the components of living things in it. Over the years, water resources have changed in terms of both quality and quantity. This can be due to population growth in addition to the natural changes in nature. The more narrow field of water absorption followed by high water consumption causes the supply of ground water reserves can be threatened. So, we need a mapping and ground water recharge calculations to assist in the monitoring of groundwater reserves.The method used in this research is the Water Balance (keseimbangan air)method. This method is based on any incoming rain water will be equal to the output evapotranspiration and runoff hereinafter this method is applied in the application. Factors affecting groundwater recharge the water balance method is precipitation, evapotranspiration and run off. Information og groundwater recharge is also displayed on the map using Google Map function are related to the database system to produce informative mapsCalculation of groundwater recharge is applied to the daily rainfall data input into the application which then included in the water balance equation method so it can be easy to determine the value of groundwater recharge. Groundwater recharge information can be displayed in the form of mapping, making them easier to understand visually.Based on testing, the highest recharge results of this research on the Kemput station is 1119,5 mm/year with rainfall of 2750 mm/year. Seyegan and Bronggang station is 1026,25 mm/year with rainfall of 2625 mm/year. Angin-angin and Prumpung station is 933 mm/year with rainfall of 2500 mm/year. Beran and Gemawang station is 839.5 mm/year with rainfall of 2375 mm/year. Plataran station is 808.42 mm/year with rainfall of 2333 mm/year. Godean station is 699.5 mm/year with rainfall of 2187 mm/year and the lowest at Tirto Tanjungand Santan stastion 560 mm / year with rainfall of 2000 mm / year.

Natural Flow Reconstruction Using Kalman Filter and Water Balance–Based Methods II: Case Studies, Results, and Discussion

AbstractDuring the prereservoir years, when limited data (neighboring basin flow and simulated flow) are available for ungauged basins, simple methods are relevant to reconstruct natural flow (NF). On the other hand, for the postreservoir years, when hydrometric data (water level in the reservoir, turbine flow, and discharged flow) are available for ungauged basins, the classic water balance equation (WBE) method is usually employed to determine NF. However, applying classic methods still produce noisy and unreliable flow data series. In an attempt to produce more reliable NF data, new methods are proposed and described in Part 1 of this paper: the state fusion Kalman filter method (prereservoir construction period) and the deterministic WBE method and the stochastic WBE method (postreservoir construction period). This paper that is presented as Part 2 deals with the execution of these new methods for three subbasins of different sizes in Quebec, Canada. Obtained results are then compared against those pr...

Analysis of the cumulative exergy consumption of an integrated oxy-fuel combustion power plant

Abstract In order to analyze the cumulative exergy consumption of an integrated oxy-fuel combustion power plant the method of balance equations was applied based on the principle that the cumulative exergy consumption charging the products of this process equals the sum of cumulative exergy consumption charging the substrates. The set of balance equations of the cumulative exergy consumption bases on the ‘input-output method’ of the direct energy consumption. In the structure of the balance we distinguished main products (e.g. electricity), by-products (e.g. nitrogen) and external supplies (fuels). In the balance model of cumulative exergy consumption it has been assumed that the cumulative exergy consumption charging the supplies from outside is a quantity known a priori resulting from the analysis of cumulative exergy consumption concerning the economy of the whole country. The byproducts are charged by the cumulative exergy consumption resulting from the principle of a replaced process. The cumulative exergy consumption of the main products is the final quantity.

Stabilized finite element discretization applied to an operator-splitting method of population balance equations

An operator-splitting method is applied to transform the population balance equation into two subproblems: a transient transport problem with pure advection and a time-dependent convection–diffusion problem. For discretizing the two subproblems the discontinuous Galerkin method and the streamline upwind Petrov–Galerkin method combined with a backward Euler scheme in time are considered. Standard energy arguments lead to error estimates with a lower bound on the time step length. The stabilization vanishes in the time-continuous limit case. For this reason, we follow a new technique proposed by John and Novo for transient convection–diffusion–reaction equations and extend it to the case of population balance equations. We also compare numerically the streamline upwind Petrov–Galerkin method and the local projection stabilization method.

Thermodynamic efficiency of use of heat pumps for comfortable conditions in indoor pools

Today it is common to use heat pumps in air conditioning systems (split systems). It is also known that heat pumps are used to maintain comfort conditions in indoor pools, but there is no sound data on the thermodynamic efficiency of their use in heating and cooling systems. The article analytically and using the method of balance equations, analyzes the thermodynamic efficiency of the system of comfortable conditions in an indoor pool using a heat pump. Graphic dependences of main parameters that characterize the efficiency of the system on temperature of the surrounding air were presented. It was determined that in order to maintain the heat balance of the scheme the more efficient and rational option is to discharge excess heat into the environment. It was found that the efficiency of the heat pump scheme is little dependent on ambient temperature and is determined by the temperature of the pool water, and as a result, by the air temperature in the pool. The results can be used in the design of heating systems, ventilation and air-conditioning of indoor pools

Connection between the deformation of paint droplets during deposition on the surface being painted and the orientation of pigment particles

In this work, we describe a new and more practically useful approach to finding the relationship between the reflective properties of a painted surface, the physical properties of the paint, and the technolog� ical parameters of painting. A simple formal dynamic model of the deformation of a droplet of a "metallic"� type paint during its interaction with the surface being painted is constructed. The physical model takes into account the main forces responsible for the deformation dynamics of a droplet, i.e., forces of surface tension, viscous friction, elasticity, and inertia; a new rheological model, which is suitable for approximating the vis� cosity of paints in a wide range of deformation rates, is used. To construct the mathematical model, we employed the method of integral balance equations of mass, momentum, and energy. The model is used to calculate the most important stages of the deformation of paint droplets during their deposition on the surface being painted, which have an effect on the orientation of pigment particles. For these stages, we compose characteristic strainapproximating functions of the Reynolds and Weber numbers, which are proved to be useful for summarizing the results of experimental studies of the entire real process of painting.

Investigation of the void reactivity effect in large-size Lead Fast Reactors

An aspect of great relevance in Lead Fast Reactors (LFRs) is the actual void reactivity evaluation. The purpose of this work is double: to inquire into the physical problem, and to evaluate the impact of different approaches and numerical methods on the calculation of the critical reactor parameters involved. Thus, results concerning void effect contributors have been evaluated through a cross-checked analysis performed by means of both a deterministic and a stochastic code. The field of investigation that has been assumed consists in the reference configuration of the 600MWe European Lead-cooled SYstem (ELSY), under development within the 6th and 7th EURATOM Framework Programmes. Calculations have been carried out on a 1500MWth MOX-fuelled core, composed by wrapper-less square Fuel Assemblies (FAs) with pins on a square lattice. The ERANOS (European Reactor Analysis Optimized System) deterministic code ver. 2.1 and the MCNP Monte Carlo code ver. 4c have been employed in conjunction with the JEFF-3.1 nuclear data library to assess the void reactivity variation and its breakdown into the most relevant nuclides, using both the neutron balance equation method and perturbation theory. Results have shown a very good agreement between ERANOS and MCNP outcomes: the huge reactivity worth determined by the core active region voiding (approximately 5000pcm) is due to the predominant contributions of even isotopes – among which 238U plays a major role, being responsible for roughly 4300pcm – as a consequence of their fission cross-section high sensitivity to spectral hardening (threshold reactions), despite their modest contribution to the total fissions.

06/00642 Sustainable and economic hydrogen cogeneration from nuclear energy in competitive power markets: Miller, A. I. and Duffey, R. B. Energy, 2005, 30, (14), 2690–2702.

An aspect of great relevance in Lead Fast Reactors (LFRs) is the actual void reactivity evaluation. The purpose of this work is double: to inquire into the physical problem, and to evaluate the impact of different approaches and numerical methods on the calculation of the critical reactor parameters involved. Thus, results concerning void effect contributors have been evaluated through a cross-checked analysis performed by means of both a deterministic and a stochastic code. The field of investigation that has been assumed consists in the reference configuration of the 600 MWe European Lead-cooled SYstem (ELSY), under development within the 6th and 7th EURATOM Framework Programmes. Calculations have been carried out on a 1500 MWth MOX-fuelled core, composed by wrapper-less square Fuel Assemblies (FAs) with pins on a square lattice. The ERANOS (European Reactor Analysis Optimized System) deterministic code ver. 2.1 and the MCNP Monte Carlo code ver. 4c have been employed in conjunction with the JEFF-3.1 nuclear data library to assess the void reactivity variation and its breakdown into the most relevant nuclides, using both the neutron balance equation method and perturbation theory. Results have shown a very good agreement between ERANOS and MCNP outcomes: the huge reactivity worth determined by the core active region voiding (approximately 5000 pcm) is due to the predominant contributions of even isotopes – among which 238U plays a major role, being responsible for roughly 4300 pcm – as a consequence of their fission cross-section high sensitivity to spectral hardening (threshold reactions), despite their modest contribution to the total fissions.

Monte Carlo calculations of hot-electron transport and diffusion noise in GaN and InN

Monte Carlo simulations of high-field transport are used to calculate the spectral density of velocity fluctuations and the diffusion coefficients of hot electrons in GaN and InN. The results of the simulations are complemented by the investigation of the velocity relaxation time through the balance equation method. It is found that the low-frequency noise spectrum remains white up to 100–300 GHz, so that the steady-state diffusion coefficient can be considered as constant in practically the whole millimetre wavelength range. It is shown that the main features of the field dependence of the longitudinal and transverse diffusion coefficients such as initial decrease of the diffusion coefficient followed by a peak near the threshold field for the intervalley transfer, etc are described well both qualitatively and quantitatively by simplified approaches based on velocity relaxation times.