Modelling of external filter cake profile along the well during drilling

2014 ◽  
Vol 54 (1) ◽  
pp. 319 ◽  
Author(s):  
Azim Kalantariasl ◽  
Abbas Zeinijahromi ◽  
Pavel Bedrikovetsky
Keyword(s):  
Mathematical Model ◽  
Velocity Profile ◽  
Filter Cake ◽  
Thickness Distribution ◽  
Material Balance ◽  
Force Balance ◽  
Predictive Tool ◽  
Physiochemical Properties ◽  
Cake Thickness ◽  
The Mathematical Model

This paper presents a new mathematical model to predict the steady-state external filter cake thickness distribution and velocity profile along the wellbore during overbalanced drilling. Several models have been suggested for the prediction of external cake thickness using the force balance method. Yet, a comprehensive literature survey reveals that electrostatic forces and the permeate force correction factor have been neglected, while both can significantly change the conditions of particle detachment from the cake surface. Torque balance of hydrodynamic (lifting, tangential and permeate drag), gravity and electrostatic (DLVO) forces along with Darcy’s law and material balance is used to investigate the conditions of particle attachment/detachment on the cake surface. The results show strong effects of mud chemistry, particle size, cake permeability, tangential flow velocity, overbalance pressure, and Young’s modulus on the external filter cake thickness and velocity profile. The mathematical model can be applied as a predictive tool for the estimation of filter cake thickness. It allows for the calculation of external filter cake distribution using the physiochemical properties of mud and particles.

scholarly journals Heat and Mass Transfer with Condensation in Capillary Porous Bodies

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Salah Larbi
Keyword(s):  
Mathematical Model ◽  
Energy Transport ◽  
Process Analysis ◽  
Theoretical Models ◽  
Liquid Interfaces ◽  
Transport Parameters ◽  
Predictive Tool ◽  
Porous Bodies ◽  
Wetting Process ◽  
The Mathematical Model

The purpose of this present work is related to wetting process analysis caused by condensation phenomena in capillary porous material by using a numerical simulation. Special emphasis is given to the study of the mechanism involved and the evaluation of classical theoretical models used as a predictive tool. A further discussion will be given for the distribution of the liquid phase for both its pendular and its funicular state and its consequence on diffusion coefficients of the mathematical model used. Beyond the complexity of the interaction effects between vaporisation-condensation processes on the gas-liquid interfaces, the comparison between experimental and numerical simulations permits to identify the specific contribution and the relative part of mass and energy transport parameters. This analysis allows us to understand the contribution of each part of the mathematical model used and to simplify the study.

scholarly journals An Optimistic Solver for the Mathematical Model of the Flow of Johnson Segalman Fluid on the Surface of an Infinitely Long Vertical Cylinder

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7798
Author(s):  
Naveed Ahmad Khan ◽  
Fahad Sameer Alshammari ◽  
Carlos Andrés Tavera Romero ◽  
Muhammad Sulaiman ◽  
Seyedali Mirjalili
Keyword(s):  
Thin Film ◽  
Neural Networks ◽  
Mathematical Model ◽  
Artificial Neural Networks ◽  
Velocity Profile ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Thin Film Flow ◽  
Sqp Algorithm ◽  
The Mathematical Model

In this paper, a novel soft computing technique is designed to analyze the mathematical model of the steady thin film flow of Johnson–Segalman fluid on the surface of an infinitely long vertical cylinder used in the drainage system by using artificial neural networks (ANNs). The approximate series solutions are constructed by Legendre polynomials and a Legendre polynomial-based artificial neural networks architecture (LNN) to approximate solutions for drainage problems. The training of designed neurons in an LNN structure is carried out by a hybridizing generalized normal distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP). To investigate the capabilities of the proposed LNN-GNDO-SQP algorithm, the effect of variations in various non-Newtonian parameters like Stokes number (St), Weissenberg number (We), slip parameters (a), and the ratio of viscosities (ϕ) on velocity profiles of the of steady thin film flow of non-Newtonian Johnson–Segalman fluid are investigated. The results establish that the velocity profile is directly affected by increasing Stokes and Weissenberg numbers while the ratio of viscosities and slip parameter inversely affects the fluid’s velocity profile. To validate the proposed technique’s efficiency, solutions and absolute errors are compared with reference solutions calculated by RK-4 (ode45) and the Genetic algorithm-Active set algorithm (GA-ASA). To study the stability, efficiency and accuracy of the LNN-GNDO-SQP algorithm, extensive graphical and statistical analyses are conducted based on absolute errors, mean, median, standard deviation, mean absolute deviation, Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE). Statistics of the performance indicators are approaching zero, which dictates the proposed algorithm’s worth and reliability.

AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

2021 ◽  
pp. 2150033
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha sohail ◽  
Andleeb Zafar ◽  
Rana Talha ◽  
Sadiq M. Sait
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Ethylene Oxide ◽  
Ethylene Glycol ◽  
Exothermic Reaction ◽  
Plug Flow ◽  
Material Balance ◽  
Chemical Species ◽  
Future Research ◽  
The Mathematical Model

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198[Formula: see text]C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129[Formula: see text]C and freezes at [Formula: see text]C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

The Spread-Mathematical Model of Special-Shaped Steel Wire during the Rolling

2011 ◽  
Vol 340 ◽  
pp. 56-63
Author(s):  
Bo Jian Wang ◽  
Wei Ke Sun ◽  
Yong Jie Wang
Keyword(s):  
Mathematical Model ◽  
Balance Equation ◽  
Steel Wire ◽  
Rolling Process ◽  
Force Balance ◽  
Stress Increment ◽  
Rolling Deformation ◽  
The Mathematical Model ◽  
Theoretical Results ◽  
Force Balance Equation

This article studied the rolling process of metal card wire, and established the spread formula of flat wire to special-shaped steel wire by rolling. The metal stress-increment in rolling deformation zone for the special-shaped steel wire was solved by the force-balance equation, and the mathematical model of rolling-piece spread was established according to the displacement increment function solved. By means of experiments to verify the mathematical model, the results show: the theoretical results of different materials through the model to calculate is closer the actual value after rolled , the error is less than 5%.

scholarly journals MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS

2019 ◽  
Vol 16 (6) ◽  
pp. 706-716
Author(s):  
D. A. Tikhov-Tinnikov ◽  
V. S. Baradiev ◽  
A. I. Fedotov ◽  
A. V. Alekseev
Keyword(s):  
Mathematical Model ◽  
Optimization Methods ◽  
Force Balance ◽  
Model Description ◽  
Harmonic Mode ◽  
Elastic Suspension ◽  
Power Characteristics ◽  
Operating Modes ◽  
Rubber Bushing ◽  
The Mathematical Model

Introduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to describe such characteristics using a mathematical model based on the classical elements of Hooke and Saint-Venant. The paper presents a mathematical description of the bushing simulation functioning results, accuracy of approach, areas of application of the mathematical model.Materials and methods. The initial data was the experimental characteristic of a cylindrical automobile rubber bushing, obtained in harmonic mode at the 0.03 to 51 Hz frequency and the 0.4 to 10 mm amplitude. The force balance of the two Hooke elements and one Saint-Venant element interacting with each other determined the mathematical model description. The authors carried out the calculations using numerical and optimization methods.Results. As a result, the authors determined functions characterizing the change in the parameters of the Hooke and Saint-Venant elements from the rubber bushings’ deformation amplitude. Moreover, the authors calculated power characteristics in the form of dependences of the rubber bushing effort and also found quantitative indicators of the reliability of the experimental data approximation by the developed mathematical model.Discussion and conclusions. The analysis of the operating modes shows the possibility of the model application to describe the rubber bushing functioning in a stationary harmonic mode with small and medium strain amplitudes. The simulation results of the Hooke’s and Saint-Venant’s parameters reveals the theoretical prerequisites for the possibility of using the model to calculate the bushing force in an unsteady mode.The authors have read and approved the final manuscript. Financial transparency: the authors have no financial interest in the presented materials or methods. There is no conflict of interest.

scholarly journals MATHEMATICAL MODELING OF TECHNOLOGICAL MODES OF HEAT-PUMPING SYSTEMS FOR TECHNOLOGICAL PROCESSES

2021 ◽  
pp. 85-91
Author(s):  
Boris Kotov ◽  
Vladimir Grishchenko ◽  
Yuriy Pantsir ◽  
Igor Garasimchuk
Keyword(s):  
Mathematical Model ◽  
Automatic Control ◽  
Heat Pump ◽  
Material Balance ◽  
Heat Pumps ◽  
Practical Implementation ◽  
Industrial Complex ◽  
Energy Potential ◽  
The Mathematical Model ◽  
Heat Carriers

One of the ways to increase the energy efficiency of the process of heat supply of technological facilities and production facilities of the agro-industrial complex is the use of heat pumps. Their use allows to increase the energy potential of heat carriers. To optimize the mode parameters and create systems for automatic control of the heat pump installation, it is necessary to establish a relationship between the parameters of the processes occurring in the elements of the installation by creating a mathematical model of non-stationary thermal modes. In the analysis of recent studies and publications, it is established that the calculations of processes in heat pumps are presented mainly for stationary modes of operation without taking into account the dynamics of the condenser. If the dynamic modes of individual elements are given, then they are described by mathematical models of considerable complexity, which greatly complicates their practical implementation. In the article, the heat pump installation, as an object of modeling, is considered as a physical system, which consists of four series-connected elements: evaporator, condenser, compressor, throttle valve forming a closed circuit. The principle of operation of a simple heat pump installation is explained by the scheme and schedule of the theoretical cycle of the steam compressor heat pump. To simplify the mathematical model, certain assumptions were made: the change in the parameters of liquid, vapor and air varies in a straight line, the thermophysical characteristics of the material of heat exchangers, air and vapor flows, heat transfer coefficients do not depend on temperature and are average for the cycle. On the basis of thermal and material balance the corresponding differential equations which make mathematical model of dynamics of change of parameters of the heat exchanger have been made. The mathematical model is supplemented by a simulation model in the MatLAB / Simulink computer environment, as well as graphical interpretations of dynamic characteristics. The developed mathematical model of dynamics of thermal processes in the heat pump installation can be used for calculation of parameters of heating and cooling of streams of heat carriers and creation of system of automatic control of them.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

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