Search results for: EKdV equation
642 Existence of Solution for Boundary Value Problems of Differential Equations with Delay
Authors: Xiguang Li
Abstract:
In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.
Keywords: Banach space, boundary value problem, differential equation, delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1220641 Two-Dimensional Observation of Oil Displacement by Water in a Petroleum Reservoir through Numerical Simulation and Application to a Petroleum Reservoir
Authors: Ahmad Fahim Nasiry, Shigeo Honma
Abstract:
We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1076640 An Approach to Correlate the Statistical-Based Lorenz Method, as a Way of Measuring Heterogeneity, with Kozeny-Carman Equation
Authors: H. Khanfari, M. Johari Fard
Abstract:
Dealing with carbonate reservoirs can be mind-boggling for the reservoir engineers due to various digenetic processes that cause a variety of properties through the reservoir. A good estimation of the reservoir heterogeneity which is defined as the quality of variation in rock properties with location in a reservoir or formation, can better help modeling the reservoir and thus can offer better understanding of the behavior of that reservoir. Most of reservoirs are heterogeneous formations whose mineralogy, organic content, natural fractures, and other properties vary from place to place. Over years, reservoir engineers have tried to establish methods to describe the heterogeneity, because heterogeneity is important in modeling the reservoir flow and in well testing. Geological methods are used to describe the variations in the rock properties because of the similarities of environments in which different beds have deposited in. To illustrate the heterogeneity of a reservoir vertically, two methods are generally used in petroleum work: Dykstra-Parsons permeability variations (V) and Lorenz coefficient (L) that are reviewed briefly in this paper. The concept of Lorenz is based on statistics and has been used in petroleum from that point of view. In this paper, we correlated the statistical-based Lorenz method to a petroleum concept, i.e. Kozeny-Carman equation and derived the straight line plot of Lorenz graph for a homogeneous system. Finally, we applied the two methods on a heterogeneous field in South Iran and discussed each, separately, with numbers and figures. As expected, these methods show great departure from homogeneity. Therefore, for future investment, the reservoir needs to be treated carefully.
Keywords: Carbonate reservoirs, heterogeneity, homogeneous system, Dykstra-Parsons permeability variations (V), Lorenz coefficient (L).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1774639 Three Computational Mathematics Techniques: Comparative Determination of Area under Curve
Authors: Khalid Pervaiz Akhter, Mahmood Ahmad, Ghulam Murtaza, Ishrat Shafi, Zafar Javed
Abstract:
The objective of this manuscript is to find area under the plasma concentration- time curve (AUC) for multiple doses of salbutamol sulphate sustained release tablets (Ventolin® oral tablets SR 8 mg, GSK, Pakistan) in the group of 18 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin® tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. AUC, an important pharmacokinetic parameter, was measured using integrated equation of multiple oral dose regimens. The approximated AUC was also calculated by using computational mathematics techniques such as repeated rectangular, repeated trapezium and repeated Simpson's rule and compared with exact value of AUC calculated by using integrated equation of multiple oral dose regimens to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin® oral tablets were 150.5819473, 157.8131756, 164.4178231 and 162.78 ng.h/ml while the closest values approximated AUC values were 149.245962, 157.336171, 164.2585768 and 162.289224 ng.h/ml, respectively as found by repeated rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the repeated rectangular rule gives slightly better approximated values of AUC as compared to repeated trapezium and repeated Simpson's rules.
Keywords: Salbutamol sulphate, Area under curve (AUC), repeated rectangular rule, repeated trapezium rule, repeated Simpson's rule.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1832638 Numerical Analysis of Rapid Gas Decompression in Pure Nitrogen using 1D and 3D Transient Mathematical Models of Gas Flow in Pipes
Authors: Evgeniy Burlutskiy
Abstract:
The paper presents a numerical investigation on the rapid gas decompression in pure nitrogen which is made by using the one-dimensional (1D) and three-dimensional (3D) mathematical models of transient compressible non-isothermal fluid flow in pipes. A 1D transient mathematical model of compressible thermal multicomponent fluid mixture flow in pipes is presented. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved in the model. Thermo-physical properties of multicomponent gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. This model is successfully validated on the experimental data [1] and shows a good agreement with measurements. A 3D transient mathematical model of compressible thermal single-component gas flow in pipes, which is built by using the CFD Fluent code (ANSYS), is presented in the paper. The set of unsteady Reynolds-averaged conservation equations for gas phase is solved. Thermo-physical properties of single-component gas are calculated by solving the Real Gas Equation of State (EOS) model. The simplest case of gas decompression in pure nitrogen is simulated using both 1D and 3D models. The ability of both models to simulate the process of rapid decompression with a high order of agreement with each other is tested. Both, 1D and 3D numerical results show a good agreement between each other. The numerical investigation shows that 3D CFD model is very helpful in order to validate 1D simulation results if the experimental data is absent or limited.Keywords: Mathematical model, Rapid Gas Decompression
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2209637 Blow up in Polynomial Differential Equations
Authors: Rudolf Csikja, Janos Toth
Abstract:
Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.
Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2167636 Another Approach of Similarity Solution in Reversed Stagnation-point Flow
Authors: Vai Kuong Sin, Chon Kit Chio
Abstract:
In this paper, the two-dimensional reversed stagnationpoint flow is solved by means of an anlytic approach. There are similarity solutions in case the similarity equation and the boundary condition are modified. Finite analytic method are applied to obtain the similarity velocity function.Keywords: reversed stagnation-point flow, similarity solutions, asymptotic solution
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1737635 Advances on LuGre Friction Model
Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane
Abstract:
LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.
Keywords: Hysteresis, LuGre model, operator, (strong) consistency.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2699634 A Convenient Model for I-V Characteristic of a Solar Cell Generator as an Active Two-Pole with Self-Limitation of Current
Authors: A. A. Penin, A. S. Sidorenko
Abstract:
A convenient and physically sound mathematical model of the external or I - V characteristic of solar cells generators is presented in this paper. This model is compared with the traditional model of p-n junction. The direct analytical calculation of load regime leads to a quadratic equation, which is importantly to simplify the calculations in the real time.
Keywords: A solar cell generator, I−V characteristic, activetwo-pole.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1259633 CFD Modeling of Air Stream Pressure Drop inside Combustion Air Duct of Coal-Fired Power Plant with and without Airfoil
Authors: Pakawhat Khumkhreung, Yottana Khunatorn
Abstract:
The flow pattern inside rectangular intake air duct of 300 MW lignite coal-fired power plant is investigated in order to analyze and reduce overall inlet system pressure drop. The system consists of the 45-degree inlet elbow, the flow instrument, the 90-degree mitered elbow and fans, respectively. The energy loss in each section can be determined by Bernoulli’s equation and ASHRAE standard table. Hence, computational fluid dynamics (CFD) is used in this study based on Navier-Stroke equation and the standard k-epsilon turbulence modeling. Input boundary condition is 175 kg/s mass flow rate inside the 11-m2 cross sectional duct. According to the inlet air flow rate, the Reynolds number of airstream is 2.7x106 (based on the hydraulic duct diameter), thus the flow behavior is turbulence. The numerical results are validated with the real operation data. It is found that the numerical result agrees well with the operating data, and dominant loss occurs at the flow rate measurement device. Normally, the air flow rate is measured by the airfoil and it gets high pressure drop inside the duct. To overcome this problem, the airfoil is planned to be replaced with the other type measuring instrument, such as the average pitot tube which generates low pressure drop of airstream. The numerical result in case of average pitot tube shows that the pressure drop inside the inlet airstream duct is decreased significantly. It should be noted that the energy consumption of inlet air system is reduced too.Keywords: Airfoil, average pitot tube, combustion air, CFD, pressure drop, rectangular duct.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1067632 Sensitivity Computations of Time Relaxation Model with an Application in Cavity Computation
Authors: Monika Neda, Elena Nikonova
Abstract:
We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).
Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1321631 Dust Acoustic Shock Waves in Coupled Dusty Plasmas with Kappa-Distributed Ions
Authors: Hamid Reza Pakzad
Abstract:
We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated.
Keywords: Shock, Soliton, Coupling, Superthermal ions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1890630 Solving Differential's Equation of Carrier Load on Semiconductor
Authors: Morteza Amirabadi, Vahid Fayaz , Fereshteh Felegary, Hossien Hossienkhani
Abstract:
The most suitable Semiconductor detector, Cadmium Zinc Teloraid , has unique properties because of high Atomic number and wide Brand Gap . It has been tried in this project with different processes such as Lead , Diffusion , Produce and Recombination , effect of Trapping and injection carrier of CdZnTe , to get hole and then present a complete answer of it . Then we should investigate the movement of carrier ( Electron – Hole ) by using above answer.Keywords: Semiconcuctor detector, Trapping, Recommbination, Diffusion
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1443629 Simulation of Sample Paths of Non Gaussian Stationary Random Fields
Authors: Fabrice Poirion, Benedicte Puig
Abstract:
Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.
Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1825628 Positive Solutions of Second-order Singular Differential Equations in Banach Space
Authors: Li Xiguang
Abstract:
In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.
Keywords: Banach space, cone, fixed point index, singular equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1235627 Process Analysis through Length Consistency
Authors: James E. Ponder
Abstract:
The requirement for consistency in physics can sometimes offer a common ground between disciplines such that their fundamental equations share a common parameter set and mathematical method for equation extraction. The parameter set shared by Relativity and Quantum Wave Mechanics enables an analysis which will be seen to be very straightforward, primarily classical in nature using linear algebra concepts, yet deriving a theoretical estimate of the value of the Gravitational Constant along with dependencies never before known.
Keywords: Gravitational Constant, Physical Consistency, Quantum Mechanics, Relativity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1532626 Quantum Ion Acoustic Solitary and Shock Waves in Dissipative Warm Plasma with Fermi Electron and Positron
Authors: Hamid Reza Pakzad
Abstract:
Ion-acoustic solitary and shock waves in dense quantum plasmas whose constituents are electrons, positrons, and positive ions are investigated. We assume that ion velocity is weakly relativistic and also the effects of kinematic viscosity among the plasma constituents is considered. By using the reductive perturbation method, the Korteweg–deVries–Burger (KdV-B) equation is derived.Keywords: Ion acoustic shock waves; Quantum plasmas
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1732625 Modeling Aggregation of Insoluble Phase in Reactors
Authors: A. Brener, B. Ismailov, G. Berdalieva
Abstract:
In the paper we submit the modification of kinetic Smoluchowski equation for binary aggregation applying to systems with chemical reactions of first and second orders in which the main product is insoluble. The goal of this work is to create theoretical foundation and engineering procedures for calculating the chemical apparatuses in the conditions of joint course of chemical reactions and processes of aggregation of insoluble dispersed phases which are formed in working zones of the reactor.
Keywords: Binary aggregation, Clusters, Chemical reactions, Insoluble phases.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1467624 Solitons in Nonlinear Optical Lattices
Authors: Tapas Kumar Sinha, Joseph Mathew
Abstract:
Based on the Lagrangian for the Gross –Pitaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4].Keywords: Double well model, nonlinear optical lattice, Solitons, tunneling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1510623 A New Method to Solve a Non Linear Differential System
Authors: Seifedine Kadry
Abstract:
In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.
Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1380622 Mathematical Modeling for the Processes of Strain Hardening in Heterophase Materials with Nanoparticles
Authors: Mikhail Semenov , Svetlana Kolupaeva, Tatiana Kovalevskaya, Olga Daneyko
Abstract:
An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.
Keywords: deformation defects, dispersion-hardened materials, mathematical modeling, plastic deformation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1481621 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)
Authors: Li Ge
Abstract:
In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1157620 Effect of Tethers Tension Force in the Behavior of a Tension Leg Platform Subjected to Hydrodynamic Force
Authors: Amr R. El-Gamal, Ashraf Essa, Ayman Ismail
Abstract:
The tension leg platform (TLP) is one of the compliant structures which are generally used for deep water oil exploration. With respect to the horizontal degrees of freedom, it behaves like a floating structure moored by vertical tethers which are pretension due to the excess buoyancy of the platform, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. In the current study, a numerical study for square TLP using modified Morison equation was carried out in the time domain with water particle kinematics using Airy’s linear wave theory to investigate the effect of changing the tether tension force on the stiffness matrix of TLP's, the dynamic behavior of TLP's; and on the fatigue stresses in the cables. The effect was investigated for different parameters of the hydrodynamic forces such as wave periods, and wave heights. The numerical study takes into consideration the effect of coupling between various degrees of freedom. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables. Nonlinear equation was solved using Newmark’s beta integration method. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether tension force, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations that is significantly dependent on wave height, and that special attention should be given to tethers fatigue because of their high tensile static and dynamic stress.
Keywords: Tethers tension, tension leg platforms, hydrodynamic wave forces, wave characteristic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2917619 Investigating the Determinants of Purchase Intention in C2C E-Commerce
Authors: Kee-Young Kwahk, Xi Ge, Jun-Hyung Park
Abstract:
This study aims to examine the determinants of purchase intention in C2C e-commerce. Specifically the role of instant messaging in the C2C e-commerce contextis investigated. In addition to instant messaging, we brought in two antecedents of purchase intention - trust and customer satisfaction - to establish a theoretical research model. Structural equation modeling using LISREL was used to analyze the data.We discussed the research findings and suggested some implications for researchers and practitioners.Keywords: E-commerce, Online marketing, C2C, Purchase Intention
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3173618 Some Geodesics in Open Surfaces Classified by Clairaut's Relation
Authors: Wongvisarut Khuangsatung, Pakkinee Chitsakul
Abstract:
In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.
Keywords: Geodesic, Surface of revolution, Clairaut's relation, Clairaut parameterization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4488617 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem
Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit
Abstract:
We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.
Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1714616 Approximate Solutions to Large Stein Matrix Equations
Authors: Khalide Jbilou
Abstract:
In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.
Keywords: IEEEtran, journal, LATEX, paper, template.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1895615 Analytical and Numerical Approaches in Coagulation of Particles
Authors: Bilal Barakeh
Abstract:
In this paper we discuss the effect of unbounded particle interaction operator on particle growth and we study how this can address the choice of appropriate time steps of the numerical simulation. We provide also rigorous mathematical proofs showing that large particles become dominating with increasing time while small particles contribute negligibly. Second, we discuss the efficiency of the algorithm by performing numerical simulations tests and by comparing the simulated solutions with some known analytic solutions to the Smoluchowski equation.
Keywords: Stochastic processes, coagulation of particles, numerical scheme.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1489614 Main Control Factors of Fluid Loss in Drilling and Completion in Shunbei Oilfield by Unmanned Intervention Algorithm
Authors: Peng Zhang, Lihui Zheng, Xiangchun Wang, Xiaopan Kou
Abstract:
Quantitative research on the main control factors of lost circulation has few considerations and single data source. Using Unmanned Intervention Algorithm to find the main control factors of lost circulation adopts all measurable parameters. The degree of lost circulation is characterized by the loss rate as the objective function. Geological, engineering and fluid data are used as layers, and 27 factors such as wellhead coordinates and Weight on Bit (WOB) used as dimensions. Data classification is implemented to determine function independent variables. The mathematical equation of loss rate and 27 influencing factors is established by multiple regression method, and the undetermined coefficient method is used to solve the undetermined coefficient of the equation. Only three factors in t-test are greater than the test value 40, and the F-test value is 96.557%, indicating that the correlation of the model is good. The funnel viscosity, final shear force and drilling time were selected as the main control factors by elimination method, contribution rate method and functional method. The calculated values of the two wells used for verification differ from the actual values by -3.036 m3/h and -2.374 m3/h, with errors of 7.21% and 6.35%. The influence of engineering factors on the loss rate is greater than that of funnel viscosity and final shear force, and the influence of the three factors is less than that of geological factors. The best combination of funnel viscosity, final shear force and drilling time is obtained through quantitative calculation. The minimum loss rate of lost circulation wells in Shunbei area is 10 m3/h. It can be seen that man-made main control factors can only slow down the leakage, but cannot fundamentally eliminate it. This is more in line with the characteristics of karst caves and fractures in Shunbei fault solution oil and gas reservoir.
Keywords: Drilling fluid, loss rate, main controlling factors, Unmanned Intervention Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 371613 Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes
Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria
Abstract:
Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1605