Nonlinear Optimal Control of a Deep Borehole Trajectory Design

2020 ◽  
Author(s):  
Valery Gulyayev ◽  
Sergii Glazunov ◽  
Olena Andrusenko
Keyword(s):  
Optimal Control ◽  
Mathematic Model ◽  
Drill String ◽  
Trajectory Design ◽  
Energy Expenditures ◽  
Total Integral ◽  
Enhance Efficiency ◽  
Step Algorithm ◽  
Curvature And Torsion ◽  
2D And 3D

Abstract In modern oil/gas producing industry, vertical, 2D and 3D directed, and multilateral (branched) boreholes are drilled. Their trajectories are designed depending on the petroleum deposit depth and structure, properties of mining rocks, their hardness, heterogeneity, fracturing anisotropy, permeability, and so on. Therefore, the borehole cost and its productivity are determined by the length, smoothness, and configuration of its trajectory. To enhance efficiency of a borehole and to reduce cost of its drivage, to enlarge rate and volume of the reservoir depletion, it is proposed to use methods of optimal control for the best tracking of its trajectory. Through application of the differential geometry correlations, the mathematic model of the borehole outline in the form of nonlinear ordinary differential equations system is elaborated. Different objective functions, representing total integral curvature of the borehole axis line, its length, and cost of its drivage, are selected; additional constraints, separating allowed and forbidden zones of passing, are chosen. The functions of the trajectory curvature and torsion are used as controlling variables. The continuous correlations of the model are discretized and, further, the techniques of nonlinear programming and optimal control are employed. On the basis of the method of objective function gradient (antigradient) projection on the linearized constraint planes, the step-by-step algorithm of approaching to the optimal trajectory is elaborated. To correct the spoilt constraints, at every step of calculations, the Newton method is used. The elaborated approach is applied to optimization of deep curvilinear borehole outlines. The results of numerical analysis are discussed. It is shown that smoothing the hole trajectory permits also to diminish the contact and frictional interaction between the drill string and bore-hole wall and, by this, to decrease the resistance forces acting on the string during tripping in/out operations performing and to diminish energy expenditures for these operations fulfillment; to decrease the rate of the drill string tube wear; and to reduce the drill string sticking occurrence probability.

Multi-Objective Optimization Method for Borehole Trajectory Design of Directional Well

2012 ◽  
Vol 152-154 ◽  
pp. 816-819
Author(s):  
Jian Bing Zhang ◽  
Xin Liu ◽  
Xiang Hong Lv
Keyword(s):  
Optimization Design ◽  
Ideal Point ◽  
Optimization Theory ◽  
Mathematic Model ◽  
Optimization Method ◽  
Drill String ◽  
Trajectory Design ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Objective Programming

To offer those who are engaged in oil development a multi-objective design method of borehole trajectory for a directional well, the author adopted optimization theory to build a multi-objective optimization mathematic model with the shortest trajectory, the lowest drill string torque and the minimum rig hook load as final objectives, and put forward an approach to seek effective solutions to these multi-objective programming problems with ideal point method. The approach proposed in the paper can help satisfy concurrently multiple objectives of drilling design for an oilfield to implement the multi-objective optimization design schemes of borehole trajectory for a directional well, and to reduce the oilfield development costs accordingly.

Analytical Model to Estimate the Downhole Casing Wear Using the Total Wellbore Energy

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Aniket Kumar ◽  
Joseph Nwachukwu ◽  
Robello Samuel
Keyword(s):  
Contact Zone ◽  
Integral Function ◽  
Drill String ◽  
Energy Model ◽  
Wear Volume ◽  
Average Wear ◽  
Casing Wear ◽  
Curved Section ◽  
Curvature And Torsion ◽  
Two Parameters

The increasing complexities of wellbore geometry imply an increasing potential of damage resulting from the casing-wear downhole. Much work has been done to quantify and estimate wear in casing; however, the results of such predictions have been mixed. While the locations of critical-wear areas along the casing string have been predicted fairly accurately, quantifying the actual amount of casing wear has been a magnitude off. A mathematical model that describes this casing wear in terms of the total wellbore energy has been developed and used to estimate the depth of the wear groove and the wear volume downhole. The wellbore energy provides a mathematical criterion to quantify the borehole quality and incorporates the parameters, borehole curvature, and the wellbore torsion. The casing wear observed downhole is also an integral function of these two parameters. Hence, a combined “wear-energy” model has been proposed to estimate the casing wear in curved sections of the wellbore that have the drill string lying on its low side. The fundamental assumption of this model is that the volume worn away from the casing wall is proportional to the work done by friction on its inner wall by the tool joints only. It also assumes that the primary mechanism for casing wear is the rotation of the drill string, and the wear caused during tripping is insignificant. The borehole torsion models of wellbore trajectory, namely spatial-arc, natural-curve, cylindrical-helix, and constant-tool face, have been incorporated separately to enhance the accuracy of estimating the wear volume downhole. The wear-energy model for a detailed analysis of a practical example using real-time well survey data will be presented. Wear zones along the wellbore have been identified using a mathematical criterion of the “contact zone parameter.” The wear-groove depths for each contact zone along with an equivalent average wear for the curved section of the wellbore have been estimated. The wear volumes predicted by the various curvature and torsion models of wellbore energy have been graphically studied. The wellbore torsion has been found to significantly impact the casing-wear downhole.

Numerical Simulation of Induction Heating Process of Continuous Casting Slab

2008 ◽  
Vol 575-578 ◽  
pp. 37-42 ◽  
Author(s):  
Hao Liu ◽  
Li Liang Chen ◽  
Jian Xin Zhou
Keyword(s):  
Finite Difference ◽  
Continuous Casting ◽  
Induction Heating ◽  
Mathematic Model ◽  
Heating Process ◽  
Power Intensity ◽  
Continuous Casting Slab ◽  
Steel Technology ◽  
Slab Temperature ◽  
Enhance Efficiency

Compared with traditional blazing furnace, the Continuous Casting-Direct Rolling is an advanced manufacturing steel technology, which can reduce energy waste, decrease pollution and enhance efficiency. The characteristics of steels during induction heating are complex, the change of material properties with temperature makes exact analysis methods very difficult to implement. Therefore, a powerful computer aided numerical tool (i.e., finite difference analysis) is selected to numerically model the induction heating process in this paper. The mathematic model coupling with electromagnetic field and thermal field was established, and it was solved by finite difference method (FDM), thus the slab temperature distribution and its variation with time were obtained, and the characteristics in whole induction heating process were studied. To validate the program feasible, the results were evaluated and compared with experiment results, which showed that the simulation results are reliable and effective. The skin effect in heating process from the two results was studied and demonstrated, the temperature change caused by different parameters such as the induced power intensity and the corner radian were also presented, which indicate that the slab temperature can be heated uniformly through adjusting these parameters, thus the continuous casting slab can meet the rolling requirement.

scholarly journals Hybrid Optimal Control for Aircraft Trajectory Design with a Variable Sequence of Modes

2011 ◽  
Vol 44 (1) ◽  
pp. 7238-7243 ◽  
Author(s):  
Maryam Kamgarpour ◽  
Manuel Soler ◽  
Claire J. Tomlin ◽  
Alberto Olivares ◽  
John Lygeros
Keyword(s):  
Optimal Control ◽  
Trajectory Design ◽  
Variable Sequence ◽  
Hybrid Optimal Control ◽  
Aircraft Trajectory

Modeling and Control of Automated Pipe Hoisting in Oil and Gas Well Construction

2015 ◽  
Author(s):  
Parham Pournazari ◽  
Pradeepkumar Ashok ◽  
Eric van Oort
Keyword(s):  
Dynamic Model ◽  
Oil And Gas ◽  
Sliding Mode ◽  
Drill String ◽  
Trajectory Design ◽  
Modeling And Control ◽  
Gas Drilling ◽  
Drilling Operations ◽  
Hoisting System ◽  
And Control

This paper presents a robust control algorithm for automatic hoisting of a drill string in oil and gas drilling operations. We demonstrate an iterative scheme for trajectory design and present a lumped dynamic model of the hoisting system. The trajectory is used along with the dynamic model to design a hybrid sliding mode and gain scheduled PI controller to deal with the frictional nonlinearities of the system. The simulation results demonstrate the feasibility of this approach in optimally performing the pipe hoisting task.

Optimal Control of a Formula One Car on a Three-Dimensional Track—Part 2: Optimal Control

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
D. J. N. Limebeer ◽  
G. Perantoni
Keyword(s):  
Optimal Control ◽  
Three Dimensional ◽  
Measurement Data ◽  
Optimal Estimation ◽  
Tangent Plane ◽  
Normal Vector ◽  
Formula One ◽  
Nearby Point ◽  
Relative Torsion ◽  
2D And 3D

The optimal control of a Formula One car on a three-dimensional (3D) track is studied. The track is described by its geodesic and normal curvatures, and its relative torsion. These curvature parameters are obtained from noisy measurement data using the optimal estimation technique described in Part 1. The optimal control calculations presented are based on the aforementioned track model and a vehicle model that is responsive to the geometric features of a 3D track. For vehicle modeling purposes, the track is treated as a plane tangent to a nearby point on the track's spine. This tangent plane moves under the car and is orthogonal to the principal normal vector m at the nearby spine point. Results are presented that compare two-dimensional (2D) and 3D minimum-lap-time results, with the two compared. The Barcelona Formula One track studied in Part 1 is used again as an illustrative example.

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