Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
|
|
- Hannah Armstrong
- 5 years ago
- Views:
Transcription
1 Downloaded from orbit.dtu.dk on: Dec 2, 217 Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir Capolei, Andrea; Völcker, Carsten; Frydendall, Jan; Jørgensen, John Bagterp Publication date: 212 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Capolei, A., Völcker, C., Frydendall, J., & Jørgensen, J. B. (212). Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir [Sound/Visual production (digital)]. 17th Nordic Process Control Workshop, Kongens Lyngby, Denmark, 25/1/212, General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
2 Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir Andrea Capolei, Carsten Völcker, Jan Frydendall, John Bagterp Jørgensen Department of Informatics and Mathematical Modeling Technical University of Denmark 17th Nordic Process Control Workshop 26th of January, / 23
3 Outline 1 Introduction 2 Optimal Control Problem Single Shooting Optimization 3 ESDIRK integration methods 4 Continuous Adjoint Method 5 Production Optimization for a Conventional Oil Field 6 Conclusions 2 / 23
4 Increasing Oil demand Introduction Production by region Million barrels daily Consumption by region Million barrels daily Asia Pacific Africa Middle East Europe & Eurasia S. & Cent. America North America (from BP statistical review 211) 3 / 23
5 An Offshore Oil Reservoir Introduction 4 / 23
6 Introduction Closed-loop reservoir management (after Jansen 25) 5 / 23
7 Introduction Water Flooding Modeled by a Two-Phase Flow Model The mass conservation of water (i w) and oil (i o) t C i(p i, S i ) = F i (P i, S i ) + Q i The mass concentrations C i = φρ i (P i )S i Fluxes through the porous medium k min :.24 Darcy, k max : Darcy log 1 (K) (Darcy) Darcy s law F i = ρ i (P i )u i (P i, S i ) u i (P i, S i ) = K k ri(s i ) µ i ( ) P i ρ i (P i )g z A general formulation of the two-phase flow problem d dt g(x(t)) = f(x(t), u(t)) 6 / 23
8 Continuous form Optimal Control Problem Consider the continuous-time constrained optimal control problem in the Bolza form min J = ˆΦ(x(t tb b )) + Φ(x(t), u(t))dt (1a) x(t),u(t) t a subject to x(t a ) = x d dt g( x(t) ) = f(x(t), u(t)), t [t a, t b ], u(t) U(t) (1b) (1c) (1d) x(t) R nx is the state vector and u(t) R nu is the control vector. The time interval I = [t a, t b ] as well as the initial state, x, are assumed to be fixed. 7 / 23
9 Path constraints Optimal Control Problem Path constraints η(x(t), u(t)) (2) are included as soft constraints using the following smooth approximation χ i (x(t), u(t)) = 1 ( ) η i (x(t), u(t)) β 2 i η i (x(t), u(t) (3) to the exact penalty function max(, η i (x(t))) for i {1,..., n η }.With this approximation of the path constraints, the resulting stage cost, Φ(x(t), u(t)), used in (11) consist of the inherent stage cost, Φ(x(t), u(t)), and terms penalizing violation of the path constraints (2) Φ(x, u) = Φ(x, u) + χ(x, u) 1,Q χ(x, u) 2 2,Q 2 (4) 8 / 23
10 Optimal Control Problem Single Shooting Discretization We introduce the function { ψ({u k } N 1 k=, x ) = J = tb t a Φ(x(t), u(t))dt + ˆΦ(x(t b )) : x(t ) = x, d dt g(x(t)) = f(x(t), u(t)), t a t t b, } u(t) = u k, t k t < t k+1, k N =,.., N 1 such that (1) can be approximated with the finite dimensional constrained optimization problem min ψ = ψ(y, x ) (6a) y:={u k } N 1 k= s.t. u min u k u max k N (6b) (5) u min u k u max k N (6c) c k (u k ) k N (6d) 9 / 23
11 Optimal Control Problem Sequential Quadratic Programming We solve the NLP (6) iteratively improving a given estimate y i of the solution by y i+1 = y i + α i p i (7) where α i ( < α 1) is determined by a linesearch (LS) strategy based on Powell s exact l 1 -merit function. The search direction p i is given by solving the KKT solution (p i, λ i, µ i ) of a quadratic approximation to (6) 1 min p 2 p H i p + ψ(y i ) p s.t h(y i ) p = h(y i ) c(y i ) c(y i ) (8) where H i R n n is an approximation for the Hessian 2 yl of the lagrangian function L(y, λ, µ) = ψ(y) λh(y) µ c(y) which starting from an initial estimate H, is updated after every step using BFGS. 1 / 23
12 ESDIRK integration methods Runge-Kutta ESDIRK Methods We use an embedded ESDIRK method c 2 a 21 γ c 3 a 31 a 32 γ b 1 b 2 b 3 γ x n+1 b 1 b 2 b 3 γ ˆx n+1 ˆb1 ˆb2 ˆb3 ˆbs 1 Solve implicit system T i = t n + h n c i, g(x i ) = g(x n ) + h n 2 Compute x n+1 = X s i 2,..., s s a ij f(t j, X j, u) j=1 3 Compute the error/tolerance ratio e n+1 = g(x n+1 ) g(ˆx n+1 ) s = h n (b j ˆb j )f(t j, X j, u) j=1 r n+1 = 1 e n+1 nx atol + g(x n+1 ) rtol 2 11 / 23
13 ESDIRK integration methods Temporal step size controller performance (after Völcker 21) 12 / 23
14 Continuous Adjoint Method Proposition (Gradients based on Continuous Adjoints) Consider the function ψ = ψ({u k } N 1 k= ; x ) defined by (5). The gradients, ψ/ u k, may be computed as ψ tk+1 ( ) Φ f = λt dt k =, 1,..., N 1 (9) u k t k u u in which x(t) is computed by solution of (1b)-(1c) and λ(t) is computed by solution of the adjoint equations dλ T g f + λt dt x x Φ x = ˆΦ x (x(t b)) + λ T (t b ) g x (x(t b)) = (1a) (1b) Remember that the dynamic model is given as d dt g(x(t)) = f(x(t), u(t)) 13 / 23
15 Production Optimization for a Conventional Oil Field Test case for waterflooding optimization squared reservoir of size 45m 45m 1m uniform cartesian grid of 25x25x1 grid blocks no flow boundaries, 4 injectors and 1 producer (rate controlled) We maximize an economic value for different discount factors b,.6,.12 min J(t b) = NPV(t b ) = x(t),u(t) tb t a Φ(x(t), u(t))dt 1 Φ = (1 + b) t/365 (r o (1 f w,j ) f w,j r w ) q j (t) j P where f w = λ w /(λ w + λ o ), λ i = ρ i kk ri /µ i, i {w, o} (11) k min :.24 Darcy, k max : Darcy log 1 (K) (Darcy) / 23
16 Production Optimization for a Conventional Oil Field Constraints The manipulated variable at time period k N is u k = {{q w,i,k } i I, {q i,k } i P } (12) with I being the set of injectors and P being the set of producers. q w,i,k q i,k injection rate (m 3 /day) of water at injector i I total flow rate (m 3 /day) at producer i P Bound constraints q w,i,k q max i I, k N (13a) q i,k q max i P, k N (13b) Rate constraints q i,k q i,k 1 5 i I P, k N (14a) q w,i,k q w,i,k 1 5 i I, k N (14b) 15 / 23
17 Production Optimization for a Conventional Oil Field Constraints (2) voidage replacement constraint q i,k = q w,i,k = q i,k i I i I i P k N (15) total injection constraint q w,i,k = q max k N (16) i I We set q max = 1 m 3 /day, t b = 427 days, T s = 35 days hence N = 122 periods. Injection of 1.5 pore volume during operation of the reservoir We consider as a reference case a fixed water injection of 1/4 = 25 m 3 /day from each injector. The prediction horizon t b is optimal in the reference case 16 / 23
18 Production Optimization for a Conventional Oil Field Optimal solution TIME: 15 (Day) TIME: 2135 (Day) TIME: 15 (Day) TIME: 2135 (Day) y x TIME: 322 (Day) y x TIME: 427 (Day) y x TIME: 322 (Day) y x TIME: 427 (Day) y x y x y x y x (a) Optimal solution (b = ). (b) Reference solution. Oil saturations at different times for the optimal solution and the reference solution. 17 / 23
19 Production Optimization for a Conventional Oil Field Cumulative oil and water production for different discount factors CUMULATIVE PRODUCTION (m 3 ) x opt oil ref oil opt water 2.5 ref water CUMULATIVE PRODUCTION (m 3 ) x opt oil ref oil opt water 2.5 ref water CUMULATIVE PRODUCTION (m 3 ) x opt oil ref oil opt water 2.5 ref water TIME (DAY) TIME (DAY) TIME (DAY) (a) Discount factor b =. (b) Discount factor b =.6. (c) Discount factor b =.12. Cumulative oil and water productions for different discount factors, b. 18 / 23
20 Production Optimization for a Conventional Oil Field NPV, Water cut, Water fraction Million dollars opt. b= ref. b= opt. b=.6 ref. b=.6 opt. b=.12 ref. b= opt. b= opt. b=.6 opt. b=.12 reference opt. b= opt. b=.6 opt. b=.12 reference days (a) NPV days (b) Water cut days (c) Water fraction (kg water/kg fluid). The net present value (NPV), water cut (accumulated water production per produced fluid), and the water fraction as function of time for the scenarios considered. 19 / 23
21 Production Optimization for a Conventional Oil Field Optimal input trajectories injector 3 (m 3 /day) injector 1 (m 3 /day) time t (Days) 1 5 b= b=.6 b=.12 reference time t (Days) injector 4 (m 3 /day) injector 2 (m 3 /day) time t (Days) time t (Days) Optimal water injection rates for different discount factors, b. 2 / 23
22 Production Optimization for a Conventional Oil Field Improvement table Table: Key indicators for the optimized cases. Improvements are compared to the base case. b NPV NPV Cum. Oil Oil Cum. water Water 1 6 USD % 1 5 m 3 % 1 5 m 3 % b Oil Rec. factor Oil Rec. factor % %-point / 23
23 Conclusions Conclusions A novel algorithm for large scale optimal control based on a novel formulation of the differential equations an ESDIRK method for integration of differential equations the continuous adjoint method for gradient computation the SQP method for optimization the single shooting principle This algorithm is applied for production optimization of oil reservoirs. For this field, optimal control improves the NPV by 8.7%. Optimal control and nonlinear model predictive control can potentially have a very big impact in oil reservoir management. 22 / 23
24 Acknowledgement Conclusions The Center for Energy Resources Engineering Consortium The Danish Research Council for Technology and Production Sciences, FTP Grant no / 23
Oil Reservoir Production Optimization using Optimal Control
Downloaded from orbit.dtu.dk on: Jun 27, 218 Oil Reservoir Production Optimization using Optimal Control Völcker, Carsten; Jørgensen, John Bagterp; Stenby, Erling Halfdan Published in: I E E E Conference
More informationAccelerating interior point methods with GPUs for smart grid systems
Downloaded from orbit.dtu.dk on: Dec 18, 2017 Accelerating interior point methods with GPUs for smart grid systems Gade-Nielsen, Nicolai Fog Publication date: 2011 Document Version Publisher's PDF, also
More informationOil Reservoir Production Optimization using Single Shooting and ESDIRK Methods
Downloaded from orbit.dtu.dk on: Jun 7, 8 Oil Reservoir Production Optimization using Single Shooting and ESDIRK Methods Capolei, Andrea; Völcker, Carsten; Frdendall, Jan; Jørgensen, John Bagterp Published
More informationBenchmarking of optimization methods for topology optimization problems
Downloaded from orbit.dtu.dk on: Feb, 18 Benchmarking of optimization methods for topology optimization problems Rojas Labanda, Susana; Stolpe, Mathias Publication date: 14 Document Version Peer reviewed
More informationReducing Uncertainty of Near-shore wind resource Estimates (RUNE) using wind lidars and mesoscale models
Downloaded from orbit.dtu.dk on: Dec 16, 2018 Reducing Uncertainty of Near-shore wind resource Estimates (RUNE) using wind lidars and mesoscale models Floors, Rogier Ralph; Vasiljevic, Nikola; Lea, Guillaume;
More informationSingle Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir
Technical Universit of Denmark, Kgs Lngb, Denmark Januar 5-7, Single Shooting and ESDIRK Methods for adjoint-based optimization of an oil reservoir Andrea Capolei Carsten Völcker Jan Frdendall John Bagterp
More informationA Trust-region-based Sequential Quadratic Programming Algorithm
Downloaded from orbit.dtu.dk on: Oct 19, 2018 A Trust-region-based Sequential Quadratic Programming Algorithm Henriksen, Lars Christian; Poulsen, Niels Kjølstad Publication date: 2010 Document Version
More informationAn Equivalent Source Method for Modelling the Lithospheric Magnetic Field Using Satellite and Airborne Magnetic Data
Downloaded from orbit.dtu.dk on: Oct 03, 2018 An Equivalent Source Method for Modelling the Lithospheric Magnetic Field Using Satellite and Airborne Magnetic Data Kother, Livia Kathleen; D. Hammer, Magnus;
More informationDynamic Asset Allocation - Identifying Regime Shifts in Financial Time Series to Build Robust Portfolios
Downloaded from orbit.dtu.dk on: Jan 22, 2019 Dynamic Asset Allocation - Identifying Regime Shifts in Financial Time Series to Build Robust Portfolios Nystrup, Peter Publication date: 2018 Document Version
More informationA Note on Powers in Finite Fields
Downloaded from orbit.dtu.dk on: Jul 11, 2018 A Note on Powers in Finite Fields Aabrandt, Andreas; Hansen, Vagn Lundsgaard Published in: International Journal of Mathematical Education in Science and Technology
More informationMatrix representation of a Neural Network
Downloaded from orbit.dtu.dk on: May 01, 2018 Matrix representation of a Neural Network Christensen, Bjørn Klint Publication date: 2003 Document Version Publisher's PDF, also known as Version of record
More informationA Mean-Variance Objective for Robust Production Optimization in Uncertain Geological Scenarios
A Mean-Variance Objective for Robust Production Optimization in Uncertain Geological Scenarios Andrea Capolei a, Eka Suwartadi b, Bjarne Foss b, John Bagterp Jørgensen a, a Department of Applied Mathematics
More informationKommerciel arbejde med WAsP
Downloaded from orbit.dtu.dk on: Dec 19, 2017 Kommerciel arbejde med WAsP Mortensen, Niels Gylling Publication date: 2002 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA): Mortensen,
More informationGlobal Wind Atlas validation and uncertainty
Downloaded from orbit.dtu.dk on: Nov 26, 20 Global Wind Atlas validation and uncertainty Mortensen, Niels Gylling; Davis, Neil; Badger, Jake; Hahmann, Andrea N. Publication date: 20 Document Version Publisher's
More informationSimulating wind energy resources with mesoscale models: Intercomparison of stateof-the-art
Downloaded from orbit.dtu.dk on: Nov 01, 2018 Simulating wind energy resources with mesoscale models: Intercomparison of stateof-the-art models Olsen, Bjarke Tobias; Hahmann, Andrea N.; Sempreviva, Anna
More informationValidation and comparison of numerical wind atlas methods: the South African example
Downloaded from orbit.dtu.dk on: Jul 18, 2018 Validation and comparison of numerical wind atlas methods: the South African example Hahmann, Andrea N.; Badger, Jake; Volker, Patrick; Nielsen, Joakim Refslund;
More informationThe dipole moment of a wall-charged void in a bulk dielectric
Downloaded from orbit.dtu.dk on: Dec 17, 2017 The dipole moment of a wall-charged void in a bulk dielectric McAllister, Iain Wilson Published in: Proceedings of the Conference on Electrical Insulation
More informationBattling Bluetongue and Schmallenberg virus Local scale behavior of transmitting vectors
Downloaded from orbit.dtu.dk on: Sep 10, 2018 Local scale behavior of transmitting vectors Stockmarr, Anders; Kirkeby, Carsten Thure; Bødker, Rene Publication date: 2015 Link back to DTU Orbit Citation
More informationModelling Salmonella transfer during grinding of meat
Downloaded from orbit.dtu.dk on: Nov 24, 2018 Modelling Salmonella transfer during grinding of meat Hansen, Tina Beck Publication date: 2017 Document Version Publisher's PDF, also known as Version of record
More informationLidar calibration What s the problem?
Downloaded from orbit.dtu.dk on: Feb 05, 2018 Lidar calibration What s the problem? Courtney, Michael Publication date: 2015 Document Version Peer reviewed version Link back to DTU Orbit Citation (APA):
More informationPrediction of airfoil performance at high Reynolds numbers.
Downloaded from orbit.dtu.dk on: Nov 04, 2018 Prediction of airfoil performance at high Reynolds numbers. Sørensen, Niels N.; Zahle, Frederik; Michelsen, Jess Publication date: 2014 Document Version Publisher's
More informationOptimizing Reliability using BECAS - an Open-Source Cross Section Analysis Tool
Downloaded from orbit.dtu.dk on: Dec 20, 2017 Optimizing Reliability using BECAS - an Open-Source Cross Section Analysis Tool Bitsche, Robert; Blasques, José Pedro Albergaria Amaral Publication date: 2012
More informationMultiple Scenario Inversion of Reflection Seismic Prestack Data
Downloaded from orbit.dtu.dk on: Nov 28, 2018 Multiple Scenario Inversion of Reflection Seismic Prestack Data Hansen, Thomas Mejer; Cordua, Knud Skou; Mosegaard, Klaus Publication date: 2013 Document Version
More informationDesign possibilities for impact noise insulation in lightweight floors A parameter study
Downloaded from orbit.dtu.dk on: Dec 23, 218 Design possibilities for impact noise insulation in lightweight floors A parameter study Brunskog, Jonas; Hammer, Per Published in: Euronoise Publication date:
More informationComparisons of winds from satellite SAR, WRF and SCADA to characterize coastal gradients and wind farm wake effects at Anholt wind farm
Downloaded from orbit.dtu.dk on: Dec 10, 2018 Comparisons of winds from satellite SAR, WRF and SCADA to characterize coastal gradients and wind farm wake effects at Anholt wind farm Hasager, Charlotte
More informationValidation of Boundary Layer Winds from WRF Mesoscale Forecasts over Denmark
Downloaded from orbit.dtu.dk on: Dec 14, 2018 Validation of Boundary Layer Winds from WRF Mesoscale Forecasts over Denmark Hahmann, Andrea N.; Pena Diaz, Alfredo Published in: EWEC 2010 Proceedings online
More informationDynamic Effects of Diabatization in Distillation Columns
Downloaded from orbit.dtu.dk on: Dec 27, 2018 Dynamic Effects of Diabatization in Distillation Columns Bisgaard, Thomas Publication date: 2012 Document Version Publisher's PDF, also known as Version of
More informationImpact of the interfaces for wind and wave modeling - interpretation using COAWST, SAR and point measurements
Downloaded from orbit.dtu.dk on: Oct 21, 2018 Impact of the interfaces for wind and wave modeling - interpretation using COAWST, SAR and point measurements Larsén, Xiaoli Guo; Du, Jianting; Bolanos, Rodolfo;
More informationNumerical modeling of the conduction and radiation heating in precision glass moulding
Downloaded from orbit.dtu.dk on: May 02, 2018 Numerical modeling of the conduction and radiation heating in precision glass moulding Sarhadi, Ali; Hattel, Jesper Henri; Hansen, Hans Nørgaard; Tutum, Cem
More informationApplication of mesoscale models with wind farm parametrisations in EERA-DTOC
Downloaded from orbit.dtu.dk on: Dec 21, 2017 Application of mesoscale models with wind farm parametrisations in EERA-DTOC Volker, Patrick; Badger, Jake; Hahmann, Andrea N.; Hansen, S.; Badger, Merete;
More informationRoom Allocation Optimisation at the Technical University of Denmark
Downloaded from orbit.dtu.dk on: Mar 13, 2018 Room Allocation Optimisation at the Technical University of Denmark Bagger, Niels-Christian Fink; Larsen, Jesper; Stidsen, Thomas Jacob Riis Published in:
More informationConceptual design of a thorium supplied thermal molten salt wasteburner
Downloaded from orbit.dtu.dk on: Dec 20, 2017 Conceptual design of a thorium supplied thermal molten salt wasteburner Schönfeldt, Troels; Klinkby, Esben Bryndt; Klenø, K.H.; Boje, Peter; Eakes, C.; Pettersen,
More informationRadioactivity in the Risø District January-June 2014
Downloaded from orbit.dtu.dk on: Dec 20, 2017 Radioactivity in the Risø District January-June 2014 Nielsen, Sven Poul; Andersson, Kasper Grann; Miller, Arne Publication date: 2014 Document Version Publisher's
More informationWaterflooding optimization in uncertain geological scenarios
DOI 1.17/s1596-13-9371-1 ORIGINAL PAPER Waterflooding optimization in uncertain geological scenarios Andrea Capolei Eka Suwartadi Bjarne Foss John Bagterp Jørgensen Received: 21 March 213 / Accepted: 21
More informationOptimal acid digestion for multi-element analysis of different waste matrices
Downloaded from orbit.dtu.dk on: Sep 06, 2018 Optimal acid digestion for multi-element analysis of different waste matrices Götze, Ramona; Astrup, Thomas Fruergaard Publication date: 2014 Document Version
More informationDetermination of packaging induced 3D stress utilizing a piezocoefficient mapping device
Downloaded from orbit.dtu.dk on: Dec 15, 2018 Determination of packaging induced 3D stress utilizing a piezocoefficient mapping device Richter, Jacob; Hyldgård, A.; Birkelund, Karen; Arnoldus, Morten Berg;
More informationThe colpitts oscillator family
Downloaded from orbit.dtu.dk on: Oct 17, 2018 The colpitts oscillator family Lindberg, Erik; Murali, K.; Tamasevicius, A. Publication date: 2008 Document Version Publisher's PDF, also known as Version
More informationPlane Wave Medical Ultrasound Imaging Using Adaptive Beamforming
Downloaded from orbit.dtu.dk on: Jul 14, 2018 Plane Wave Medical Ultrasound Imaging Using Adaptive Beamforming Voxen, Iben Holfort; Gran, Fredrik; Jensen, Jørgen Arendt Published in: Proceedings of 5th
More informationAlkali Release from Typical Danish Aggregates to Potential ASR Reactive Concrete
Downloaded from orbit.dtu.dk on: Nov 30, 2018 Alkali Release from Typical Danish Aggregates to Potential ASR Reactive Concrete Thomsen, Hans Christian Brolin; Grelk, Bent; Barbosa, Ricardo Antonio; Hansen,
More informationBerøringsløs optisk måling af gassammensætning ved UV og IR spektroskopi
Downloaded from orbit.dtu.dk on: Dec 21 2017 Berøringsløs optisk måling af gassammensætning ved UV og IR spektroskopi Clausen Sønnik Publication date: 2008 Document Version Publisher's PDF also known as
More informationExtreme sea levels and the assessment of future coastal flood risk
Downloaded from orbit.dtu.dk on: Dec 18, 2017 Extreme sea levels and the assessment of future coastal flood risk Nilsen, J. E. Ø. ; Sørensen, Carlo Sass; Dangendore, S. ; Andersson, H. ; Arns, A. ; Jensen,
More informationReflection of sound from finite-size plane and curved surfaces
Downloaded from orbit.dtu.dk on: Sep, 08 Reflection of sound from finite-size plane and curved surfaces Rindel, Jens Holger Published in: Journal of the Acoustical Society of America Publication date:
More informationThe Wien Bridge Oscillator Family
Downloaded from orbit.dtu.dk on: Dec 29, 207 The Wien Bridge Oscillator Family Lindberg, Erik Published in: Proceedings of the ICSES-06 Publication date: 2006 Link back to DTU Orbit Citation APA): Lindberg,
More informationRadioactivity in the Risø District July-December 2013
Downloaded from orbit.dtu.dk on: Jan 02, 2019 Radioactivity in the Risø District July-December 2013 Nielsen, Sven Poul; Andersson, Kasper Grann; Miller, Arne Publication date: 2014 Document Version Publisher's
More informationRealtime 3D stress measurement in curing epoxy packaging
Downloaded from orbit.dtu.dk on: Dec 17, 2017 Realtime 3D stress measurement in curing epoxy packaging Richter, Jacob; Hyldgård, A.; Birkelund, Karen; Hansen, Ole; Thomsen, Erik Vilain Published in: International
More informationSound absorption properties of a perforated plate and membrane ceiling element Nilsson, Anders C.; Rasmussen, Birgit
Aalborg Universitet Sound absorption properties of a perforated plate and membrane ceiling element Nilsson, Anders C.; Rasmussen, Birgit Published in: Proceedings of Inter-Noise 1983 Publication date:
More informationDiffusion of sulfuric acid in protective organic coatings
Downloaded from orbit.dtu.dk on: Nov 03, 2018 Diffusion of sulfuric acid in protective organic coatings Wang, Ting; Møller, Victor Buhl; Dam-Johansen, Kim; Frankær, Sarah M.; Kiil, Søren Publication date:
More informationAalborg Universitet. Land-use modelling by cellular automata Hansen, Henning Sten. Published in: NORDGI : Nordic Geographic Information
Aalborg Universitet Land-use modelling by cellular automata Hansen, Henning Sten Published in: NORDGI : Nordic Geographic Information Publication date: 2006 Document Version Publisher's PDF, also known
More informationA systematic methodology for controller tuning in wastewater treatment plants
Downloaded from orbit.dtu.dk on: Dec 2, 217 A systematic methodology for controller tuning in wastewater treatment plants Mauricio Iglesias, Miguel; Jørgensen, Sten Bay; Sin, Gürkan Publication date: 212
More informationApplication of the MCNPX-McStas interface for shielding calculations and guide design at ESS
Downloaded from orbit.dtu.dk on: Nov 22, 2017 Application of the MCNPX-McStas interface for shielding calculations and guide design at ESS Klinkby, Esben Bryndt; Willendrup, Peter Kjær; Bergbäck Knudsen,
More informationGeometry of power flows and convex-relaxed power flows in distribution networks with high penetration of renewables
Downloaded from orbit.dtu.dk on: Oct 15, 2018 Geometry of power flows and convex-relaxed power flows in distribution networks with high penetration of renewables Huang, Shaojun; Wu, Qiuwei; Zhao, Haoran;
More informationMeasurements of the angular distribution of diffuse irradiance
Downloaded from orbit.dtu.dk on: Nov 02, 2018 Measurements of the angular distribution of diffuse irradiance Nielsen, Elsabet Nomonde Noma; Nielsen, Kristian Pagh ; Dragsted, Janne; Furbo, Simon Published
More informationFeasibility of non-linear simulation for Field II using an angular spectrum approach
Downloaded from orbit.dtu.dk on: Aug 22, 218 Feasibility of non-linear simulation for using an angular spectrum approach Du, Yigang; Jensen, Jørgen Arendt Published in: 28 IEEE Ultrasonics Symposium Link
More informationAdvantages and Challenges of Superconducting Wind Turbine Generators
Downloaded from orbit.dtu.dk on: Apr 10, 2018 Advantages and Challenges of Superconducting Wind Turbine Generators Jensen, Bogi Bech; Mijatovic, Nenad; Abrahamsen, Asger Bech Publication date: 2012 Link
More informationGenerating the optimal magnetic field for magnetic refrigeration
Downloaded from orbit.dtu.dk on: Oct 17, 018 Generating the optimal magnetic field for magnetic refrigeration Bjørk, Rasmus; Insinga, Andrea Roberto; Smith, Anders; Bahl, Christian Published in: Proceedings
More informationHigher-order spectral modelling of the diffraction force around a vertical circular cylinder
Downloaded from orbit.dtu.dk on: Apr 10, 2018 Higher-order spectral modelling of the diffraction force around a vertical circular cylinder Bredmose, Henrik; Andersen, Søren Juhl Publication date: 2017
More informationA practical implementation of microphone free-field comparison calibration according to the standard IEC
Downloaded from orbit.dtu.dk on: Jun 08 2018 A practical implementation of microphone free-field comparison calibration according to the standard IEC 61094-8 Barrera Figueroa Salvador; Torras Rosell Antoni;
More informationA zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees
Downloaded from orbit.dtu.dk on: Sep 02, 2018 A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees Perrett, Thomas Published in: Discrete Mathematics Link to article, DOI:
More informationRobustness of a cross contamination model describing transfer of pathogens during grinding of meat
Downloaded from orbit.dtu.dk on: Jan 25, 2019 Robustness of a cross contamination model describing transfer of pathogens during grinding of meat Møller, Cleide Oliveira de Almeida; Sant'Ana, A. S.; Hansen,
More informationCrack Tip Flipping: A New Phenomenon yet to be Resolved in Ductile Plate Tearing
Downloaded from orbit.dtu.dk on: Jan 06, 2019 Crack Tip Flipping: A New Phenomenon yet to be Resolved in Ductile Plate Tearing Nielsen, Kim Lau Published in: Proceedings of the 30th Nordic Seminar on Computational
More informationOn the Einstein-Stern model of rotational heat capacities
Downloaded from orbit.dtu.dk on: Jan 06, 2018 On the Einstein-Stern model of rotational heat capacities Dahl, Jens Peder Published in: Journal of Chemical Physics Link to article, DOI: 10.1063/1.77766
More informationSpace charge fields in DC cables
Downloaded from orbit.dtu.dk on: Sep 25, 2018 Space charge fields in DC cables McAllister, Iain Wilson; Crichton - Fratrådt, George C; Pedersen, Aage Published in: Conference Record of the IEEE International
More informationIrregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope
Downloaded from orbit.dtu.dk on: Dec 04, 2017 Irregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope Schløer, Signe; Bredmose, Henrik; Bingham, Harry B. Published in:
More informationSolar radiation and thermal performance of solar collectors for Denmark
Downloaded from orbit.dtu.dk on: Feb 01, 2018 Solar radiation and thermal performance of solar collectors for Denmark Dragsted, Janne; Furbo, Simon Publication date: 2012 Document Version Publisher's PDF,
More informationValidity of PEC Approximation for On-Body Propagation
Downloaded from orbit.dtu.dk on: Nov, 208 Validity of PEC Approximation for On-Body Propagation Kammersgaard, Nikolaj Peter Brunvoll; Kvist, Søren Helstrup; Thaysen, Jesper; Jakobsen, Kaj Bjarne Published
More informationSteady State Comparisons HAWC2 v12.2 vs HAWCStab2 v2.12
Downloaded from orbit.dtu.dk on: Jan 29, 219 Steady State Comparisons v12.2 vs v2.12 Verelst, David Robert; Hansen, Morten Hartvig; Pirrung, Georg Publication date: 216 Document Version Publisher's PDF,
More informationOn numerical evaluation of two-dimensional phase integrals
Downloaded from orbit.dtu.dk on: Nov 28, 2018 On numerical evaluation of two-dimensional phase integrals Lessow, H.; Rusch, W.; Schjær-Jacobsen, Hans Published in: E E E Transactions on Antennas and Propagation
More informationPractical Implementations of Advanced Process Control for Linear Systems
Downloaded from orbitdtudk on: Jul 01, 2018 Practical Implementations of Advanced Process Control for Linear Systems Knudsen, Jørgen K H ; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp Published in:
More informationPotential solution for rain erosion of wind turbine blades
Downloaded from orbit.dtu.dk on: Jun 28, 2018 Potential solution for rain erosion of wind turbine blades Hasager, Charlotte Bay; Bech, Jakob Ilsted; Kusano, Yukihiro; Sjöholm, Mikael; Mikkelsen, Torben
More informationDevelopment of a Dainish infrastructure for spatial information (DAISI) Brande-Lavridsen, Hanne; Jensen, Bent Hulegaard
Aalborg Universitet Development of a Dainish infrastructure for spatial information (DAISI) Brande-Lavridsen, Hanne; Jensen, Bent Hulegaard Published in: NORDGI : Nordic Geographic Information Publication
More informationVindkraftmeteorologi - metoder, målinger og data, kort, WAsP, WaSPEngineering,
Downloaded from orbit.dtu.dk on: Dec 19, 2017 Vindkraftmeteorologi - metoder, målinger og data, kort, WAsP, WaSPEngineering, meso-scale metoder, prediction, vindatlasser worldwide, energiproduktionsberegninger,
More informationPhase Equilibrium in Amino Acid Salt Systems for CO2 Capture
Downloaded from orbit.dtu.dk on: Dec 22, 217 Phase Equilibrium in Amino Acid Salt Systems for CO2 Capture Sengeløv, Louise With; Thomsen, Kaj Publication date: 211 Document Version Early version, also
More informationWake decay constant for the infinite wind turbine array Application of asymptotic speed deficit concept to existing engineering wake model
Downloaded from orbit.dtu.dk on: Jul 22, 208 Wake decay constant for the infinite wind turbine array Application of asymptotic speed deficit concept to existing engineering wake model Rathmann, Ole Steen;
More informationAnalytical Studies of the Influence of Regional Groundwater Flow by on the Performance of Borehole Heat Exchangers
Analytical Studies of the Influence of Regional Groundwater Flow by on the Performance of Borehole Heat Exchangers Claesson, Johan; Hellström, Göran Published in: [Host publication title missing] Published:
More informationAdaptive Stepsize Control in Implicit Runge-Kutta Methods for Reservoir Simulation
Proceedings of the 9th International Symposium on Dynamics and Control of Process Systems (DYCOPS 21), Leuven, Belgium, July 5-7, 21 Mayuresh Kothare, Moses Tade, Alain Vande Wouwer, Ilse Smets (Eds.)
More informationProving in the Isabelle Proof Assistant that the Set of Real Numbers is not Countable
Downloaded from orbit.dtu.dk on: Mar 18, 2019 Proving in the Isabelle Proof Assistant that the Set of Real Numbers is not Countable Villadsen, Jørgen Publication date: 2018 Document Version Publisher's
More informationNeutronics calculations for the ITER Collective Thomson Scattering Diagnostics
Downloaded from orbit.dtu.dk on: Sep 04, 2018 Neutronics calculations for the ITER Collective Thomson Scattering Diagnostics Nonbøl, Erik; Klinkby, Esben Bryndt; Lauritzen, Bent; Santos, R. Publication
More informationExposure Buildup Factors for Heavy Metal Oxide Glass: A Radiation Shield
Downloaded from orbit.dtu.dk on: Jan 16, 2019 Exposure Buildup Factors for Heavy Metal Oxide Glass: A Radiation Shield Manonara, S. R.; Hanagodimath, S. M.; Gerward, Leif; Mittal, K. C. Published in: Journal
More informationDesign of Robust AMB Controllers for Rotors Subjected to Varying and Uncertain Seal Forces
Downloaded from orbit.dtu.dk on: Nov 9, 218 Design of Robust AMB Controllers for Rotors Subjected to Varying and Uncertain Seal Forces Lauridsen, Jonas Skjødt; Santos, Ilmar Published in: Mechanical Engineering
More informationStrongly 2-connected orientations of graphs
Downloaded from orbit.dtu.dk on: Jul 04, 2018 Strongly 2-connected orientations of graphs Thomassen, Carsten Published in: Journal of Combinatorial Theory. Series B Link to article, DOI: 10.1016/j.jctb.2014.07.004
More informationAalborg Universitet. Publication date: Document Version Publisher's PDF, also known as Version of record
Aalborg Universitet Experimental Investigation of the Influence of Different Flooring Emissivity on Night- Time Cooling using Displacement Ventilation Dreau, Jerome Le; Karlsen, Line Røseth; Litewnicki,
More informationA Procedure for Classification of Cup-Anemometers
Downloaded from orbit.dtu.dk on: Dec, 17 A Procedure for Classification of Cup-Anemometers Friis Pedersen, Troels; Paulsen, Uwe Schmidt Published in: Proceedings of EWEC 97 Publication date: 1997 Link
More informationRadiometric Measurements of Environmental Radioactivity Beta Counting, Alpha and Gamma Spectrometry
Downloaded from orbit.dtu.dk on: Jan 31, 2018 Radiometric Measurements of Environmental Radioactivity Beta Counting, Alpha and Gamma Spectrometry Nielsen, Sven Poul Publication date: 2013 Link back to
More informationA numerical study of vortex-induced vibrations (viv) in an elastic cantilever
A numerical study of vortex-induced vibrations (viv) in an elastic cantilever Lorentzon, Johan; Austrell, Per Erik; Szász, Robert-Zoltán; Revstedt, Johan 2009 Link to publication Citation for published
More informationApplication of the wind atlas for Egypt
Downloaded from orbit.dtu.dk on: Dec 19, 2017 Application of the wind atlas for Egypt Mortensen, Niels Gylling Publication date: 2005 Document Version Peer reviewed version Link back to DTU Orbit Citation
More informationAalborg Universitet. Lecture 14 - Introduction to experimental work Kramer, Morten Mejlhede. Publication date: 2015
Aalborg Universitet Lecture 14 - Introduction to experimental work Kramer, Morten Mejlhede Publication date: 2015 Document Version Publisher's PDF, also known as Version of record Link to publication from
More informationMulti (building)physics modeling
Multi (building)physics modeling van Schijndel, A.W.M. Published: 01/01/2010 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check
More informationTransmuted distributions and extrema of random number of variables
Transmuted distributions and extrema of random number of variables Kozubowski, Tomasz J.; Podgórski, Krzysztof Published: 2016-01-01 Link to publication Citation for published version (APA): Kozubowski,
More informationA comparison study of the two-bladed partial pitch turbine during normal operation and an extreme gust conditions
Downloaded from orbit.dtu.dk on: Jul 12, 2018 A comparison study of the two-bladed partial pitch turbine during normal operation and an extreme gust conditions Kim, Taeseong; Pedersen, Mads Mølgaard; Larsen,
More informationGraphs with given diameter maximizing the spectral radius van Dam, Edwin
Tilburg University Graphs with given diameter maximizing the spectral radius van Dam, Edwin Published in: Linear Algebra and its Applications Publication date: 2007 Link to publication Citation for published
More informationReflection and absorption coefficients for use in room acoustic simulations
Downloaded from orbit.dtu.dk on: May 1, 018 Reflection and absorption coefficients for use in room acoustic simulations Jeong, Cheol-Ho Published in: Proceedings of Spring Meeting of the Acoustical Society
More informationGIS Readiness Survey 2014 Schrøder, Anne Lise; Hvingel, Line Træholt; Hansen, Henning Sten; Skovdal, Jesper Høi
Aalborg Universitet GIS Readiness Survey 2014 Schrøder, Anne Lise; Hvingel, Line Træholt; Hansen, Henning Sten; Skovdal, Jesper Høi Published in: Geoforum Perspektiv DOI (link to publication from Publisher):
More informationAnalysis of Biaxially Stressed Bridge Deck Plates
Downloaded from orbit.dtu.dk on: Dec 14, 2018 Analysis of Biaxially Stressed Bridge Deck Plates Jönsson, Jeppe; Bondum, Tommi Højer Published in: Proceedings of Nordic Steel Construction Conference 2012
More informationGeneralized Nonlinear Wave Equation in Frequency Domain
Downloaded from orbit.dtu.dk on: Dec 03, 208 Generalized Nonlinear Wave Equation in Frequency Domain Guo, Hairun; Zeng, Xianglong; Bache, Morten Publication date: 203 Document Version Early version, also
More informationUnknown input observer based scheme for detecting faults in a wind turbine converter Odgaard, Peter Fogh; Stoustrup, Jakob
Aalborg Universitet Unknown input observer based scheme for detecting faults in a wind turbine converter Odgaard, Peter Fogh; Stoustrup, Jakob Published in: Elsevier IFAC Publications / IFAC Proceedings
More informationDetermination of the minimum size of a statistical representative volume element from a fibre-reinforced composite based on point pattern statistics
Downloaded from orbit.dtu.dk on: Dec 04, 2018 Determination of the minimum size of a statistical representative volume element from a fibre-reinforced composite based on point pattern statistics Hansen,
More informationComparison between Multitemporal and Polarimetric SAR Data for Land Cover Classification
Downloaded from orbit.dtu.dk on: Sep 19, 2018 Comparison between Multitemporal and Polarimetric SAR Data for Land Cover Classification Skriver, Henning Published in: Geoscience and Remote Sensing Symposium,
More informationThe new worldwide microscale wind resource assessment data on IRENA s Global Atlas. The EUDP Global Wind Atlas
Downloaded from orbit.dtu.dk on: Dec 25, 2017 The new worldwide microscale wind resource assessment data on IRENA s Global Atlas. The EUDP Global Wind Atlas Badger, Jake; Davis, Neil; Hahmann, Andrea N.;
More informationSurface composition of ordered alloys: An off-stoichiometric effect
Downloaded from orbit.dtu.dk on: Dec 17, 2017 Surface composition of ordered alloys: An off-stoichiometric effect Ruban, Andrei Published in: Physical Review B (Condensed Matter and Materials Physics)
More informationAalborg Universitet. The number of independent sets in unicyclic graphs Pedersen, Anders Sune; Vestergaard, Preben Dahl. Publication date: 2005
Aalborg Universitet The number of independent sets in unicyclic graphs Pedersen, Anders Sune; Vestergaard, Preben Dahl Publication date: 2005 Document Version Publisher's PDF, also known as Version of
More information