Topology Optimization of an Actively Cooled Electronics Section for Downhole Tools
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1 Topology Optimization of an Actively Cooled Electronics Section for Downhole Tools S. Soprani*, J. H. K. Haertel, B. S. Lazarov, O. Sigmund, K. Engelbrecht
2 Table of contents Introduction Method and COMSOL model Analysis of the results Choice of the final design Conclusions November October 2014
3 Introduction Topology Optimization: mathematical approach that optimizes the material layout within a given design space and boundary conditions November October 2014
4 Introduction Downhole Tool: cylindrical robotic tool used to increase or restore the production of oil and gas wells (well cleaning, pipe cutting, installation of valves). I feed Q TEC - Thermoelectric (Peltier) cooler: upgrade the maximum operating temperature from 175 C to 200 C November October 2014
5 Problem formulation Metallic housing (o.d. 80mm) Optimizable chassis TEC Heat spreader + soft thermal pad Design Criteria: Use aluminum to enhance Axial thesection cooler s of heat the downhole rejection tool s the implemented well. geometry. Structural chassis (o.d. 60mm) T-sensitive electronics (PCB) Use thermal insulation to protect the cooled electronics. Optimize the distribution of aluminum-thermal insulation within the chassis Minimize the average PCB temperature November October 2014
6 Governing equations Heat conduction k T = Q source (1) Modified heat conduction JST k T = Q JouleHeating (2) Convective heat flux (T fluid, h) TEC feed current I feed Boundary conditions Thermal insulation Thermal (contact) resistance Heat source (1 W) November October 2014
7 Topology Optimization Implementation (SIMP method) minimize: f obj T, ρ design = 1 A PCB Ω PCB T dω PCB (3) constraints: 0 ρ design 1 (4) ρ design Density filter f(r) ρ Projection function p(η,β) ρ interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
8 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) p(η,β = 1) p(η,β = 8) I feed = 4 A h = 50 Wm -2 K November October 2014
9 Simulation results T fluid = 200 C h = 25, 50, 100, 500 Wm -2 K -1 I feed = 1, 2, 3, 4 A ρ optimized distribution I feed = 2 A h = 100 Wm -2 K -1 ρ optimized distribution I feed = 4 A h = 50 Wm -2 K -1 Aluminum Insulator Design 1 Design 2 Low I feed / High h High I feed / Low h Aluminum pad length grows with I feed and decreases with h. Aluminum layer thickness grows with I feed and decreases with h November October 2014
10 Choice of the final design Axial section of the finally chosen design. h (Wm -2 K -1 ) Opt - 1A T PCB ( C) Design - 1A T PCB ( C) ΔT (K) h (Wm -2 K -1 ) Opt - 2A T PCB ( C) Design - 2A T PCB ( C) ΔT (K) h (Wm -2 K -1 ) Opt - 3A T PCB ( C) Design - 3A T PCB ( C) ΔT (K) h (Wm -2 K -1 ) Opt - 4A T PCB ( C) Design - 4A T PCB ( C) ΔT (K) ΔT = T PCB,design - T PCB,Opt November October 2014
11 Conclusions The topology optimization (SIMP) approach supported the development of a chassis for actively cooled downhole electronics. Two main design concepts were found and analyzed. A parametric study evaluated the sensitivity of the optimized topologies to the boundary conditions. The final design was defined according to the optimization results and proved to perform very closely to the optimized systems November October 2014
12 Thank you for the attention November October 2014
13 Extra slides November October 2014
14 COMSOL Multiphysics representation of the longitudinal section of the downhole tool (left side) and particular of the TEC device with the two plates and the semiconducting material layer highlighted in blue (right side) November October 2014
15 Governing equations Heat conduction k T = Q source (1) Modified heat conduction JST k T = Q JouleHeating (2) Convective heat flux (T fluid, h) TEC feed current I feed Boundary conditions Thermal insulation Thermal (contact) resistance Heat source (1 W) November October 2014
16 Cross-Check analysis Evaluate the performance of the optimized designs at different boundary conditions The optimization process is negligibly sensitive to the well fluid convection regime, at a given I feed. The TEC feed current influences significantly the optimized design. But we can control it! An optimal feed current I feed,opt was found. I feed,opt varies with h and ranges between 2 and 3 A November October 2014
17 R vs. well fluid convective coefficient, for different TEC feed currents. Different symbols refer to the different optimized design concepts. = Design 1, = Design 2. HTS electronics temperature vs. well fluid convective coefficient for four different systems, optimized for I feed = 2 A and h = 25, 50, 100 and 500 Wm -2 K November October 2014
18 HTS electronics temperature vs. TEC feed current for four different systems, optimized for I feed h = 25 Wm -2 K -1 (left side) and 50 Wm -2 K -1 (right side). = 1, 2, 3 and 4 A, and November October 2014
19 Characteristic curve of the finally designed electronics unit. The plot reports the performance of the cooling system as HTS electronics temperature vs. Convective coefficient and TEC feed current. The minimum HTS electronics temperatures for each operating condition are highlighted with a red line November October 2014
20 J = NI feed A tot = NI feed A tot NA leg = I feed A BiTe = J x NA leg A leg A BiTe tot J S = J S S = S x BiTe k A air A BiTe = k air + k A BiTe = k tot A air (1 x BiTe ) + k BiTe x BiTe tot σ = σ BiTe x BiTe + σ air x air = σ BiTe x BiTe (Gordon 2002) November October 2014
21 Topology Optimization Implementation (SIMP method) minimize: f obj T, ρ design = 1 A PCB Ω PCB T dω PCB (3) constraints: 0 ρ design 1 (4) r T, ρ design = 0 (5) density filter: r 2 2 ρ + ρ = ρ design (Lazarov 2011) (6) projection function: ρ i = tanh βη +tanh(β( ρ i η) tanh βη +tanh β 1 η (Wang 2011) (7) interpolation function: k SIMP = k ins + k Al k ins ρ p (8) November October 2014
22 Topology Optimization Implementation (SIMP method) projection function: ρ i = tanh βη +tanh(β( ρ i η) tanh βη +tanh β 1 η (Wang 2011) (7) November October 2014
23 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
24 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
25 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
26 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
27 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
28 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
29 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
30 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) November October 2014
31 Simulation results interpolation function: k SIMP = k ins + k Al k ins ρ p (5) p(η,β = 1) p(η,β = 8) November October 2014
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