681.51: (043) 6D Prof. Dr. hab. inz. Waldemar Wójcik
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1 : (043) 6D (PhD),.. Prof. Dr. hab. inz. (, ) Waldemar Wójcik, 2017
2 Matlab ( ) ( ) COMSOL Multiphysics
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8 SCADA, ,,.,.., : ( ) ( ) ;, ; ; ;, ; (),, ( ) ;, ;, ;... ( ) Comsol.., 8
9 ,,,,,. : Matlab, Comsol Multiphysics. : ; ( ) ; ; ; ;. Comsol; ( ) ; ; : ; ( ) ( ), ( ) ( ); Comsol Multiphysics; ( ) ; ; 9
10 :, ( ) ( )..,.,. :, , : «.», 3927/ 4, : ;,. ; Comsol Multiphysics; ;.. 10
11 - (, 2015); The 15th International Scientific Conference Information Technologies and Management ( Riga, 2017); - ( 80-. ) (, 2017); Lubelskie Dni Nauki i Biznesu. Pod patronatem honorowym Polskiego stowarzyszenia tomografii procesowej I Komitetu elektrotechniki polskiej akademii nauk. Warsztaty doktoranckie. WD2016. Science conference (Lublin, 2016); Environmental engineering V : proceedings of the fifth National Congress of Environmental Engineering, (Lublin, Poland, 2016) , 5, 2 (, ), 3,, 1 -, 3, Scopus. :,,, , 67 2.,,,.,,,. : «-»; ;,.. -. MATLAB.., 11
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24 .,.,,, (.., : )...,,,,,,,,.., [24-30]., :..,..,..,..,..,..,..,..,..,..,..,..,..,. - University of Texas at Austin (P. M. Bommer, R. S. Schechter, L. W. Lake. [24-26]), US Bureau of Mines, Minneapolis (R. D. Schmidt, S. E. Follin. [28-30]), Research Institute of University of Petroleum Minerals, Saudi Arabia.,,. ( 2.1).,., -... ( )..,.,.. 24
25 ,.,,,.,,....,.,,,,.,,.,.. 1.4,,,.,,,. 25
26 2. 2.1,.., [19]., -,,.,.,,,, [20].,,.,,,., [21-22]..,,, (5) 1. (4),. ( ) (1) ( ),,. -, (3)., 26
27 . ( ). (2). ( ).. 2. Q Pо, Qо H H H Q т 4 Q Qо ,8 0,01. : dh W dt i 27 Q i Q i (2.1)
28 , H i ( ); W (м ); Q i (м / ); Q i (м / ); Q i = Q i, H = H i. : P i H g (2.2) i : = H. + H (2.3), H. i-.., : P i Q i Ri ( H i ) (2.4), 1 P i Q i 2 Ri ( H i ) (2.5), 1 P i Q i 3 Ri ( H i ) (2.6) : ( H i ) = + H i + H i (2.7), ( H i ) - i-. 28
29 . - : = (2.8), ( );, (м /ч);,,,. l ; : H = + м g (2.9) = H + H g (2.10), 0 l l- ( ); H ( ); м. ( ); ( );
30 .,,,, ( ),,, [31]., :,,., : Pp. i R p. i Q i (2.10), R p. i -. P. P P (2.11) p i i l, ( );. 6., : 6 = = (2.12) :.., H < H.., (2.13) =,,.. i- ; H.. i- ; j-. 30
31 (2.2)-(2.12) «- -». 2.2,,.,.,. (,,, -..) : ( ),.. [].,, : ( ) :,,..,. ( )., (, )., - : ( ), ( ).. 31
32 ,,. : [ ] = d + d Р [ ] + d [ ] + d Р. [ ] (2.14), ; d, d, d, d. : = Р [ ] = Ф Р [ ] (2.15), Ф Р [ ]. (2.14) ( ). 3% 5%.,., :,
33 З - (1) (2),..,,. (3). - (5), (4). - (6). 6 ВУ 5 4 H Q ,, : dh W dt (2.16), H ( ); (м ); Q (м / ); Q Q 33
34 Q (м / ); Q Q, H k = H, H k -. : P H g (2.17) : Q = ` (2.18),. H.,. : Q = b + b Q + b Q (2.19) [ b i ] (H ). H (2.18) (2.19) Q. : 2 ( Q 1 ) = b + b Q 1 + b Q 2 Q 2 = b + b Q 2 + b Q (2.20) 2 Q 3 = b + b Q 3 + b Q (2.20) b, b, b Q. ( 2.6),
35 (3) (2). (6). (5), (4).. 6 PI 5 4 ВУ Q одукт т о
36 -, = + + +, (2.21),,,, ;. - Matlab atlab Simulink Simulink - ( 2.10):
37 ,., -.,.,. 2.4 Matlab. -.,,.,,,, -,,,. (2.2) - (2.12) Matlab. :,, 7, , = 6, +,6,, (2.22) Matlab 37
38 ,.,,.,..,,
39 , ( 14,15): ,. 2.5.,., : 39
40 F = = max (2.23), m ; - i- (.); i- ( 3/ );, (2.23). ( ), ( ). : F = = max (2.24), n ; - j- ( 3/ ); i- (%);, (2.24)..,,. F = =. [ ]. [ ] C u.. [ ] :. -,j-, [ / ];. -, j- [ 3]; 40
41 . - j-, [ / ]; n. ;,,.. : : - ( ) ( ), ( ); -, ; -. - ; , ; -, ; -, ; -., ( ). 41
42 .,. 2.6 : «-»; ;,.. -. MATLAB.. 42
43 3 3.1,... : - ; -.., ( - ).,, : / ; /. : - ; - ; -.,,. : - ; - ; - ; 43
44 -,, ; - ( ) ( ) ; /,..,. 20 /,. 20 /,. 1 ( 2,4 5 / )., /. ( 85%) 15 /. 1-2 /.. «2 (.1)», «6 (.2)», «5 (.3)» «2 (.4)»., (, ),
45 К ч. 1-6 З 102 К З ч. 2 З З К-1 ч. 3 З 90 З 93 Ц Ц ч. 4 З З ч. 5 К З 1 З ,
46 Ве у о е одел ле е то Comsol Multiphysics Matlab ед у о е одел ле е то L Q P Q Н у о е одел ле е то ия ия Li Q 1 i L i Q 1 i L i Q 1 i L i Q 1 i З к ч е к лок 1 Отк ч е к лок 1 З к ч е к лок N Отк ч е к лок M dl dt i W Q 1i Q2 i Li... Q 1 i dl dt i W Q 1i Q3 i уд ое тело P=R(Q)*Q P =a 0+a 1Q+a 2 Q 2 L i Q 1 i... P =a0+a1q+a2 Q 2... dl dt i W Q 1i Q2 i L i... Q 1 i dl dt i W Q 1i Q3 i P=R(Q)*Q P =a 0+a 1Q+a 2 Q 2 Li... P =a0+a1q+a2 Q 2 Q 1 i (2.20). 46
47 ия dl dt Li i W Q 1i Q2 i Q 1 i З к ч е к лок 1... dl dt i W Q 1i Q3 i L i P =a 0 +a 1 Q +a 2 Q 2 Q 1 i Отк ч е к лок 1... P =a 0 +a 1 Q +a 2 Q 2 Li Q 1 i Li Q 1 i уд ое тело P=R(Q)*Q 3.3,,. 3.3,,. Comsol Multiphysics Matlab 3.4 : - ; 47
48 -,,.,. 3.2 ( ).. (2.23), -, 3.5. ( ) 1 2 j- 3 Δ 4 Q i- l, j- 1 1 N Q j- 1 1 M
49 : 1. P ; (2.23). 2, P, - ; (2.8) (2.9). 3 : P t = P P (3.1) 4 Q, (3.1). 5 l, j-. 6 l, l Q c = = Q (3.2) l,. Q c = = Q c (3.3), Q c - j-.. : = Q = Ф РI (3.4), : : : F = = P t Q (3.5) : P t = P P (3.6) 49
50 l- ; j- ; (3.5) (3.7) : = Q = Ф Р (3.7) F = = P t Q λ = Q Ф (3.8) F Q = P λ = F Q = P λ = F Q 3 = P λ = (3.9) F Q n = P λ = F λ : F = Q Ф = (3.10) (3.10),,,. 3.3 ( )., [ ], γ -, γ -. F = = (3.11) = d + d + d + d (3.12) 50
51 = = Ф (3.13) З (3.10) - (3.12) : F = = [ d + d + d + d ] + [ = Ф ], (3.14) F 1 c1 = d + d + d + = (3.15) F = d + d + d + =.. (3.16). F = d + d + d + = F = = Ф = (3.17) m,. (3.16) j-. (3.15) = =., 3.6. = 51
52 1 2 (3*) () 3 (3*) : 1 (3.12),, (3.16) (3.16) j-, j=1..m. 3.4,. -,.,.. 52
53 : - ; - ; ρ + divρ =, (4.1) = grad + ρg (4.2), u,,, g /. (4.2) (4.1),, ( 2 3 ), : β t div grad p = f x, t, (4.3) β. f x, t / t div grad p = q N q = t ψ x, x Ω, t, T], (4.4) q, /, i-,, i-, ψ x, N, T > 0 Ω R α, α = 2, 3. (4.4) 53
54 =, x, t, T], (4.5) p x, = p x, x Ω, (4.6) Γ Ω, n Γ., p x, t, t, T], T >,, (4.5), (4.6) k, µ, c, p, q t, ψ x, i =,,..., N. - (4.4) (4.6)., : - ; -. :,...,.. -,.,,., D,,, ( ). -,..: = + = =, (4.7) -, -. (.. ). : + + =, =, = (4.8) 54
55 = h (4.9) Y + ρ + = d + (4.10) ρ = (4.11), H/ 2,, / 3,, /,, /,, /,, ρ, / 3, ( > ( ), < ),. ( ),,,,, /,. (4.8) (4.11) - : = =, = =, = =,, Ω, (4.12) Y =, =, > (4.13) Ω,,. : = L = L + L T + L T = L L T +, +, +. (4.14) L, L T,,,,, /, = +, /. 55
56 4.2 COMSOL Multiphysics :, ; ;, -., (,,,.). : ; ;,,. COMSOL Multiphysics (PDE)., ( )., PDE, :,,,.... (GUI), COMSOL Script MATLAB., [48]. PDE, COMSOL Multiphysics (FEM). 56
57 . PDE, :,,,,,,,,,, [35]., (coupling variables). Comsol Multiphysics. Comsol Multiphysics,. [36]..,,. = / щ.,., ρ + d (ρ ) = (4.15) ρ + d (ρ ) = (4.16) W.,, : ρ ; P ; g ; = d (4.17) Ф = + ρ H (4.17) 57
58 ; ; k,..., (4.15), (4.17) m = const. Ф,..,. ( ), ( ),.,.. ( = ).,., [2]: + + N = = (4.18) = (4.19)., ρ ; μ - ; k ; p ; W ;. Comsol Multiphics : 58
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59 . Comsol: (dl), - (ale)...,,,.,., [33]. Comsol Multiphysics,.. : - ; - ; - ; -. В
60 PDE -,
61 щ,,,, , ( 4.5) 2D- -,.. 61
62 4.5-3D :, ( 4.6). З к ч е к Отк ч я к Под е ые оды У а о оде аш е пе к Гл а а 4.6 3D,,. 62
63 ,,.. ё.., :,. : 1., ; 2.,,.., ; 3.,.,,
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70 ,., (1),. (2)..,,,.. (3).,,.,,,,, ( ).,,..,.,..,,. ( ),. :,,,,,. 70
71 .,,, Q i = Q i, H = H i. : P i H i g (4.19) 4.17,,,,
72 ( H i =130, H 1 =4., i=1..6;) ( H i =130, H 1 =4., i=1..6;) 72
73 ( H i =130, H 1 =4., i=1..6;),,,., 73
74 ,.,,..,,. Comsol, , ё ( H i =130, H 1 =4., i=1..6;), (. 4.20). 74
75 4.20 ( H i =130, H 1 =4., i=1..6;) ,, ( H i =130, H 1 =4., i=1..6;) 75
76 ,. 4.22,. 4.23,,,,
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78 )., /,.,,, ( ), 100.., (168 ),.,,.. ( ).. ( ) ,. ( ).. 78
79 ( H , H , H =150, H , H , H =120, H 1 =4.) ( H H , H, =150, H , H H , =120, H 1 =4.) 79
80 ( H , H , H =150, H , H , H =150, H 1 =4.) ( H , H , H =120, H , H , H =150, H 1 =4.) 80
81 ( H H , H, =120, H , H H , =150, H 1 =4.) ( H H , H, =120, H , H H , H =150, 1 81 =4.)
82 ,,,. 4.1, , ,
83 -4.2 ( ) ( ), 1 ( ) ( ), 2 ( ), 1 ( ), 2 ( ), ( ), 1 ( ), ,
84 5 5.1.,,., 20%,, 40%, 70%,,.,..,...,... : ; ; ; ;.., -,,,., 84
85 ,., [36].,.,,.,.,., [37]., ( ) SCADA-., : ;..,. :, ;, [].,,. 85
86 5.1 -,. ( ). [38].. : 1. (Matlab) 2. (WinCC). WinCC......,.. ( ).,,. : 5.2 : - ; -. 86
87 1 2 3 SCADA До туп 4 Web ,,.. in-situ. 5.3(a).,,. 5.3( b). Matlab / Simulink+ omsol. omsol,, : -, ; - ; -,. MatLab,, : - ; - ; - ; -. 87
88 а 1 b d оток д SCADA До туп оче о п о е e До туп оче о п о е Web Кл е т к до туп (a) ; (b) ; (c) OPC- ; d) SCADA ; (e) -. : ; ; ; ; ; ; ;. -..., 5.3 ( ) : OPC- ;. :,,,, 88
89 ;,,,, ;, :, ;, ; ( ) ;, ). ( ) : ;, :,,,, ;,, ; : ( ), ( ), ( ); (,,,,, ); (, );,,,, ; 89
90 (,. SCADA WinCC. Matlab. ( -5.4). WinCC Server Comsol OPC Matlab :,, - Grundfos (W=7,5 ) 90
91 ,., ( )., ( ) ,. :, ;, ; 2-.,,. : ; Fatek FBs-24MC; 91
92 24 -. Wi-Fi. : ; ; ;. : Wi-Fi MOXA :, - 1.; 1 ESP , RS > Ethernet Moxa5130 Wi-Fi MOXA-3121 Wi-Fi MOXA : 1 FATEK-24-MC : FATEK Memory Card, 3,3 FLASH, 4 FBS-6AD,, 6 3 : PROSTAR : : /4-20 (,. ) , 1.; , , , -160/4-20 ( 160 ). ( ). 92
93 : Windows Server 2008; WINCC 7.3(Siemens); - Winproladder v.3.0; -221 OWEN Modbus ; Matlab 2014; Comsol;,,. (WinCC Server, MS SQL Server Windows Server 2008).,,..... (. 5.6). Prostar (. 5.7) Grundfos.. 93
94 Prostar (. 5.8)
95 5.9 Fatek, WiFi. WiFi 5.10 WiFi, ( ) %, ( 5.11)
96 5.4,..,.. 96
97 ,, 2D 3D.,,,.,,. :, ; ( ) ;.,.. - ( ).,. Comsol Multiphysics; ( ) ; ; 97
98 1.... // -, :, : :...., :, /...:, // -,.:, ,..,..,..,../, :, 1992., /,, 2006., , , ,..,... // -., , ,...-.:, ,...- :,2011., 13...,.. : -. - :, ,... // " ", 2006,
99 15...:, :., ,.., // «XXI :», , ,..,... : " і", Manual of acid in situ leach uranium mining technology., IAEA,VIENNA, 2001., p /....:., ,..,..,..,,. :, ,... M.:, / , mm r.., Schechter R. S, Mathematical modeling of in-situ uranium leaching, Society of Petroleum Engineers Journal., 1979., 19. p Schechter S., P. M. Bommer, Optimization of uranium leach mining, Society of Petroleum Engineers Journal., 1982., 22., p Kabir M.I., Lake L. W., Schechter R. S, Evaluation of one-well uranium leaching test restoration, Society of Petroleum Engineers Journal , 22., p Walsh M.P., Schechter., R. S., Humenick M. J., Hill A. D., Silberberg I. H. A Model For Predicting The Restoration Of And Ammonium Migration From In Situ Mine Sites., AIME, South Texas Uranium Seminar - Corpus Christi, Texas., 1978., p Schmidt D., Follin S. E., Peterson K. A., Level E.V. Geochemical kinetics model for in-situ leach mining. // SPE Journal P Kurth D. J., Schmidt R. D., Computer modeling of five-spot well pattern fluid flow during in situ uranium leaching. - Washington: US Bureau of Mines, P
100 30. Kurth D. J., Schmidt R. D., Computer modeling of fluid flow during production and environmental restoration phases of in situ uranium leaching. - Washington: US Bureau of Mines p ,..,.., // - ( - ),, 2000, 5, Arriaga M.C.. Introduction to the Numerical Modeling of Groundwater and Geothermal Systems., 2010., p :, Mukhanov B.K., Omirbekova Zh.Zh., Usenov K.A., Wójcik W. Simulating In-situ Leaching Process Using COMSOL Multiphysics, INTL International Journal of Electronics and Telecommunications, 2014, Vol. 60, 3, p Mukhanov B.K., Usenov.., Omirbekova Zh.Zh., Process of in-situ leaching modeling in a Comsol Multiphysics environment., The 2nd International Virtual Conference on Advanced Scientific Results (SCIECONF-2014), 2014 (held in Zilina, Slovakia)., p Mukhanov B., Omirbekova Zh., Alimanova M., Jumadilova S., Kozhamzharova D., Baimuratov O., A model of virtual training application for simulation of technological processes. Procedia Computer Science, 2015, Vol. 56, p Lisunets N.L., Smirnov O.M., Tsepin M.A. Simulation of the processes of aluminum alloys preforms and semi-finished products manufacture under influence of technological heredity and phase transitions, Physical and Numerical Simulation of Materials Processing, 2008, Vol , p ,. 38. Kim Y.S, Kim H.M. Design of a New Virtual Interaction Based PLC Training Using Virtual Sensors and Actuators: System and Its Application. International Journal of Distributed Sensor Networks, 2013, Vol Mashkov V., Smolarz A., Lytvynenko V., DEVELOPMENT ISSUES IN ALGORITHMS FOR SYSTEM LEVEL SELF-DIAGNOSIS., Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska., 2016., Vol. 6, 1, p Joung-souk S., Doo-hun L. Adaptive Tutoring and Training System Based on Intelligent Agent., International Journal of Multimedia and Ubiquitous Engineering., 2006.,Vol. 1, 3, p Dongfeng SH., Fugee T. Modelling and diagnosis of feedbackcontrolled processes using dynamic PCA and neural networks., INT. J. PROD. RES., 2003, Vol. 41, 2, p // ,.,..,.,.,.,.,., ё. 100
101 . //.., :....., Nuclear share figures, / World Nuclear Association, IAEA p. 46. Forty Years of Uranium Resources, Production and Demand in Perspective/ OECD p : -., ,... :, , :, ,..,..,... : Grewal M.S., Andrews A.P., Kalman filtering: Theory and practice // Wiley-Interscience , 105 p. 53.., -.:, // ,....:, ,..,... :.. -, // ,... // ,.....:..., ,... :...,
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