globals [ dt_s k hmin hmax rad pen-number] breed [particles particle] breed [waters water] patches-own [ h vx vy ] waters-own [ ux uy dispx dispy ] particles-own [ ux uy dispx dispy ] to setup ;; (for this model to work with NetLogo's new plotting features, ;; __clear-all-and-reset-ticks should be replaced with clear-all at ;; the beginning of your setup procedure and reset-ticks at the end ;; of the procedure.) __clear-all-and-reset-ticks ; default values set r 1.0 set dt 1 set n 1000 set q 0.05 set T 5e-3 set ep 50 set a 0.1 set p 0.15 set xs 0 set ys 200 set xu 200 set yu 300 ; time step into seconds set dt_s dt * 24 * 3600 ; permeability (m/s) set k T / ep ; minimum value of hydraulic head (m) set hmin 0.0 ; maximum value of hydraulic head (m) set hmax 0.0 ; radius of the well influence (patches) set rad 3 velocity end to velocity ask patches [ ; underground x and y velocities if pycor >= 0 [ ifelse pycor = ys and pxcor = 0 [ set vx 0 set vy 0 ] [ set vy ( a - q * ys * ( ys ^ 2 - pycor ^ 2 + pxcor ^ 2) / (pi * T * ( (ys - pycor) ^ 2 + pxcor ^ 2) * ( (ys + pycor) ^ 2 + pxcor ^ 2) ) ) set vx ( 2 * q * pxcor * pycor * ys / (pi * T * ( ( (ys - pycor) ^ 2 + pxcor ^ 2) * ( (ys + pycor) ^ 2 + pxcor ^ 2) ) ) ) ] ] ] end to aquifer ask patches [ ; well, waste repository and river positions ifelse pxcor = xu and pycor = yu [ set pcolor red ] [ ifelse pxcor = xs and pycor = ys [ set pcolor black ] [ifelse pycor <= 0 [ set pcolor blue] [ set pcolor brown]] ] ] end to head ask patches [ ifelse pycor >= 0 [ ifelse pycor = ys and pxcor = 0 [ set h -100 ] [ set h ( a * pycor - q * ln( ((ys + pycor) ^ 2 + pxcor ^ 2) / ((ys - pycor) ^ 2 + pxcor ^ 2) ) / (4 * pi * T) ) if hmax < h [ set hmax h ] if hmin > h [ set hmin h ] ] ] [ set h 0.0 ] ] ask patches [ ifelse pycor > 0 [ set pcolor scale-color blue h hmin hmax ] [ set pcolor scale-color blue h hmin hmax ] ] end to line velocity ask patches [ let casex remainder pxcor 20 let casey remainder pycor 20 if casex = 0 and casey = 0 [ sprout-waters 1 [set color blue set size 3 set pen-mode "down"] ] ] end to move ifelse any? waters [ ask waters [ ifelse ycor > 0.0 [ set ux ( - k * vx / p ) set uy ( - k * vy / p ) set dispy ( 0 ) set dispx ( 0 ) set xcor ( xcor + ( random-normal 0 1 ) * sqrt(2 * dispx * dt_s) + ux * dt_s ) set ycor ( ycor + ( random-normal 0 1 ) * sqrt(2 * dispy * dt_s) + uy * dt_s ) if sqrt((xcor - xs) ^ 2 + (ycor - ys) ^ 2) < rad [ die ] ] [ die ] ] ] [ stop ] end to pollutant velocity reset-ticks create-particles n [ set xcor xu set ycor yu set color red set shape "circle" set size 3 set heading 180 ifelse pathway [pen-down] [pen-up] ] end to go ifelse any? particles [ ask particles [ ifelse pathway [pen-down] [pen-up] ifelse ycor >= 0 [ set ux ( - k * vx / (p * R) ) set uy ( - k * vy / (p * R) ) set dispy ( alpha * abs(uy) / R ) set dispx ( alpha * abs(ux) / R ) set xcor ( xcor + ( random-normal 0 1 ) * sqrt(2 * dispx * dt_s) + ux * dt_s ) set ycor ( ycor + ( random-normal 0 1 ) * sqrt(2 * dispy * dt_s) + uy * dt_s ) if sqrt((xcor - xs) ^ 2 + (ycor - ys) ^ 2) < rad [ die ] ] [ die ] ] ] [ set pen-number pen-number + 1 stop ] do-plots tick end to do-plots set-current-plot "Pollutant" set-current-plot-pen "river" set-plot-pen-color 3 + (pen-number * 10) plotxy (ticks * dt) ((count particles with [ ycor < 0 ]) / n) end @#$#@#$#@ GRAPHICS-WINDOW 195 10 656 452 -1 -1 1.0 1 10 1 1 1 0 1 1 1 -50 400 -10 400 0 0 1 ticks 30.0 BUTTON 670 75 810 108 Upper aquifer view aquifer NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 670 390 747 423 Simulate go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 0 25 172 58 r r 0.1 5 1 0.1 1 NIL HORIZONTAL SLIDER 0 80 172 113 alpha alpha 0.1 2 0.8 0.1 1 (m) HORIZONTAL SLIDER 0 135 172 168 dt dt 0 100 1 0.01 1 (days) HORIZONTAL SLIDER 0 190 172 223 n n 0 50000 1000 1 1 NIL HORIZONTAL SLIDER 0 245 172 278 q q 0 0.1 0.1 0.005 1 (m3/s) HORIZONTAL SLIDER 0 300 172 333 T T 0.0022 0.01 0.002201 0.0001 1 (m2/s) HORIZONTAL SLIDER 0 355 172 388 ep ep 50 300 50 10 1 (m) HORIZONTAL SLIDER 0 410 172 443 a a 0.1 1 0.1 0.01 1 NIL HORIZONTAL SLIDER 0 465 172 498 p p 0.01 1 0.15 0.01 1 NIL HORIZONTAL SLIDER 0 520 172 553 xs xs min-pxcor max-pxcor 0 10 1 NIL HORIZONTAL SLIDER 0 575 172 608 ys ys min-pycor max-pycor 200 10 1 NIL HORIZONTAL SLIDER 0 630 172 663 xu xu min-pxcor max-pxcor 200 10 1 NIL HORIZONTAL SLIDER 0 685 172 718 yu yu min-pycor max-pycor 300 10 1 NIL HORIZONTAL BUTTON 670 200 827 233 Setup water pathways line NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 670 235 827 268 Watch water pathways move T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 670 115 812 148 Hydraulic head view head NIL 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 190 470 655 720 Pollutant Time (days) C/C0 0.0 10.0 0.0 0.0 true false "" "" PENS "river" 1.0 0 -16777216 true "" "" TEXTBOX 5 10 155 28 Delay factor of pollutant 11 0.0 1 TEXTBOX 5 65 170 91 Aquifer dispersivity (m) 11 0.0 1 TEXTBOX 5 120 155 138 Time step (days) 11 0.0 1 TEXTBOX 5 175 155 193 Number of particles 11 0.0 1 TEXTBOX 5 230 155 248 Flow rate of the well (m3/s) 11 0.0 1 TEXTBOX 5 285 155 303 Transmisivity (m2/s) 11 0.0 1 TEXTBOX 5 340 155 358 Aquifer thickness (m) 11 0.0 1 TEXTBOX 5 395 155 413 Hydraulic head slope (m/m) 11 0.0 1 TEXTBOX 5 450 155 468 Aquifer porosity 11 0.0 1 TEXTBOX 5 505 155 523 X coordinate of the well (m) 11 0.0 1 TEXTBOX 5 560 155 578 Y coordinate of the well (m) 11 0.0 1 TEXTBOX 5 615 170 641 X coordinate of the repository (m) 11 0.0 1 TEXTBOX 5 670 180 696 Y coordinate of the repository (m) 11 0.0 1 SWITCH 670 355 772 388 pathway pathway 1 1 -1000 BUTTON 665 685 747 718 Clear plot clear-plot NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 670 10 742 43 Clear all setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 670 320 825 353 Create a cloud of particles pollutant NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 670 60 820 78 Choose a view 11 0.0 1 TEXTBOX 675 185 825 203 See water pathways 11 0.0 1 TEXTBOX 675 305 825 323 See cloud of particles 11 0.0 1 @#$#@#$#@ ## WHAT IS IT? This model computes the 2D underground flows through a porous aquifer. ## HOW IT WORKS The study area consists of an aquifer (top view) in which a well was located (the user can choose its X and Y coordinates). According to the aquifer properties, the user can: - To watch the hydraulic head properties (Darcy law) - To watch the water pathways - To create clouds of pollutant (the user can choose X and Y coordinates of the source as well as the pollutant properties) Assumptions: - The aquifer has uniform properties and isotropic characteristics ; - A river (coordinates with Y < 0) induces Dirichlet boundary conditions: a constant hydraulic head (h = 0 m) along the entire river. ## HOW TO USE IT Here is a rough explanation of the model variables: - "r" is a delay factor (no dimension) compare to groundwater flow. If "r" = 1, the cloud of particles (pollutant or not) has a hydrodynamic behavior like groundwater (basically the same velocity and dispersion). If "r" > 1, particles are constrained through porous media (it is called chromatographic effect). If "r" < 1, particles go faster than groundwater (in average)! This last case is observed with colloidal particles for instance. - "alpha" is the aquifer dispersivity (m). The dispersivity is a scale-dependant parameter of the dispersion in porous media. - "dt" is the time step (days). - "n" is the number of particles (no dimension) when user create a cloud. - "q" is the well's flow rate (m3/s). Increasing "q" will create a depression cone of the hydraulic head values. - "T" is the transmissivity (m2/s) which is computed by T = k * ep, with "k" the aquifer permeability (m/s) and "ep" the aquifer thickness (m). - "ep" is the aquifer thickness (m). - "a" is the slope of the hydraulic head's aquifer when the flow rate of the well is nil. Then "a" is the slope of the aquifer in natural conditions. - "p" is the aquifer porosity (no dimension). - "xs" and "xy" are the X and Y coordinates (m) of the well respectively. - "xu" and "yu" are the X and Y coordinates (m) of the particles' source. Here is a quick description of the functions (buttons on the right): - "Clear all": clear all! - You can choose the type of the aquifer view by clicking "Upper aquifer view", then you see a geographic view: positions of the well (a black dot), of the waste repository (a red dot) and of the river (blue rectangle at the bottom of the screen). If you click on "Hydraulic head view", then you see how hydraulic head is computed according to the set of parameters (e.g. "q", "T" or "a"). - To see how groundwater goes through the aquifer according to the computed hydraulic head, click on "Setup water pathways" (uniform distribution of water particles over the aquifer area) and then on "Watch water pathways" (water particles move along the flow lines). - Add a cloud of particles by clicking the button "Create a cloud of particles". The particles move according to the simulation parameters by clicking "Simulate". The concentration (C/C0: the actual concentration divided by the initial concentration) is then computed when particles reach the river. You can follow the particles' pathways by choosing "On" in the switch button. ## THINGS TO TRY - The number of particles "n": for a given set of parameters (default), only change the number of particles "n" = 100, "n" = 1000 and "n" = 10000. Then you can see how the output concentration curve becomes smoother. - The well's flow rate value "q": for a given set of parameters (default), only change the flow rate of the well "q" = 0.0 m3/s, "q" = 0.005 m3/s and "q" = 0.01 m3/s. Then you can see that output concentration is more and more delayed and dispersed. You can also observe on the view how the cloud of particles behaves spatially. ## CREDITS AND REFERENCES Copyright 2011 Cyril Fleurant. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 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