01 - Results Visualization

One simulation, shown five different ways. This example is not about the chemistry – it reuses the cation exchange column of 11 - Transport and Cation Exchange – but about what can be done with the results once they exist.

A reactive transport run produces a table with three independent axes: distance along the column, time, and chemical species. No single plot shows all three, so every figure here is a decision about which one to collapse. That choice is the subject.

TITLE Phreeqc Example 11.-- Transport and cation exchange.
SOLUTION 0  CaCl2
	units            mmol/kgw
	temp             25.0
	pH               7.0     charge
	pe               12.5    O2(g)   -0.68
	Ca               0.6
	Cl               @{$ini_conc$}@
SOLUTION 1-40  Initial solution for column
	units            mmol/kgw
	temp             25.0
	pH               7.0     charge
	pe               12.5    O2(g)   -0.68
	Na               1.0
	K                0.2
	N(5)             1.2
END
EXCHANGE 1-40
	-equilibrate 1
	X                0.0011
END
TRANSPORT
	-cells           40
	-lengths         0.002
	-shifts          100
	-time_step       720.0
	-flow_direction  forward
	-boundary_conditions   flux  flux
	-diffusion_coefficient 0.0e-9
	-dispersivities  @{$dispersivity$}@
	-correct_disp    true
END

Pick two of three

Chloride, sodium, potassium and calcium against pore volumes at one cell, with the analytical chloride

Fix the place, vary time. Concentrations at the boundary cell against pore volumes – the breakthrough curve, and the form in which a column experiment is measured. The analytical chloride is drawn with it as the check described in 11 - Transport and Cation Exchange.

Potassium as a colour map over distance and time

Keep both, drop the species. Potassium over distance and time as a colour map: one species, the whole run. Fronts appear here as diagonal bands, and their slope is a velocity – which is the thing neither a breakthrough curve nor a profile shows directly.

Concentration surfaces of several species over distance and time

The same, as a surface. Several species at once over the same two axes. Harder to read a value from, easier to see the shape of; useful for finding where something interesting happens before plotting it properly.

Percentage of exchange sites held by calcium, sodium and potassium along the column at one time

Fix the time, vary the place. The exchanger composition along the column at step 12, as percentages of the sites.

This is the complement of the first figure and the one that explains it. The breakthrough curve shows what came out; this shows what the column is holding, and the replacement of sodium and potassium by calcium moving along as a front is the mechanism behind the effluent curve.

Exchanger composition of four cells plotted as paths on a ternary diagram

Drop the axes entirely. The three exchangeable cations sum to 100 %, so their composition is two independent numbers and fits on a ternary diagram. Each cell traces a path across it as time passes.

Four cells are drawn – 1, 10, 20 and 40. Their paths lie close to one another, which says that every part of the column passes through essentially the same sequence of exchanger compositions, just at different times. That is a statement about the process rather than about any one location, and none of the four figures above can make it.

The table

table_ex1

Time (sec)

Cl (mmoles)

Na (mmoles)

K (mmoles)

Ca (mmoles)

0

0

1

0.2

0

720

0

1

0.2

0

1440

0

1

0.2

0

2160

0

1

0.2

0

2880

0

1

0.2

0

3600

0

1

0.2

0

4320

0

1

0.2

0

5040

0

1

0.2

0

5760

3.099695935216e-19

1

0.2

0

6480

1.500905973391e-14

1

0.2

0

7200

6.3378101301940005e-12

1

0.2

0

7920

4.494806174889e-10

1

0.2

0

8640

1.148716182625e-08

1

0.2

0

9360

1.502206811058e-07

1

0.2

0

10080

1.22254281191e-06

1

0.2

0

10800

6.992469583284e-06

0.9999999999999001

0.2000000000001

0

11520

3.0480434402039997e-05

0.9999999999998

0.2000000000002

0

12240

0.0001071736884874

0.9999999999996

0.2000000000004

0

12960

0.0003167880505857

0.9999999999990999

0.2000000000009

0

13680

0.0008119152403764

0.9999999999981001

0.2000000000019

0

14400

0.001847753784

0.9999999999954999

0.2000000000045

0

15120

0.003804229075475

0.9999999999815

0.2000000000185

0

15840

0.007191769366246

0.9999999999194

0.20000000008069999

0

16560

0.012635060222689998

0.9999999996769

0.2000000003232

0

17280

0.020834137170530002

0.9999999988263

0.2000000011738

0

18000

0.03250742767479

0.9999999961114001

0.2000000038887

0

18720

0.04832522920503

0.9999999881420999

0.20000001185779998

0

19440

0.06884373211788

0.9999999664316

0.20000003356819998

0

20160

0.09444901160173

0.9999999111043

0.20000008889530002

0

20880

0.1253179893805

0.9999997783000001

0.20000022169929998

0

21600

0.1614000573129

0.9999994762263

0.2000005237725

0

22320

0.20241969718269998

0.9999988216498

0.2000011783484

0

23040

0.24789764663570002

0.9999974639168

0.20000253607989998

0

23760

0.2971862880203

0.9999947567684

0.200005243227

0

24480

0.3495140484272

0.9999895484264999

0.2000104515675

0

25200

0.40403357709590004

0.9999798465372999

0.2000201534554

0

25920

0.45986908597389997

0.9999622949276

0.2000377050638

0

26640

0.5161592448412999

0.9999313715105

0.2000686284796

0

27360

0.5720931802482

0.9998781779365

0.20012182205239998

0

28080

0.6269382550202

0.9997886375294001

0.2002113624584

0

28800

0.6800592808307

0.9996408433259

0.2003591566607

0

29520

0.7309295762311

0.9994011963713001

0.2005988036142

0

30240

0.7791348087955

0.9990188398079001

0.2009811601767

0

30960

0.824370867474

0.9984177243093

0.2015822756744

0

31680

0.8664371340724

0.9974854440118

0.2025145559711

0

32400

0.9052265038216

0.9960577965183

0.2039422034634

0

33120

0.9407133877476

0.9938979448207

0.20610205515990002

0

33840

0.9729407531493001

0.9906693148514

0.2093306851283

0

34560

1.0020070550459999

0.9859023902485

0.2140976097306

0

35280

1.028053705196

0.9789581360882

0.2210418638904

0

36000

1.051253532901

0.9689960047788

0.2310039951996

0

36720

1.071800523379

0.9549633446588

0.24503665531950003

0

37440

1.0899009800300001

0.9356347669942

0.2643652329843

0

38160

1.105766147279

0.909738463714

0.2902615362648

0

38880

1.1196062494930001

0.8761960898604

0.323803910119

0

39600

1.131625845338

0.8344533299762

0.365546670004

0

40320

1.142020362045

0.7847919648582

0.4152080351229

0

41040

1.150973656035

0.7284538370877001

0.4715461628945

3.527692818409e-25

41760

1.158656441394

0.6674661293038999

0.5325338706794

4.210831922196e-23

42480

1.165225432016

0.6042301756361

0.5957698243484999

2.1112644179359998e-21

43200

1.170823053923

0.5410707040733

0.6589292959126001

9.153155272165e-20

43920

1.175577598779

0.47991770646410004

0.7200822935230999

3.5143308904239995e-18

44640

1.179603706072

0.42217463625970003

0.7778253637289

1.2072133357479998e-16

45360

1.183003078326

0.3687296863928

0.831270313597

3.694071189028e-15

46080

1.1858653501440002

0.3200378092874

0.8799621907034

1.035721727649e-13

46800

1.188269047044

0.27622844301579996

0.9237715569711

2.657316513578e-12

47520

1.190282583742

0.23719604397229999

0.9628039558955

6.272120759453e-11

48240

1.1919652634100002

0.20268026595570002

0.9973197312302001

1.4041082268950001e-09

48960

1.193368249524

0.1723175378763

1.0276824027

2.9709432256e-08

49680

1.194535490349

0.14569865254900002

1.054300174308

5.865691926516e-07

50400

1.195504582884

0.1223834694148

1.077593517021

1.1506780068630001e-05

51120

1.19630756853

0.1019262302484

1.09765724114

0.0002082643040654

51840

1.196971656898

0.08381480430459

1.109525476356

0.0033298596681490002

52560

1.197519877322

0.06668225215375

1.024937205368

0.05419027123916

53280

1.197971659937

0.05053198361894

0.7350507092904

0.207208653549

54000

1.1983433497520002

0.03879701353344

0.5356918133817

0.31275558654860003

54720

1.1986486582040001

0.03007678319726

0.40211880019659996

0.3839022083108

55440

1.198899057198

0.023444635472219998

0.30685223670469997

0.4348515639204

56160

1.199104120993

0.01834047970582

0.2366187844776

0.4725203679181

56880

1.199271821253

0.01438416332256

0.1838015686767

0.5009071340114001

57600

1.199408780438

0.01130287551729

0.1435541335456

0.5225714954803

58320

1.199520488471

0.008894854146136

0.1125953624841

0.5392548916968001

59040

1.199611487223

0.007008145844608

0.08861328626373001

0.5521892839574001

59760

1.199685527006

0.005526939763041

0.06993373970834

0.5622696602753

60480

1.199745698858

0.004362237384878

0.05532050322144

0.5701586297071001

61200

1.1997945459900001

0.0034452316226400003

0.043847402190319996

0.576353683103

61920

1.1998341573940001

0.002722483621173

0.03481279238995

0.5812323620030001

62640

1.199866246232

0.0021523437323109997

0.02768046310685

0.5850835965882

63360

1.199892215323

0.0017022599005469998

0.022037745425940003

0.5881299973437

64080

1.199913211686

0.001346733077458

0.017565220330539998

0.590544023302

64800

1.1999301718820001

0.0010657521983839999

0.01401446576925

0.5924598910212999

65520

1.199943859609

0.0008435890590553

0.01119149962915

0.5939824556603001

66240

1.199954896813

0.000667865908903

0.008944331671829

0.5951939012134

66960

1.1999637893780002

0.0005288312741436999

0.007153523667664

0.5961588225322

67680

1.1999709483010002

0.0004187957410809

0.005724978921465999

0.5969281126714

68400

1.199976707113

0.0003316912253529

0.004584400975147

0.5975419539019999

69120

1.1999813361849998

0.0002627259547465

0.003673012862258

0.5980321305934

69840

1.199985054462

0.0002081138872308

0.00294423532525

0.5984238253953

70560

1.199988039067

0.0001648621778509

0.002361099157963

0.5987370193334001

71280

1.199990433149

0.00013060402175539998

0.001894222604932

0.5989875866877

72000

1.199992352295

0.0001034670377818

0.0015202257368670002

0.5991881536136

Results are also available as a table, which is what to use when a number is wanted rather than a shape.

What it shows

That choosing a plot is choosing a question. The same results support a breakthrough curve, a profile, a map and a composition path, and each discards something the others keep.

Source

  • Parkhurst, D. L. and Appelo, C. A. J. (2013). Description of input and examples for PHREEQC version 3. U.S. Geological Survey Techniques and Methods, book 6, chapter A43. The model is Example 11 of that manual.

  • Appelo, C. A. J. and Postma, D. (2005). Geochemistry, Groundwater and Pollution, 2nd edition. Balkema, Leiden.