NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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To submit a request, click below on the link of the version you wish to order.
Only liaison officers are authorised to submit online requests. Rules for requesters are
available here.

Program name | Package id | Status | Status date |
---|---|---|---|

PHREEQE | NESC9674/02 | Tested | 24-MAY-1985 |

PHREEQE | NESC9674/06 | Tested | 13-JUN-1990 |

Machines used:

Package ID | Orig. computer | Test computer |
---|---|---|

NESC9674/02 | CDC 7600 | DEC VAX 11/780 |

NESC9674/06 | IBM PC | IBM PC |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

PHREEQE is a program designed to model geochemical reactions. Based on an ion pairing aqueous model, PHREEQE can calculate pH, redox potential, and mass transfer as a function of reaction progress. It can be used to describe geochemical processes for both far-field and near-field performance assessment and to evaluate data acquisition needs and test data. The composition of solutions in equilibrium with multiple phases can be calculated. The aqueous model, including elements, aqueous species, and mineral phases, is exterior to the computer code and is completely user definable.

PHREEQE is a program designed to model geochemical reactions. Based on an ion pairing aqueous model, PHREEQE can calculate pH, redox potential, and mass transfer as a function of reaction progress. It can be used to describe geochemical processes for both far-field and near-field performance assessment and to evaluate data acquisition needs and test data. The composition of solutions in equilibrium with multiple phases can be calculated. The aqueous model, including elements, aqueous species, and mineral phases, is exterior to the computer code and is completely user definable.

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4. METHOD OF SOLUTION

The code solves a reduced set of simultaneous non-linear equations.The conceptual model embodied in PHREEQE is the ion-association model of Pearson and Noronha to obtain values for a set of key independent variables. These results are then used to solve for all other unknowns sought. The key independent variables are:

1) aH+, the activity of hydrogen ion in solution

2) ae-, the activity of electrons in solution

3) the activity of a single aqueous species (called the master species) for each element

4) the amount of mass transferred between each mineral phase and solution to achieve equilibrium.

From these data, the code calculates the dependent variables, including activities of all other aqueous species specified, activity coefficients of these species, molal concentrations of these species at equilibrium, and the activity of water. The equations used to solve for the key independent variables are:

1) Electrical neutrality

2) Electron balance (one equation)

3) Mass balance

4) Mineral equilibrium

PHREEQE solves the equations for the set of key independent variables using two iterative methods to approximate the solutions:

1) a continued fraction approach for the mass balance equations and 2) a modified Newton-Raphson approach for the remaining equations.

The activity coefficient expressions in PHREEQE include the extended Debye-Huckel, WATEQ Debye-Huckel, and Davies equations from the original United State Geological Survey version of the program. The molal concentrations of all secondary species can be calculated from the equilibrium concentration of the master species thus obtained. This is done by evaluating the reactions in the data base of the code.

The code solves a reduced set of simultaneous non-linear equations.The conceptual model embodied in PHREEQE is the ion-association model of Pearson and Noronha to obtain values for a set of key independent variables. These results are then used to solve for all other unknowns sought. The key independent variables are:

1) aH+, the activity of hydrogen ion in solution

2) ae-, the activity of electrons in solution

3) the activity of a single aqueous species (called the master species) for each element

4) the amount of mass transferred between each mineral phase and solution to achieve equilibrium.

From these data, the code calculates the dependent variables, including activities of all other aqueous species specified, activity coefficients of these species, molal concentrations of these species at equilibrium, and the activity of water. The equations used to solve for the key independent variables are:

1) Electrical neutrality

2) Electron balance (one equation)

3) Mass balance

4) Mineral equilibrium

PHREEQE solves the equations for the set of key independent variables using two iterative methods to approximate the solutions:

1) a continued fraction approach for the mass balance equations and 2) a modified Newton-Raphson approach for the remaining equations.

The activity coefficient expressions in PHREEQE include the extended Debye-Huckel, WATEQ Debye-Huckel, and Davies equations from the original United State Geological Survey version of the program. The molal concentrations of all secondary species can be calculated from the equilibrium concentration of the master species thus obtained. This is done by evaluating the reactions in the data base of the code.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

PHREEQE is an extremely general geochemical model and is applicable to most hydro- chemical environments. There are, however, several conceptual and numerical limitations which must be considered.

A. Water (Masses of H and O)

The single most important set of limitations results from the fact that PHREEQE deals with masses of elements in terms of their concentrations in the aqueous phase and uses electrical neutrality and electron balance relations to complete the set of equations needed to solve a given problem. A consequence of this is that the masses of H and O are not considered in the numerical solution to the set of simultaneous equations. Although this does not pose a significant problem in the vast majority of systems to which PHREEQE will be applied, there are certain artifacts of the computations that can, under certain circumstances, be misleading. These are discussed below.

(1) Formation of O2 and/or H2

A potential problem stemming from the lack of mass balance on O and H lies in working with redox systems involving chemical reac- tions that produce or consume H2 or O2. Because the only constraints on H2 and O2 in the calculations are equilibrium and electron balance constraints, there are no numerical limits on the amounts of H2 or O2 that can be made or destroyed (mathematically) to satisfy the constraint in a given simulation. If the masses of H2 and O2 in- volved in chemical reactions become significant relative to 1 kg of water, then the simulations may begin to deviate significantly from reality.

(2) Hydrated minerals

A generally more significant problem occurs if PHREEQE is used to model systems in which large amounts of water are involved in mineral precipitation or dissolution. The most obvious examples are reactions occurring in brines; for example, equilibrium phase- boundary precipitation of 1 mole of natron (Na2CO3 . 10H2O) from 1 liter of solution would remove 1 0 moles of H2O from aqueous phase with a resulting increase in concentration of constituents other than Na and C of about 20 per cent (independent of other reactions). This increase in concentration would not be taken into account in PHREEQE's present computation system.

B. Convergence Problems

Due to the non-linear nature of the equations involved, on some problems the program may not converge. This is much more likely to occur in problems involving redox because of the fact that equili- brium concentrations of some species can vary by more than 100 orders of magnitude from a fully oxidizing to a fully reducing en- vironment. In general the less the redox potential of the solution has to change during a simulation the better the convergence possi- bilities. If problems arise, alternative paths to the same final solution should be tried if possible. If some idea of the final solution characteristics is available, simply start the calculations with the same concentrations but at a pH and pe close to the final anticipated composition. Also make sure that the problem is truly a redox problem. If one is modelling an (NH4)+ solution and there is no need to consider (NO3)- or other valences of nitrogen, then the data base can be rewritten with (NH4)+ as the master species, eliminating all other valences of N, and the problem is considerably simpler for the program to solve.

C. Ion Exchange

There are limitations in the way PHREEQE deals with ion exchange. The user should explore these limitations in detail before actually trying to run such calculation.

D. Water Stability Limits

Although in principle PHREEQE's calculations are not limited to the water stability field, it should be pointed out that because O2, H2, and H2O are coupled via mass-action equations, the only way the program can deal with solutions outside of the normal thermodynamic stability limits of water (1 atmosphere total pressure) is to invoke partial pressures of O2 and H2 greater than 1 atm. As these partial pressures vary exponentially with the departure of pe from the water stability boundary, calculated solution properties rapidly become physically meaningless for comparison with natural environments.

E. Titration and Mixing

The problem lies in the fact that the titration equations are valid for volume and molarity or normality, but not for volume and molality. The errors introduced in these calculations will be pro- portional to one minus the density of the solutions involved in the titration.

F. Activity of Water

The activity of water function used by PHREEQE is the same as that used in WATEQ (Truesdell and Jones, 1974), taken originally from Garrels and Christ (1965).

G. Uniqueness of Solutions

A final precaution should be discussed at this point. This is really a general commentary on chemical modelling, and not unique to the program PHREEQE.

Experience acquired to date in using PHREEQE to simulate natural water systems has shown that in many cases a reaction, or reaction path, that models a given set of observed chemical changes is not mathematically unique. That is, the observed changes in water chemistry can often be modelled exactly by two or (in most cases) more distinct reactions or reaction paths. Thus, the PHREEQE user really faces two distinct questions: (1) can a model be found that simulates the desired chemical system (natural or laboratory), and (2) if a satisfactory model is found, is it the only model that simulates the system in question. The second question is often as difficult to answer, and as important, as the first.

PHREEQE is an extremely general geochemical model and is applicable to most hydro- chemical environments. There are, however, several conceptual and numerical limitations which must be considered.

A. Water (Masses of H and O)

The single most important set of limitations results from the fact that PHREEQE deals with masses of elements in terms of their concentrations in the aqueous phase and uses electrical neutrality and electron balance relations to complete the set of equations needed to solve a given problem. A consequence of this is that the masses of H and O are not considered in the numerical solution to the set of simultaneous equations. Although this does not pose a significant problem in the vast majority of systems to which PHREEQE will be applied, there are certain artifacts of the computations that can, under certain circumstances, be misleading. These are discussed below.

(1) Formation of O2 and/or H2

A potential problem stemming from the lack of mass balance on O and H lies in working with redox systems involving chemical reac- tions that produce or consume H2 or O2. Because the only constraints on H2 and O2 in the calculations are equilibrium and electron balance constraints, there are no numerical limits on the amounts of H2 or O2 that can be made or destroyed (mathematically) to satisfy the constraint in a given simulation. If the masses of H2 and O2 in- volved in chemical reactions become significant relative to 1 kg of water, then the simulations may begin to deviate significantly from reality.

(2) Hydrated minerals

A generally more significant problem occurs if PHREEQE is used to model systems in which large amounts of water are involved in mineral precipitation or dissolution. The most obvious examples are reactions occurring in brines; for example, equilibrium phase- boundary precipitation of 1 mole of natron (Na2CO3 . 10H2O) from 1 liter of solution would remove 1 0 moles of H2O from aqueous phase with a resulting increase in concentration of constituents other than Na and C of about 20 per cent (independent of other reactions). This increase in concentration would not be taken into account in PHREEQE's present computation system.

B. Convergence Problems

Due to the non-linear nature of the equations involved, on some problems the program may not converge. This is much more likely to occur in problems involving redox because of the fact that equili- brium concentrations of some species can vary by more than 100 orders of magnitude from a fully oxidizing to a fully reducing en- vironment. In general the less the redox potential of the solution has to change during a simulation the better the convergence possi- bilities. If problems arise, alternative paths to the same final solution should be tried if possible. If some idea of the final solution characteristics is available, simply start the calculations with the same concentrations but at a pH and pe close to the final anticipated composition. Also make sure that the problem is truly a redox problem. If one is modelling an (NH4)+ solution and there is no need to consider (NO3)- or other valences of nitrogen, then the data base can be rewritten with (NH4)+ as the master species, eliminating all other valences of N, and the problem is considerably simpler for the program to solve.

C. Ion Exchange

There are limitations in the way PHREEQE deals with ion exchange. The user should explore these limitations in detail before actually trying to run such calculation.

D. Water Stability Limits

Although in principle PHREEQE's calculations are not limited to the water stability field, it should be pointed out that because O2, H2, and H2O are coupled via mass-action equations, the only way the program can deal with solutions outside of the normal thermodynamic stability limits of water (1 atmosphere total pressure) is to invoke partial pressures of O2 and H2 greater than 1 atm. As these partial pressures vary exponentially with the departure of pe from the water stability boundary, calculated solution properties rapidly become physically meaningless for comparison with natural environments.

E. Titration and Mixing

The problem lies in the fact that the titration equations are valid for volume and molarity or normality, but not for volume and molality. The errors introduced in these calculations will be pro- portional to one minus the density of the solutions involved in the titration.

F. Activity of Water

The activity of water function used by PHREEQE is the same as that used in WATEQ (Truesdell and Jones, 1974), taken originally from Garrels and Christ (1965).

G. Uniqueness of Solutions

A final precaution should be discussed at this point. This is really a general commentary on chemical modelling, and not unique to the program PHREEQE.

Experience acquired to date in using PHREEQE to simulate natural water systems has shown that in many cases a reaction, or reaction path, that models a given set of observed chemical changes is not mathematically unique. That is, the observed changes in water chemistry can often be modelled exactly by two or (in most cases) more distinct reactions or reaction paths. Thus, the PHREEQE user really faces two distinct questions: (1) can a model be found that simulates the desired chemical system (natural or laboratory), and (2) if a satisfactory model is found, is it the only model that simulates the system in question. The second question is often as difficult to answer, and as important, as the first.

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6. TYPICAL RUNNING TIME

Although the length of this for each run depends on the number of elements, the number of phases, and largely on the size of the change of redox potential, times for routine runs average of the order of 1 second execution time.

NEA-DB executed the test cases included in the package on a VAX-11/780. The following CPU times were found:

PHREEQE PHRQINPT

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test case 1 16.4 1.8 seconds

test case 2 19.4 2.2 seconds

(original test case 72.1 seconds)

Although the length of this for each run depends on the number of elements, the number of phases, and largely on the size of the change of redox potential, times for routine runs average of the order of 1 second execution time.

NEA-DB executed the test cases included in the package on a VAX-11/780. The following CPU times were found:

PHREEQE PHRQINPT

------- --------

test case 1 16.4 1.8 seconds

test case 2 19.4 2.2 seconds

(original test case 72.1 seconds)

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8. RELATED AND AUXILIARY PROGRAMS

The auxiliary preprocessor program PHTL, which is derived from EQTL, converts EQ3/6 (NESC 886) thermodynamic data to PHREEQE format so that the two programs can be compared. PHREEQE can be used to determine solubility limits on the radionuclides present in the waste form. These solubility constraints may be input to the WAPPA (NESC 9673) leach model.

The auxiliary preprocessor program PHTL, which is derived from EQTL, converts EQ3/6 (NESC 886) thermodynamic data to PHREEQE format so that the two programs can be compared. PHREEQE can be used to determine solubility limits on the radionuclides present in the waste form. These solubility constraints may be input to the WAPPA (NESC 9673) leach model.

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Package ID | Status date | Status |
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NESC9674/02 | 24-MAY-1985 | Tested at NEADB |

NESC9674/06 | 13-JUN-1990 | Tested at NEADB |

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10. REFERENCES

- Parkhurst, D.L., D.C., Thorstenson and L.N. Plummer,

PHREEQE: A Computer Program for Geochemical Calculations,

Water-Resources Investigation 80-96,

US Geological Survey, 1980, 210p.

- INTERA Environmental Consultants, Inc.,

PHREEQE: A Geochemical Speciation and Mass Transfer Code Suitable

for Nuclear Wastw Performance Assessment,

ONWI-435, April 1983.

- Parkhurst, D.L., D.C., Thorstenson and L.N. Plummer,

PHREEQE: A Computer Program for Geochemical Calculations,

Water-Resources Investigation 80-96,

US Geological Survey, 1980, 210p.

- INTERA Environmental Consultants, Inc.,

PHREEQE: A Geochemical Speciation and Mass Transfer Code Suitable

for Nuclear Wastw Performance Assessment,

ONWI-435, April 1983.

NESC9674/02, included references:

- D.L.Parkhurst, D.C. Thorstenson and L.N. Plummer:PHREEQE - A Computer Program for Geochemical Calculations.

USGS/WRI-80-96 (Rev. January 1985)

- G.W. Fleming and L.N. Plummer:

PHRQINPT - An Interactive Computer Program for Constructing Input

Data Sets to the Geochemical Simulation Program PHREEQE

USGS/WRI-83-4236 (1983)

- K. Ollila:

Dissolution of UO2 at various parametric conditions: a comparison

between calculated and experimental results

Reprint from Materials Research Society Symp. Proc. Vol. 127,

pp. 337-342 (1989)

NESC9674/06, included references:

- J.W. Ball and D.K. Nordstrom :WATEQ4F--: A Personal Computer Fortran Translation of the

Geochemical Model WATEQ2 with Revised Data Base

US Geological Survey Open-File Report 87-50 (1987)

- J.W. Ball :

Erata and Revision Sheet for Open-File 87-50 WATEQ4F

(March 7, 1988)

- D.L. Parkhurst, L.N. Plummer and D.C. Thorstenson:

BALANCE - A Computer Program for Calculating Mass Transfer for

Geochemical Reactions in Ground Water

US Geological Survey Report 82-14 (1982)

- D.L. Parkhurst, D.C. Thorstenson and L.N. Plummer:

PHREEQE - A Computer Program for Geochemical Calculations.

USGS/WRI-80-96 (Rev. January 1985)

- G.W. Fleming and L.N. Plummer:

PHRQINPT - An Interactive Computer Program for Constructing Input

Data Sets to the Geochemical Simulation Program PHREEQE

USGS/WRI-83-4236 (1983)

- K. Ollila:

Dissolution of UO2 at various parametric conditions: a comparison

between calculated and experimental results

Reprint from Materials Research Society Symp. Proc. Vol. 127,

pp. 337-342 (1989)

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Package ID | Computer language |
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NESC9674/02 | FORTRAN-IV |

NESC9674/06 | FORTRAN-77 |

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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

NOS 1.4-531 (CDC CYBER 170/740).

VMS (DEC VAX-11/780).

NOS 1.4-531 (CDC CYBER 170/740).

VMS (DEC VAX-11/780).

NESC9674/06

All five test cases included in this package have been compiled and executed on an IBM PC/AT microcomputer running under MSDOS 3.2 using the following compilers:- Profession FORTRAN

- Microsoft Optimizing Compiler version 4.01

- Ryan-McFarland RM/FORTRAN version 2.4.2

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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

PHREEQE uses several non-standard IBM FORTRAN H extended enhancements to FORTRAN IV in an effort to conserve memory and shorten the card deck. If the source code is to be used on another computer, the non- standard features may have to be modified. This section only points out known problem areas and so is not necessarily complete. No attempt is made to give complete statement by statement modifica- tions which might be necessary if problems occur.

FORTRAN H allows various word lengths for variables and PHREEQE uses the shortest word lengths which give the necessary precision for the numerical method. All integers are implicitly declared as 2 byte words, all variables beginning with the letter "D" are declared as double precision, "REAL*8" (17-18 decimal digits), and all other real numbers are implicitly single precision, "REAL*4" (7 decimal digits). Other "REAL*8" variables are declared explicitly at the beginning of each subroutine. Some computers may not allow the INTEGER*2 or the REAL*8 statements. Care should be taken to ensure there is no loss of precision when redefining the word length for REAL*8 variables. Function names for REAL*8 variables, absolute value (DABS) and minimum of two numbers (DMIN1) are not standard.

Another possible problem in compiling the code on another machine is the ENTRY statement. Two of PHREEQE's subroutines, PTOT and THORIT, are really collections of subroutines which use ENTRY in- common blocks and declaration statements do not have to be repeated for each subroutine. Each computer handles entry points differently and some do not allow argument lists in the ENTRY statement. Im most cases, making each entry point a separate subroutine with all the common blocks and declarations will eliminate any problems. In making each entry point into a subroutine, a call to SPUM must be inserted at the end of PSPEC. ENTRY RDATA, however, cannot beeasily separated from subroutine READ. The logic of the entry point must be maintained in re-writing this entry point (perhaps with a call to READ instead of RDATA and a jump to the point where the ENTRY state- ment is in the code).

Subroutine CHECK returns to three different points in subroutine MODEL by using a RETURN n statement. This statement may have a different form or may be illegal on another computer.

The program assumes there is a file, labeled in the Fortran Code as 10, from which it will read the basic thermodynamic data. If no file exists then the call to entry RDATA must be removed from the main program and all data must be read with the rest of the input data stream (file 5, or the card reader).

PHREEQE uses several non-standard IBM FORTRAN H extended enhancements to FORTRAN IV in an effort to conserve memory and shorten the card deck. If the source code is to be used on another computer, the non- standard features may have to be modified. This section only points out known problem areas and so is not necessarily complete. No attempt is made to give complete statement by statement modifica- tions which might be necessary if problems occur.

FORTRAN H allows various word lengths for variables and PHREEQE uses the shortest word lengths which give the necessary precision for the numerical method. All integers are implicitly declared as 2 byte words, all variables beginning with the letter "D" are declared as double precision, "REAL*8" (17-18 decimal digits), and all other real numbers are implicitly single precision, "REAL*4" (7 decimal digits). Other "REAL*8" variables are declared explicitly at the beginning of each subroutine. Some computers may not allow the INTEGER*2 or the REAL*8 statements. Care should be taken to ensure there is no loss of precision when redefining the word length for REAL*8 variables. Function names for REAL*8 variables, absolute value (DABS) and minimum of two numbers (DMIN1) are not standard.

Another possible problem in compiling the code on another machine is the ENTRY statement. Two of PHREEQE's subroutines, PTOT and THORIT, are really collections of subroutines which use ENTRY in- common blocks and declaration statements do not have to be repeated for each subroutine. Each computer handles entry points differently and some do not allow argument lists in the ENTRY statement. Im most cases, making each entry point a separate subroutine with all the common blocks and declarations will eliminate any problems. In making each entry point into a subroutine, a call to SPUM must be inserted at the end of PSPEC. ENTRY RDATA, however, cannot beeasily separated from subroutine READ. The logic of the entry point must be maintained in re-writing this entry point (perhaps with a call to READ instead of RDATA and a jump to the point where the ENTRY state- ment is in the code).

Subroutine CHECK returns to three different points in subroutine MODEL by using a RETURN n statement. This statement may have a different form or may be illegal on another computer.

The program assumes there is a file, labeled in the Fortran Code as 10, from which it will read the basic thermodynamic data. If no file exists then the call to entry RDATA must be removed from the main program and all data must be read with the rest of the input data stream (file 5, or the card reader).

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NESC9674/02

File name | File description | Records |
---|---|---|

NESC9674_02.003 | INFORMATION FILE | 166 |

NESC9674_02.004 | PHREEQE SOURCE PROGRAM | 2684 |

NESC9674_02.005 | COMMAND PROCEDURE | 121 |

NESC9674_02.006 | PHREEQE TEST CASE 1 INPUT DATA | 20 |

NESC9674_02.007 | PHREEQE TEST CASE 2 INPUT DATA | 20 |

NESC9674_02.008 | PHREEQE ORIGINAL TEST CASE INPUT DATA | 504 |

NESC9674_02.009 | PHREEQE TEST CASE 1 PRINTED OUTPUT | 586 |

NESC9674_02.010 | PHREEQE TEST CASE 2 PRINTED OUTPUT | 790 |

NESC9674_02.011 | PHREEQE ORIGINAL TEST CASE PRINTED OUTPUT | 6912 |

NESC9674_02.012 | PHRQINPT SOURCE PROGRAM | 2621 |

NESC9674_02.013 | DATA LIBRARY 1 (PHREEQE DATA BASE) | 579 |

NESC9674_02.014 | DATA LIBRARY 2 (USED FOR PHRQINPT) | 81 |

NESC9674/06

File name | File description | Records |
---|---|---|

NESC9674_06.001 | Information file. | 238 |

NESC9674_06.002 | Batch file, compile and link Microsoft vers. | 3 |

NESC9674_06.003 | Batch file, compile Ryan-McFarland version. | 21 |

NESC9674_06.004 | Batch file, link Ryan-McFarland version. | 4 |

NESC9674_06.005 | PLINK86 input file, used by LINKRM.BAT. | 3 |

NESC9674_06.006 | Batch file to execute test cases,Prof. FORT. | 6 |

NESC9674_06.007 | Batch file to execute test cases,Microsoft. | 6 |

NESC9674_06.008 | Batch file to execute test cases,Ryan-McFarl | 6 |

NESC9674_06.009 | FORTRAN source file. | 102 |

NESC9674_06.010 | FORTRAN source file. | 119 |

NESC9674_06.011 | FORTRAN source file. | 107 |

NESC9674_06.012 | FORTRAN source file. | 110 |

NESC9674_06.013 | FORTRAN source file. | 94 |

NESC9674_06.014 | FORTRAN source file. | 95 |

NESC9674_06.015 | FORTRAN source file. | 59 |

NESC9674_06.016 | FORTRAN source file. | 128 |

NESC9674_06.017 | FORTRAN source file. | 218 |

NESC9674_06.018 | FORTRAN source file. | 292 |

NESC9674_06.019 | FORTRAN source file. | 15 |

NESC9674_06.020 | FORTRAN source file. | 469 |

NESC9674_06.021 | FORTRAN source file. | 145 |

NESC9674_06.022 | FORTRAN source file. | 79 |

NESC9674_06.023 | FORTRAN source file. | 114 |

NESC9674_06.024 | FORTRAN source file. | 124 |

NESC9674_06.025 | FORTRAN source file. | 52 |

NESC9674_06.026 | FORTRAN source file. | 126 |

NESC9674_06.027 | FORTRAN source file. | 212 |

NESC9674_06.028 | FORTRAN source file. | 10 |

NESC9674_06.029 | FORTRAN source file. | 54 |

NESC9674_06.030 | Executable file, Professional FORTRAN vers. | 1802 |

NESC9674_06.031 | Executable file, Microsoft version. | 905 |

NESC9674_06.032 | Executable file, Ryan-McFarland version. | 770 |

NESC9674_06.033 | Thermodynamic library. | 579 |

NESC9674_06.034 | Minerals library. (Used by PHRQINPT only.) | 82 |

NESC9674_06.035 | Input data, test case 1. | 84 |

NESC9674_06.036 | Input data, test case 2. | 48 |

NESC9674_06.037 | Input data, test case 3. | 19 |

NESC9674_06.038 | Input data, test case 4. | 82 |

NESC9674_06.039 | Input data, test case 5. | 271 |

NESC9674_06.040 | Output from test case no. 1,Ryan-McFarland. | 243 |

NESC9674_06.041 | Output from test case no. 2,Ryan-McFarland. | 633 |

NESC9674_06.042 | Output from test case no. 3,Ryan-McFarland. | 589 |

NESC9674_06.043 | Output from test case no. 4, Ryan-McFarland. | 1921 |

NESC9674_06.044 | Output from test case no. 4,Microsoft vers. | 1943 |

NESC9674_06.045 | Output from test case no. 4, Prof. FORT. v. | 1921 |

NESC9674_06.046 | Output from test case 4, CDC version. | 1905 |

NESC9674_06.047 | Output from test case no. 5, Ryan-McFarland. | 3520 |

NESC9674_06.048 | DOS file-names | 47 |

Keywords: chemical reactions, geochemistry, radioactive effluents, radionuclide migration.