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Functions

 

HGA+ provides a number of built-in functions to automatically calculate a variety of commonly used metrics for geochemical samples.

 

Please Note: The built-in Functions for samples are only available in HGA+.

 

The Functions tab in the Project Properties window lists all of the internal calculations performed by Hydro GeoAnalyst, with reference information for each calculation provided in the discussion below. All of the active functions (as indicated by a checkmark) will be available as "calculated parameters" which can be included in statistical comparisons and for plotting data.  In this dialogue, you may manage which calculations should appear in the lists and in what order. For example, if you never use the enthalpy calculations, you may deactivate them here. In addition, you may define the units in which some of the functions are reported.

The calculated values of functions are displayed in the Calculated tab of the Sample Details window.

The calculated parameters are treated by Hydro GeoAnalyst as regular database parameters with respect to plotting, searches, or statistical calculations. However, in order for the built-in calculations to work, their corresponding database parameters must be included in the database and mapped to the required parameters in the Project Properties window. For example, the database must include calcium and magnesium in order to calculate hardness, and both of these parameters must be identified with an internal name of `Ca' and `Mg' respectively.  

You may edit the name of the function or hide/show a function. Hidden functions will not appear in the list of functions within Hydro GeoAnalyst. To edit the name of the function, press Project > Properties, select the appropriate function in the Functions tab and edit the Label input.  For functions that can be expressed in different units (e.g. hardness as meq/L, mmol/L CaCO3, or mg/L CaCO3) you may specify a default unit.  

Hydro GeoAnalyst includes a number of common calculations for determining common geochemical parameters. Each of the available calculations (functions) is explained below.

 

Ions, Hardness, and Alkalinity Calculations

Sum of Ions

Sum of Anions

Sum of Cations

Electroneutrality

Total Hardness

Carbonate Hardness

Non-Carbonate Hardness

Calculated Alkalinity

Calculated TDS

 

Agricultural and Irrigation Calculations

Sodium Adsorption Ratio (SAR)

Magnesium Hazard (MH)

Residual Sodium Carbonate (RSC)

 

Scaling and Corrosion Calculations

Langelier Saturation Index (LSI)

Larson-Skold Index (LSkI)

Puckorius Scaling Index (PSI)

Ryznar Stability Index (RSI)



 

Organic Calculations

Calculated Total Organic Carbon (TOC)

Calculated Total Organic Halides (TOX)


 

Isotope Infiltration Calculations

z(18O)

T(18O)

z(2H)

T(2H)



 

Enthalpy Calculations

Calculated Total Organic Carbon (TOC)

Calculated Total Organic Halides (TOX)


 

Exceedances and Comparisons

Exceeds Any Standard

Exceeds Natural Occurrence


 

Date Time Calculations

Year

Season

Month

 

Ions, Hardness, and Alkalinity Calculations

 

Note: Ions, Cations, and Anions in AquaChem

Ions, Anions, and Cations are specified in Hydro GeoAnalyst using the Valency value in the Parameter settings:

Ions are any parameter with a non-zero parameter valency

Anions are any parameter with a negative parameter valency

Cations are any parameter with a positive parameter valency

Valencies are always integer values.  New parameters are assumed to have a valency of zero and are therefore not considered Ions unless/until otherwise specified.

 

Sum of Ions:

Sum of the concentration of all measured ion concentrations in the sample, given by the equation:

 

 

where:Xi is the volumetric concentration of the ith ion parameter in units of meq/L [Default], mmol/L, or mg/L

 

Sum of Anions:

Sum of the concentration of all measured anion concentrations in the sample, given by the equation:

 

 

where:Ai is the volumetric concentration of the ith anion parameter measured in the solution in units of meq/L [Default], mmol/L, or mg/L

 

Sum of Cations:

Sum of the concentration of all measured anion concentrations in the sample, given by the equation:

 

 

where:Ci is the volumetric concentration of the ith cation parameter measured in the solution in units of meq/L [Default], mmol/L, or mg/L

 

Electroneutrality

The principal of electroneutrality is one of the foundations of aquatic chemistry. This principle states that the sum of positive and negative charges within a solution must balance to zero. The electroneutrality ratio (E.N.) is the relative difference in the ionic charge of the solution and is given by the following equation:

 

 

Electroneutrality is expressed in terms of percent. According to Appelo and Postma (1994), electroneutrality differences of up to ±2% are nearly inevitable but differences of more than ±5% mean that sampling and analytical procedures should be reviewed as this may indicate that:

the sample was subjected to sampling and/or analytical procedural errors, or

there are other (less common/un-analyzed) major ions in the solution

 

Total Hardness

The sum of ions that can precipitate from water as calcite or dolomite. Generally, the sum of Ca2+ and Mg2+, expressed in meq/L or mg/L CaCO3, or mol/L CaCO3.

 

 

where:TH is in units of meq/L
               [Ca2+] is the concentration of calcium ions in solution in mmol/L
               [Mg2+] is the concentration of magnesium ions in solution in mmol/L
 
               TH unit conversion 1 meq/L [CaCO3] = 50 mg/L [CaCO3] = 0.5 mmol/L [CaCO3]

 

Carbonate (Temporary) Hardness:

Carbonate Hardness (CH) is the portion of total hardness that is balanced by carbonate [CO32-] and bicarbonate [HCO3-] and thus can precipitate as calcium carbonate, magnesium carbonate, or related minerals.

 

where:CH is in units of meq/L
               TH is total hardness in units of meq/L
               [CO32-] is the concentration of carbonate ions in solution in mmol/L
               [HCO3-] is the concentration of bicarbonate ions in solution in mmol/L
 
               CH unit conversion 1 meq/L [CaCO3] = 50 mg/L [CaCO3] = 0.5 mmol/L [CaCO3]

 

Non Carbonate (Permanent) Hardness:

Non carbonate hardness (NCH), also known as permanent hardness, is the portion of calcium and magnesium hardness in excess of carbonate [CO32-] and bicarbonate [HCO3-].

 

where:NCH is in units of meq/L
               TH is total hardness in units of meq/L
               CH is carbonate hardness in units of meq/L
 
               NCH unit conversion 1 meq/L [CaCO3] = 50 mg/L [CaCO3] = 0.5 mmol/L [CaCO3]

 

Calculated Alkalinity

Alkalinity is a measure of the acid neutralizing capacity of the solution. Alkalinity is most commonly measured by titration, but can be estimated using the following equation:

 

where:Alkalinity is in units of meq/L
               pH = -log10[H+]
               pOH = -log10[OH-] 14 - pH (@ 25oC, 1 atm)
               Alk unit conversion 1 meq/L [CaCO3] = 50 mg/L [CaCO3] = 0.5 mmol/L [CaCO3]

 

Calculated Total Dissolved Solids (TDS)

TDS is a measure of the evaporation residue at a given temperature. It can also be thought of as the mass of all ions in solution. TDS is calculated as the sum of all ions plus dissolved silica less the amount of bicarbonate that will outgas under the following reaction (Hounslow, 1995, p 57):

 

So, the formula to estimate total dissolve solids is as follows:

 

 

 

where:TDS is in units of mg/L
               FMW = formula molecular weight (mg/mmol)

 

Please Note: calculated TDS is only an approximation; it is always better to have a measured value.

 

Agricultural and Irrigation Calculations

 

Sodium Adsorption Ratio (SAR)

The sodium adsorption ratio (SAR) is an empirical water quality criterion that is important for irrigation waters. It is used in the Wilcox Plot.

 

where:SAR is in units of (meq/L)0.5, but the units are not traditionally reported
               Inputs are in units of meq/L

 

Magnesium Hazard (MH)

Magnesium is considered to be harmful for plants, but the effect is reduced by the presence of calcium. Magnesium Hazard was proposed by Szabolcs and Darab (1964) and is calculated as follows:

 

where:MH is dimensionless.
               Inputs are in units of meq/L

 

Waters with values of MH that exceed 50 are generally considered to be harmful for use in irrigation.

 

Residual Sodium Carbonate (RSC)

Residual sodium carbonate (RSC) is similar to the SAR in that it expresses the sodium content in relation with calcium and magnesium (Richards, 1954). This value may appear in some water quality reports, although it is not frequently used. Residual sodium carbonate (RSC) has the following equation:

 

where: RSC is in units of meq/L

 

Waters are categorized using RSC as follows:

RSC Value

Significance

< 1.25 meq/L

waters are generally considered safe for irrigation, although some crops may require lower values

1.25 – 2.5 meq/L

waters are considered are considered marginal

> 2.5 meq/L

waters are generally not appropriate for irrigation without treatment

 

Scaling and Corrosion Calculations

 

Please Note: The scaling and corrosion indices presented below are only approximations of the real saturation state and should only be used in preliminary analyses. Modeled (e.g. PHREEQC) saturation index values of calcite or dolomite will generally provide more reliable results since they are based on a thermodynamic dataset and include more corrosion/scaling-relevant minerals and parameters such as Eh, Mn, Fe, iron hydroxides, etc.

 

Langelier Saturation Index (LSI)

The Langelier index is a popular way of expressing the equilibrium state of a solution in respect to calcite (Langelier, 1936) and is given by:

 

where:LSI is in standard pH units
               pH is the measured pH
               pHs is the estimated pH at calcite saturation

 

The value of pHs is estimated using temperature, alkalinity, hardness and total dissolved solids values as follows:

 

where: TDS is total dissolved solids in units of mg/L
               T is temperature in units of Kelvin
               Ca is the concentration of calcium in mg/L-CaCO3
               Alk is the alkalinity in mg/L-CaCO3
               

Waters are categorized using LSI as follows (Belitz et al., 2016):

LSI Value

Significance

< -0.5

potentially corrosive

-0.5 – +0.5

indeterminate

> +0.5

potentially scale-forming

 

Larson-Skold Index (LSkI)

The Larson-Skold Index (LSkI) is used to describe the corrosivity of water towards mild steel and was developed based on in situ measurements of corrosion in steel lines transporting Great Lakes water (Larson and Skold, 1958).  The index describes the ratio of concentration of chloride and sulfate ions to the concentration of bicarbonate and carbonate ions. Because the LSkI is an empirical correlation, its utility for describing corrosion for other types of water is questionable. The following equation is used to calculate the LSkI:

 

where:LSkI is dimensionless
               All inputs are concentrations in meq/L

 

 

The following table describes the criteria for evaluating values of L&SkI (Larson and Skold, 1958):

 

LSkI Value

Significance

< 0.8

Chloride and sulfate concentrations will not interfere with natural film formation

0.8 – 1.2

Chloride and sulfate concentrations may interfere with natural film formation; corrosion may occur

> 1.2

High corrosion rates are anticipated

 

Ryznar Stability Index (RSI)

The Ryznar stability index (RSI) attempts to correlate an empirical database of scale thickness observed in municipal water systems to water chemistry (Ryznar, 1944). Like the LSI, the RSI has its basis in the concept of saturation level. Ryznar attempted to quantify the relationship between calcium carbonate saturation state and scale formation. The Ryznar stability index is calculated as follows:

 

where:LSI is in standard pH units
               pHs is the pH at calcite saturation
               pH is the measured pH in standard units

The value of pHs is estimated from temperature, alkalinity, hardness and total dissolved values using the following empirical formula:

 

where: TDS is total dissolved solids in units of mg/L
               T is temperature in units of Kelvin
               Ca is the concentration of calcium in mg/L-CaCO3
               Alk is the alkalinity in mg/L-CaCO3

 

The empirical correlation of the Ryznar Stability Index can be summarized as follows:

 

RSI Value

Significance

< 6

the scale tendency increases as the index decreases

> 7

the calcium carbonate formation probably does not lead to a protective corrosion inhibitor film

> 8

mild steel corrosion becomes an increasing problem

 

Puckorius Scaling Index (PSI)

The Puckorius Scaling Index (PSI) is based on estimates of the maximum quantity of precipitate that can form and the buffering capacity of the water. The PSI index is calculated in a manner similar to the Ryznar Stability Index, described above, except that it incorporates the equilibrium pH and is calculated as follows:

 

 

where:PSI is in standard pH units
               pHs is the estimated pH at calcite saturation
               pHeq is the estimated pH at equilibrium

 

The value of pHs is estimated using temperature, alkalinity, hardness and total dissolved solids values as follows:

 

where: TDS is total dissolved solids in units of mg/L
               T is temperature in units of Kelvin
               Ca is the concentration of calcium in mg/L-CaCO3
               Alk is the alkalinity in mg/L-CaCO3

 

The value of pHeq is based on the buffering capacity of the solution and is estimated using alkalinity:

 

where: pHeq is in standard units
               Alk is alkalinity in mg/L CaCO3

 

The empirical correlation of the Puckorius Scaling Index can be summarized as follows:

PSI Value

Significance

< 6

the scale tendency increases as the index decreases

> 7

the calcium carbonate formation probably does not lead to a protective corrosion inhibitor film

> 8

mild steel corrosion becomes an increasing problem

 

Organic Calculations

 

Calculated Total Organic Carbon (TOC)

This function calculates the total carbon associated with organic parameters. Organic carbon is assumed to be present in parameters with a molecular formula containing carbon and excluding the following specific inorganic species: HCO3, CO3, and CO2. Values are reported in mg/L or µg/L.

 

Calculated Total Organic Halogens (TOX)

This function estimates the total halogens associated with organic parameters. Organic halogen are assumed to be those parameters with a molecular formula containing halogens (i.e. Cl, Br, I) and excluding inorganic species containing only halogens (thus, chloride mass from Cl- and Cl2 is excluded). Values are reported in mg/L or µg/L.

 

Isotope Infiltration Calculations

Hydro GeoAnalyst includes functions to estimate infiltration elevation and temperature based on linear relationships with the measured fractionation of oxygen-18 (18O) and deuterium (2H) isotopes. The slope and intercept fitting parameters are valid only for a very limited zone that must be established for your area of interest using empirical data and are specified in Hydro GeoAnalyst using the project settings for Regional Chemistry.

 

z(18O)

Average infiltration height as a function of oxygen-18 isotopic composition.

 

where:zinfiltration is a length unit in meters or feet, depending on the fitting parameter values
               18O is the fractionation of oxygen-18, usually expressed in units of permille (‰).

         m and b are regression fitting parameters based on regional/site-specific data

 

T(18O)

Average temperature of infiltration zone as a function of oxygen-18 isotopic composition.

 

where:Tinfiltration is a temperature unit in oC or oF, depending on the fitting parameter values
               18O is the fractionation of oxygen-18, usually expressed in units of permille (‰).

         m and b are regression fitting parameters based on regional/site-specific data

 

z(2H)

Average infiltration elevation of the infiltration zone as a function of deuterium (2H) isotopic composition.

 

where:zinfiltration is a length unit in meters or feet, depending on the fitting parameter values
               2H is the fractionation of deuterium, usually expressed in units of permille (‰).

         m and b are regression fitting parameters based on regional/site-specific data

 

T(2H)

Average temperature of infiltration zone as a function of deuterium isotopic composition.

 

where:Tinfiltration is a temperature unit in oC or oF, depending on the fitting parameter values
               2H is the fractionation of deuterium, usually expressed in units of permille (‰).
               m and b are regression fitting parameters based on regional/site-specific data

 

Enthalpy Calculations

 

Temp > H H2O(l)

The enthalpy (H) of liquid water as a function of temperature (T) in Kelvin is approximated using the following function:

 

where:temperature is in units of Kelvin
               a1 = 418.84
               a2 = 10.286
               a3 = -0.05092
               a4 = 0.00026309
               a5 = -0.00000069303
               a6 = 0.00000000074566
               a7 = -1209.8
               a8 = 11.99
               a9 = -353.76

 

For more details please refer to Fournier and Potter (1972).

 

Temp > H H2O(v)

The enthalpy (H) of water vapor as a function of temperature (T) in Kelvin is approximated using the following function:

 

where:temperature is in units of Kelvin
               a1 = 2035
               a2 = -5.0499
               a3 = 0.057399
               a4 = -0.00030426
               a5 = 0.00000079095
               a6 = -0.00000000086968
               a7 = 1342.4
               a8 = -13.298
               a9 = 396.29

 

For more details please refer to Fournier and Potter (1972).

 

SiO2 > H H2O(l)

The enthalpy (H) of liquid water as a function of dissolved silica in mmol/L is approximated using the following function:

 

where:SiO2 is the concentration of dissolved silica in units of mmol/L
               a1 = -42.198
               a2 = 0.28831
               a3 = -0.00036686
               a4 = 0.00000031665
               a5 = 77.034

 

For more details please refer to Fournier and Potter (1972).

 

SiO2 > H H2O(v)

The enthalpy (H) of water vapor as a function of dissolved silica is approximated using the following formula:

 

where:SiO2 is the concentration of dissolved silica in units of mmol/L
               a1 = -3.5532
               a2 = 0.146
               a3 = -0.0004927
               a4 = 0.0000012305
               a5 = -0.00000000049421

 

For more details, please refer to Fournier and Potter (1972).

 

Exceedance Calculations

 

Exceeds Natural Occurrence Range (NO)

Returns the number of measured parameters in a given sample that fall outside of a specified natural occurrence range. The natural occurrence range can be defined for a given parameter using the Parameter Editor.

 

Exceeds Standard

Returns the number of measured parameters in a given sample that exceed the active standard(s) as specified in the Water Quality Standards view.

 

Date Calculations

 

Year

Returns the calendar year of the sample collection date.

 

Season

Returns a season index number (1-4) for the sample collection date, based on the time of year as follows:

 

Index

Date Range

Season

Northern
Hemisphere

Southern
Hemisphere

1

Mar 21 - Jun 20

Spring

Fall

2

Jun 21 - Sep 20

Summer

Winter

3

Sep 21 - Dec 20

Fall

Spring

4

Dec 21 - Mar 20

Winter

Summer

 

The season index is a convenient metric to find and select samples that were sampled in the same season but in different years.

 

Month

Returns the index of the month of the sample collection date, where the index is the ordinal number of the month (i.e. January=1, February=2, March=3, etc.). Using this function is a convenient metric to find and select sample data for calculating month-based statistics over several years.

 

 


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