# Assessment of Groundwater Quality Based on Matter Element Extension Model

Authors: Jin Jing; Qian Hui; Chen Yu-Fei; Xi Wen-Juan
Journal: Journal of Chemistry
 (2013)

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## Abstract

The basic theory and calculating processes of matter element extension method are discussed in detail. Mass balance simulation is used to study the changes of groundwater chemistry. Results show that calcite and dolomite are oversaturated, while gypsum, fluorite, and halite are unsaturated in the simulation path; so calcite precipitates, while gypsum, fluorite, halite, and dolomite dissolve. The changing tendency of Ca2+/Na+ is apparent. Because of the dissolution and precipitation of minerals, the content of each ion changes. Parameters of groundwater are basically within the permissible limits and meet the requirement of drinking water standards. By comparing the evaluation results obtained from matter element extension method, osculating value method based on entropy weight, and principal component analysis method, it is proved that matter element extension is an effective and reasonable method for groundwater quality assessment. The converting tendency of groundwater quality is judged based on the extension indexes; this characteristic is unique of matter element extension method.


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## Body

## 1. Introduction

Groundwater is the most important water resource for human. Groundwater quality problems have intensified through the ages in response to the increased growth on concentration of populations and industrial centres and unreasonable exploitation and utilization of groundwater. Thus finding an objective and reasonable method to evaluate water quality is a hot issue at the present time.Today there are a lot of methods to evaluate goundwater quality, such as water quality index method [1], grey correlation method [2], principal component analysis method [3], and fuzzy theory method [4] and fuzzy synthetic evaluation method [5]; every method has its weakness, such that water quality index evaluation method is subjective, and grey clustering method and fuzzy theory method neglect some important information in the process of calculation and need special program to finish the complicated calculation. Matter element extension method can solve the realistic contradiction qualitatively and quantitatively [6]. It has been applied to many fields, such as environmental quality assessment [7], land suitability evaluation [8], and risk assessment of urban network planning [9], but the application on evaluating groundwater quality is less. In this paper, we combine the method and information entropy to evaluate groundwater quality of water source of Shizuishan city NW China; the grade of groundwater quality is obtained by calculating the comprehensive correlation degrees and extension indexes [6]. The comprehensive analysis is done based on parameters analysis and mass balance simulation.


## 2. Method

Matter element extension, incorporating the matter element theory with extension theory [3], was proposed by Mr. Cai in the 1980s. Its basic theory is outlined below.


### 2.1. Definition of Matter Element

A given thing is namedM, whose characteristic c is valued ν, the orderly ternary group R=(M,C,V) is named as the matter element. M has n characteristics c1,c2,…,cn  and the corresponding values are ν1,ν2,…,νn; thus the matter element can be expressed as [7–11]:
(1)R(x)=[Mc1ν1c2ν2MMcnνn]
according to the definition of matter element, the classical domain R0 and section domain Rc  can be determined.


### 2.2. Construction of the Correlation Function

The correlation degree of each characteristic to each class can be calculated by using the following functions [7–11]:
(2)Kj(xi)={-ρ(xj,xij)|xij|xj∈xijρ(xj,xij)ρ(xj,xpj)-ρ(xj,xij)xj∉xij,
where |xij|=|aij-bij|,
(3)ρ(xj,xij)=|xj-12(aij-bij)|-12(bij-aij)i=1,2,…,m,j=1,2,…,nρ(xj,xpj)=|xj-12(apj-bpj)|-12(bpj-apj)j=1,2,…,n.


### 2.3. Weight Determination

There are many widely used methods, such as principal component analysis [3], and AHP [12]. These methods are subjective and random to some extent. Information entropy [13] is used to determine the weights of evaluated indexes in this study; it minimizes the subjective influence, and the result is more objective and reasonable.


### 2.4. Comprehensive Correlation DegreeKi(P) and Extension Index j* Calculation

The comprehensive correlation degrees of evaluated samples can be obtained(4)Ki(p)=∑j=1nWj·Kj(xi)i=1,2,…,m;j=1,2,…,n.
Suppose
(5)Ki(p)-=Ki(p)-minKi(p)maxKi(p)-minKi(p)i=1,2,…,m.
The formula for calculating the extension index j* is
(6)j*=∑i=1mi·Ki(p)-∑i=1mKi(p)-i=1,2,…,m.
The grade of evaluated object and the attributive degree of the evaluated matter element tend to convert into adjacent levels can be judged from j* [14, 15].


## 2.1. Definition of Matter Element

A given thing is namedM, whose characteristic c is valued ν, the orderly ternary group R=(M,C,V) is named as the matter element. M has n characteristics c1,c2,…,cn  and the corresponding values are ν1,ν2,…,νn; thus the matter element can be expressed as [7–11]:
(1)R(x)=[Mc1ν1c2ν2MMcnνn]
according to the definition of matter element, the classical domain R0 and section domain Rc  can be determined.


## 2.2. Construction of the Correlation Function

The correlation degree of each characteristic to each class can be calculated by using the following functions [7–11]:
(2)Kj(xi)={-ρ(xj,xij)|xij|xj∈xijρ(xj,xij)ρ(xj,xpj)-ρ(xj,xij)xj∉xij,
where |xij|=|aij-bij|,
(3)ρ(xj,xij)=|xj-12(aij-bij)|-12(bij-aij)i=1,2,…,m,j=1,2,…,nρ(xj,xpj)=|xj-12(apj-bpj)|-12(bpj-apj)j=1,2,…,n.


## 2.3. Weight Determination

There are many widely used methods, such as principal component analysis [3], and AHP [12]. These methods are subjective and random to some extent. Information entropy [13] is used to determine the weights of evaluated indexes in this study; it minimizes the subjective influence, and the result is more objective and reasonable.


## 2.4. Comprehensive Correlation DegreeKi(P) and Extension Index j* Calculation

The comprehensive correlation degrees of evaluated samples can be obtained(4)Ki(p)=∑j=1nWj·Kj(xi)i=1,2,…,m;j=1,2,…,n.
Suppose
(5)Ki(p)-=Ki(p)-minKi(p)maxKi(p)-minKi(p)i=1,2,…,m.
The formula for calculating the extension index j* is
(6)j*=∑i=1mi·Ki(p)-∑i=1mKi(p)-i=1,2,…,m.
The grade of evaluated object and the attributive degree of the evaluated matter element tend to convert into adjacent levels can be judged from j* [14, 15].


## 3. Case Study and Materials

### 3.1. Study Area

The water source of Shizuishan City is located between latitude 38°57′18′′–39°04′04′′ N and longitude 106°25′09′′–106°33′33′′ E. It covers an area of about 75.23 km2, 10.03 km from east to west, and 7.50 km from north to south. It is situated in the arid continental climate area with little rain and intensive evaporation. The average annual rainfall is 160.94 mm and the average annual evaporation value is 1792.64 mm. The maximum and minimum temperatures are 25.18°C and −6.73°C, respectively. The ground elevation varies from 1120 m to 1123 m and tilts smoothly from northwest to southeast. The area consists of diluvial inclined plain and flood-lacustrine plain.


### 3.2. Materials

The water source of Shizuishan City pumps water from the confined aquifer, so we must evaluate the groundwater quality to make sure whether the groundwater is drinkable. Ten groundwater samples were collected from the water source in April 2009, which were taken from the third confined aquifer. Samples were collected in precleaned plastic polyethylene bottles for physicochemical analysis. Prior to sampling, all the sampling containers were washed and rinsed thoroughly with the groundwater to be taken for analysis.


## 3.1. Study Area

The water source of Shizuishan City is located between latitude 38°57′18′′–39°04′04′′ N and longitude 106°25′09′′–106°33′33′′ E. It covers an area of about 75.23 km2, 10.03 km from east to west, and 7.50 km from north to south. It is situated in the arid continental climate area with little rain and intensive evaporation. The average annual rainfall is 160.94 mm and the average annual evaporation value is 1792.64 mm. The maximum and minimum temperatures are 25.18°C and −6.73°C, respectively. The ground elevation varies from 1120 m to 1123 m and tilts smoothly from northwest to southeast. The area consists of diluvial inclined plain and flood-lacustrine plain.


## 3.2. Materials

The water source of Shizuishan City pumps water from the confined aquifer, so we must evaluate the groundwater quality to make sure whether the groundwater is drinkable. Ten groundwater samples were collected from the water source in April 2009, which were taken from the third confined aquifer. Samples were collected in precleaned plastic polyethylene bottles for physicochemical analysis. Prior to sampling, all the sampling containers were washed and rinsed thoroughly with the groundwater to be taken for analysis.


## 4. Result and Discussion

### 4.1. Parameters Analysis

Groundwater quality depends on various chemical constituents and their concentrations, which are mostly derived from the geological stratum of the particular region. Thus it is necessary to find some useful indicators, both chemical and physical, to monitor groundwater quality changes. The individual parameters are given as minimum, maximum, average, and standard deviation of the collected samples in the specific area.Seen from Table1 and Figure 1, there are mainly six ions in the groundwater (Na+, Mg2+, Ca2+, Cl−, SO42-, HCO3-). They have indirect influence on other parameters of groundwater, such as TDS, TH, and conductivity, thus they can affect groundwater quality to some extent.Table 1
Statistical analysis for physicochemical parameters of groundwater.
Parameters
Max
Min
Average
Std. Dev.
TH
400.05
84.1
199.08
102.43
TDS
665
259.31
504.67
132.05
COD
2.84
0.44
1.37
0.79
Na+
200
57
123.5
48.52
K+
4.87
0.94
2.25
1.33
Mg2+
29.68
7.8
17.29
8.98
Ca2+
103.67
20.8
49.44
26.15
Cl−
160.9
34.09
89.79
33.93
S
O
4
2
-
213.4
2.45
98.91
81.08
HC
O
3
-
395.96
192.2
264.22
57.41
F−
1.13
0.1
0.58
0.46
Note: Unit mg/L for all parameters.Figure 1
Pipe chart of groundwater ions equivalents.Total hardness (TH) is closely related to daily life and industry; water with high TH is not suitable for drinking, washing, and industry. Besides, it may lead to some diseases. The maximum TH is 400.05 mg/L in W741; the minimum is 84.1 mg/L in W44. TDS reflects the total concentration of dissolved solids; the high TDS is maybe caused by mineral weathering. The TDS ranges from a minimum of 259.31 mg/L in W279 to a maximum of 665 mg/L in W75.COD reflects the organic matter’s concentration; whether water is polluted by organics can be judged from the value of COD. The highest value of COD is 2.84 mg/L in W44; the lowest value is 0.44 mg/L in W279. COD is slightly higher, which may be due to the organic pollution.Fluoride in small amount is good for preventing dental caries, but high concentration causes health risk such as dental fluorosis and skeletal fluorosis [16]. Fluoride-bearing minerals in the rocks and their interaction with water and agricultural activities are considered to be the main cause for fluoride in groundwater. In this case, the fluoride ranges from 0.1 mg/L to 1.13 mg/L, and there is no values exceed the permissible limits.Volatile phenol, As, Hg, Cr, Ag, and other heavy metals are important for assessing groundwater quality; if their concentrations are too high, human health will be under threat. Fortunately, these indexes in this study are all within the permissible limits.Hydrochemical concepts help to elucidate mechanisms of flow and transport in groundwater systems. In this paper, Piper plot is used to infer hydrogeochemical facies of groundwater. Seen from Figure2 that the major chemical types of water samples fall into Cl·HCO3-Na type, Cl·HCO3-Na·Ca type, Cl·SO4·HCO3-Na·Ca, Cl·SO4·HCO3-Na·Ca·Mg type and some mixed. Seen from the plot, alkalis (Na and K) exceed alkaline earths (Ca and Mg) and strong acids (Cl and SO4) exceed weak acids (HCO3 and CO3).Figure 2
Piper plot of groundwater samples.


### 4.2. Mass Balance Simulations

Mass balance simulation is mainly used for studying the chemical reaction during the process of groundwater flow. In the method, two points (e.g., A and B) in the flow path are considered to be the study subjects. The chemistry of A in the upstream is considered to be the initial water quality, and the chemistry of B in the downstream is considered to be the final water quality. According to the chemical reactions between groundwater and aquifer, the quantities of mineral dissolution and precipitation between A and B can be calculated using the mass balance principle. On the basis of that, the chemistry changes in groundwater can be analyzed. In general, mass balance simulation is based on the following equation [17]:
(7)∑j=1naijxj=bi,
where aij is the stoichiometric number of theith element in the jth mineral. xj is the dissolved mole of the jth mineral, if the value is positive, it means that the jth mineral is dissolved, whereas the negative value indicates the jth mineral is precipitated. bi is the increments of the ith element between A and B.In this case, groundwater flows from northwest to southeast, W279 is in the upstream, W75 is in the downstream, so the simulation path is from W279 to W75. The chemical analysis results of sample W279 and W75 are showed in Table2. Saturation index (SI) is the common index to do the hydro-geochemical research, and it is applied to determine the saturation state of minerals in groundwater [17].Table 2
Groudwater chemical analysis results in the simulation path (mg/L).
pH
K+
Na+
Ca2+
Mg2+
HC
O
3
-
Cl−
S
O
4
2
-
F−
W279
8.15
1
57
34.56
10.47
238.83
34.09
2.45
0.12
W75
7.91
1.88
128
65.7
29.2
219.2
102.1
213.4
1The mineral facies are chosen based on the analysis result of groundwater quality, the main components of groundwater, and the occurrences conditions [18]. In the study area, the main cations are Na+, Ca2+, Mg2+, the main anions are HCO3-, SO42-, Cl−; thus halite, gypsum, calcite, and dolomite are chosen to be the mineral facies. Although fluoride is the required element for human body, considering its pathogenetic role, fluorite is also decided to be analyzed. Above all, there are five minerals selected.During the process of groundwater flow, the cations existed in groundwater can be exchanged by other cations existed in the surface of aquifer media. The cation exchange reactions plays important role in the chemical evolution of groundwater [17], so it is included in the mass balance simulation. If the ratio of Ca2+ to Na+ decreases in the flow path, it indicates that Ca2+ existed in groundwater may exchange with Na+ existed in clay; if the ratio of Ca2+ to Na+ increases, it indicates that Na+ existed in groundwater may exchange with Ca2+ existed in clay [19]. The reactions which may occur in the simulation path are listed in Table 3.Table 3
Reaction equations.
Reaction equation
Gypsum
CaSO4·2H2O = Ca2++ SO42-+ 2H2O
Fluorite
CaF2 = Ca2++ 2F−
Calcite
CaCO3 = Ca2++ CO32-
Halite
NaCl = Na++ Cl−
Dolomite
CaMg(CO3)2 = Ca2++ Mg2++ 2CO32-
Ion exchange
2NaX + Ca2+↔2Na++ CaX2Seen from Table4, Na+, Ca2+, and Cl− increase in the simulation path, and the increase degree of Na+ is greater than that of Cl+, which indicates that there are some other reactions related to Na+ occur in the simulation path besides halite’s dissolution. The value of Ca2+/Na+ in W279 is 0.3486, and the value of Ca2+/Na+ in W75 is 0.2951; it indicates that the cation exchange reaction may occur in the path.Table 4
Ratios of Ca2+/Na+ and Na+/Cl−.
Na+(mmol/L)
Ca2+(mmol/L)
Cl−(mmol/L)
Ca2+/Na+
Na+/Cl−
W279
2.4783
0.8640
0.9603
0.3486
0.3875
W75
5.5652
1.6425
2.8761
0.2951
0.5168
Difference
3.0870
0.7785
1.9158
−0.0535
0.1293The mass balance simulation is done by PHREEQC, and the simulation results are listed below.Seen from Table5, calcite and dolomite are always oversaturated in the simulation path and have the tendency to precipitate; meanwhile gypsum, fluorite and halite are unsaturated in the simulation path and have the tendency to dissolve into groundwater.Table 5
Saturation indices.
Gypsum
Fluorite
Calcite
Halite
Dolomite
CO2(g)
W279
−3.44
−3.13
0.61
−7.28
1.06
−2.79
W75
−1.42
−1.16
0.48
−6.49
0.96
−2.61Known from Table6, calcite precipitates while gypsum, fluorite, halite, and dolomite dissolve in the simulation path. The cation exchange reaction between Na+ and Ca2+ occurs at the same time. During the process, F− increases due to the fluorite’s dissolution, Cl− increases due to the halite’s dissolution, Mg2+ increases due to the dolomite’s dissolution, and SO42- increases due to the gypsum’s dissolution. Na+ increases because of the combined effect of halite’s dissolution and the cation exchange reaction. Since the influences of gypsum, fluorite, and dolomite’s dissolution on the content of Ca2+ are greater than that of calcite’s dissolution and the cation exchange reaction, the concentration of Ca2+ increases. The precipitation of calcite and the dissolution of dolomite together decrease HCO3-. Because the groundwater in this case is confined water and the burial depth is large, it is less connected with the atmosphere, so pH of the groundwater is mainly affected by the content of alkaline anions, such as HCO3-.Table 6
Dissolution of the mineral facies (mmol/L).
Calcite
Dolomite
Fluorite
Halite
Gypsum
NaX
CaX2
−1.612
0.781
0.023
1.907
2.199
1.138
−0.569
Note: Positive means dissolution, negative means precipitation.Judged from the dissolution of NaX and CaX2, the cation exchange reactions is extensive, and the change of Ca2+ is smaller, while the change of Na+ is greater, and the changing tendency of Ca2+/Na+ is apparent. Thus we can determine again that Na+ increase is due to the combined effect of halite’s dissolution and cation exchange reaction.


### 4.3. Assessment of Groundwater Quality

In this study, eight typical indexes are selected to be the evaluation indexes, which can reflect the physical and chemical characteristics of groundwater. There are TH, TDS, COD, Ca2+, Cl−, SO42-, HCO3-, and F−. The state standard of groundwater quality GB/T14848-93 is chosen to be the evaluation criterion, which is divided into five levels. Considering that there is no evaluation index exceeded the fifth level limit in this study, thus only the first fourth levels are chosen to build the matter elements.Based on matter element extension method, groundwater quality is evaluated. The comprehensive correlation degreeKi(P) and extension index j* are calculated and shown in Table 7.Table 7
Comprehensive correlation degrees and extension indexes.
Samples
K
i
(
P
)
j
*
Level
I
II
III
IV
W279
0.9374
−0.7077
−0.8589
−0.9026
1.1359
I
W390
0.7434
−0.4621
−0.6973
−0.8297
1.305
I
W719
0.5338
−0.1644
−0.7095
−0.8132
1.4078
I
W741
−0.1117
−0.2959
0.119
−0.4583
2.2124
II
W16
−0.132
0.3749
−0.451
−0.4885
1.7464
I
W43
0.0962
0.3431
−0.5084
−0.7263
1.7135
I
W44
0.4992
−0.2544
−0.5663
−0.7411
1.4398
I
W66
−0.2628
0.0508
0.2968
−0.1565
2.7885
II
W75
−0.1554
0.0453
0.2501
−0.2702
2.4265
II
W69
−0.3968
0.0186
0.2233
−0.1476
2.8706
IIKnown from Table7, groundwater quality of W279, W390, W719, W16, W43, and W44 belong to level I, and W741, W66, W75, and W69 belong to level II. The result indicates that groundwater quality in the study area is good as a whole and can be drinkable. Because of the great depth and the protection of aquitard, the confined water is not easy to be polluted. Judged from the value of extension index j*, water samples W16 and W43 tend to convert from level I into level II. W741 and W75 tend to convert from level II into level I, while W66 and W69 tend to convert from level II into level III.Which water sample’s quality is better than other’s at the same level can be judged by comparing the values of extension indexes. For instance, groundwater quality of both W279 and W16 belongs to level I, but the extension index value of sample W16 is higher than that of W279. It indicates that the attributive degree of W16 to convert into II level water is higher than that of W279. In other words, groundwater quality of W16 is worse than that of W279. The rest can be done in the same way. So groundwater quality of water samples from good to bad can be expressed in the order ofW279>W390>W719>W44>W43>W16>W741>W75>W66>W69.Osculating value method based on entropy weight [13] and principal component analysis method (PCA) [20] are the popular methods to assess groundwater quality, so we also use the two methods to assess groundwater quality of study area and then compare the results obtained from the three methods.Seen from Table8, the results obtained from the three different methods are basically similar. Principal component analysis method (PCA) neglects some important information, which may lead some result unreasonable; the evaluated result obtained by using osculating value method based on entropy weight is too restrict. Based on the reasons presented above, the evaluated results obtained from the three methods are different from each other more or less. But on the whole the comparison confirms that the results obtained from matter element extension are reliable and scientific.Table 8
Comparison of the results of the two methods.
Samples
W279
W390
W719
W741
W16
W43
W44
W66
W75
W69
Matter element extension
I
I
I
II
I
I
I
II
II
II
Osculating value method
I
I
I
II
II
I
I
III
III
III
PCA
I
I
I
II
II
II
III
II
II
II


## 4.1. Parameters Analysis

Groundwater quality depends on various chemical constituents and their concentrations, which are mostly derived from the geological stratum of the particular region. Thus it is necessary to find some useful indicators, both chemical and physical, to monitor groundwater quality changes. The individual parameters are given as minimum, maximum, average, and standard deviation of the collected samples in the specific area.Seen from Table1 and Figure 1, there are mainly six ions in the groundwater (Na+, Mg2+, Ca2+, Cl−, SO42-, HCO3-). They have indirect influence on other parameters of groundwater, such as TDS, TH, and conductivity, thus they can affect groundwater quality to some extent.Table 1
Statistical analysis for physicochemical parameters of groundwater.
Parameters
Max
Min
Average
Std. Dev.
TH
400.05
84.1
199.08
102.43
TDS
665
259.31
504.67
132.05
COD
2.84
0.44
1.37
0.79
Na+
200
57
123.5
48.52
K+
4.87
0.94
2.25
1.33
Mg2+
29.68
7.8
17.29
8.98
Ca2+
103.67
20.8
49.44
26.15
Cl−
160.9
34.09
89.79
33.93
S
O
4
2
-
213.4
2.45
98.91
81.08
HC
O
3
-
395.96
192.2
264.22
57.41
F−
1.13
0.1
0.58
0.46
Note: Unit mg/L for all parameters.Figure 1
Pipe chart of groundwater ions equivalents.Total hardness (TH) is closely related to daily life and industry; water with high TH is not suitable for drinking, washing, and industry. Besides, it may lead to some diseases. The maximum TH is 400.05 mg/L in W741; the minimum is 84.1 mg/L in W44. TDS reflects the total concentration of dissolved solids; the high TDS is maybe caused by mineral weathering. The TDS ranges from a minimum of 259.31 mg/L in W279 to a maximum of 665 mg/L in W75.COD reflects the organic matter’s concentration; whether water is polluted by organics can be judged from the value of COD. The highest value of COD is 2.84 mg/L in W44; the lowest value is 0.44 mg/L in W279. COD is slightly higher, which may be due to the organic pollution.Fluoride in small amount is good for preventing dental caries, but high concentration causes health risk such as dental fluorosis and skeletal fluorosis [16]. Fluoride-bearing minerals in the rocks and their interaction with water and agricultural activities are considered to be the main cause for fluoride in groundwater. In this case, the fluoride ranges from 0.1 mg/L to 1.13 mg/L, and there is no values exceed the permissible limits.Volatile phenol, As, Hg, Cr, Ag, and other heavy metals are important for assessing groundwater quality; if their concentrations are too high, human health will be under threat. Fortunately, these indexes in this study are all within the permissible limits.Hydrochemical concepts help to elucidate mechanisms of flow and transport in groundwater systems. In this paper, Piper plot is used to infer hydrogeochemical facies of groundwater. Seen from Figure2 that the major chemical types of water samples fall into Cl·HCO3-Na type, Cl·HCO3-Na·Ca type, Cl·SO4·HCO3-Na·Ca, Cl·SO4·HCO3-Na·Ca·Mg type and some mixed. Seen from the plot, alkalis (Na and K) exceed alkaline earths (Ca and Mg) and strong acids (Cl and SO4) exceed weak acids (HCO3 and CO3).Figure 2
Piper plot of groundwater samples.


## 4.2. Mass Balance Simulations

Mass balance simulation is mainly used for studying the chemical reaction during the process of groundwater flow. In the method, two points (e.g., A and B) in the flow path are considered to be the study subjects. The chemistry of A in the upstream is considered to be the initial water quality, and the chemistry of B in the downstream is considered to be the final water quality. According to the chemical reactions between groundwater and aquifer, the quantities of mineral dissolution and precipitation between A and B can be calculated using the mass balance principle. On the basis of that, the chemistry changes in groundwater can be analyzed. In general, mass balance simulation is based on the following equation [17]:
(7)∑j=1naijxj=bi,
where aij is the stoichiometric number of theith element in the jth mineral. xj is the dissolved mole of the jth mineral, if the value is positive, it means that the jth mineral is dissolved, whereas the negative value indicates the jth mineral is precipitated. bi is the increments of the ith element between A and B.In this case, groundwater flows from northwest to southeast, W279 is in the upstream, W75 is in the downstream, so the simulation path is from W279 to W75. The chemical analysis results of sample W279 and W75 are showed in Table2. Saturation index (SI) is the common index to do the hydro-geochemical research, and it is applied to determine the saturation state of minerals in groundwater [17].Table 2
Groudwater chemical analysis results in the simulation path (mg/L).
pH
K+
Na+
Ca2+
Mg2+
HC
O
3
-
Cl−
S
O
4
2
-
F−
W279
8.15
1
57
34.56
10.47
238.83
34.09
2.45
0.12
W75
7.91
1.88
128
65.7
29.2
219.2
102.1
213.4
1The mineral facies are chosen based on the analysis result of groundwater quality, the main components of groundwater, and the occurrences conditions [18]. In the study area, the main cations are Na+, Ca2+, Mg2+, the main anions are HCO3-, SO42-, Cl−; thus halite, gypsum, calcite, and dolomite are chosen to be the mineral facies. Although fluoride is the required element for human body, considering its pathogenetic role, fluorite is also decided to be analyzed. Above all, there are five minerals selected.During the process of groundwater flow, the cations existed in groundwater can be exchanged by other cations existed in the surface of aquifer media. The cation exchange reactions plays important role in the chemical evolution of groundwater [17], so it is included in the mass balance simulation. If the ratio of Ca2+ to Na+ decreases in the flow path, it indicates that Ca2+ existed in groundwater may exchange with Na+ existed in clay; if the ratio of Ca2+ to Na+ increases, it indicates that Na+ existed in groundwater may exchange with Ca2+ existed in clay [19]. The reactions which may occur in the simulation path are listed in Table 3.Table 3
Reaction equations.
Reaction equation
Gypsum
CaSO4·2H2O = Ca2++ SO42-+ 2H2O
Fluorite
CaF2 = Ca2++ 2F−
Calcite
CaCO3 = Ca2++ CO32-
Halite
NaCl = Na++ Cl−
Dolomite
CaMg(CO3)2 = Ca2++ Mg2++ 2CO32-
Ion exchange
2NaX + Ca2+↔2Na++ CaX2Seen from Table4, Na+, Ca2+, and Cl− increase in the simulation path, and the increase degree of Na+ is greater than that of Cl+, which indicates that there are some other reactions related to Na+ occur in the simulation path besides halite’s dissolution. The value of Ca2+/Na+ in W279 is 0.3486, and the value of Ca2+/Na+ in W75 is 0.2951; it indicates that the cation exchange reaction may occur in the path.Table 4
Ratios of Ca2+/Na+ and Na+/Cl−.
Na+(mmol/L)
Ca2+(mmol/L)
Cl−(mmol/L)
Ca2+/Na+
Na+/Cl−
W279
2.4783
0.8640
0.9603
0.3486
0.3875
W75
5.5652
1.6425
2.8761
0.2951
0.5168
Difference
3.0870
0.7785
1.9158
−0.0535
0.1293The mass balance simulation is done by PHREEQC, and the simulation results are listed below.Seen from Table5, calcite and dolomite are always oversaturated in the simulation path and have the tendency to precipitate; meanwhile gypsum, fluorite and halite are unsaturated in the simulation path and have the tendency to dissolve into groundwater.Table 5
Saturation indices.
Gypsum
Fluorite
Calcite
Halite
Dolomite
CO2(g)
W279
−3.44
−3.13
0.61
−7.28
1.06
−2.79
W75
−1.42
−1.16
0.48
−6.49
0.96
−2.61Known from Table6, calcite precipitates while gypsum, fluorite, halite, and dolomite dissolve in the simulation path. The cation exchange reaction between Na+ and Ca2+ occurs at the same time. During the process, F− increases due to the fluorite’s dissolution, Cl− increases due to the halite’s dissolution, Mg2+ increases due to the dolomite’s dissolution, and SO42- increases due to the gypsum’s dissolution. Na+ increases because of the combined effect of halite’s dissolution and the cation exchange reaction. Since the influences of gypsum, fluorite, and dolomite’s dissolution on the content of Ca2+ are greater than that of calcite’s dissolution and the cation exchange reaction, the concentration of Ca2+ increases. The precipitation of calcite and the dissolution of dolomite together decrease HCO3-. Because the groundwater in this case is confined water and the burial depth is large, it is less connected with the atmosphere, so pH of the groundwater is mainly affected by the content of alkaline anions, such as HCO3-.Table 6
Dissolution of the mineral facies (mmol/L).
Calcite
Dolomite
Fluorite
Halite
Gypsum
NaX
CaX2
−1.612
0.781
0.023
1.907
2.199
1.138
−0.569
Note: Positive means dissolution, negative means precipitation.Judged from the dissolution of NaX and CaX2, the cation exchange reactions is extensive, and the change of Ca2+ is smaller, while the change of Na+ is greater, and the changing tendency of Ca2+/Na+ is apparent. Thus we can determine again that Na+ increase is due to the combined effect of halite’s dissolution and cation exchange reaction.


## 4.3. Assessment of Groundwater Quality

In this study, eight typical indexes are selected to be the evaluation indexes, which can reflect the physical and chemical characteristics of groundwater. There are TH, TDS, COD, Ca2+, Cl−, SO42-, HCO3-, and F−. The state standard of groundwater quality GB/T14848-93 is chosen to be the evaluation criterion, which is divided into five levels. Considering that there is no evaluation index exceeded the fifth level limit in this study, thus only the first fourth levels are chosen to build the matter elements.Based on matter element extension method, groundwater quality is evaluated. The comprehensive correlation degreeKi(P) and extension index j* are calculated and shown in Table 7.Table 7
Comprehensive correlation degrees and extension indexes.
Samples
K
i
(
P
)
j
*
Level
I
II
III
IV
W279
0.9374
−0.7077
−0.8589
−0.9026
1.1359
I
W390
0.7434
−0.4621
−0.6973
−0.8297
1.305
I
W719
0.5338
−0.1644
−0.7095
−0.8132
1.4078
I
W741
−0.1117
−0.2959
0.119
−0.4583
2.2124
II
W16
−0.132
0.3749
−0.451
−0.4885
1.7464
I
W43
0.0962
0.3431
−0.5084
−0.7263
1.7135
I
W44
0.4992
−0.2544
−0.5663
−0.7411
1.4398
I
W66
−0.2628
0.0508
0.2968
−0.1565
2.7885
II
W75
−0.1554
0.0453
0.2501
−0.2702
2.4265
II
W69
−0.3968
0.0186
0.2233
−0.1476
2.8706
IIKnown from Table7, groundwater quality of W279, W390, W719, W16, W43, and W44 belong to level I, and W741, W66, W75, and W69 belong to level II. The result indicates that groundwater quality in the study area is good as a whole and can be drinkable. Because of the great depth and the protection of aquitard, the confined water is not easy to be polluted. Judged from the value of extension index j*, water samples W16 and W43 tend to convert from level I into level II. W741 and W75 tend to convert from level II into level I, while W66 and W69 tend to convert from level II into level III.Which water sample’s quality is better than other’s at the same level can be judged by comparing the values of extension indexes. For instance, groundwater quality of both W279 and W16 belongs to level I, but the extension index value of sample W16 is higher than that of W279. It indicates that the attributive degree of W16 to convert into II level water is higher than that of W279. In other words, groundwater quality of W16 is worse than that of W279. The rest can be done in the same way. So groundwater quality of water samples from good to bad can be expressed in the order ofW279>W390>W719>W44>W43>W16>W741>W75>W66>W69.Osculating value method based on entropy weight [13] and principal component analysis method (PCA) [20] are the popular methods to assess groundwater quality, so we also use the two methods to assess groundwater quality of study area and then compare the results obtained from the three methods.Seen from Table8, the results obtained from the three different methods are basically similar. Principal component analysis method (PCA) neglects some important information, which may lead some result unreasonable; the evaluated result obtained by using osculating value method based on entropy weight is too restrict. Based on the reasons presented above, the evaluated results obtained from the three methods are different from each other more or less. But on the whole the comparison confirms that the results obtained from matter element extension are reliable and scientific.Table 8
Comparison of the results of the two methods.
Samples
W279
W390
W719
W741
W16
W43
W44
W66
W75
W69
Matter element extension
I
I
I
II
I
I
I
II
II
II
Osculating value method
I
I
I
II
II
I
I
III
III
III
PCA
I
I
I
II
II
II
III
II
II
II


## 5. Conclusion

From the mass balance simulation, calcite and dolomite are oversaturated, meanwhile gypsum, fluorite and halite are unsaturated in the simulation path, and the changing tendency of Ca2+/Na+ is apparent. Calcite precipitates, while gypsum, fluorite, halite, and dolomite dissolve in the simulation path. Because of the dissolution and precipitation of minerals, the contents of chemical compositions are changed. Groundwater quality in the study area is evaluated by using the matter element extension method, and results show the groundwater meets the requirement of drinking water standards. It is proved that matter element extension is a reasonable and effective method to evaluate groundwater quality by comparing the results obtained from the other methods. The application of information entropy minimizes the subjective interferences and makes the result more objective and accurate. According to the values of extension indexes, groundwater quality of water samples in the same level can be compared and the tendency of conversion can be judged; it is the unique characteristic of matter element extension method used in this study.



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*Source: 715647-2012-09-27.xml*