# Analysis of the Erosion Law of Karst Groundwater Using Hydrogeochemical Theory in Liulin Spring Area, North China

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Liulin Spring Area

#### 2.1. Physical Geography

^{2}, and its average annual runoff is 194 million m

^{3}/a.

#### 2.2. Geology and Hydrogeology

#### 2.3. Sampling and Analysis

_{3}

^{−}, SO

_{4}

^{2−}, Cl, Na

^{+}+ K

^{+}, Ca

^{2+}, Mg

^{2+}and TDS (Total Dissolved Solids) was accomplished in the water environmental monitoring center of Shanxi province.

_{3}

^{−}was measured using the Gran titration method in the sampling day. Samples for cation analysis were acidified using 1:1 nitric acid to pH < 2 in field. The cations (K

^{+}+ Na

^{+}, Ca

^{2+}, Mg

^{2+}) and anions (Cl

^{−}, SO

_{4}

^{2−}) were determined by atomic absorption spectrometry (PERSEE TAS990F) and ion chromatography (CIC300), respectively. The uncertainties of measurements were all within 5%.

## 3. Model Building and Feature Analysis of Hydrogeochemistry

#### 3.1. Hydrogeochemical Partition and the Construction of Its Model

#### 3.2. Geochemical Characteristics Analysis

#### 3.2.1. βc ≤ 1 (Zone I)

_{2}open system. The karst water chemistry reactions, including the reaction of CO

_{2}dissolved in phreatic water and the reaction between H

^{+}generated by CO

_{2}dissolution and the calcite and dolomite in carbonate rocks, nevertheless, have little effect on the process of gypsum dissolution. The main equations of chemical reaction models in zone I are as follows:

_{2}+ H

_{2}O = H

_{2}CO

_{3}

_{2}CO

_{3}= H

^{+}+ HCO

_{3}

^{−}

_{3}

^{−}= H

^{+}+ CO

_{3}

^{2−}

_{3}+ H

^{+}= Ca

^{2+}+ HCO

_{3}

^{−}

_{3})

_{2}+ 2H

^{+}= Ca

^{2+}+ Mg

^{2+}+ 2HCO

_{3}

^{−}

_{4}·2H

_{2}O = Ca

^{2+}+ SO

_{4}

^{2−}+ 2H

_{2}O

#### 3.2.2. βc > 1 ~ βd ≤ 1 (Zone II)

_{2}cannot directly pass into, so the hydrogeochemical environment of this zone is a relatively closed system. The karst water chemistry reaction mainly consumes CO

_{2}that dissolved in zone I, including the precipitation of calcite and dissolution of dolomite and gypsum. The main equations of chemical reaction models of zone II are as follows:

_{2}CO

_{3}= H

^{+}+ HCO

_{3}

^{−}

_{3}

^{−}= H

^{+}+ CO

_{3}

^{2−}

_{3})

_{2}+ 2H

^{+}= Ca

^{2+}+ Mg

^{2+}+ 2HCO

_{3}

^{−}

_{4}·2H

_{2}O = Ca

^{2+}+ SO

_{4}

^{2−}+ 2H

_{2}O

^{2+}+ CO

_{3}

^{2−}= CaCO

_{3}

#### 3.2.3. βd > 1 ~ βg ≤ 1 (Zone III)

_{4}·2H

_{2}O = Ca

^{2+}+ SO

_{4}

^{2−}+ 2H

_{2}O

^{2+}+ CO

_{3}

^{2−}= CaCO

_{3}

^{2+}+ Mg

^{2+}+ 2CO

_{3}

^{2−}= CaMg(CO

_{3})

_{2}

#### 3.2.4. βg > 1 (Zone IV)

^{2+}+ CO

_{3}

^{2−}= CaCO

_{3}

^{2+}+ Mg

^{2+}+ 2CO

_{3}

^{2−}= CaMg(CO

_{3})

_{2}

^{2+}+ SO

_{4}

^{2−}= CaSO

_{4}

## 4. Calculation and Discussion of Corrosion Modulus

#### 4.1. βc ≤ 1 (Zone I)

^{2+}computed by water quality analysis is supposed to be the total quantities of Ca

^{2+}(T

_{Ca2+}) dissolved from calcite, dolomite and gypsum. The amount of Ca

^{2+}and SO

_{4}

^{2−}dissolved from gypsum is equivalent, so that this part of Ca

^{2+}can be expressed as (T

_{Ca2+/SO42−}). Based on the previous analysis, the content of Ca

^{2+}dissolved from carbonate rocks, which has correlativity with the content of HCO

_{3}

^{−}, can be computed by deducting T

_{Ca2+/SO42−}from T

_{Ca2+}. Assuming that the contents of gypsum, calcite and dolomite dissolved into groundwater are m

_{1}, m

_{2}and m

_{3}respectively, the dissolution equations of three kinds of minerals are presented as follows:

_{1}CaSO

_{4}·2H

_{2}O = m

_{1}Ca

^{2+}+ m

_{1}SO

_{4}

^{2−}+ 2m

_{1}H

_{2}O

_{2}CaCO

_{3}= m

_{2}Ca

^{2+}+ m

_{2}CO

_{3}

^{2−}

_{3}CaMg(CO

_{3})

_{2}= m

_{3}Ca

^{2+}+ m

_{3}Mg

^{2+}+ 2m

_{3}CO

_{3}

^{2−}

_{1}CaSO

_{4}·2H

_{2}O + m

_{2}CaCO

_{3}+ m

_{3}CaMg(CO

_{3})

_{2}+ (2m

_{3}+ m

_{2})CO

_{2}+ (2m

_{3}+ m

_{2})H

_{2}O

=(m

_{1}+ m

_{2}+ m

_{3})Ca

^{2+}+ m

_{1}SO

_{4}

^{2−}+ m

_{3}Mg

^{2+}+ (2m

_{2}+ 4m

_{3})HCO

_{3}

^{−}+ 2m

_{1}H

_{2}O

^{2+}and SO

_{4}

^{2−}are identical is reasonable, namely:

_{1}= A

_{1}X

_{1}+ B

_{1}

_{1}denotes the average content of SO

_{4}

^{2−}(mmol/L), X

_{1}represents the average content of T

_{Ca2+/SO42-}(mmol/L), and A

_{1}and B

_{1}are a constant that usually equal 1 and 0, respectively.

_{3}

^{−}, Ca

^{2+}and Mg

^{2+}, so the correlation equations are established as follows:

_{2}= A

_{2}X

_{2}+ B

_{2}

_{3}= A

_{3}X

_{2}+ B

_{3}

_{2}and y

_{3}are the contents of Ca

^{2+}dissolved from calcite and Mg

^{2+}dissolved from dolomite (mmol/L), X

_{2}denotes the average content of HCO

_{3}

^{−}(mmol/L), A

_{2}and A

_{3}are the regression coefficients, B

_{2}and B

_{3}are constant.

^{2+}with SO

_{4}

^{2−}, Ca

^{2+}(Ca

^{2+}− SO

_{4}

^{2−}) with HCO

_{3}

^{−}and Mg with HCO

_{3}

^{−}(shown in Figure 3). The following correlation equations can be observed in Figure 3.

_{2}= 0.4012X

_{2}− 0.1921

_{3}= 0.0603X

_{2}+ 0.3328

_{1}X

_{1}for m

_{1}, A

_{2}X

_{2}for m

_{2}, A

_{3}X

_{2}for m

_{3}, Equation (4) changes to:

_{1}X

_{1}CaSO

_{4}·2H

_{2}O + A

_{2}X

_{2}CaCO

_{3}+ A

_{3}X

_{2}CaMg(CO

_{3})

_{2}+ (2A

_{3}+ A

_{2})X

_{2}CO

_{2}+ (2A

_{3}+ A

_{2})X

_{2}H

_{2}O + ∑C = A

_{1}X

_{1}Ca

^{2+}+ A

_{1}X

_{1}SO

_{4}

^{2−}+ 2A

_{1}X

_{1}H

_{2}O + (A

_{2}+ A

_{3})X

_{2}Ca

^{2+}+ A

_{3}X

_{2}Mg

^{2+}+ (2A

_{2}+ 4A

_{3})X

_{2}HCO

_{3}

^{−}+ B

_{2}Ca

^{2+}+ B

_{3}Mg

^{2+}

_{2}Ca

^{2+}+ B

_{3}Mg

^{2+}, ∑C can be seen as the constant in Equations (6) and (7), and is also the product of carbonate rock dissolution and has nothing to do with the dissolution of sulphate rocks. The following comprehensive chemical equation is established in the form of Equation (4):

_{2}− B

_{3})CaCO

_{3}+ B

_{3}CaMg(CO

_{3})

_{2}+ (B

_{2}+ 2B

_{3})CO

_{2}+ (B

_{2}+ 2B

_{3})H

_{2}O = B

_{2}Ca

^{2+}+ B

_{3}Mg

^{2+}+ (2B

_{2}+ 4B

_{3})HCO

_{3}

^{−}

_{2}Ca

^{2+}represents the total content of Ca

^{2+}dissolved from calcite and dolomite, B

_{3}represents the content of Ca

^{2+}dissolved from the dolomite, and (B

_{2}− B

_{3}) represents the content of Ca

^{2+}dissolved from calcite.

_{1}X

_{1}CaSO

_{4}·2H

_{2}O = A

_{1}X

_{1}Ca

^{2+}+ A

_{1}X

_{1}SO

_{4}

^{2−}+ 2A

_{1}X

_{1}H

_{2}O

_{2}X

_{2}CaCO

_{3}+ (B

_{2}− B

_{3})CaCO

_{3}= (A

_{2}X

_{2}+ B

_{2}− B

_{3})CaCO

_{3}

_{3}X

_{2}CaMg(CO

_{3})

_{2}+ B

_{3}CaMg(CO

_{3})

_{2}= (A

_{3}X

_{2}+ B

_{3})CaMg(CO

_{3})

_{2}

_{g}, M

_{d}, M

_{c}):

_{g}= 0.5A

_{1}X

_{1}CaSO

_{4}·2H

_{2}O = 86.09X

_{1}= 86.09 × 0.15 = 12.914(g/m

^{3})

_{d}= 0.25(A

_{3}X

_{2}+ B

_{3})CaMg(CO

_{3})

_{2}= 46.1(A

_{3}X

_{2}+ B

_{3}) = 46.1 × (0.0603 × 3.65 + 0.3328) = 25.489(g/m

^{3})

_{c}= 0.5(A

_{2}X

_{2}+ B

_{2}− B

_{3})CaCO

_{3}= 50.045(A

_{2}X

_{2}+ B

_{2}− B

_{3}) = 50.045 × (0.4012 × 3.65 − 0.1921 − 0.3328) = 47.016(g/m

^{3})

_{1}) is the sum of each mineral modulus. Namely:

_{1}= M

_{c}+ M

_{d}+ M

_{g}= 12.914 + 47.016 + 25.489 = 85.418(g/m

^{3})

_{d}, N

_{c}) of gypsum, dolomite and calcite are computed as follows:

_{g}= M

_{g}/γ

_{g}= 86.09X

_{1}/2.3 × 10

^{−6}= 3.743X

_{1}× 10

^{−5}= 3.743 × 10

^{−5}× 0.15 = 5.615 × 10

^{−6}

_{d}= M

_{d}/γ

_{d}= 46.1/2.8 × (A

_{3}X

_{2}+ B

_{3}) × 10

^{−6}= 1.646(A

_{3}X

_{2}+ B

_{3}) × 10

^{−5}

^{−5}= 9.103 × 10

^{−6}

_{c}= M

_{c}/γ

_{c}= 50.045/2.7 × (A

_{2}X

_{2}+ B

_{2}− B

_{3}) × 10

^{−6}= 1.845(A

_{2}X

_{2}+ B

_{2}− B

_{3}) × 10

^{−5}

^{−5}= 1.741 × 10

^{−5}

_{1}) is computed as:

_{1}= N

_{g}+ N

_{d}+ N

_{c}= 5.615 × 10

^{−6}+ 9.103 × 10

^{−6}+ 1.741 × 10

^{−5}= 3.213 × 10

^{−5}

_{g}equals 12.914 g/m

^{3}and N

_{g}equals 5.615 × 10

^{−6}, and the dissolved quantities of dolomite are such that M

_{d}equals 25.489 g/m

^{3}and N

_{d}equals 9.103 × 10

^{−6}. The dissolved quantities of calcite in the unit volume of water is maximal with M

_{c}equal to 47.016 g/m

^{3}and N

_{c}equals 1.741 × 10

^{−5}. The total weight modulus and volume modulus of the three minerals are 85.418 g/m

^{3}and 3.213 × 10

^{−5}, respectively. Evidently, calcite dissolution, whose dissolved quantity is larger than that of dolomite and gypsum, is more likely given priority in this zone. The mineral dissolution lead to the new space increasing, and the analysis which is mentioned above indicates that the volume modulus of new space created by calcite dissolution is one order of magnitude larger than that of dolomite and gypsum dissolution.

#### 4.2. βc >1 ~ βd ≤ 1 (Zone II)

^{2+}and CO

_{3}

^{2−}are in the supersaturated state, so that the dissolution of calcite does not occur in this zone but the dissolution of dolomite and gypsum still exist. Based on the same principle as zone I, the comprehensive chemical equations (in zone II) about the dissolution of dolomite and gypsum are as follows:

_{4}CaMg(CO

_{3})

_{2}= m

_{4}Ca

^{2+}+ m

_{4}Mg

^{2+}+ 2m

_{4}CO

_{3}

^{2−}

_{5}CaSO

_{4}·2H

_{2}O = m

_{5}Ca

^{2+}+ m

_{5}SO

_{4}

^{2−}+ 2m

_{5}H

_{2}O

_{4}CaMg(CO

_{3})

_{2}+ m

_{5}CaSO

_{4}·2H

_{2}O = m

_{4}CaCO

_{3}+ (m

_{5}Ca

^{2+}+ m

_{4}CO

_{3}

^{2−}) + m

_{4}Mg

^{2+}+ m

_{5}SO

_{4}

^{2−}+ 2m

_{5}H

_{2}O

_{4}CaCO

_{3}(i.e., m

_{4}CaCO

_{3}+ m

_{4}Ca

^{2+}+ m

_{4}CO

_{3}

^{2−}) represents the precipitation of calcite when m

_{5}Ca

^{2+}≥ m

_{4}CO

_{3}

^{2−}and the extra quantity of (m

_{5}− m

_{4}) Ca

^{2+}saves in the karst water, while (m

_{4}+ m

_{5}) CaCO

_{3}(i.e., m

_{4}CaCO

_{3}+ m

_{5}Ca

^{2+}+ m

_{5}CO

_{3}

^{2−}) represents the quantity of calcite precipitation when m

_{5}Ca

^{2+}> m

_{4}CO

_{3}

^{2−}and the extra quantity of (m

_{4 −}m

_{5}) CO

_{3}

^{2−}saves in the karst water.

^{2+}dissolved from gypsum from total content in zone II, the rest is the sum content of Ca

^{2+}which consists of the part inputted from zone I and the other part dissolved from dolomite in zone II. It is difficult to determine the quantity of CaCO

_{3}which formed by Ca

^{2+}and CO

_{3}

^{2−}, so the values of A

_{4}and B

_{4}are computed by the relationship between Mg

^{2+}and HCO

_{3}

^{−}based on the equation as follows:

_{4}= A

_{4}X

_{4}+ B

_{4}

_{4}and X

_{4}are the content of Mg

^{2+}and HCO

_{3}

^{−}(mmol/L). A

_{4}and B

_{4}are the coefficient of regression and constant, respectively.

^{2+}and SO

_{4}

^{2−}dissolved from gypsum and accumulated from zone I are still few. Assuming that the dissolved quantities of Ca

^{2+}and SO

_{4}

^{2−}are identical, the correlation equation of Ca

^{2+}and SO

_{4}

^{2−}is presented as follows:

_{5}= A

_{5}X

_{5}+ B

_{5}

_{5}and X

_{5}denote the content of SO

_{4}

^{2−}and Ca

^{2+}, which are equivalent (mmol/L). A

_{5}and B

_{5}are constants of 1 and 0, respectively.

^{2+}with SO

_{4}

^{2−}and Mg with HCO

_{3}

^{−}are drawn (Figure 4). The following correlation equations can be observed from Figure 4.

_{4}= 0.7429X

_{4}− 2.0786

_{4}X

_{4}CaMg(CO

_{3})

_{2}+ A5X5CaSO

_{4}·2H

_{2}O + ∑C = A

_{4}X

_{4}CaCO

_{3}↓ + A

_{4}X

_{4}CO

_{3}

^{2−}+ A

_{5}X

_{5}Ca

^{2+}+ A

_{4}X

_{4}Mg

^{2+}+ A

_{5}X

_{5}SO

_{4}

^{2−}+ 2ª

_{5}X

_{5}H

_{2}O + B

_{4}Ca

^{2+}+ B

_{4}Mg

^{2+}

_{4}Ca

^{2+}+ B

_{4}Mg

^{2+}is the product of carbonate rock dissolution and has nothing to do with the dissolution of sulphate:

_{4}CaMg(CO

_{3})

_{2}= B

_{4}Ca

^{2+}+ B

_{4}Mg

^{2+}+ B

_{4}CO

_{3}

^{2−}

_{4}X

_{4}CaMg(CO

_{3})

_{2}+ B

_{4}CaMg(CO

_{3})

_{2}= (A

_{4}X

_{4}+ B

_{4})CaMg(CO

_{3})

_{2}

_{5}X

_{5}CaSO

_{4}·2H

_{2}O = A

_{5}X

_{5}Ca

^{2+}+ A

_{5}X

_{5}SO

_{4}

^{2−}+ 2A

_{5}X

_{5}H

_{2}O

_{g}and M

_{d}:

_{g}= 0.5A

_{5}X

_{5}CaSO

_{4}·2H

_{2}O = 86.09X

_{5}= 86.09 × 0.25 = 21.523(g/m

^{3})

_{d}= 0.25(A

_{4}X

_{4}+ B

_{4})CaMg(CO

_{3})

_{2}= 46.1(A

_{4}X

_{4}+ B

_{4}) = 46.1 × (0.7429 × 3.85 − 2.0786) = 36.030(g/m

^{3})

_{4}

^{2−}is two times less than that of Mg

^{2+}, so M

_{c}can be computed as:

_{c}= −50.045 × (0.7429 × 3.85 + 0.25 − 2.0786) = −51.625(g/m

^{3})

_{2}) can be calculated as:

_{2}= M

_{g}+ M

_{d}+ M

_{c}= 21.523 + 36.030 − 51.625 = 5.928(g/m

^{3})

_{g}, N

_{d}, N

_{c}are computed as follows:

_{g}= 3.743 × 10

^{−5}X

_{5}= 3.743 × 10

^{−5}× 0.25 = 9.358 × 10

^{−6}

_{d}= 1.646(A4X4 + B4) × 10

^{−5}= 1.646 × (0.7429 × 3.85 − 2.0786) × 10

^{−5}= 1.287 × 10

^{−5}

_{c}= −1.854(A

_{4}X

_{4}+ A

_{5}X

_{5}+ B

_{4}) × 10

^{−5}= −1.854 × (0.7429 × 3.85 + 0.25 − 2.0786) × 10

^{−5}= −1.912 × 10

^{−5}

_{2}) can be calculated as:

_{2}= N

_{g}+ N

_{d}+ N

_{c}= 9.358 × 10

^{−6}+ 1.287 × 10

^{−5}− 1.912 × 10

^{−5}= 3.105 × 10

^{−6}

_{g}equals 21.523 g/m

^{3}and N

_{g}equals 9.358 × 10

^{−6}. The dissolved quantity of dolomite is increased, which can be seen from M

_{d}(36.030 g/m

^{3}) and N

_{d}(1.278 × 10

^{−5}). The dissolution of calcite begins to be subside since it has already reached the supersaturated state and the values of M

_{c}and N

_{c}equal −51.625 g/m

^{3}and −1.912 × 10

^{−5}respectively. The total weight modulus and volume modulus of the three minerals are 5.928 g/m

^{3}and 3.105 × 10

^{−6}. Evidently, dolomite dissolution, whose dissolved quantity is larger than that of gypsum, is more likely given priority in this zone while calcite starts to precipitate. Generally speaking, the new space created by the dissolution of dolomite and gypsum is larger than the space filled by the precipitation of calcite, which can be seen from the value of N

_{2}(3.105 × 10

^{−6}> 0).

#### 4.3. βd >1 ~ βg ≤ 1 (Zone III)

_{6}CaSO

_{4}·2H

_{2}O = m

_{6}Ca

^{2+}+ m

_{6}SO

_{4}

^{2−}+ 2m

_{6}H

_{2}O

_{7}CaMg(CO

_{3})

_{2}+ m

_{7}Ca

^{2+}= m

_{7}Mg

^{2+}+ 2m

_{7}CaCO

_{3}↓

^{2+}(in Equation (23)) is far lower than the quantity of Ca

^{2+}(in Equation (22)), that is to say, m

_{6}> m

_{7}. Combining the Equation (22) and (23) then obtains the following equation:

_{6}CaSO

_{4}·2H

_{2}O + m

_{7}CaMg(CO

_{3})

_{2}= (m

_{6}·− m

_{7})Ca

^{2+}+ m

_{6}SO

_{4}

^{2−}+ 2m

_{6}H

_{2}O + m

_{7}Mg

^{2+}+ 2m

_{7}CaCO

_{3}

_{6}= 0.7253X

_{6}+ 1.0131

_{7}= 0.2590X

_{7}+ 0.8869

_{6}X

_{6}+ B

_{6})CaSO

_{4}·2H

_{2}O

_{7}X

_{7}+ B

_{7})CaMg(CO

_{3})

_{2}

_{6}X

_{6}+ B

_{7})CaCO

_{3}

^{2+}in groundwater. The two kinds of chemistry reaction of the dissolution of gypsum and precipitation of calcite are main considerations for the rock reconstruction in zone III. Equations (25) and (27) are used to compute M

_{g}and M

_{c}:

_{g}= 86.09(A

_{6}X

_{6}+ B

_{6}) = 86.09 × (0.7253 × 2.16 + 1.0131) = 222.091(g/m

^{3})

_{c}= −100.089(A

_{6}X

_{6}+ B

_{7}) = −100.089 × (0.7253 × 2.16 + 0.8869) = −245.573(g/m

^{3})

_{3}) can be calculated as:

_{3}= M

_{g}+ M

_{c}= 222.091 − 245.573 = −23.482(g/m

^{3})

_{g}and N

_{c}are computed based on the weight modulus:

_{g}= 3.743(A

_{6}X

_{6}+ B

_{6}) × 10

^{−5}= 3.743 × (0.7253 × 2.16 + 1.0131) × 10

^{−5}= 9.656 × 10

^{−5}

_{c}= −3.707(A

_{6}X

_{6}+ B

_{7}) × 10

^{−5}= −3.707 × (0.7253 × 2.16 + 0.8869) × 10

^{−5}= −9.095 × 10

^{−5}

_{3}) can be calculated as:

_{3}= N

_{g}+ N

_{c}= 9.656 × 10

^{−5}− 9.095 × 10

^{−5}= 5.61 × 10

^{−6}

_{g}equals to 222.091 g/m

^{3}and N

_{g}equal to 9.656 × 10

^{−5}. Calcite (M

_{c}and N

_{c}are −245.573 g/m

^{3}and −9.095 × 10

^{−5}, respectively) is still in the supersaturated state and is accompanied by dedolomitization. The total weight modulus in this zone is −23.482 g/m

^{3}, so the quantity of calcite precipitation is greater than that of gypsum dissolution. The value of the total volume modulus (5.61 × 10

^{−6}) indicates that the groundwater influence on the aquifer will still form little amounts of new pore space. It is of significant importance to get a more comprehensive understanding of interaction between water and rocks by combining these two kinds of moduli (the weight modulus and volume modulus) for the evaluation of the dissolution quantities in zone III.

_{c}reduced from 47.016 g/m

^{3}to −51.625 g/m

^{3}, then to −245.573 g/m

^{3}, and the value of N

_{c}reduced from 1.7 × 10

^{−5}to −1.912 × 10

^{−5}, then to −9.095 × 10

^{−5}, which indicates that the corrosion modulus of calcite decreased and the chemical reaction transformed dissolution into precipitation, and the ability of calcite precipitation continued strengthening from zone II to III. Secondly, the value of M

_{d}increased from 25.489 g/m

^{3}to 36.030 g/m

^{3}, and N

_{d}increased from 9.103 × 10

^{−6}to 1.287 × 10

^{−5}, which reveals that the corrosion modulus of dolomite was increasing gradually, and the ability of dolomite dissolution continued strengthening from zone I to zone II, then dolomite reached the state of supersaturation with weak dedolomitization. Thirdly, the value of M

_{g}increased from 12.914 g/m

^{3}to 21.523 g/m

^{3}, then to 222.091 g/m

^{3}and N

_{g}increased from 5.615 × 10

^{−6}to 9.358 × 10

^{−6}, then to 9.656 × 10

^{−5}, which shows that the corrosion modulus of gypsum increased gradually, however, its dissolution ability is weaker than that of carbonate rocks. Fourthly, the total weight modulus reduced from 85.418 g/m

^{3}to 5.928 g/m

^{3}, and finally to −23.482 g/m

^{3}, and the total volume modulus reduced from 3.213 × 10

^{−5}to 3.105 × 10

^{−6}, then increased to 5.61 × 10

^{−6}, which manifests that the quantities of precipitation of carbonate rocks minerals was greater than that of sulphate rocks, but a tiny amount of new pore space would still be produced by the interaction between the groundwater and karst aquifer.

## 5. Conclusions

- (1)
- In zone I where βc ≤ 1, three kinds of minerals (viz. calcite, dolomite and gypsum) are in the dissolved state. The corrosion modulus of calcite is maximum and the second is that of dolomite, and the value of corrosion modulus of gypsum is minimum; in zone II where βc ~ 1 > βd ≤ 1, the value of corrosion modulus of calcite is negative, which indicates that the reaction of calcite transforms dissolution to precipitation. The corrosion modulus of dolomite and gypsum increased, and the corrosion reaction was dominated by carbonate rocks dissolution; in the third zone where βd > 1 ~ βg ≤ 1, calcite and dolomite achieved a supersaturated state and the corrosion modulus of gypsum increased remarkably.
- (2)
- From zone I to zone III, the corrosion modulus of calcite decreased gradually along the direction of groundwater flow, however, the corrosion modulus of dolomite increased at first then decreased, and the corrosion modulus of gypsum was augmented with the increase in aquifer depth. The dissolution law of karst groundwater in the Liulin spring area shows that the hydrogeochemical environment plays an important role in mineral corrosion. However, there is less work in the hydrodynamic analysis of the spring system, and more efforts in this regard should be made in the future.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Cao, Y.Q.; Hu, K.R. Karst Chemistry Environment Hydrogeology; Jilin University Press: Changchun, China, 1994. (In Chinese) [Google Scholar]
- Sappa, G.; Ferranti, F.; De Filippi, F.M.; Cardillo, G. Mg
^{2+}-based method for the Pertuso spring discharge evaluation. Water**2017**, 9, 67. [Google Scholar] [CrossRef] - Xie, Y.H.; Yang, M.D. Human Activity and Karst Environment; Beijing Science and Technology Press: Beijing, China, 1994. (In Chinese) [Google Scholar]
- Dreybrodt, W. Processes in Karst Systems: Physics, Chemistry, and Geology; Springer: New York, NY, USA, 1988. [Google Scholar]
- Appelo, C.A.J.; Postma, D. Geochemistry, Groundwater and Pollution; A.A. Balkema Publishers: Avereest, The Netherlands, 1993. [Google Scholar]
- Allred, K. Some carbonate erosion rates of Southeast Alaska. J. Cave Karst Stud.
**2004**, 66, 89–97. [Google Scholar] - Gil-Márquez, M.; Barberá, J.A.; Andreo, B.; Mudarra, M. Hydrological and geochemical processes constraining groundwater salinity in wetland areas related to evaporitic (karst) systems. A case study from Southern Spain. J. Hydrol.
**2017**, 544, 538–554. [Google Scholar] [CrossRef] - Barbieri, M.; Nigro, A.; Petitta, M. Groundwater mixing in the discharge area of San Vittorino Plain (Central Italy): Geochemical characterization and implication for drinking uses. Environ. Earth Sci.
**2017**, 76, 393. [Google Scholar] [CrossRef] - Mottershead, D.N. Rates and patterns of bedrock denudation by coastal salt spray weathering: A seven year record. Earth Surf. Proc. Land.
**1989**, 14, 383–398. [Google Scholar] [CrossRef] - Stephenson, W.J.; Kirk, R.M. Measuring erosion rates using the micro-erosion meter: 20 years of data from shore platforms, Kaikoura Peninsula, South Island, New Zealand. Mar. Geol.
**1996**, 131, 209–218. [Google Scholar] [CrossRef] - Liu, Z.H. Field experimental research on the corrosion kinetics of limestone and dolomite in allogenic water—Case from Yaoshan Mt. Carsol. Sin.
**2000**, 19, 1–4. (In Chinese) [Google Scholar] - Plan, L. Factors controlling carbonate dissolution rates quantified in a field test in the Austrian alps. Geomorphology
**2005**, 68, 201–212. [Google Scholar] [CrossRef] - Webb, A.H.; Bawden, R.J.; Busby, A.K.; Hopkins, J.N. Studies on the effects of air pollution on limestone degradation in Great Britain. Atmos. Environ.
**1992**, 26, 165–181. [Google Scholar] [CrossRef] - Pulina, M.; Sauro, U. Modello dell’ erosione chimica potenziale di rocce carbonatiche in Italia. Memorie della Soc. Geol. Italiana
**1993**, 49, 313–323. [Google Scholar] - Gombert, P. Role of karstic dissolution in global carbon cycle. Glob. Planet. Chang.
**2002**, 33, 177–184. [Google Scholar] [CrossRef] - Li, J.Z.; Lin, J.S.; Fang, J.F. Karst corrosion strength analysis and estimation. Geogr. Res.
**1994**, 13, 90–97. (In Chinese) [Google Scholar] - Cao, Y.Q.; Hu, K.R. A preliminary study on karst hydrochemical field modeling and quantitative evaluation of erosion of carbonate-sulfate formation. J. Changchun Univ. Earth Sci.
**1988**, 18, 53–62. (In Chinese) [Google Scholar] - Mercado, A.; Billings, G.K. Kinetics of mineral dissolution in carbonate aquifers as a tool for hydrological invertigations, I. concentration-time relationships. J. Hydrol.
**1975**, 24, 303–331. [Google Scholar] [CrossRef] - Mercado, A.; Billings, G.K. Kinetics of mineral dissolution in carbonate aquifers as a tool for hydrological invertigations, II. hydrogeochemcal models. J. Hydrol.
**1975**, 24, 365–384. [Google Scholar] [CrossRef] - Hu, K.R.; Cao, Y.Q. The study of water quality and chemical dynamics model in carbonate area. Hydrogeol. Eng. Geol.
**1993**, 3, 8–14. (In Chinese) [Google Scholar]

**Figure 1.**The partition map of hydrogeology-hydrogeochemical of Liulin spring area.

**1.**zone I;

**2.**zone II;

**3**. zone III;

**4.**zone IV;

**5.**river;

**6.**section line;

**7.**the boundary of Lulin spring area;

**8.**county boundary;

**9.**the segmentation borderline;

**10.**county;

**11.**water-sample point;

**12.**Liulin spring.

**Figure 2.**The model diagram of hydrogeology-hydrogeochemical of Liulin spring area.

**1.**Karst groundwater table;

**2.**flow directions of groundwater;

**3.**recharge of precipitation;

**4.**recharge of surface water;

**5.**spring.

**Figure 3.**The relationship plots of Ca

^{2+}vs. SO

_{4}

^{2−}and Ca

^{2+}(Ca

^{2+}− SO

_{4}

^{2−}) vs. HCO

_{3}

^{−}, and Mg

^{2+}vs. HCO

_{3}

^{−}.

Zone | Water Sample | Mineral ion Concentration (mmol/L) | Mineral ion Dissolved Quantity (mmol/L) | ||||||
---|---|---|---|---|---|---|---|---|---|

HCO_{3}^{−} | SO_{4}^{2−} | Ca^{2+} | Mg^{2+} | HCO_{3}^{−} | SO_{4}^{2−} | Ca^{2+} | Mg^{2+} | ||

βc ≤ 1 | Jiuliwan | 3.20 | 0.20 | 1.15 | 0.61 | 2.79 | 0.09 | 0.99 | 0.52 |

Liujiagou | 4.35 | 0.18 | 1.58 | 0.61 | 3.94 | 0.07 | 1.42 | 0.52 | |

Sanjiaozhuang | 4.20 | 0.18 | 1.75 | 0.63 | 3.79 | 0.07 | 1.59 | 0.54 | |

Shizhuang | 3.90 | 0.38 | 1.58 | 0.63 | 3.49 | 0.27 | 1.42 | 0.54 | |

Chemingyu | 4.65 | 0.35 | 1.83 | 0.73 | 4.24 | 0.24 | 1.67 | 0.64 | |

βc > 1 ~ βd ≤ 1 | Youpingfang | 4.45 | 0.45 | 1.55 | 0.96 | 4.04 | 0.34 | 1.39 | 0.87 |

Chejiawan | 3.95 | 0.12 | 1.40 | 0.61 | 3.54 | 0.01 | 1.24 | 0.52 | |

Tianjiahui | 3.85 | 0.30 | 1.63 | 0.73 | 3.44 | 0.19 | 1.47 | 0.64 | |

Nancun | 4.15 | 0.15 | 1.58 | 0.58 | 3.74 | 0.04 | 1.42 | 0.49 | |

Liujiagou | 4.00 | 0.25 | 1.25 | 0.71 | 3.59 | 0.14 | 1.09 | 0.62 | |

Shang’an | 4.49 | 0.86 | 1.61 | 1.07 | 4.08 | 0.75 | 1.45 | 0.98 | |

Tuanshuitou | 4.90 | 2.25 | 2.46 | 1.42 | 4.49 | 2.14 | 2.30 | 1.33 | |

βd > 1 ~ βg ≤ 1 | Mazewan | 5.35 | 1.30 | 1.80 | 1.17 | 4.94 | 1.19 | 1.64 | 1.08 |

Loumenhui | 4.05 | 0.68 | 1.63 | 0.96 | 3.64 | 0.57 | 1.47 | 0.87 | |

Shangqinglong | 4.10 | 1.00 | 1.83 | 1.09 | 3.69 | 0.89 | 1.67 | 1.00 | |

Zhaidong | 4.35 | 1.40 | 1.91 | 1.12 | 3.94 | 1.29 | 1.75 | 1.03 | |

Yangjiagang | 4.40 | 0.95 | 1.75 | 0.99 | 3.99 | 0.84 | 1.59 | 0.90 | |

Liujiagata | 3.75 | 2.18 | 2.51 | 1.95 | 3.34 | 2.07 | 2.35 | 1.86 | |

Yangjiagang | 3.60 | 6.48 | 5.36 | 2.41 | 3.19 | 6.37 | 5.20 | 2.32 | |

Zhangjiazhuang | 4.10 | 1.55 | 2.23 | 1.60 | 3.69 | 1.44 | 2.07 | 1.51 | |

Luotuoju | 4.35 | 4.33 | 4.81 | 2.05 | 3.94 | 4.22 | 4.65 | 1.96 | |

Jucaita | 4.85 | 2.88 | 3.61 | 2.05 | 4.44 | 2.77 | 3.45 | 1.96 | |

ion quantity in rainfall | 0.41 | 0.11 | 0.16 | 0.09 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zheng, X.; Wang, K.; Zhang, F.; Chen, J.; Li, A.; Chen, Y.
Analysis of the Erosion Law of Karst Groundwater Using Hydrogeochemical Theory in Liulin Spring Area, North China. *Water* **2018**, *10*, 674.
https://doi.org/10.3390/w10060674

**AMA Style**

Zheng X, Wang K, Zhang F, Chen J, Li A, Chen Y.
Analysis of the Erosion Law of Karst Groundwater Using Hydrogeochemical Theory in Liulin Spring Area, North China. *Water*. 2018; 10(6):674.
https://doi.org/10.3390/w10060674

**Chicago/Turabian Style**

Zheng, Xiuqing, Kai Wang, Fei Zhang, Junfeng Chen, Aimin Li, and Yanping Chen.
2018. "Analysis of the Erosion Law of Karst Groundwater Using Hydrogeochemical Theory in Liulin Spring Area, North China" *Water* 10, no. 6: 674.
https://doi.org/10.3390/w10060674