Introduction: Why This Reaction Matters
In the study of groundwater geochemistry, the interaction between calcite (calcium carbonate) and CO₂-charged water is perhaps the most fundamental and significant process.
As rainwater infiltrates through the soil, it absorbs CO₂ produced by biological activity, becoming slightly acidic. When this acidic water comes into contact with carbonate rocks (such as limestone), calcite dissolves, releasing \(\mathrm{Ca^{2+}}\) and \(\mathrm{HCO_3^-}\) into the water. This is the primary reason why much of the world’s groundwater is “hard water.”
Crucially, the progression of this reaction depends heavily on whether the system is “open” or “closed” to CO₂ gas.
Chemical Equations
Let’s summarize the chemistry involved in this system.
Dissolution of CO₂:
\[\mathrm{CO_2(g) + H_2O \rightleftharpoons H_2CO_3^* \rightleftharpoons H^+ + HCO_3^-}\]
Dissolution of Calcite:
\[\mathrm{CaCO_3 + H^+ \rightleftharpoons Ca^{2+} + HCO_3^-}\]
Net Reaction (Open System):
\[\mathrm{CaCO_3 + CO_2(g) + H_2O \rightleftharpoons Ca^{2+} + 2HCO_3^-}\]
- \(\mathrm{H_2CO_3^*}\): Sum of dissolved \(\mathrm{CO_2(aq)}\) and true carbonic acid \(\mathrm{H_2CO_3}\) \([mol/kg]\)
- \(\mathrm{CaCO_3}\): Calcite (solid phase)
- \(\mathrm{CO_2(g)}\): Carbon dioxide in the gas phase
In an open system, the continuous supply of CO₂ drives the reaction to the right, promoting dissolution. In a closed system, the limited amount of dissolved CO₂ is quickly consumed, often resulting in a higher final pH and lower mineral dissolution.
Setting the Partial Pressure of CO₂
The partial pressure of CO₂ (\(P_{CO_2}\)) in soil can reach 30 to 100 times that of the atmosphere. In this tutorial, we will use a representative value:
\[P_{CO_2} = 10^{-1.5} \approx 0.032 \text{ atm}\]
This is a typical value for soil in limestone regions (roughly 100 times the atmospheric value of \(10^{-3.5}\) atm).
In PHREEQC, CO₂ gas is identified as CO2(g). By writing CO2(g) -1.5 in the EQUILIBRIUM_PHASES block, we specify the condition \(\log P_{CO_2} = -1.5\).
Configuration of Simulation Scenarios
| Scenario | CO₂ Condition | Calcite Condition | PHREEQC Block |
|---|---|---|---|
| Open System | Constant equilibrium with CO₂(g) (P = 10⁻¹·⁵ atm) |
Calcite (SI=0, 10 mol) | SOLUTION 1 EQUILIBRIUM_PHASES 1 (Simultaneous CO2 + Calcite) |
| Closed System | Pre-equilibrate with CO₂(g) → Then isolate from gas |
Separate EQ_PHASES for Calcite only |
SOLUTION 2 EQUILIBRIUM_PHASES 1 SAVE → USE EQUILIBRIUM_PHASES 2 |
GUI Procedure
Open System Configuration
Step 1: Define pure water (SOLUTION 1).
Step 2: Click the EQUILIBRIUM_PHASES icon and set the following: - CO2(g): Target SI = -1.5, Amount = 10 - Calcite: Target SI = 0, Amount = 10
The instruction CO2(g) -1.5 means “dissolve CO₂ until the water reaches equilibrium with \(\log P_{CO_2} = -1.5\).” In an open system, CO₂ is maintained at this partial pressure throughout the reaction.
Closed System Configuration
A closed system is simulated in two stages:
Stage 1: Dissolve CO₂ (Gas phase present) Define SOLUTION 2, equilibrate with CO₂ only using EQUILIBRIUM_PHASES, and save the state using SAVE solution 2.
Stage 2: React with Calcite (No gas phase) Use USE solution 2 to recall the carbonated water, then equilibrate with Calcite only in a new EQUILIBRIUM_PHASES block. Do not include CO2(g) in this second block.
Full PHREEQC Code
# ===================================
# Open System
# Simultaneous equilibrium with CO2 and Calcite
# ===================================
SOLUTION 1 Open system - Pure water
temp 25
pH 7
pe 4
redox pe
units mmol/kgw
density 1
-water 1 # kg
EQUILIBRIUM_PHASES 1
CO2(g) -1.5 10 # log P(CO2) = -1.5 atm, constant supply
Calcite 0 10 # Equilibrium with calcite
END
# ===================================
# Closed System
# Stage 1: Initial CO2 dissolution
# ===================================
SOLUTION 2 Closed system - Pure water
temp 25
pH 7
pe 4
redox pe
units mmol/kgw
density 1
-water 1 # kg
EQUILIBRIUM_PHASES 1
CO2(g) -1.5 10 # Equilibrate with CO2 only (no calcite yet)
SAVE solution 2 # Save water after CO2 dissolution
END
# ===================================
# Closed System Stage 2:
# Reaction with Calcite after isolation from gas
# ===================================
USE solution 2 # Use the saved carbonated water
EQUILIBRIUM_PHASES 2
Calcite 0 10 # Equilibrate with calcite only (no gas phase)
ENDSAVE and USE
The SAVE solution 2 command stores the current state of the water (pH, ion concentrations, temperature, etc.) in memory. USE solution 2 recalls that state for further calculations. This is essential for simulating “step-wise reactions” like the closed system scenario.
Reading the Results
After running the calculation, you can compare the outputs for the two scenarios.
Open System Results (SOLUTION 1 after)
pH = 6.97
Ca²⁺ (mol/kgw) = 2.39e-03
HCO₃⁻ (mol/kgw) = 4.88e-03
Calcite SI = 0.00 ← Equilibrium reached
CO2(g) SI = -1.5 ← CO2(g) maintained at -1.5Closed System Results (SOLUTION 2 after Stage 2)
pH = 7.68
Ca²⁺ (mol/kgw) = 9.94e-04
HCO₃⁻ (mol/kgw) = 1.99e-03
Calcite SI = 0.00 ← Equilibrium reached
CO2(g) SI = -2.58 ← CO2 is undersaturated (consumed)Comparison Summary
| Parameter | Open System | Closed System |
|---|---|---|
| Final pH | 6.97 | 7.68 |
| Ca²⁺ Concentration | 2.39×10⁻³ mol/kg ≈ 96 mg/L |
9.94×10⁻⁴ mol/kg ≈ 40 mg/L |
| HCO₃⁻ Concentration | 4.88×10⁻³ mol/kg | 1.99×10⁻³ mol/kg |
| Calcite Dissolved | High (~2.5x) | Low |
| CO₂(g) SI | -1.5 (Input condition) | −2.58 (Consumed) |
Discussion
1. Why the Open System has a Lower pH
In an open system, CO₂ is maintained at \(P_{CO_2} = 10^{-1.5}\) atm. Even as calcite dissolves and consumes \(\mathrm{H^+}\), additional CO₂ is supplied from the gas phase to regenerate \(\mathrm{H^+}\). This maintains the acidity and promotes further dissolution of calcite. Consequently, the final Calcium concentration (2.39×10⁻³ mol/kgw) is significantly higher than in the closed system.
\[\mathrm{CO_2(g) \rightarrow CO_2(aq) \rightarrow H^+ + HCO_3^- \xrightarrow{Calcite} Ca^{2+} + 2HCO_3^-}\]
2. Why the Closed System has a Higher pH
In a closed system, the amount of CO₂ dissolved in Stage 1 is the total available carbon. As calcite dissolves, \(\mathrm{H^+}\) is consumed. However, because the system is isolated, there is no new supply of CO₂. The acidity is quickly neutralized, the solution pH rises, and the reaction halts much earlier.
3. Application to Natural Groundwater
Natural groundwater systems often transition between these two states: - Soil Zone (Shallow): Rich in soil CO₂ with constant replenishment → Approaches an Open System. - Deep Aquifers: Isolated from the atmosphere and soil gas → Approaches a Closed System.
As groundwater moves deeper, it often becomes more alkaline (higher pH) and can become supersaturated with respect to calcite. In cave environments, when this deep groundwater emerges and comes into contact with low-CO₂ air, it “degasses” CO₂, causing calcite to precipitate and form speleothems like stalagmites.
Key Mechanism Comparison
Next Time: Mixing Groundwater and Seawater
In the next tutorial, we will calculate what happens when carbonated groundwater (from limestone areas) meets seawater.
We will explore the phenomenon of “Mixing Corrosion”—where the simple mixture of two calcite-saturated solutions becomes undersaturated (corrosive). This process is vital for understanding the formation of coastal limestone caves.
References
Other articles in this series:
- #1 Installation and Initial Calculation
- #2 Analyzing Seawater with Speciation
- #3 Mineral Equilibrium and Temperature Effects
- #4 Calcite–CO₂ Interaction (Open vs. Closed Systems) (This article)
- #5 Mixing Groundwater and Seawater
DeepFlow | Science beneath the surface