Reactive transport occurs when a species flow through a porous media and reacts with the stationary phase, in this case the rock. Several codes can simulate this coupling between flow through porous medias and reactions in different phases (Liu et al., 2019). In this work, simulations were carried out to evaluate how seawater could react with a carbonated rock, using the flow simulator COORES™ coupled to the geochemical simulator ARXIM.
COORES™ is a 3-D thermal, multiphase (oil, water, gas and rock) and compositional flow simulator developed by IFP Energies Nouvelles. It can work with relative permeabilities, diffusion and hydrodynamic dispersion, flexible boundary conditions (pressure, flow rate, concentration, and temperature) and injection wells, either horizontal or vertical. It can be coupled with a geochemical simulator called ARXIM to account for chemical reactions that can occur in a carbonate reservoir under fluid injection (MAURAND et al., 2014). Its equations are based on conservation laws of continuum mechanics, but the viscous fluid-solid interaction is modeled using Darcy’s empirical equation.To solve the equations, COORES™ uses finite differences and can calculate flow rates, pressure, and chemical species concentrations in multiphase flow.
ARXIM is a geochemical software developed by the École des Mines de Saint-Étienne in partnership with IFP Energies Nouvelles. Two classical approaches are used to calculate the thermodynamic equilibrium of a multi-component system and the speciation of a solution: minimization of Gibbs free energy and Law of mass action. ARXIM calculates activities coefficients as functions of ionic strength by different models: Pitzer, Davies, Debye-Hückel and their modified equations to neutral species such as CO2. For equilibrium calculations, the software can use the logarithm of equilibrium constant (logK's) database or derive them from equations of state (EOS). The limit pressure is 5000 bar, and the limit temperature, 1000°C. The database can be changed, and new reactions can be added (Moutte, 2009).
By coupling COORES™ and ARXIM it is possible to evaluate chemical reactions, rock properties such as porosity and permeability variations, and the produced water composition. ARXIM solves the reactive part of the problem. Chemical reactions can be defined only by equilibrium (such as the partition of CO2 between oil and water) or require the definition of a kinetic law (like the ones involving the mineral phase). They can also be homogeneous (elements in the same phase) or heterogeneous (elements in different phases).
The model used in the simulation was an extract of a fullfield model, consisting of 23490 cells (Grid XYZ: 29x30x27) and one pair of wells (one injector and one producer). The reservoir temperature was 130°C and the pressure was 450 bar. Figure 1 shows a view of the extracted grid and the wells.
An equation of state represented the oil and its composition was based on field data. The formation and injected water compositions were also based on field samples and are shown in Table 1. Reservoir mineralogy consisted initially of calcite, dolomite, and quartz. All the reactions represented by equations 1 to 4 are available in the geochemical database.
Table 1
Formation and injected waters
Component
|
Formation Water (mg/kgw)
|
Injected Water (mg/kgw)
|
Na+
|
70300
|
11800
|
K+
|
4050
|
398
|
Ca2+
|
15200
|
448
|
Mg2+
|
1376
|
1390
|
Cl−
|
143000
|
21200
|
HCO3−
|
325
|
151
|
SO42−
|
217
|
2860
|
Originally, the reservoir is in equilibrium. It means that no changes are expected: the initial aqueous phase at the reservoir, the formation water, is thermodynamically equilibrated with gas, oil and rock and no chemical reactions take place. Also, there is a momentum equilibrium, so there is no mass transfer along the rock. Once the equilibrium is disturbed by injection and production, reactivity becomes important, affecting the composition and the pH of produced fluids. The most important reactions considered in the simulations are represented by Equations 1 (calcite dissolution), 2 (dolomite precipitation), 3 (anhydrite precipitation) and 4 (dolomitization).
$$CaC{O}_{3}\rightleftarrows {Ca}^{2+}+C{O}_{3}$$
1
$${Ca}^{2+}+{Mg}^{2+}+ 2C{O}_{3}\rightleftarrows CaMg{\left(C{O}_{3}\right)}_{2}$$
2
$${Ca}^{2+}+S{O}_{4}^{2-}\rightleftarrows CaS{O}_{4}$$
3
$$2Ca{CO}_{3}+{Mg}^{2+}+\rightleftarrows {Ca}^{2+}+CaMg{\left(C{O}_{3}\right)}_{2}$$
4
At high temperatures, reactions represented by Equations 3 (anhydrite precipitation) and 4 (dolomitization) are favored. Anhydrite precipitation is a fluid-fluid reaction and depends on the amount of calcium and sulphate. Dolomitization, on the other hand, is a rock-fluid reaction, such as calcite dissolution (Eq. 1). Those reactions are expected in the injection zone, where fresh water is reaching the reservoir. Both reactions (Equations 1 and 4) release calcium, increasing its concentration in the water. Therefore, anhydrite precipitation will also be stronger in the injection zone.
Figures 2 and 3 show, respectively, the results for sulphate and magnesium, in mg/L, as a function of the percentage of injected water (IW) in produced water (PW). Blue diamonds represent the reactive case. The light red squares represent the non-reactive case where chemical reactions are not allowed: the produced water is simply a mixture between injected and formation water.
Figure 4 shows a comparison, in terms of sulphate concentration, for three different scenarios: non-reactive (red squares), reactive (blue diamonds), and reactive but with no dolomitization (green circles). In this last case, dolomitization (Eq. 4) was intentionally blocked. All the other reactions were still possible.
Comparing the green and blue curves is possible to conclude that when dolomitization occurs, sulphate concentration in the produced water is smaller. In other words, anhydrite precipitation is stronger. Experiments were carried out to confirm this behavior.