Simulation of End-member Scenarios of Density-driven flow: Prediction of Dolostone Geobody Dimensions Using Comsol

Conxita Taberner, Mayur Pal, and Christian Tueckmantel
Carbonate Reservoir Research, Shell GSNL, Rijswijk, The Netherlands

Density-driven flows occur in nature and are initiated due to (i) density contrast and (ii) even minor heterogeneities present in sediments and rocks. Salinity and temperature differences are remarkably effective to initiate density-driven flow, which may instigate convective flow. In turn, convective flow is seen by many authors as key for solute and mass transport (References). Usually, during the evaluation of scenarios of dolomitization from observed diagenetic patterns in carbonate reservoirs, both the hydrological model and the conceptually predicted dolomitization pattern are reviewed to come up with plausible architecture, geobody dimensions and rock property distributions in static models. More specifically, two key dolomitization models rely on the application of density-driven flow concepts: 1) dolomitization by shallow or by deep reflux of hypersaline brines in coastal ramp settings and 2) fault-related dolomitization by the inflow of deep-seated fluids.

Outcrop analogs are of great value to provide constraints on expected geometries and size of dolostone geobodies (e.g. References). A different approach derives from the use of fluid flow and/or reactive transport models (e.g. references), where a process and fluid flow based approach provides possible end member scenarios of the geometry and size of dolostone geobodies. This is an “old geological problem”, which appears still unsolved. To avoid the prediction uncertainties associated to chemical reactions and geochemical data bases, we have followed a step approach, where we first have evaluated flow and flow pathways as key constraints of dolomitization and potential geometries of dolomitized geobodies. Flow provides a combined solution to overcome three key restrictions for dolomitization, namely (i) mass (required fluid volumes), (ii) solute (mostly Mg²⁺) and (iii) heat transport. The last being relevant to overcome the kinetic barriers as shown experimentally (e.g. Usdowski, 1994).

This contribution focuses on the application of numerical models to evaluate the plausible applicability of specific dolomitization models/mechanisms in different geological scenarios. We shall discuss end member results of flow simulations using the numerical code Comsol. These results will be compared to outcrops that suggest (i) reflux dolomitization by hypersaline brines along large epeiric ramps and (ii) fault-related dolomitization by convective/thermally driven flow.

1. Key controlling factors for density-driven flow, mathematical concepts and dolomitization

Density variations between two fluids can initiate flow even in a still fluid. Two main physical parameters that can initiate density driven flow are: salinity and temperature. Listed below are two very well-known examples in surface and subsurface:

• Hypersaline brine reflux. – Typically favoured by the density contrast between a highly saline shallow aquifer (e.g. highly evaporated brines formed in hypersaline lagoons, salinas and salt pans) and lower salinity aquifers (seawater incursion and/or freshwater aquifers).
• Thermally-driven flow. - Mostly relates to the change in buoyancy of fluids at different temperatures. Typical subsurface examples involve the generation of convective cells due to (i) heat flow anomalies and (ii) variations in geothermal gradients (e.g. due to the presence of thick salt units). In these scenarios, the generation of convective cells may be favoured by (iii) lateral migration of subsurface fluids due to compaction, and (iv) presence of major faults that may sustain the circulation of over-pressured deep-seated fluids

Both scenarios, hypersaline brine reflux and thermally-driven flow, have been traditionally claimed as possible driving forces for dolomitization. These models support the flow, across lime sediments/rocks, of significant volumes of fluids, which may supply the Mg²⁺ required for dolomitization. In this contribution we shall not discuss the modification in the chemical boundary conditions favouring dolomitization that are associated to brine reflux or to thermally-driven flow. The contribution will focus on (i) the approach that has been used for density-driven flow simulation, (ii) the model results and (iii) the implications for the most favourable areas for dolomitization.

Elder (1966, 1967) was first to study thermal convection in a laboratory experiment. Voss and Souza (1987) re-casted the Elder’s problem for salt concentration and this became the benchmark for many researchers to test variable-density driven flow models. In this contribution, the Elder’s formulation has been used and modified to model brine reflux and thermally-driven flow. The brine reflux circulation model for dolomitization has been created by examining the Elder’s problem for magnesium-rich brines via a two way coupling between Darcy’s law for fluid flow in porous media, solute transport and heat transport equations for both scenarios (further details in Pal and Taberner, 2011).

2. Dolomitization by hypersaline brine reflux – simulation results

The simulations were performed on 2D domains. In these simulations it was assumed that a denser (more saline) fluid (magnesium-rich) moved downward and caused complete dolomitization by replacement of calcite (CaCO3) with dolomite (CaMg (CO3)2). This way the dolomitized rock fraction, due to brine reflux processes, was predicted. The fingering effects (as commonly observed in outcrops) are commonly interpreted as related to density contrast of saline fluid rich in magnesium moving downward to the underground water. In order to verify this effect of density differences, simulations were performed with varying density difference between the saline fluid and underground water. Interestingly, the model results show that as density difference decreases the fingering effect vanishes. The interplay between hydraulic gradient and fingering has been evaluated, with the following outcome: in the model with hydraulic gradient this fingering effect is not seen, as the presence of hydraulic gradient dictates the direction of the fluid flow and therefore the geometry and distribution of dolomite geobodies.

3. Dolomitization by convective-thermally driven flow – simulation results

As above, the simulations were performed in 2D domains. In these simulations it was assumed that a lighter (hotter) magnesium-rich fluid moved upward and caused complete dolomitization by replacement of calcite with dolomite. These simulations are aiming to reproduce dolomitization associated to the movement of the deep-seated fluids along (i) the “upward branches” of convective cells and (ii) along deep-seated faults. Modelled dolomite patterns are very much linked to the magnitude of geothermal heat flux. For lower values of geothermal heat flux more layered dolomite bodies are predicted compared to the irregular finger like bodies predicted at higher values of geothermal heat flux.

4. Considerations and way forward

Results presented in this paper reproduce geometries resulting from two of the most relevant processes that cause dolomitization in nature; namely brine reflux and geothermally driven flow. The next step in our modeling effort is the incorporation of chemical reactions (coupling Comsol with Phreeqc) and the validation of the model results with outcrop analogs and subsurface data.

5. References

Elder, J.W., 1966. Numerical experiments with free convection in a vertical slot, J. Fluid Mech., 24, 823-843.
Elder, J.W., 1967 Transient convection in porous medium, J. Fluid Mech., 27, 609-623.
Pal, M. and Taberner, C. 2011. Simulation of Brine Reflux and Geothermal Circulation in Large Carbonate Platforms: An Attempt to Predict Dolomite Geobodies. Proceedings of Comsol conference, Stuttgart: 11 pp.
Usdowski, E.1994. Synthesis of dolomite and geochemical implications. In: Dolomites. A volume in honour of Dolomieu. IAS Spec. Publ.: 21, 345-360.
Voss, C.I. and Souza, W.R., 1987. Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone, Water Resources Research, 23, 10

AAPG Search and Discovery Article #120034©2012 AAPG Hedberg Conference Fundamental Controls on Flow in Carbonates, Saint-Cyr Sur Mer, Provence, France, July 8-13, 2012