Modelling porosity and permeability in early cemented carbonates
Hosa, Aleksandra Maria
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Cabonate-hosted hydrocarbon reservoirs will play an increasingly important role in the energy supply, as 60% of the world's remaining hydrocarbon resources are trapped within carbonate rocks. The properties of carbonates are controlled by deposition and diagenesis, which includes calcite cementation that begins immediately after deposition and may have a strong impact on subsequent diagenetic pathways. This thesis aims to understand the impact of early calcite cementation on reservoir properties through object-based modelling and Lattice Boltzmann ow simulation to obtain permeability. A Bayesian inference framework is also developed to quantify the ability of Lattice Boltzmann method to predict the permeability of porous media. Modelling focuses on the impact of carbonate grain type on properties of early cemented grainstones and on the examination of the theoretical changes to the morphology of the pore space. For that purpose process-based models of early cementation are developed in both 2D (Calcite2D) and 3D (Calcite3D, which also includes modelling of deposition). Both models assume the existence of two grain types: polycrystalline and monocrystalline, and two early calcite cement types specific to these grain types: isopachous and syntaxial, respectively. Of the many possible crystal forms that syntaxial cement can take, this thesis focuses on two common rhombohedral forms: a blocky form 01¯12 and an elongated form 40¯41. The results of the 2D and 3D modelling demonstrate the effect of competition of growing grains for the available pore space: the more monocrystalline grains present in the sample, the stronger this competition becomes and the lesser the impact of each individual grain on the resulting early calcite cement volume and porosity. The synthetic samples with syntaxial cements grown of the more elongated crystal form 40¯41 have lower porosity for the same monocrystalline grains content than synthetic samples grown following more blocky crystal form 01¯12. Moreover, permeability at a constant porosity is reduced for synthetic samples with the form 40¯41. Additionally, synthetic samples with form 40¯41 exhibit greater variability in the results as this rhombohedral form is more elongated and has the potential for producing a greater volume of cement. The results of the 2D study suggest that for samples at constant porosity the higher the proportion of monocrystalline grains are in the sample, the higher the permeability. The 3D study suggests that for samples with crystal form 01¯12 at constant porosity the permeability becomes lower as the proportion of monocrystalline grains increase, but this impact is relatively minor. In the case of samples with crystal form 40¯41 the results are inconclusive. This dependence of permeability on monocrystalline grains is weaker than in the 2D study, which is most probably a result of the bias of flow simulation in the 2D as well as of the treatment of the porous medium before the cement growth model is applied. The range of the permeability results in the 2D modelling may be artificially overly wide, which could lead to the dependence of permeability on sediment type being exaggerated. Poroperm results of the 2D modelling (10-8000mD) are in reasonable agreement with the data reported for grainstones in literature (0.1-5000mD) as well as for the plug data of the samples used in modelling (porosity 22 - 27%, permeability 200 - 3000mD), however permeability results at any given porosity have a wide range due to the bias inherent to the 2D flow modelling. Poroperm results in the 3D modelling (10 - 30, 000mD) exhibit permeabilities above the range of that reported in the literature or the plug data, but the reason for that is that the initial synthetic sediment deposit has very high permeability (58, 900mD). However, the trend in poroperm closely resembles those reported in carbonate rocks. As the modelling depends heavily on the use of Lattice Boltzmann method (flow simulation to obtain permeability results), a Bayesian inference framework is presented to quantify the predictive power of Lattice Boltzmann models. This calibration methodology is presented on the example of Fontainebleau sandstone. The framework enables a systematic parameter estimation of Lattice Boltzmann model parameters (in the scope of this work, the relaxation parameter τ ), for the currently used calibrations of Lattice Boltzmann based on Hagen-Poiseuille law. Our prediction of permeability using the Hagen-Poiseuille calibration suggests that this method for calibration is not optimal and in fact leads to substantial discrepancies with experimental measurements, especially for highly porous complex media such as carbonates. We proceed to recalibrate the Lattice Boltzmann model using permeability data from porous media, which results in a substantially different value of the optimal τ parameter than those used previously (0.654 here compared to 0.9). We augment our model introducing porosity-dependence, where we find that the optimal value for τ decreases for samples of higher porosity. In this new semi-empirical model one first identifies the porosity of the given medium, and on that basis chooses an appropriate Lattice Boltzmann relaxation parameter. These two approaches result in permeability predictions much closer to the experimental permeability data, with the porosity-dependent case being the better of the two. Validation of this calibration method with independent samples of the same rock type yields permeability predictions that fall close to the experimental data, and again the porosity-dependent model provides better results. We thus conclude that our calibration model is a powerful tool for accurate prediction of complex porous media permeability.