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Summary This study aims to improve our understanding of the seismic signature (i.e., variations in acoustic velocity) as a result of variations in the brine and oil saturation. To this scope, we utilized a customized core flooding system and measured P- and S-wave velocity (Vp and Vs respectively) under reservoir pressure and as function of brine and oil saturation during drainage and imbibition, in three carbonate samples. Our results show that both Vp and Vs decrease as oil displaces brine (imbibition) and then increase as brine displaces oil (drainage). The Vp-saturation trend during imbibition followed the lower bound predicted by Gassmann theory assuming uniform fluid distribution, while drainage data followed the upper bound assuming patchy fluid distribution. Since oil production or EOR processes can be represented by the drainage process (i.e., gas or brine displacing oil), patchy fluid distribution should be considered in Gassmann theory when performing feasibility studies to predict changes in Vp as function of saturation changes. Despite the success of Gassmann theory in predicting Vp here, the results obtained for Vs show that Gassmann theory fails significantly to predict Vs as function of saturation. This suggests that the constant-shear-modulus condition in Gassmann is violated as fluid saturation changes.

Summary Three-dimensional (3D) information on rock microstructures is important for a better understanding of physical phenomena and for rock characterization on the micro-scale. Digital rock physics (DRP) can directly image rock microstructures across a continuous range of length scales and can be used to predict rock properties. In most cases, the simulated results from rock images can agree well with their lab measurements. However, some properties, such as the effective elastic moduli, strongly depend on the microstructural details of rock, which can lead to a dissatisfied comparison between numerical simulations and lab measurements. High-resolution images can provide more detailed microstructures of rocks but they may not represent the whole sample as their physical sizes are very small. In addition, some unresolved phases, containing many micro-porosities and cement, may have an impact on the calculation of elastic moduli of digital rocks. In this paper, we use multi-scale CT images of a heterogeneous carbonate rock sample to study its heterogeneity and the impact of unresolved phases on the calculation of rock properties. Besides, we study the upscaling methods for multi-scale image analysis in DRP.

Summary Carbonate reservoirs are considered extremely complex due to their texture heterogeneity. Using new approaches in Digital Rock Physics (DRP) is possible to compute core plug sample properties and study the heterogeneity from digital image data generated from X-ray computed tomography (CT) scan. Some numerical methods are effective to calculate and analyze these samples properties. However, there is a limitation when the simulations are run at the scale of the whole core plug, especially for fluid flow simulation, due to the large amount of calculation and consequent large computer memory requirement. Therefore, simulations are often done only in subsamples of the core plug. To get the dynamic properties of the whole core plug samples and study their heterogeneity, we propose a combined approach of DRP. Digital imaging processing is used to run digital core models for the calculation of porosity and permeability. The Lattice Boltzmann Method (LBM) is used to simulate fluid flow and calculate the absolute permeability. Experimental measurements are used to compare with simulated results of subsamples which are selected from the whole core plug sample. By comparing and analyzing the results of subsamples, the dynamic properties of the whole core samples are obtained and the heterogeneity is studied.

Due to the complex pore structures with a large portion of nano pores, flow mechanics of shale gas in organic-rich shale kerogen pores may involve in some nanoscale effects that could not be accounted for by classic Darcy’s law. In this study, we present a parallel lattice Boltzmann method (PLBM) to study these effects and to simulate 3D flow process of natural gas in real pore geometry of a shale reservoir rock. The numerical advantages of LBM make it a powerful tool to simulate gas flow in such nano pores. The new parallel implementation with standard Message Passing Interface (MPI) communication routines has been well tested. By simulating the flow process of shale gas in a tube model and real geometry of shale core through PLBM on high performance computing cluster, the results show that many factors (such as rarefaction effect, slippage effect and roughness effect, etc.) have a great impact on the flow process of shale gas in nano pores and LBM is an effective way to simulate shale gas flow in kerogen pores, and compared to other physical experimental methods, it has great convenience and accuracy.

Scaling in general is referred as mathematical transformations that allow calculating object characteristics from one scale to another. In Earth Sciences, we are interested to scale rock properties from the scale of measurement to the scale of modelling, as they are usually different. In particular, when there are only rock fragments or cuttings available, porosity can be extracted from SEM and/or thin sections using image processing. When there are cores available, porosity can also be measured from core plugs using, for example, gas porosimeters (Boyle’s law) or NMR lab measurements. However, the main issue is how to extrapolate these values to the wells and field scales. In other words, is there any scaling law or transformation that can be used for going from lab scale measurements to field scales or vice-versa? Previous works have shown fractal behaviour in pore space of some soils, sandstones and carbonates (e.g. Thompson et al. 1987; Posadas et al. 2001; Xie et al. 2010). As fractal geometry involves self-similarity and its corresponding power laws, it seems that scaling using this mathematical formalism is a promising implication. As a matter of fact, fractal porosity in sandstones has been found to be proportional to the ratio between the minimum and maximum limits of self-similarity to the power of D-Do, where D is the Euclidian dimension (2 for SEM and thins section images and 3 for full core plugs images) and Do is the corresponding fractal dimension or capacity dimension (Thompson et al. 1987). However, this fractal porosity relation implies that self-similarity might be limited or constrain to certain scales. If it is not constrained to the measure scales, which is indeed the need; it is very difficult to find. Few studies have shown multifractal behaviour in carbonate rocks. Multifractal systems are more complex than fractals. The multifractal systems present more than one exponent and one singularity, while the fractals possess only one. Xie et al. (2010) have presented an analysis of SEM images from Permian-Triassic carbonate rocks, showing that all their samples behave as fractal/multifractal. However, their samples have a very small range of porosities – between 0.4 to 8.8 %. On the other hand, it is not clear yet if the found power laws could be used to scale rock properties as porosity and permeability to field scales, except for Muller et al. (1995). Muller et al. (1995) have found a good and clear correlation between the multifractal exponent (D1) from SEM images and permeability from core plugs in chalk samples. In this paper, we aim to investigate if it is acceptable to generalize multifractal behaviour to all type of carbonate rocks, and if it is possible to estimate porosity at different scales using fractal geometry. To accomplish this, we use a set of carbonate samples from the Upper Cretaceous with a considerable range of porosities – between 1 to 31 %, and different type of rocks (mudstones, packstones, grainstones, wackestones, and rudstones).

Predicting the elastic properties of carbonate rocks is crucial for the oil industry. However, the standard models that estimate effective elastic properties in porous media present many limitations in carbonate rocks. One of the main possible reasons is the presence of heterogeneous pore space structures. Recently, image acquisition systems based on X-ray computed tomography have been developed and allowed describing grains and pores geometries at high resolutions. Numerical simulations can then be conducted to predict the elastic properties. In this paper, we apply a new automatic image segmentation technique based on bi-level thresholding in order to separate grains and pores. Then we assess the ability of a commonly used numerical simulation technique on sandstones, based on a static method, to estimate the elastic properties of carbonate core plug samples from a Middle East reservoir under different fluid saturation conditions. Thirty three samples were available and four of them could be used to predict elastic properties. Results show that a good agreement was found in relatively homogeneous samples whereas a mismatch was revealed for heterogeneous ones. Mismatches were due to a lack of representativity related to a partial image acquisition and to a misdetection of microporosity related to the acquisition resolution.