Sandra Vega

Numerical estimation of carbonate rock properties using multiscale images

Characterizing the pore space of rock samples using three-dimensional (3D) X-ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X-ray microtomography images at multiple resolutions.We perform a three-phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples.

Sensitivity of flow and elastic properties to fabric heterogeneity in carbonates

ABSTRACT Carbonate rocks are heterogeneous at various levels from deposition to diagenesis. Any existing depositional heterogeneity becomes more complex when carbonate rocks are in contact with polar fluids. Our experiments on carbonate rocks show that change in textural heterogeneity leads to heterogeneity in the distribution of storage and flow properties that may govern changes in saturation patterns. This would be akin to any carbonate reservoir with a mix of heterogeneous and homogeneous facies within a formation and their control on saturation distribution in response to a standard imbibition process. Associated with the saturation pattern heterogeneities, the resultant elastic property distributions also change. We quantify this heterogeneity and its effects on flow and seismic properties based on a few textural extremes of fabric heterogeneity in samples that can exist in any typical carbonate reservoir system. Our measurements show that textural heterogeneity can lead to anisotropy in permeability and in acoustic velocities. Permeability anisotropy measurements varied between 40% and 100% while acoustic velocity anisotropy measurements varied between 8% and 30% with lower values for homogeneous samples respectively. Under similar conditions of the saturation experiment (spontaneous imbibition at the benchtop and undrained pressure imbibition at 1000 psi), the imbibing brine replaced 97% of the pore volume in a homogeneous sample (porosity 20% and permeability 2.6 mD) compared to 80% pore volume in a heterogeneous sample (porosity 29% and permeability 23.4 mD). Furthermore, after pressure saturation, a change of +79% in the bulk modulus and ‐11% in the shear modulus is observed for homogeneous samples in comparison to +34% in the bulk modulus and −1% in the shear modulus for heterogeneous samples, with respect to the dry state moduli values of the samples. We also examined the uncertainties associated with Gassmann models of elastic properties due to variations in fluid saturations. Our results provide significant information on the saturation and, with it, modulus variations that are often ignored during fluid substitution modelling in time‐lapse seismic studies in carbonate reservoirs. We show that the bulk modulus could vary by 45% and the shear modulus by 10% between homogeneous and heterogeneous patches of a reservoir after a water flooding sequence for secondary recovery. Our findings demonstrate the need to incorporate and couple such fabric‐controlled saturation heterogeneities in reservoir simulation and in seismic fluid substitution models.

Detection of stress-induced velocity anisotropy in unconsolidated sands

Velocity anisotropy in rocks and soft sediments can indicate stress anisotropy and can be more sensitive to stress in soft sediments than in rocks. Most of the experimental studies on velocity anisotropy in soft sediments have been focused in the S-wave response. However, S-waves are highly attenuated in soft sediments under field conditions. P-waves are less attenuated and frequently acquired using in-situ geophysical methods. Hence, detecting stress anisotropy with P-waves in soft sediments would be of great value.

Simulation of elastic properties in carbonates

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 have many limitations in carbonate rocks. One main reason is highly complex pore-space structures, produced in carbonates by diagenesis and other geological processes, which create heterogeneities at several scales. Recently developed image acquisition systems, based on X-ray computed tomography, allow description of the spatial distribution of grains and pores in scanned samples at high resolution. Numerical simulations can then predict the elastic properties using the geometry of each phase (grains matrix and pore space). In this paper, we apply a new efficient automatic segmentation technique based on bi-level thresholding to separate grains and pores phases in 3D X-ray CT scans. Then we assess the ability of a finite-element simulation technique commonly used on sandstones to estimate the elastic properties of carbonate rocks unde...

Preliminary experiments to evaluate the Gassmann equation in carbonate rocks: calcite and dolomite

Fluid substitution is used to predict potential changes in seismic data due to production in oil reservoirs. The fluid changes in clastic rocks are often predicted by the Gassmann equation. However, the applicability of Gassmanns equation in carbonates is not well understood. Apparently, part of this failure is due to the violation of the assumption of a constant shear modulus for different fluids (Baechle et al., 2005; Adam et al., 2006), but it is not clear yet.

A Study of Permeability And Velocity Anisotropy In Carbonates

Abstract The ability to predict permeability anisotropy through seismic can assist engineers in having a deeper understanding of fluid flow dynamics and developing oil fields. However, carbonate rocks, which constitute important petroleum reservoirs in the Middle East, have complex textures and properties distribution due to their diagenetic processes. Indeed, relationships between seismic properties and permeability need to be better understood. Hence, this study investigates the relationship between permeability and seismic velocity anisotropy. An experimental procedure to measure this anisotropy on a set of samples from a carbonate reservoir is presented. The relationship between permeability and seismic velocity is complex. Compressional (P-wave) velocity response was found to be independent of permeability anisotropy. However, a trend was observed between the shear (S-wave) velocity and permeability at each measurement location in some samples. An inverse relationship was found between shear velocity and permeability when the velocity is measured perpendicular to the preferential permeability direction, whereas the relationship was proportional when the velocity is measured parallel to the preferential permeability direction. This could have important applications in application of seismic multicomponents integrated to reservoir simulation. 1. Introduction Carbonate rocks constitute important petroleum reservoirs in the Middle East. These rocks are characterized by complex textures and properties distribution such as permeability that resulted mainly from the various diagenetic processes such as dissolution, cementation, and precipitation. These complexities make it difficult to understand the relationships of seismic velocity and permeability for carbonate rocks. Accordingly, the ability to predict permeability anisotropy of carbonate reservoirs may assist engineers in developing oil fields and having a deeper understanding of the dynamics of fluid flow. The petrophysical properties of reservoir formations containing hydrocarbons dictate the quantities of fluids trapped within their pore space. The ability of these fluids to flow through rocks together with the ability of rocks to transmit fluids via the interconnected pores is called permeability. Permeability is considered one of the most important petrophysical rock properties as it is essential to estimate flow rates and fluid recovery. Most experimental studies conducted in laboratories to understand rock properties have been carried out on sandstones (1). However, applying the relationships developed for sandstones to carbonate rocks is challenging as it works in only some cases and it does not work in others. From the engineering point of view, rock heterogeneity, which is common in carbonate reservoirs, makes it difficult to obtain representative permeability of the reservoir formation far away from the wellbore. In this paper, an experimental procedure to measure permeability anisotropy on a set of samples from a carbonate reservoir is presented. The paper investigates the relationship between seismic wave velocities and permeability anisotropy for each sample. Finally, it is found that an inverse relationship between shear velocity and permeability when the velocity is measured perpendicular to the preferential permeability direction, whereas the relationship was proportional when the velocity is measured parallel to the preferential permeability direction. Bastos et al. (2) established a relationship to estimate permeability from seismic wave velocity for an offshore Brazilian field. Measurements of compressional wave velocity and shear wave velocity were made on limestone core samples and supplemented with measurements of porosity and permeability. Using this experimental data, Bastos et al developed empirical relationships between permeability and porosity and between compressional wave velocity and porosity. Then, Bastol et al used these relationships to estimate permeability from compressional wave velocity.

Is Gassmann the Best Model For Fluid Substitution In Heterogeneous Carbonates

Fluid substitution is used to predict potential changes in seismic due to production in oil reservoirs. Gassmann’s model has been successfully applied to 4D-time lapse seismic in clastic reservoirs. However, the applicability of this model in carbonates is not well understood. To evaluate alternative models, we compare Gassmann, Generalize Gassmann, and Patchy saturation models in a carbonate reservoir in the Middle East. We estimated seismic changes due to substitution of oil by water after 5 and 18 years of production. We found that Gassmann’s model generally predicts the lowest seismic variation. Therefore, a 4D-time lapse seismic would not be recommended here, according to Gassmann’s model. Generalized Gassmann’s model results corroborates that seismic response depends on porosity type. Finally, Patchy saturation model shows favourable results for a 4D-time lapse seismic in both studied scenarios. Consequently, if we are going to use 4D-time lapse seismic as a production management tool in this type of carbonate reservoirs we need more information about pore structure and saturation distribution.

Is it Possible to Predict Porosity at Different Scales

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).

Comparative Study of Velocities Under Hydrostatic And Non-hydrostatic Stress In Sands

In this paper, we compare Vp measured under hydrostatic and non-hydrostatic stress conditions in a sand. We describe how we apply isotropic stress using a polyaxial apparatus. We examine velocities in three perpendicular directions as function of stress and find that Vp under hydrostatic pressure is higher than Vp measured under nonhydrostatic isotropic stress. Furthermore, we observe that velocity anisotropy revealed the intrinsic anisotropy in the sands.

Evaluation of Gassmann and Patchy Saturation Models in Carbonates from an Oil Field in the Middle East

The applicability of rock physics models in carbonates is not well understood yet. The aim of this study is to carry out an evaluation of different rock physics models in carbonate rocks from an oil field in the Middle East. We evaluate three rock physics models including Gassmann, Patchy saturation and the Voigt approximation of Patchy model. We use well log data as well as lab measurements on dry samples to perform the evaluation. Our results reveal that while all tested models underestimate bulk modulus in general, Voigt approximation of Patchy model makes the best predictions. Moreover, we observe that the relative difference between the predicted and measured bulk modulus decreases as the rock heterogeneity decreases. We found that predictions of bulk modulus in homogenous rocks show good match with measured modulus.