Porositeit classificatie en upscaling strategie voor travertijn reservoir gesteenten

Heterogeneity is an inherent characteristic of carbonate reservoir rocks, which is determined by their geological evolution, e.g. sedimentary origin, diagenetic processes and burial history. These processes relate to the economic relevance of reservoir rocks as well as to the degradation of building stones. Different porosity types in sedimentary rocks exist on a spectrum of different spatial scales. An example of the lower end of the spectrum is very fine micro-porosity in mic- ritic textures, characterised by pore diameters on sub-μm scale. On the other hand of the spectrum are the large pores in sedimentary rocks, e.g. karst and shelter porosity with diameters up to meter scale. In this study a unique dataset comprising several orders of spatial scale (from μm till m) is used to develop a new descriptive pore shape classification in order to assess the representativeness of porosity at different spatial scales. The major aim of this study was to characterise complex pore systems in 3D in carbonate rocks, framed in a well-established upscaling strategy. Additionally, the aspect of the Representative Elementary Volume (REV) was addressed since in CT-technology sample size is linked to resolution. An up- scaling strategy has been developed in which data on porosity acquired at different resolutions (from micro- to macro-porosity) and sample sizes are aligned. This will help to understand the major controlling factors on pore development, permeability, acoustic properties and other petrophysical characteristics. In order to achieve a 3D interpretation of porosity and mineralogy, samples were scanned using medical and micro-CT. While both systems are non-destructive and pro- vide 3D data, medical and micro-CT scanners have a different hardware set-up and reach different resolutions. The medical CT scans are performed in collaboration with the department of radiology, UZ Leuven. For the micro-CT scans a GE Nanotom of the Material Engineering Department, KU Leu- ven is used. Samples scanned with a medical CT scanner have a resolution around 250 μm while with a micro-CT scanner resolutions between 20 and 1 μm can be obtained. The first aim of the project was to develop an objective description of pore shapes based on 3D data. This is achieved by analysing the ratios of the longest, intermediate, shortest dimensions and compactness of the pore shapes, based on an approximating ellipsoid, in order to obtain a thorough and objective description of pore shapes. This classification differs from traditional pore classifications because it is based on 3D data and uses solely the shape of the pores. In the traditional classifications of Choquette and Pray (1970), Lucia (1999) and Lønøy (2006), the parameters that are used are descriptive and relative to each other. They describe the rock, i.e. the solid constituents, to extract information about the porosity type rather than describing the pore itself, e.g. intercrystal or interparticle porosity. By using intrinsic properties, the classification based on CT data can be used at every resolution scale. Five shape classes are defined: i.e. rod, blade, plate, cuboid and cube. An additional advantage of this classification is that the data provide information about the orientation of the pores. This permits the assessment of the anisotropy of the porosity parameter. The new 3D classification (Claes et al., 2015b) allows a better understanding of the influence of the porosity parameter on other petrophysical parameters, e.g. the acoustic properties of rock samples (Soete et al., 2015). In this study it was shown that rod and cuboid shaped pores increase compressional wave velocities, while flattened pore shapes such as blade and plate-like shaped pores decrease the acoustic wave propagations. These observations help us to understand more accurately acoustic properties of reservoir rocks. Additionally, the surface area of the pore is an important parameter since it plays a crucial role in the connectivity of pores as well as the reactive surface. Addressing the shape of the surface area is highly dependent on the resolution of the dataset. Hence the voxel representation of smooth continuous surfaces is generally jagged, so the total area of exposed voxel faces is usually greater than that of the original continuous surface. This can be solved by a triangulation of the surface but literature indicates this is not the ideal solution. When using the marching cubes algorithm to create the triangulated representation, topological ambiguities may occur and holes may be generated due to the complex shapes of the pores. Secondly, the surface area estimate, produced by summing up the area of the resulting triangles, does not converge to the true surface area as the resolution increases due to the locality of the marching cubes algorithm. The extension of Fourier series to 3D results in the definition of spherical harmonic surfaces. Based on this new iterative approach, additional parameters such as surface area and circularity are calculated. Moreover the accuracy of the calculated parameters is sufficiently increased compared to other estimating methods. In a second research step the aspect of Representative Elementary Volume (REV) was studied. This is an important parameter in several research fields such as reservoir properties and structural property determination. In the former the porosity parameter will be the most crucial. High-resolution LIDAR data of quarry walls were used to assess the porosity on the upper end of the spatial spectrum, while medical CT, micro-CT scans and thin- sections are used to cover the middle and lower end of the spectrum. For each spatial scale the REV is calculated (i.e. the smallest value that can be taken as a representation for the entire sample area/volume that does not respond to small changes in volume or location). In this study two approaches to calculate the REV were developed and compared. Both methods are applicable to 2D as well as 3D datasets. This is important for linking the results of the new 3D approach with data of traditional studies. The first method uses the chi-square criterion to measure how much a single randomly chosen sub-sample diverges from the mean value of all realisations. This method is closely related to the original definition proposed by Bear. The second method uses the relationship between the REV and geo- statistical interpretations. A volume Vi falls within the REV domain if Y(x,Vi) can be treated as a stationary random function for any x in the domain. The advantage of both methods is that they allow to calculate 95 % confidence bounds for the REV parameter. The results of both methods are in the same order of magnitude and vary depending on the scale of the sample. Nevertheless the geostatistical method provides additional information on the shape of the REV based on the spatial distribution of the porosity parameter, i.e. the anisotropy. Additionally both approaches can be used on 2D as well as 3D datasets. This is an important feature because CT only allows to obtain 3D information of samples, which have a sample size between mm and m. In order to be able to perform further down- scaling or upscaling, 2D datasets are more common such as scanning electron microscopy images and LiDAR datasets. This study illustrates the complexity of the application of the REV parameter in geo- logical studies. Only by calculating the REV at different scales, reservoir properties in complex carbonate rocks can be evaluated correctly. In order to link results from LIDAR, medical CT, micro-CT and thin-sections and to accurately predict adequate REV sizes, a new upscaling strategy to incorporate 3D CT data was developed. Hence the necessity to establish a link between different datasets, acquired at different resolutions is required. This can be achieved by using a workflow derived from multiple point geostatistical studies. This approach combines the strengths of pixel-based and object-based techniques. The shape of the pores is re- produced, while retaining the flexibility of a pixel-based method. Scans of the 2.5 cm diameter plugs are used as a training image while data from 10 cm diameter cores are used for conditioning. The quality of the simulated datasets is determined by com- paring pore shape distributions and the simulated permeability values of a corresponding part of both the original dataset and the simulated dataset. The simulated samples provide further information about the size of the REV over the studied scale range and bridge the gap between 10 cm and 2.5 cm diameter samples. This upscaling approach allows us to counter one of the main disadvantages of using CT data. To achieve μm resolutions only small samples (7 mm diameter) can be scanned. The technique described above allows to artificially improve the resolution of CT datasets as long as a representative training image of the desired resolution is present. This again proves the importance of an accurate calculation of the REV. An extra research topic that was added to the project was the use of the developed techniques to establish a workflow in order to simulate rock volumes based on a single thin-section. It is important that these simulated “numerical-rock” volumes have the same petrophysical characteristics as the original rock from which the thin-section was made. In this project, the used work- flow can be best described as a 2.5D approach, where 2D slices are simulated using some selected pore centres as conditioning data for the next slice. Because of this simplified approach, less computation time is needed compared to other pure 3D techniques. Heterogeneity is an inherent characteristic of carbonate reservoir rocks, which is determined by their geological evolution, e.g. sedimentary origin, diagenetic processes and burial history. These processes relate to the economic relevance of reservoir rocks as well as to the degradation of building stones. Different porosity types in sedimentary rocks exist on a spectrum of different spatial scales. An example of the lower end of the spectrum is very fine micro-porosity in micritic textures, characterised by pore diameters on sub-μm scale. On the other hand of the spectrum are the large pores in sedimentary rocks, e.g. karst and shelter poros- ity with diameters up to meter scale. In this study a unique dataset comprising several orders of spatial scale (from μm till m) is used to develop a new descriptive pore shape classification in order to assess the representativeness of porosity at different spatial scales. The major aim of this study was to charac- terise complex pore systems in 3D in carbonate rocks, framed in a well-established upscaling strategy. Additionally, the aspect of the Representative Elementary Volume (REV) was addressed since in CT-technology sample size is linked to resolution. An up- scaling strategy has been developed in which data on porosity acquired at different resolutions (from micro- to macro-porosity) and sample sizes are aligned. This will help to understand the major controlling factors on pore development, permeability, acous- tic properties and other petrophysical char- acteristics. In order to achieve a 3D interpretation of porosity and mineralogy, samples were scanned using medical and micro-CT. While both systems are non-destructive and pro- vide 3D data, medical and micro-CT scan- ners have a different hardware set-up and reach different resolutions. The medical CT scans are performed in collaboration with the department of radiology, UZ Leuven. For the micro-CT scans a GE Nanotom of the Material Engineering Department, KU Leu- ven is used. Samples scanned with a medi- cal CT scanner have a resolution around 250 μm while with a micro-CT scanner resolu- tions between 20 and 1 μm can be ob- tained. The first aim of the project was to develop an objective description of pore shapes based on 3D data. This is achieved by ana- lysing the ratios of the longest, intermedi- ate, shortest dimensions and compactness of the pore shapes, based on an approximating ellipsoid, in order to obtain a thor- ough and objective description of pore shapes. This classification differs from tradi- tional pore classifications because it is based on 3D data and uses solely the shape of the pores. In the traditional classifications of Choquette and Pray (1970), Lucia (1999) and Lønøy (2006), the parameters that are used are descriptive and relative to each other. They describe the rock, i.e. the solid constituents, to extract information about the porosity type rather than describing the pore itself, e.g. intercrystal or interparticle porosity. By using intrinsic properties, the classification based on CT data can be used at every resolution scale. Five shape classes are defined: i.e. rod, blade, plate, cuboid and cube. An additional advantage of this classification is that the data provide infor- mation about the orientation of the pores. This permits the assessment of the anisot- ropy of the porosity parameter. The new 3D classification (Claes et al., 2015b) allows a better understanding of the influence of the porosity parameter on other petrophysical parameters, e.g. the acoustic properties of rock samples (Soete et al., 2015). In this study it was shown that rod and cuboid shaped pores increase com- pressional wave velocities, while flattened pore shapes such as blade and plate-like shaped pores decrease the acoustic wave propagations. These observations help us to understand more accurately acoustic prop- erties of reservoir rocks. Additionally, the surface area of the pore is an important parameter since it plays a crucial role in the connectivity of pores as well as the reactive surface. Addressing the shape of the surface area is highly depen- dent on the resolution of the dataset. Hence the voxel representation of smooth conti- nuous surfaces is generally jagged, so the total area of exposed voxel faces is usually greater than that of the original continuous surface. This can be solved by a triangula- tion of the surface but literature indicates this is not the ideal solution. When using the marching cubes algorithm to create the triangulated representation, topological ambiguities may occur and holes may be generated due to the complex shapes of the pores. Secondly, the surface area estimate, produced by summing up the area of the resulting triangles, does not converge to the true surface area as the resolution increases due to the locality of the marching cubes algorithm. The extension of Fourier series to 3D results in the definition of spherical harmonic surfaces. Based on this new itera- tive approach, additional parameters such as surface area and circularity are calcu- lated. Moreover the accuracy of the calcu- lated parameters is sufficiently increased compared to other estimating methods. In a second research step the aspect of Rep- resentative Elementary Volume (REV) was studied. This is an important parameter in several research fields such as reservoir properties and structural property determi- nation. In the former the porosity parame- ter will be the most crucial. High-resolution LIDAR data of quarry walls were used to assess the porosity on the upper end of the spatial spectrum, while medical CT, micro-CT scans and thin- sections are used to cover the middle and lower end of the spectrum. For each spatial scale the REV is calculated (i.e. the smallest value that can be taken as a representation for the entire sample area/volume that does not respond to small changes in vol- ume or location). In this study two approaches to calculate the REV were developed and compared. Both methods are applicable to 2D as well as 3D datasets. This is important for linking the results of the new 3D approach with data of traditional studies. The first method uses the chi-square crite- rion to measure how much a single ran- domly chosen sub-sample diverges from the mean value of all realisations. This method is closely related to the original definition proposed by Bear. The second method uses the relationship between the REV and geo- statistical interpretations. A volume Vi falls within the REV domain if Y(x,Vi) can be treated as a stationary random function for any x in the domain. The advantage of both methods is that they allow to calculate 95 % confidence bounds for the REV parameter. The results of both methods are in the same order of magnitude and vary depending on the scale of the sample. Nevertheless the geostatistical method provides additional information on the shape of the REV based on the spatial distribution of the porosity parameter, i.e. the anisotropy. Additionally both approaches can be used on 2D as well as 3D datasets. This is an im- portant feature because CT only allows to obtain 3D information of samples, which have a sample size between mm and m. In order to be able to perform further down- scaling or upscaling, 2D datasets are more common such as scanning electron micro- scopy images and LiDAR datasets. This study illustrates the complexity of the application of the REV parameter in geo- logical studies. Only by calculating the REV at different scales, reservoir properties in complex carbonate rocks can be evaluated correctly. In order to link results from LIDAR, medical CT, micro-CT and thin-sections and to accu- rately predict adequate REV sizes, a new upscaling strategy to incorporate 3D CT data was developed. Hence the necessity to es- tablish a link between different datasets,acquired at different resolutions is required. This can be achieved by using a workflow derived from multiple point geostatistical studies. This approach combines the strengths of pixel-based and object-based techniques. The shape of the pores is reproduced, while retaining the flexibility of a pixel-based method. Scans of the 2.5 cm diameter plugs are used as a training image while data from 10 cm diameter cores are used for conditioning. The quality of the simulated datasets is determined by comparing pore shape distributions and the simulated permeability values of a corre- sponding part of both the original dataset and the simulated dataset. The simulated samples provide further information about the size of the REV over the studied scale range and bridge the gap between 10 cm and 2.5 cm diameter samples. This upscaling approach allows us to counter one of the main disadvantages of using CT data. To achieve μm resolutions only small samples (7 mm diameter) can be scanned. The technique described above allows to artificially improve the resolution of CT datasets as long as a representative training image of the desired resolution is present. This again proves the importance of an accurate calculation of the REV. An extra research topic that was added to the project was the use of the developed techniques to establish a workflow in order to simulate rock volumes based on a single thin-section. It is important that these simu- lated “numerical-rock” volumes have the same petrophysical characteristics as the original rock from which the thin-section was made. In this project, the used work- flow can be best described as a 2.5D ap- proach, where 2D slices are simulated using some selected pore centres as conditioning data for the next slice. Because of this simplified approach, less computation time is needed compared to other pure 3D tech- niques.status: publishe