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Digital core reconstruction research: challenges and prospects

Digital core reconstruction research: challenges and prospects GEOLOGY, ECOLOGY, AND LANDSCAPES INWASCON https://doi.org/10.1080/24749508.2022.2086201 RESEARCH ARTICLE a b a b b b A.A. Ponomarev , М.А. Kadyrov , O.A. Tugushev , D.A. Drugov , Y. V. Vaganov , D.S. Leontiev and M. D Zavatsky a b Department of Oil and Gas Deposits Geology, Tyumen Industrial University, Tyumen, Russia; Department of Drilling of Oil and Gas Wells, Tyumen Industrial University, Tyumen, Russia ABSTRACT ARTICLE HISTORY Received 1 April 2022 In this review we have briefly reviewed the state of the art of “digital core” technology. In Accepted 31 May 2022 particular, we reviewed the main artefacts that can occur in the analysis of rocks by computed X-ray microtomography. Next, we highlighted the existing approaches of direct mathematical KEYWORDS modelling of core filtration characteristics using digital model and poroset models. Literature Digital petrophysics; digital analysis has shown that the most justified in the ratio of required technical resources (compu- core; X-ray ter power) and reliability of results is the integrated approach. Unfortunately, when calculating microtomography; filtration phase permeabilities using digital core models, it is necessary to calibrate simulation results properties using standard laboratory methods. We also analysed some approaches to modelling enhanced oil recovery methods such as hydrochloric acid and hydraulic fracturing, as well as thermal stimulation of oil matrix rocks. In conclusion, we noted that the main challenge of today’s “digital core” technology is reliable calculation of phase permeabilities, and further development of the technology should be towards 4D modelling of EOR methods using digital core models. Introduction In this review, we will highlight the current state of At present, due to the commissioning of oil and gas research in the field of “digital petrophysics”: consider reservoirs with hard-to-recover reserves (Gajica et al., the main problems that may arise in obtaining a digital 2022; Sun et al., 2022; G. Wang et al., 2022), there is model (scanning artifacts), the state of research on the a need to improve the quality of petrophysical studies determination of filtration-volume properties by digi- (Brailovskaya & Oks, 2021; D. Wang et al., 2020). This tal core model and assess the prospects for the devel- applies first of all to reservoirs represented by poorly opment of this field. consolidated rocks, clay-bituminous rocks and rocks with a complex lithological structure. The problem in Problems of computed X-ray core this case is that when working with these rocks there are microtomography difficulties when preparing samples for analysis and their subsequent study by standard petrophysical meth- Before it was possible to examine rock samples at ods: the core of poorly consolidated rocks – crumbles a high resolution by computed X-ray microtomogra- (Peixoto Filho et al., 2021), clay-bituminous rocks after phy (A. A. Ponomarev et al., 2022; Ibrahim et al., extraction with organic solvents crack, and samples of 2021), first geologists were studying rocks by conven- rocks with complex lithological structure due to tional computed X-ray tomography (Mees et al., a complex combination of permeable and impermeable 2003), the principle of which was identical as in med- interlayers can show understated relative to the forma- icine. Before turning to the problems encountered tion values of permeability and permeability properties when examining cores by computed X-ray microto- With the development of scientific and technical sup- mography, we present the principle of operation of port of petrophysical laboratories and the need for reli- X-ray microtomography, Figure 1. X-rays pass able determination of filtration-volume properties in the through the object under study, hit the detector, above rock types, a new trend “digital petrophysics” or which captures the shadow projection. The sample is “digital core” has been actively developing over the last then rotated by a certain angle and the procedure is decade (Kadyrov et al., 2022; Pal et al., 2022; Payton et al., repeated. Scanning results in a database of shadow 2022). This trend implies obtaining a digital core model projections of the sample from different angles. by means of computer X-ray microtomography and its Further during reconstruction special mathematical mathematical processing in specialized software for cal- algorithms are used to present the shadow projections culating filtration-volume properties. in the form of tomographic slices of 1 pixel thickness. CONTACT М.А. Kadyrov kadyrov-marsel@bk.ru Department of Drilling of Oil and Gas Wells, Tyumen Industrial University, Tyumen, Russia © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the International Water, Air & Soil Conservation Society(INWASCON). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 A. A. PONOMARYOV ET AL. Figure 1. Principle of the computed micro-tomography system (Soltani et al., 2015). This makes it possible to work with a digital model, The artifacts shown in Figure 2 occur when the X-ray which is a set of consecutive tomographic slices that source is not powerful enough to sufficiently illuminate can be handled both in 3D and in 2D. a dense object with X-rays. When examining rocks, There is probably little point in listing all the pos- similar scanning artefacts can occur when large, heavy sible types of artefacts that can arise from tomographic (dense) minerals are present in the rock. In such cases, scanning, as they are known and already well as shown in Figure 2(c,d), these artifacts distort the described (Stock, 2019). We want to highlight some structure of the void space. Those areas in the vicinity of them that are characteristic of working with rocks. of which such distortions are observed cannot be used In particular, we should highlight artifacts that can for modeling and calculating rock filtration-volume occur when very heavy (dense) minerals are present properties. This is due to the fact that the mineral in rocks. These artifacts can create a distortion of the framework of the rock is segmented as a void space real rock structure, which in turn leads to errors in and causes overestimation of the defined properties. further numerical modeling of filtration-volume prop- Circular artefacts can also occur on tomographic erties. An example of such an artifact will be found in images when working with rocks. These should be medicine, but similar artifacts are also found in rocks, avoided and, if possible, eliminated. An example of see, Figure 2. circular artefacts is shown in Figure 3. Figure 2. Trabecular bone with metal implants of different diameters: (a) No visible artefacts, (b) With small visible artefacts, (c) With large artefacts, (d) With very large artefacts (arrows indicate artefacts; Grandmougin et al., 2020). GEOLOGY, ECOLOGY, AND LANDSCAPES 3 In tomographic images the boundary between media “pore space” – “mineral skeleton” or “mineral” – “mineral” is a step-by-step colour transition – gradual intensity gradients. Firstly, it is due to the fact that the actual media interface in the tomographic image is represented as several voxels, whose colour intensity corresponds to the average value of neighbouring voxels from it. This is the so-called partial volume effect, resulting in unresolved morphological features, including pore space wall roughness. Secondly, the finite resolu- tion of the imaging blurs the material interface by several voxels in width (Schlüter et al., 2014). In addition, the abrupt density transitions of the materials produce different refractive indices on either side of the interface, leading to so-called edge enhancement, which manifests as an over and under gray level immediately adjacent to the Figure 3. Example of circular artefacts (Kornilov et al., 2020). interface (Banhart, 2008). Based on this, the mor- phology of the void space in tomographic images is somewhat different from the real morphology in To combat ring artifacts, the following recommen- the material specimen (Soulaine et al., 2016). dations should be considered: 1. Fix the specimen Although these effects can be minimized, they securely on the slide so that the specimen does not cannot be excluded from the imaging process move during scanning; 2. Increase the number of (Perez et al., 2022). random frames in scanning settings; 3. Optimize All of the artefacts listed above can greatly reconstruction parameters. influence further mathematical modelling and cal- Also in this section we briefly highlight a problem culation of key petrophysical characteristics, so in the segmentation of void space or minerals in researchers need to keep artefacts to a minimum. a rock. This is very important because an incorrectly Where this cannot be done, an “area of interest” chosen X-ray density or colour interval in in the sample volume that is free of artifacts a tomographic image can greatly affect the results of should be selected for modeling. When selecting mathematical calculations of filtration-volume prop- direct filtration-capacitance modeling approaches, erties. Figure 4 shows a classic example of uncertainty proper void space segmentation greatly influences in the selection of the boundary between the void simulation results. space and the mineral skeleton of a rock. Figure 4. Example of an enlarged image of a “pore space”-”mineral skeleton” rock interface (Perez et al., 2022). 4 A. A. PONOMARYOV ET AL. volume method (VoF; Bilger et al., 2017); 3) phasefield The main approaches to modelling method (Rokhforouz & Akhlaghi Amiri, 2017); 4) filtration-capacitance properties density functional (Dinariev & Evseev, 2010). Currently, there are two main approaches for Due to the fact that “digital core” technology modelling filtration-capacitative properties from implies high-quality and fast calculation of filtration a digital core model: 1. direct numerical modelling characteristics, the use of direct calculation methods in based on the numerical solution of the Navier- multiphase filtration is inefficient in these technologi- Stokes equation and its simplification/modifica - cal possibilities. In this regard, scientists most often tion, or using the Boltzmann lattice method and use poroset modelling to solve the set problems 2. modelling based on mesh models (Gerke et al., (Bembel et al., 2019; Kohanpur & Valocchi, 2020; 2021). X. Wang et al., 2021; H. Zhang et al., 2021; The easiest in terms of mathematical modelling is W. Zhang et al., 2022). In contrast to direct modelling, to calculate absolute permeability from a digital core the main advantage of grid-based modelling is the model. Typically, this involves solving the Navier- speed of calculation, the possibility of working with Stokes equation for a single fluid whose flow obeys representative numerical models and the absence of Darcy’s law. Most often the following approaches are the requirement to carry out the calculation on used for modeling and absolute permeability calcula- a supercomputer. A standard, modern personal com- tion: 1) LBM (Khirevich et al., 2015); 2) finite element puter will be sufficient for calculations on the basis of and volume methods (FVM/FEM; Sedaghat et al., grid models. Despite rather high calculation speed, 2016); 3) smoothed particle methods (SPH; Holmes grid computing has a lower accuracy in comparison et al., 2016); 4) finite difference scheme (FDM) based to direct mathematical modelling. This is due to calculation codes (Eichheimer et al., 2019). Usually, to a large number of simplifications in reconstruction solve the problem at hand and use the listed of poroset models from digital core model. To approaches, the computer power is sufficient to per- improve the quality of calculations of filtration- form the calculation in a sufficiently representative capacitative properties from digital core models, the sample volume. use of an integrated modeling approach is considered When relative phase permeabilities need to be cal- to be the most modern approach. This approach culated, the use of direct calculation methods is greatly implies the use of direct modelling methods to esti- complicated by the need to use supercomputers for the mate filtration-volume properties in elementary filtra - calculations. However, even in this case, the calcula- tion channels with a certain structural characteristic; tion time can be excessively long. This is due to the then, using machine learning, pores with known struc- fact that when multiphase filtration is simulated on ture and filtration-volume properties are segmented a pore scale (two, three or more phases), in addition to from tomography data and the properties of the sam- solving the flow problem itself, it is also necessary to ple as a whole are calculated using them (Miao et al., describe in time the evolution of the interface of the 2017). This approach reduces the time required for filtering fluids. In this case, different approaches are direct modelling by evaluating the filtration properties used for direct numerical simulation because it is of individual pores, and further improves the accuracy necessary to describe the interaction of phases with of porosity modelling. An example of pore network the rock solid skeleton. In this case, the most common topology extraction in a particular pore-network approaches are as follows: 1) Boltzmann lattice simulation for calculating filtration-capacitative prop- method (Zakirov & Khramchenkov, 2020); 2) fluid erties is shown in Figure 5. Figure 5. Identification of the pore throat network topology by the “maximum balloon” method: (a) pore bodies filled with spheres of different sizes, (b) schematic of the pore-throat-pore structure (L. Wang et al., 2020). GEOLOGY, ECOLOGY, AND LANDSCAPES 5 Figure 5 shows a particular case of poroset model- this review, we will not dwell on the problem of deter- ling, where the void space of a rock is broken up into mining the mechanical properties of rocks, but will large pores in the form of spheres and throats. In talk in more detail about the capabilities of the tech- practice, there are various approaches to porous nology in modelling enhanced oil recovery methods. mesh modelling, where the void space can be trans- There are papers in the literature on the use of formed into shapes of different geometries. digital core technology for fracture modelling, mainly It is important to remember that the computed focused on determining mechanical properties of the X-ray microtomography method has limitations in core using digital modelling (Lin et al., 2022; Rassouli imaging resolution, which entails an inaccurate digital & Lisabeth, 2021). It is also noted that computed X-ray core model. As a rule, when working with low- microtomography can be used to improve the effi - permeability reservoirs, some of the pores that are ciency of hydraulic fracturing in terms of the most involved in filtration are beyond the resolution of the optimal proppant selection (Ramandi et al., 2021). micro-CT. In such cases, the results of focused ion In a generalised sense, the use of computed X-ray beam scanning electron microscopy (FIP-SEM) are microtomography in conjunction with digital core used in conjunction with X-ray microtomography technology can be used to conduct experiments before data (Jacob et al., 2021). This is necessary to obtain and after core exposure using various methods. For information on the morphology of the void space, example, thermal treatment of oil-bearing rocks which cannot be seen by microtomography. As (Gafurova et al., 2021) or hydrochloric acid core treat- a result of this integrated approach, it is possible to ment (Ivanov et al., 2020, 2021). The results of these complement the porosette model in order to improve kinds of laboratory experiments on the core can be the determination of core filtration properties (Gerke extrapolated to the reservoir as a whole to optimise et al., 2017). pilot testing. Figure 6 shows 3D models of the void space of oil-bearing rocks as a result of heating to 100, 200, 300 and 400°C. In the presented models, the Modelling of enhanced oil recovery methods colouring corresponds to the pore size (red are the and other properties smallest, green and blue are the largest). Analysis of Figure 6 indicates that the transforma- We would like to point out that the digital core tech- tion of the void space occurs as a result of heat expo- nology, in addition to calculating the filtration-volume sure of organic-rich oil-bearing rocks: new, larger properties of rocks, also allows calculating the pores and fractures are formed. This example does mechanical properties (Shulakova et al., 2013). In Figure 6. 3D models of the void space structure of heated samples with colour differentiation by the size of the pore channels (cubes with 1 mm edge): 1 – “nodules” of voids, 2 – crack (A. Ponomarev et al., 2021). 6 A. A. PONOMARYOV ET AL. not simulate filtration properties, but given that per- To optimise the calculation of filtration-volume proper- ties from a digital core model, it is advisable to use meability is a function of pore size distribution, we can a combined approach of direct mathematical modelling infer an increase in the filtration properties of the and poroset models samples as a result of heating. This laboratory experi- At present, without standard laboratory tests to deter- ment suggests that heat treatment of an oil-bearing mine phase permeabilities, mathematical calculations are reservoir should be used to increase its filtration char- not very accurate acteristics and shale oil production. Acknowledgments Prospects for the development of digital core This article was prepared as part of the Digital Core tech- technology nology project at the West Siberian Interregional World- class Science and Education Centre A comprehensive review of the “digital core” study showed that the current technology allows to deter- mine absolute permeability with high accuracy, as Disclosure statement for relative phase permeability – the main problem No potential conflict of interest was reported by the is imperfect mathematical modelling methods. In the author(s). first case, in direct calculations of phase permeabil- ity – insufficient computing power of computers, and in the second case, when using porosity model- Funding ing approach – there is an oversimplification of the This work was supported by the West Siberian Interregional real structure of the void space of rocks, which leads World-class Science and Education Centre; to inaccuracies in the calculations. 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Digital core reconstruction research: challenges and prospects

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GEOLOGY, ECOLOGY, AND LANDSCAPES INWASCON https://doi.org/10.1080/24749508.2022.2086201 RESEARCH ARTICLE a b a b b b A.A. Ponomarev , М.А. Kadyrov , O.A. Tugushev , D.A. Drugov , Y. V. Vaganov , D.S. Leontiev and M. D Zavatsky a b Department of Oil and Gas Deposits Geology, Tyumen Industrial University, Tyumen, Russia; Department of Drilling of Oil and Gas Wells, Tyumen Industrial University, Tyumen, Russia ABSTRACT ARTICLE HISTORY Received 1 April 2022 In this review we have briefly reviewed the state of the art of “digital core” technology. In Accepted 31 May 2022 particular, we reviewed the main artefacts that can occur in the analysis of rocks by computed X-ray microtomography. Next, we highlighted the existing approaches of direct mathematical KEYWORDS modelling of core filtration characteristics using digital model and poroset models. Literature Digital petrophysics; digital analysis has shown that the most justified in the ratio of required technical resources (compu- core; X-ray ter power) and reliability of results is the integrated approach. Unfortunately, when calculating microtomography; filtration phase permeabilities using digital core models, it is necessary to calibrate simulation results properties using standard laboratory methods. We also analysed some approaches to modelling enhanced oil recovery methods such as hydrochloric acid and hydraulic fracturing, as well as thermal stimulation of oil matrix rocks. In conclusion, we noted that the main challenge of today’s “digital core” technology is reliable calculation of phase permeabilities, and further development of the technology should be towards 4D modelling of EOR methods using digital core models. Introduction In this review, we will highlight the current state of At present, due to the commissioning of oil and gas research in the field of “digital petrophysics”: consider reservoirs with hard-to-recover reserves (Gajica et al., the main problems that may arise in obtaining a digital 2022; Sun et al., 2022; G. Wang et al., 2022), there is model (scanning artifacts), the state of research on the a need to improve the quality of petrophysical studies determination of filtration-volume properties by digi- (Brailovskaya & Oks, 2021; D. Wang et al., 2020). This tal core model and assess the prospects for the devel- applies first of all to reservoirs represented by poorly opment of this field. consolidated rocks, clay-bituminous rocks and rocks with a complex lithological structure. The problem in Problems of computed X-ray core this case is that when working with these rocks there are microtomography difficulties when preparing samples for analysis and their subsequent study by standard petrophysical meth- Before it was possible to examine rock samples at ods: the core of poorly consolidated rocks – crumbles a high resolution by computed X-ray microtomogra- (Peixoto Filho et al., 2021), clay-bituminous rocks after phy (A. A. Ponomarev et al., 2022; Ibrahim et al., extraction with organic solvents crack, and samples of 2021), first geologists were studying rocks by conven- rocks with complex lithological structure due to tional computed X-ray tomography (Mees et al., a complex combination of permeable and impermeable 2003), the principle of which was identical as in med- interlayers can show understated relative to the forma- icine. Before turning to the problems encountered tion values of permeability and permeability properties when examining cores by computed X-ray microto- With the development of scientific and technical sup- mography, we present the principle of operation of port of petrophysical laboratories and the need for reli- X-ray microtomography, Figure 1. X-rays pass able determination of filtration-volume properties in the through the object under study, hit the detector, above rock types, a new trend “digital petrophysics” or which captures the shadow projection. The sample is “digital core” has been actively developing over the last then rotated by a certain angle and the procedure is decade (Kadyrov et al., 2022; Pal et al., 2022; Payton et al., repeated. Scanning results in a database of shadow 2022). This trend implies obtaining a digital core model projections of the sample from different angles. by means of computer X-ray microtomography and its Further during reconstruction special mathematical mathematical processing in specialized software for cal- algorithms are used to present the shadow projections culating filtration-volume properties. in the form of tomographic slices of 1 pixel thickness. CONTACT М.А. Kadyrov kadyrov-marsel@bk.ru Department of Drilling of Oil and Gas Wells, Tyumen Industrial University, Tyumen, Russia © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the International Water, Air & Soil Conservation Society(INWASCON). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 A. A. PONOMARYOV ET AL. Figure 1. Principle of the computed micro-tomography system (Soltani et al., 2015). This makes it possible to work with a digital model, The artifacts shown in Figure 2 occur when the X-ray which is a set of consecutive tomographic slices that source is not powerful enough to sufficiently illuminate can be handled both in 3D and in 2D. a dense object with X-rays. When examining rocks, There is probably little point in listing all the pos- similar scanning artefacts can occur when large, heavy sible types of artefacts that can arise from tomographic (dense) minerals are present in the rock. In such cases, scanning, as they are known and already well as shown in Figure 2(c,d), these artifacts distort the described (Stock, 2019). We want to highlight some structure of the void space. Those areas in the vicinity of them that are characteristic of working with rocks. of which such distortions are observed cannot be used In particular, we should highlight artifacts that can for modeling and calculating rock filtration-volume occur when very heavy (dense) minerals are present properties. This is due to the fact that the mineral in rocks. These artifacts can create a distortion of the framework of the rock is segmented as a void space real rock structure, which in turn leads to errors in and causes overestimation of the defined properties. further numerical modeling of filtration-volume prop- Circular artefacts can also occur on tomographic erties. An example of such an artifact will be found in images when working with rocks. These should be medicine, but similar artifacts are also found in rocks, avoided and, if possible, eliminated. An example of see, Figure 2. circular artefacts is shown in Figure 3. Figure 2. Trabecular bone with metal implants of different diameters: (a) No visible artefacts, (b) With small visible artefacts, (c) With large artefacts, (d) With very large artefacts (arrows indicate artefacts; Grandmougin et al., 2020). GEOLOGY, ECOLOGY, AND LANDSCAPES 3 In tomographic images the boundary between media “pore space” – “mineral skeleton” or “mineral” – “mineral” is a step-by-step colour transition – gradual intensity gradients. Firstly, it is due to the fact that the actual media interface in the tomographic image is represented as several voxels, whose colour intensity corresponds to the average value of neighbouring voxels from it. This is the so-called partial volume effect, resulting in unresolved morphological features, including pore space wall roughness. Secondly, the finite resolu- tion of the imaging blurs the material interface by several voxels in width (Schlüter et al., 2014). In addition, the abrupt density transitions of the materials produce different refractive indices on either side of the interface, leading to so-called edge enhancement, which manifests as an over and under gray level immediately adjacent to the Figure 3. Example of circular artefacts (Kornilov et al., 2020). interface (Banhart, 2008). Based on this, the mor- phology of the void space in tomographic images is somewhat different from the real morphology in To combat ring artifacts, the following recommen- the material specimen (Soulaine et al., 2016). dations should be considered: 1. Fix the specimen Although these effects can be minimized, they securely on the slide so that the specimen does not cannot be excluded from the imaging process move during scanning; 2. Increase the number of (Perez et al., 2022). random frames in scanning settings; 3. Optimize All of the artefacts listed above can greatly reconstruction parameters. influence further mathematical modelling and cal- Also in this section we briefly highlight a problem culation of key petrophysical characteristics, so in the segmentation of void space or minerals in researchers need to keep artefacts to a minimum. a rock. This is very important because an incorrectly Where this cannot be done, an “area of interest” chosen X-ray density or colour interval in in the sample volume that is free of artifacts a tomographic image can greatly affect the results of should be selected for modeling. When selecting mathematical calculations of filtration-volume prop- direct filtration-capacitance modeling approaches, erties. Figure 4 shows a classic example of uncertainty proper void space segmentation greatly influences in the selection of the boundary between the void simulation results. space and the mineral skeleton of a rock. Figure 4. Example of an enlarged image of a “pore space”-”mineral skeleton” rock interface (Perez et al., 2022). 4 A. A. PONOMARYOV ET AL. volume method (VoF; Bilger et al., 2017); 3) phasefield The main approaches to modelling method (Rokhforouz & Akhlaghi Amiri, 2017); 4) filtration-capacitance properties density functional (Dinariev & Evseev, 2010). Currently, there are two main approaches for Due to the fact that “digital core” technology modelling filtration-capacitative properties from implies high-quality and fast calculation of filtration a digital core model: 1. direct numerical modelling characteristics, the use of direct calculation methods in based on the numerical solution of the Navier- multiphase filtration is inefficient in these technologi- Stokes equation and its simplification/modifica - cal possibilities. In this regard, scientists most often tion, or using the Boltzmann lattice method and use poroset modelling to solve the set problems 2. modelling based on mesh models (Gerke et al., (Bembel et al., 2019; Kohanpur & Valocchi, 2020; 2021). X. Wang et al., 2021; H. Zhang et al., 2021; The easiest in terms of mathematical modelling is W. Zhang et al., 2022). In contrast to direct modelling, to calculate absolute permeability from a digital core the main advantage of grid-based modelling is the model. Typically, this involves solving the Navier- speed of calculation, the possibility of working with Stokes equation for a single fluid whose flow obeys representative numerical models and the absence of Darcy’s law. Most often the following approaches are the requirement to carry out the calculation on used for modeling and absolute permeability calcula- a supercomputer. A standard, modern personal com- tion: 1) LBM (Khirevich et al., 2015); 2) finite element puter will be sufficient for calculations on the basis of and volume methods (FVM/FEM; Sedaghat et al., grid models. Despite rather high calculation speed, 2016); 3) smoothed particle methods (SPH; Holmes grid computing has a lower accuracy in comparison et al., 2016); 4) finite difference scheme (FDM) based to direct mathematical modelling. This is due to calculation codes (Eichheimer et al., 2019). Usually, to a large number of simplifications in reconstruction solve the problem at hand and use the listed of poroset models from digital core model. To approaches, the computer power is sufficient to per- improve the quality of calculations of filtration- form the calculation in a sufficiently representative capacitative properties from digital core models, the sample volume. use of an integrated modeling approach is considered When relative phase permeabilities need to be cal- to be the most modern approach. This approach culated, the use of direct calculation methods is greatly implies the use of direct modelling methods to esti- complicated by the need to use supercomputers for the mate filtration-volume properties in elementary filtra - calculations. However, even in this case, the calcula- tion channels with a certain structural characteristic; tion time can be excessively long. This is due to the then, using machine learning, pores with known struc- fact that when multiphase filtration is simulated on ture and filtration-volume properties are segmented a pore scale (two, three or more phases), in addition to from tomography data and the properties of the sam- solving the flow problem itself, it is also necessary to ple as a whole are calculated using them (Miao et al., describe in time the evolution of the interface of the 2017). This approach reduces the time required for filtering fluids. In this case, different approaches are direct modelling by evaluating the filtration properties used for direct numerical simulation because it is of individual pores, and further improves the accuracy necessary to describe the interaction of phases with of porosity modelling. An example of pore network the rock solid skeleton. In this case, the most common topology extraction in a particular pore-network approaches are as follows: 1) Boltzmann lattice simulation for calculating filtration-capacitative prop- method (Zakirov & Khramchenkov, 2020); 2) fluid erties is shown in Figure 5. Figure 5. Identification of the pore throat network topology by the “maximum balloon” method: (a) pore bodies filled with spheres of different sizes, (b) schematic of the pore-throat-pore structure (L. Wang et al., 2020). GEOLOGY, ECOLOGY, AND LANDSCAPES 5 Figure 5 shows a particular case of poroset model- this review, we will not dwell on the problem of deter- ling, where the void space of a rock is broken up into mining the mechanical properties of rocks, but will large pores in the form of spheres and throats. In talk in more detail about the capabilities of the tech- practice, there are various approaches to porous nology in modelling enhanced oil recovery methods. mesh modelling, where the void space can be trans- There are papers in the literature on the use of formed into shapes of different geometries. digital core technology for fracture modelling, mainly It is important to remember that the computed focused on determining mechanical properties of the X-ray microtomography method has limitations in core using digital modelling (Lin et al., 2022; Rassouli imaging resolution, which entails an inaccurate digital & Lisabeth, 2021). It is also noted that computed X-ray core model. As a rule, when working with low- microtomography can be used to improve the effi - permeability reservoirs, some of the pores that are ciency of hydraulic fracturing in terms of the most involved in filtration are beyond the resolution of the optimal proppant selection (Ramandi et al., 2021). micro-CT. In such cases, the results of focused ion In a generalised sense, the use of computed X-ray beam scanning electron microscopy (FIP-SEM) are microtomography in conjunction with digital core used in conjunction with X-ray microtomography technology can be used to conduct experiments before data (Jacob et al., 2021). This is necessary to obtain and after core exposure using various methods. For information on the morphology of the void space, example, thermal treatment of oil-bearing rocks which cannot be seen by microtomography. As (Gafurova et al., 2021) or hydrochloric acid core treat- a result of this integrated approach, it is possible to ment (Ivanov et al., 2020, 2021). The results of these complement the porosette model in order to improve kinds of laboratory experiments on the core can be the determination of core filtration properties (Gerke extrapolated to the reservoir as a whole to optimise et al., 2017). pilot testing. Figure 6 shows 3D models of the void space of oil-bearing rocks as a result of heating to 100, 200, 300 and 400°C. In the presented models, the Modelling of enhanced oil recovery methods colouring corresponds to the pore size (red are the and other properties smallest, green and blue are the largest). Analysis of Figure 6 indicates that the transforma- We would like to point out that the digital core tech- tion of the void space occurs as a result of heat expo- nology, in addition to calculating the filtration-volume sure of organic-rich oil-bearing rocks: new, larger properties of rocks, also allows calculating the pores and fractures are formed. This example does mechanical properties (Shulakova et al., 2013). In Figure 6. 3D models of the void space structure of heated samples with colour differentiation by the size of the pore channels (cubes with 1 mm edge): 1 – “nodules” of voids, 2 – crack (A. Ponomarev et al., 2021). 6 A. A. PONOMARYOV ET AL. not simulate filtration properties, but given that per- To optimise the calculation of filtration-volume proper- ties from a digital core model, it is advisable to use meability is a function of pore size distribution, we can a combined approach of direct mathematical modelling infer an increase in the filtration properties of the and poroset models samples as a result of heating. This laboratory experi- At present, without standard laboratory tests to deter- ment suggests that heat treatment of an oil-bearing mine phase permeabilities, mathematical calculations are reservoir should be used to increase its filtration char- not very accurate acteristics and shale oil production. Acknowledgments Prospects for the development of digital core This article was prepared as part of the Digital Core tech- technology nology project at the West Siberian Interregional World- class Science and Education Centre A comprehensive review of the “digital core” study showed that the current technology allows to deter- mine absolute permeability with high accuracy, as Disclosure statement for relative phase permeability – the main problem No potential conflict of interest was reported by the is imperfect mathematical modelling methods. In the author(s). first case, in direct calculations of phase permeabil- ity – insufficient computing power of computers, and in the second case, when using porosity model- Funding ing approach – there is an oversimplification of the This work was supported by the West Siberian Interregional real structure of the void space of rocks, which leads World-class Science and Education Centre; to inaccuracies in the calculations. 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Journal

Geology Ecology and Landscapes – Taylor & Francis

Published: Jun 12, 2022

Keywords: Digital petrophysics; digital core; X-ray microtomography; filtration properties

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