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Estimation of porosity at a millimeter scale would be an order of magnitude finer resolution than traditional logging techniques. This enables proper description of reservoirs with thin layers and fine scale heterogeneities. To achieve this, we propose an end-to-end convolutional neural network (CNN) regression model that automatically predicts continuous porosity at a millimeter scale resolution using two-dimensional whole core CT scan images. More specifically, a CNN regression model is trained to learn from routine core analysis (RCA) porosity measurements. To characterize the performance of such approach, we compare the performance of this model with two linear regression models trained to learn the relationship between the average attenuation and standard deviation of the same two-dimensional images and RCA porosity. Our investigations reveal that the linear models are outperformed by the CNN, indicating the capability of the CNN model in extracting textures that are important for porosity estimations. We compare the predicted porosity results against the total porosity logs calculated from the density log. The obtained results show that the predicted porosity values using the proposed CNN method are well correlated with the core plug measurements and the porosity log. More importantly, the proposed approach can provide accurate millimeter scale porosity estimations, while the total porosity log is averaged over an interval and thus do not show such fine scale variations. Thus, the proposed method can be employed to calibrate the porosity logs, thereby reducing the uncertainties associated with indirect calculations of the porosity from such logs.

A data-driven automatic well planner procedure is implemented to develop complex well trajectories by efficiently adapting to near-well reservoir properties and geometry. The procedure draws inspiration from geosteering drilling operations, where modern logging-while-drilling tools enable the adjustment of well trajectories during drilling. Analogously, the proposed procedure develops well trajectories based on a selected geology-based fitness measure using an artificial neural network as the decision maker in a virtual sequential drilling process within a reservoir model. While neural networks have seen extensive use in other areas of reservoir management, to the best of our knowledge, this work is the first to apply neural networks on well trajectory design within reservoir models. Importantly, both the input data generation used to train the network and the actual trajectory design operations conducted by the trained network are efficient calculations, since these rely solely on geometric and initial properties of the reservoir, and thus do not require additional simulations. Therefore, the main advantage over traditional methods is the highly articulated well trajectories adapted to reservoir properties using a low-order well representation. Well trajectories generated in a realistic reservoir by the automatic well planner are qualitatively and quantitatively compared to trajectories generated by a differential evolution algorithm. Results show that the resulting trajectories improve productivity compared to straight line well trajectories, both for channelized and geometrically complex reservoirs. Moreover, the overall productivity with the resulting trajectories is comparable to well solutions obtained using differential evolution, but at a much lower computational cost.

Motivation A tanglegram is a plot of two-tree-like diagrams, one facing the other, and having their labels connected by inter-tree edges. These two trees, which could be both phylogenetic trees and dendrograms stemming from hierarchical clusterings, have thus identically labelled leaves but different topologies. As a result, the inter-tree edges of a tanglegram can be intricately tangled and difficult to be analysed and explained by human readers. To better visualize the tanglegram (and thus compare the two dendrograms) one may try to untangle it, i.e. search for that series of flippings of the various branches of the two trees that minimizes the number of crossings among the inter-tree edges. The untanglement problem has received significant interest in the past decade, and several techniques have been proposed to address it. These techniques are computationally efficient but tend to fail at finding the global optimum configuration generating the least tangly tanglegram. Results We leverage the existing results to propose untanglement methods that are characterized by an overall slower convergence method than the ones in the literature, but that produce tanglegrams with lower entanglements. Availability and implementation One of the algorithms is implemented in Python, and available from https://github.com/schlegelp/tanglegram.

This article considers upscaling of polymer adsorption. Input to adsorption values employed in reservoir simulation models are typically obtained from core plug measurements. There are several orders of magnitude in scale difference between core plugs and grid cells in reservoir simulation models, which foster a need for upscaling of the adsorption values. Polymer concentration distribution on the lithofacies scale is investigated in this article. The effect of diffusion on concentration distribution is investigated analytically. The slow diffusion of polymer molecules retards mixing even at the lithofacies scale. We introduce a formula to estimate the redistribution of polymer due to capillary forces in a layered model, and this formula is validated through numerical simulations. From our considerations we conclude that it is questionable to assume a constant polymer concentration in lithofacies models. This impedes applying steady-state upscaling techniques. Such upscaling techniques will over-predict polymer adsorption. Different methods for upscaling adsorption are presented in this paper, and applied to a simplified layered model and to more realistic fine-scale numerical models based on the SPE10 model. These numerical models were populated with adsorption values obtained from published experiments conducted on samples from the Brent sequence modeled in SPE10. Simulations of tertiary polymer flooding on the upscaled models were compared to simulations of the same flooding sequences on the original fine scale models. The tested upscaling methods include a volume averaging technique employed by other authors, and a method were we distribute the adsorption values by the same functional relationship as in the fine scale model. In addition we introduce upscaling methods were we assign zero adsorption to fine scale grid cells with permeability below a given cut-off value. The cut-off value is obtained from a single phase simulation on the fine scale model. In our models the cut-off value methods yield the best match between the coarse scale and fine scale simulation results. The volume averaging technique over-predict the polymer adsorption. Results from both the lithofacies and geomodel scale indicate a tendency to over-predict polymer adsorption, which could lead to conservative estimates for the effect of polymer flooding.

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ([Formula: see text]), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

An Automatic Well Planner (AWP) is used to efficiently adjust pre-determined well paths to honor near-well properties and increase overall production. AWP replicates modern geosteering decision-making where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. In this work, AWP is combined into a robust optimization scheme to develop trajectories that follow reservoir properties in a more realistic manner compared to common well representations for optimization purposes. Core AWP operation relies on an artificial neural network coupled with a geology-based feedback mechanism. Specifically, for each well path candidate obtained from an outer-loop optimization procedure, AWP customizes trajectories according to the particular geological near-well properties of each realization in an ensemble of models. While well placement searches typically rely on linear well path representations, AWP develops customized trajectories by moving sequentially from heel to the toe. Analog to realistic drilling operations, AWP determines subsequent trajectory points by efficiently processing neighboring geological information. Studies are performed using the Olympus ensemble. AWP and the two derivative-free algorithms used in this work, Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO), are implemented using NTNU’s open-source optimization framework FieldOpt. Results show that, with both APPS and PSO, the AWP solutions outperform the solutions obtained with a straight-line parameterization in all the three tested well placement optimization scenarios, which varied from the simplest scenario with a sole producer in a single-realization environment to a scenario with the full ensemble and multiple producers.

The efficiency of a displacement is the fraction of applied work over the change in free energy. This displacement efficiency is essential for linking wettability to applied work during displacement processes. We quantify the efficiency of slow immiscible displacements in porous media from pore space geometry. For this end, we introduce pore-scale definitions for thermodynamically reversible (ison) and irreverisble (rheon) processes. We argue that the efficiency of slow primary displacement is described by the geometry of the pore space for porous media with a sufficient number of pore bodies. This article introduces how to calculate such geometry-based efficiency locally, and integrating this local efficiency over the pore space yields an aggregate efficiency for the primary displacement in the porous medium. Further, we show how the geometrical characterization of the displacement efficiency links the efficiency to the constriction factor from transport processes governed by the Laplace equation. This enables estimation of displacement efficiency from traditional and widely available measurements for porous media. We present a thermodynamically based wettability calculation based on the local efficiency and a method to approximate this thermodynamically based wettability from traditional experiments.

In this work we apply a recently developed machine learning routine for automatic well planning to simplify well parameterization in reservoir simulation models. This reduced-order parameterization is shown to be beneficial for well placement optimization, both in terms of convergence and final well configuration. The proposed machine learning routine maps trajectories that honor predefined engineering requirements by exploiting spatial information about the reservoir and prior domain-knowledge about the problem. In this paper, the well planner creates wells that traverse high-permeable parts of the reservoir, thereby increasing well productivity. Previous work found that small changes to the start- and end-points of the well had limited impact on most of the resulting well trajectories, since development of trajectories is chiefly determined by local information around the digital drill bit. In particular, changes in the depth component of the start- and end-points had limited impact on the trajectory away from the end-points. Based on these observations, this work reduces well parameterization to only include horizontal coordinates. The main assumption is that the perforated part of the well always enters the reservoir at the upper reservoir boundary, while the stopping criteria in the machine learning routine is a perforation length only. This formulation reduces the number of decision variables from six to four coordinates for each well. The resulting reduced search space enables a more efficient exploration effort at the cost of less freedom over the start and end points of the well path. However, we show that the highly-refined well trajectory developed by the well planning routine is robust and compensates for fewer degrees of freedom at the overarching parameterization. This robustness is tested by investigating the effect of different start locations on the automatic well planning routines. Moreover, the effect of the reduced well parameterization for well placement optimization is explored. Two optimization scenarios using four different optimizations algorithms are presented. Results show the implementation of the reduced well parameterization for optimization purposes consistently produces high quality solutions.

This article provides an overview of the current state of digital rock technology, with emphasis on industrial applications. We show how imaging and image analysis can be applied for rock typing and modeling of end-point saturations. Different methods to obtain a digital model of the pore space from pore scale images are presented, and the strengths and weaknesses of the different methods are discussed. We also show how imaging bridges the different subjects of geology, petrophysics and reservoir simulations, by being a common denominator for results in all these subjects. Network modeling is compared to direct simulations on grid models, and their respective strengths are discussed. Finally we present an example of digital rock technology applied to a sandstone oil reservoir. Results from digital rock modeling are compared to results from traditional laboratory experiments. We highlight the mutual benefits from conducting both traditional experiments and digital rock modeling., Comment: 36 pages, 18 figures

In this work, we calculate contact angles in X-ray tomography images of two-phase flow in order to investigate the wettability. Triangulated surfaces, generated using the images, are smoothed to calculate the contact angles. As expected, the angles have a spread rather than being a constant value. We attempt to shed light on sources of the spread by addressing the overlooked mesh corrections prior to smoothing, poorly resolved image features, cluster-based analysis, and local variations of contact angles. We verify the smoothing algorithm by analytical examples with known contact angle and curvature. According to the analytical cases, point-wise and average contact angles, average mean curvature and surface area converge to the analytical values with increased voxel grid resolution. Analytical examples show that these parameters can reliably be calculated for fluid–fluid surfaces composed of roughly 3000 vertices or more equivalent to 1000 pixel2. In an experimental image, by looking into individual interfaces and clusters, we show that contact angles are underestimated for wetting fluid clusters where the fluid–fluid surface is resolved with less than roughly 500 vertices. However, for the fluid–fluid surfaces with at least a few thousand vertices, the mean and standard deviation of angles converge to similar values. Further investigation of local variations of angles along three-phase lines for large clusters revealed that a source of angle variations is anomalies in the solid surface. However, in the places least influenced by such noise, we observed that angles tend to be larger when the line is convex and smaller when the line is concave. We believe this pattern may indicate the significance of line energy in the free energy of the two-phase flow systems. Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-mons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Permeability and formation factor are important properties of a porous medium that only depend on pore space geometry, and it has been proposed that these transport properties may be predicted in terms of a set of geometric measures known as Minkowski functionals. The well-known Kozeny–Carman and Archie equations depend on porosity and surface area, which are closely related to two of these measures. The possibility of generalizations including the remaining Minkowski functionals is investigated in this paper. To this end, two-dimensional computer-generated pore spaces covering a wide range of Minkowski functional value combinations are generated. In general, due to Hadwiger’s theorem, any correlation based on any additive measurements cannot be expected to have more predictive power than those based on the Minkowski functionals. We conclude that the permeability and formation factor are not uniquely determined by the Minkowski functionals. Good correlations in terms of appropriately evaluated Minkowski functionals, where microporosity and surface roughness are ignored, can, however, be found. For a large class of random systems, these correlations predict permeability and formation factor with an accuracy of 40% and 20%, respectively. © The Author(s) 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

The objective of this paper is to describe experiments conducted to investigate osmosis as a mechanism for low-salinity enhanced oil recovery (EOR). For this purpose, an experiment was designed to facilitate enhanced oil recovery by osmosis-induced connate water expansion, while at the same time reducing the contributions of other proposed low-salinity mechanisms. Considerations were also made to achieve osmotic water transport rates comparable to what is expected at reservoir temperature. The correlation between enhanced oil recovery and the surface-to-volume ratio was of particular interest. Because the osmotic pressure gradients occur over distances comparable to the pore size, it is plausible that fluid redistribution due to osmosis would lead to a fairly local redistribution of oil, and thereby have a small impact on overall enhanced recovery in the field. However, near exposed surfaces, this local redistribution may result in oil production. Previous investigations of osmosis as an underlying low-salinity mechanism have consisted of visualization experiments, where water transport and oil movement under influence of osmotic gradients have been observed. Our experiments are intended to increase the understanding of the relative importance of osmosis in both small-scale low-salinity experiment results, and for field-scale low-salinity flooding. In the experiments, oil-wet sandstone samples with different surface-to-volume ratios were saturated with high-salinity water and oil to irreducible water saturation. The samples were first left to spontaneous imbibe in high-salinity water and afterward in low-salinity water. Additional oil production from spontaneous imbibition of low-salinity was recorded and compared with the surface-to-volume ratio. The experiment was performed twice, at both ambient and elevated temperatures. The experiments at ambient temperature resulted in increased oil production values of 8-22% of pore volume by low-salinity spontaneous imbibition. No clear correlation was found between increased oil recovery and the surface-to-volume ratio. A correlation was, however, seen between increased oil production and the pore volume. Thus, increased oil production by low-salinity imbibition seems to be proportionate to the pore volume. The experiments at elevated temperature resulted in low values of increased oil production by low-salinity spontaneous imbibition, and the values do not seem to correlate with either surface area or pore volume. The low response is believed to be caused by thermal effects from repeated heating and cooling of the samples during the preparations. Our results cannot dismiss osmosis as an important mechanism for low-salinity EOR. Possible explanations for the correlation between increased oil production and pore volume are hysteresis and simultaneous connate water expansion throughout the core.

In integral geometry, intrinsic volumes are a set of geometrical variables to characterize spatial structures, for example, distribution of fluids in two‐fluid flow in porous media. McClure et al. (2018, https://doi.org/10.1103/PhysRevFluids.3.084306) utilized this principle and proposed a geometric state function based on the intrinsic volumes. In a similar approach, we find a geometrical description for free energy of a porous system with two fluids. This is also an extension of the work by Mecke (2000, https://doi.org/10.1007/3-540-45043-2_6) for energy of a single fluid. Several geometrical sets of spatial objects were defined, including bulk of the two fluids, interfaces, and three‐phase contact lines. We have simplified the description of free energy by showing how the intrinsic volumes of these sets are geometrically related. We obtain a description for energy as a function of seven microscopic geometrically independent variables. In addition, using a thermodynamic approach, we find an approximation for the free energy as a function of macroscopic parameters of saturation and pressure under quasi‐static conditions. The combination of the two energy descriptions, by integral geometry and thermodynamics, completes the relation between the associated variables and enables us to find the unknown coefficients of the intrinsic volumes and to calculate the amount of dissipated energy in drainage and imbibition processes. We show that the theory is consistent with a set of experiments performed by Schlüter et al. (2016a, https://doi.org/10.1002/2015WR018254, 2017a, https://doi.org/10.1002/2016WR019815). However, in order to be more conclusive, it needs to be tested with larger data sets. ©2018. The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distri- bution in any medium, provided the original work is properly cited, the use is non-commercial and no modi fi cations or adaptations are made.

Steady-state upscaling of relative permeability is studied for a range of reservoir models. Both rate-dependent upscaling and upscaling in the capillary and viscous limits are considered. In particular, we study fluvial depositional systems, which represent a large and important class of reservoirs. Numerical examples show that steady-state upscaling is rate dependent, in accordance with previous work. In this respect we introduce a scale-dependent capillary number to estimate the balance between viscous and capillary forces. The difference between the limit solutions can be large, and we show that the intermediate flow rates can span several orders of magnitude. This substantiate the need for rate-dependent steady-state upscaling in a range of flow scenarios. We demonstrate that steady-state upscaling converges from the capillary to the viscous limit solution as the flow rate increases, and we identify a simple synthetic model where the convergence fails to be monotone. Two different sets of boundary conditions were tested, but had only minor effects on the presented reservoir models. Finally, we demonstrate the applicability of steady-state upscaling by performing dynamic flow simulation at the reservoir scale, both on fine-scaled and on upscaled models. The considered model is viscous dominated for realistic flow rates, and the simulation results indicate that viscous limit upscaling is appropriate., Comment: 25 pages, 18 figures, 4 tables

Flow diagnostics refers to a family of numerical methods that within a few seconds can compute visually intuitive quantities illuminating flow patterns and well connections for full 3D reservoir models. The starting point is a flow field, extracted from a previous multiphase simulation or computed by solving a simplified pressure equation with fixed mobilities. Time-of-flight (TOF) and stationary tracer equations are then solved to determine approximate time lines and influence regions. From these, one can derive sweep or drainage regions, injector–producer regions, and well allocation factors, as well as dynamic heterogeneity measures that characterize sweep and displacement efficiency and correlate (surprisingly) well with oil recovery from waterflooding processes. This work extends flow diagnostics to polymer flooding. Our aim is to develop inexpensive flow proxies that can be used to optimize well placement, drilling sequence, and injection strategies. In particular, we seek proxies that can distinguish the effects of improved microscopic and macroscopic displacement. To account for the macroscopic effect of polymer injection, representative flow fields are computed by solving the reservoir equations with linearized flux functions. Although this linearization has a pronounced smearing effect on water and polymer fronts, we show that the heterogeneity of the total flux field is adequately represented. Subsequently, transform the flow equations to streamline coordinates, map saturations from physical coordinates to time-of-flight, and (re)solve a representative 1D flow problem for each well-pair region. A recovery proxy is then obtained by accumulating each 1D solution weighted by a distribution function that measures the variation in residence times for all flow paths inside each well-pair region. We apply our new approach to 2D and 3D reservoir simulation models, and observe close agreements between the suggested approximations and results obtained from full multiphase simulations. Furthermore, we demonstrate how two different versions of the proxy can be utilized to differentiate between macroscopic and microscopic sweep improvements resulting from polymer injection. For the examples considered, we demonstrate that macroscopic sweep improvements alone correlate better with measures for heterogeneity than the combined improvements. This is the authors' accepted and refereed manuscript to the article. The final publication is available at link.springer.com via https://doi.org/10.1007/s10596-017-9681-9 . Locked until 05 July 2018 due to copyright restrictions.

We show that every k-linear abelian Ext-finite hereditary category with Serre duality which is generated by preprojective objects is derived equivalent to the category of representations of a strongly locally finite thread quiver., Comment: 32 pages, 12 pictures

In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g., brine), usually described using the Archie cementation exponent. We show how the electrical conductance depends on changes in the drift velocity and the length of the electric field lines, in addition to the porosity and the conductance of the electrolyte. We characterized the length of the electric field lines by a tortuosity and the changes in drift velocity by a constriction factor. Both the tortuosity and the constriction factor are descriptors of the pore microstructure. We define a conductance reduction factor to measure the local contributions of the pore microstructure to the global conductance. It is shown that the global conductance reduction factor is the product of the tortuosity squared divided by the constriction factor, thereby proving that the combined effect of tortuosity and constriction, in addition to the porosity and conductance of the electrolyte, fully describes the effective electrical conductance of a porous medium. We show that our tortuosity, constriction factor, and conductance reduction factor reproduce the electrical conductance for idealized porous media. They are also applied to Bentheimer sandstone, where we describe a microstructure-related correlation between porosity and conductivity using both the global conductance reduction factor and the distinct contributions from tortuosity and constriction. Overall, this work shows how the empirical Archie cementation exponent can be substituted by more descriptive, physical parameters, either by the global conductance reduction factor or by tortuosity and constriction., Comment: 9 pages, 8 figures, 1 table

In this article we investigate the permeability of a porous medium as given in Darcy's law. The permeability is described by an effective hydraulic pore radius in the porous medium, the fluctuation in local hydraulic pore radii, the length of streamlines, and the fractional volume conducting flow. The effective hydraulic pore radius is related to a characteristic hydraulic length, the fluctuation in local hydraulic radii is related to a constriction factor, the length of streamlines is characterized by a tortuosity, and the fractional volume conducting flow from inlet to outlet is described by an effective porosity. The characteristic length, the constriction factor, the tortuosity and the effective porosity are thus intrinsic descriptors of the pore structure relative to direction. We show that the combined effect of our pore structure description fully describes the permeability of a porous medium. The theory is applied to idealized porous media, where it reproduces Darcy's law for fluid flow derived from the Hagen-Poiseuille equation. We also apply this theory to full network models of Fontainebleau sandstone, where we show how the pore structure and permeability correlate with porosity for such natural porous media. This work establishes how the permeability can be related to porosity, in the sense of Kozeny-Carman, through fundamental and well-defined pore structure parameters: characteristic length, constriction, and tortuosity., Comment: 20 pages, 8 figures, 1 table

We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-linear (k algebraically closed) hereditary category with Serre duality and enough projectives is equivalent to the category of finitely presented representations of a thread quiver. In this way, we obtain an explicit construction of a new class of hereditary categories with Serre duality., Comment: As accepted by the Proceedings of the London Mathematical Society; some differences in label and page numbering may occur between this version and the published version

Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to rep_k Q for a so called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form \mathbb{Z} Q., Comment: 16 pages, as accepted by Journal of Pure and Applied Algebra

This thesis evaluates the possibility of automated permeability estimation by utilizing the information obtained from whole core 2D and 3D CT-scan images of wells on the Norwegian continental shelf. To evaluate this possibility, end-to-end convolutional neural network (CNN) regression models were proposed. These models used two-dimensional image slices and three-dimensional sub-cube images of 3D whole core CT scan images to automatically predict continuous permeability at a millimeter scale resolution. More specifically, CNN regression models were trained to learn permeability obtained from routine core analysis (RCA) measurements. Initially, a suggested CNN regression model was trained on 2D image slices belonging to a subclass of data to learn the relationship between convolution-derived features and RCA-derived permeability values. In the next methodology applied, the CNN regression model was further trained on 2D images belonging to the entire well. In the final methodology, a model was trained on 3D sub-cube images belonging to the entire well by utilizing a classical and a modified CNN architecture. The preliminary results from all models utilized in the three aforementioned methodologies demonstrate degrees of deviation from the RCA permeability values. Therefore, a post-processing stage was executed to enhance the performance of the models and to decrease the discrepancy between the measured and predicted permeabilities. This is done by initially including image augmentation of the test set data and then ultimately averaging the predicted permeability values of those test set images. The results depict that the models are predominantly prone to be erratic prior to applying the post-processing stage. However, once the post-processing procedure was implemented, the results exhibit a relatively good correlation between the predicted permeability values obtained utilizing the proposed method and the core plug permeability measurements. To summarize, this thesis confirms that the models show consistent predictive results, and are able to identify a substantial portion of the variation in permeability measurements. It is indicative that the models are able to learn the relationship between the distribution of grey-level attenuations of the images and the permeability measurements. However, it is important to note that the proposed models were only trained on a subset of data from a single well. Ideally, we assume a model trained on the whole well and multiple wells would result in a more robust model with higher generalization capabilities. Furthermore, there are some limitations and uncertainties associated with the image artifacts in the training dataset, and image complexities that can negatively impact the training process and generalization capabilities of the proposed model. This thesis evaluates the possibility of automated permeability estimation by utilizing the information obtained from whole core 2D and 3D CT-scan images of wells on the Norwegian continental shelf. To evaluate this possibility, end-to-end convolutional neural network (CNN) regression models were proposed. These models used two-dimensional image slices and three-dimensional sub-cube images of 3D whole core CT scan images to automatically predict continuous permeability at a millimeter scale resolution. More specifically, CNN regression models were trained to learn permeability obtained from routine core analysis (RCA) measurements. Initially, a suggested CNN regression model was trained on 2D image slices belonging to a subclass of data to learn the relationship between convolution-derived features and RCA-derived permeability values. In the next methodology applied, the CNN regression model was further trained on 2D images belonging to the entire well. In the final methodology, a model was trained on 3D sub-cube images belonging to the entire well by utilizing a classical and a modified CNN architecture. The preliminary results from all models utilized in the three aforementioned methodologies demonstrate degrees of deviation from the RCA permeability values. Therefore, a post-processing stage was executed to enhance the performance of the models and to decrease the discrepancy between the measured and predicted permeabilities. This is done by initially including image augmentation of the test set data and then ultimately averaging the predicted permeability values of those test set images. The results depict that the models are predominantly prone to be erratic prior to applying the post-processing stage. However, once the post-processing procedure was implemented, the results exhibit a relatively good correlation between the predicted permeability values obtained utilizing the proposed method and the core plug permeability measurements. To summarize, this thesis confirms that the models show consistent predictive results, and are able to identify a substantial portion of the variation in permeability measurements. It is indicative that the models are able to learn the relationship between the distribution of grey-level attenuations of the images and the permeability measurements. However, it is important to note that the proposed models were only trained on a subset of data from a single well. Ideally, we assume a model trained on the whole well and multiple wells would result in a more robust model with higher generalization capabilities. Furthermore, there are some limitations and uncertainties associated with the image artifacts in the training dataset, and image complexities that can negatively impact the training process and generalization capabilities of the proposed model.

Fenomenet med borevæske som slipper ut fra brønnen og inn i formasjonen under boring av en oljebrønn er kjent som tapt sirkulasjon (lost circulation). Ved siden av økonomiske tap på grunn av tapt tid ved boring, er det også mulighet for å skade formasjonen. En potensiell løsning for å hindre tap av borevæske er å tilsette partikler til borevæsken, kjent som Lost Circulation Materials (LCM). Disse kan tette brudd og permeable soner. I denne oppgaven er formasjonen forenklet til en kule-pakke. Den numeriske simuleringen utføres med en Dense Discrete Phase Model (DDPM), som løser væskestrøm ligningene og partikkel-væskeinteraksjonene, koblet til en Discrete Element Method (DEM), som løser partikkel interaskjoner; kontakter mellom partikler og mellom partikler og pore-vegger. Karakteriseringen av væske-partikkel strømmen oppnås ved å variere trykkforskjellen over modellen. Væskehastighet, partikkelmassestrøm, permeabilitet og volumetrisk strømningshastighet på væsken overvåkes under tilstoppingsprosessen. Økningen i trykkforskjellen på innløpsoverflaten resulterer i en høyere væskehastighet ved innløpsoverflaten og en høyere massehastighet for faste partikler. Det reduserer også den volumetriske strømningshastigheten ved utløpet, noe som resulterer i en mer effektiv tetting av det porøse mediet. During the drilling of an oil well, the phenomenon of drilling fluid escaping from the annular region into the formation is known as lost circulation. Besides the financial and time losses due to mitigation procedures, there is also the possibility of damaging the formation. A potential solution to the lost circulation problem is adding solid particles to the drilling fluid, known as Lost Circulation Materials (LCM). These particles can seal fractures and highly permeable zones. In this work, the rock formation is simplified to a spheres pack. The numerical simulation is performed via the Dense Discrete Phase Model (DDPM), which solves the fluid flow equations and the particle-fluid interactions, coupled to the Discrete Element Method (DEM), which solves the interaction between particles and between particles and walls. Characterization of the liquid-solid flow is obtained by varying the pressure difference in the numerical domain. Fluid velocity, solid particle flow rate, and normalized fluid flow rate are monitored throughout the clogging process. The effectiveness of changing some parameters is studied in this work. Increasing particle diameters shows to be a good solution to reduce fluid loss. The variation in particle-fluid density ratio on the other hand presented little change in the final fluid flow rate. Injecting particles of different sizes can be effective if all particles are larger that the pore throat. The increase in the pressure difference on the domain results in a lower fluid flow rate, but also in fewer particles trapped in the porous medium.

Forskningsspørsmålet i dette arbeidet var effekten av vannkvalitet på spontan oppsuging (SI) i karbonatkjerner. Målet var å endre fra oljefuktende til vannfuktende tilstand kjerner for å oppnå mer spontan oppsuging av vann og forbedret produksjon av olje. Hovedmålet var å forstå hvordan den ioniske sammensetningen av oppsugd vann dikterer fuktighetsendringen. For å gjennomføre disse eksperimentene var det nødvendig å bygge en rigg designet for å operere ved 96°C for en uavbrutt SI. Vi brukte kjerner fra to steder; fra Ainsa i Spania og fra Angola. Disse kjernene ble ansett som representative for et Equinor-operert oljefelt utenfor Brasil. Basert på petrofysiske egenskaper var kjernematerialet fra Angola mer heterogent enn det fra Ainsa. X-ray diffraction (XRD) og back-scatter electron imaging (SEM) resultater klassifiserte kjernematerialene som kalkstein uten anhydrid. Dette prosjektet sammenligner også to aldringsprosesser, og design for den mest effektive prosessen. Effekten av ionisk sammensetning på fukting ble studert ved å analysere utvinning av olje fra SI av formasjonsvann (FW), syntetisk sjøvann (SSW) eller modifiserte versjoner av syntetisk vann ved 96°C. Den ioniske sammensetningen av SSW ble endret ved å øke magnesium (Mg2+) og sulfat (SO2−4) ion konsentrasjonene. Tre forskjellige modifiserte syntetiske sjøvann; en med to ganger sulfatkonsentrasjon og fire ganger magnesiumkonsentrasjon (SSW-2S4Mg), et annet vann med to ganger sulfatkonsentrasjon og åtte ganger magnesiumkonsentrasjon (SSW-2S8Mg), og til slutt et med lavt saltinnhold der NaCl-konsentrasjonen ble redusert til 10% av SSW-konsentrasjon (0,1-NaCl-SSW). For reproduserbarhet av resultatene ble to kjerner brukt i hver runde av SI-eksperimentene. Kontaktvinkelmålinger utført ved romtemperatur på polerte steinprøver eldet ved både 25°C (romtemperatur) og ved 96°C ble også utført ved bruk av samme salt-vann løsninger for å supplere resultatene av spontan oppsuging. Zeta-potensiale målinger ble utført på Angola 8μm stein-partikler suspendert i hver av test-vannene for å studere stein-vann overflaten ved 25°C og 70°C. En forbedret SI-rigg som tillater en uavbrutt SI-prosess ble bygget, og fungerte jevnt uten lekkasjer, trykk opp-bygging og uten å koke vannet. Fra SI-eksperiment fikk vi økt oljeproduksjon på 6-10% med SSW etter FW, noe som viser at SSW er en EOR-væske i kalksteinkjerner. Utvinning på 4-6% og 4-10% med SSW-2S4Mg og SSW-2S8Mg, viste henholdsvis at berikelse av SSW med Mg2+ og SO2−4 ioner gir økt vannfukt i kalksteinkjerner, noe som forårsaker mer spontan oppsuging. Eksperimentet med Ainsa-kjerner ga en ekstra utvinning på 5% med 0,1-NaCl-SSW etter SSW, noe som viser virkningen av selektiv fortynning. Ytterligere utvinning av 13% med SSW-2S4Mg bekreftet at reduksjon av NaCl-innholdet i SSW forbedrer aktiviteten til potensielt bestemmende ioner i fuktigendrings-prosessen i kalksteinskjerner. Dette ble også bekreftet med kontaktvinkel målinger på vannvåte prøver etter aldring i 0,1-NaCl-SSW i 3 dager. Ulike aldrings-metoder ble studert ved å elde to Ainsa-kjerner med enten dynamisk eller statisk elding. For denne sammenligningen ble et nytt eksperimentelt oppsett for dynamisk aldring designet og bygget. Dette oppsettet kan takle høye temperaturer og trykk under 35 bar. Spontane oppsuging resultater viste at dynamisk aldring er en bedre aldringsprosess for å forandre fuktighet enn statisk elding. En produksjon på 12% ble registrert i kjernen eldet dynamisk, mot 4% for statisk elding, da SSW ble introdusert i tertiær modus. The research topic in this work was the effect of water quality on spontaneous imbibition (SI)in carbonate cores. The target was to alter the oil wetting state in outcrop cores to a more water wet state in order to have spontaneous imbibition of brine and improved crude oil recovery. The main aim was to understand how the ionic composition of imbibing brine dictates the wettability change. In order to carry out these experiments a rig designed to operate at 96°C for an uninterrupted SI was needed. Outcrop cores used were of two origins; outcrop cores from Ainsa in Spain and from Angola, and these outcrop cores were considered representative of an Equinor operated oil field off-shore Brazil. Based on petrophysical properties, the core material sourced from Angola was more heterogeneous than that from Ainsa. X-ray diffraction (XRD) and back-scatter electron imaging (SEM) results classified the rock materials as limestone without anhydrite. The research also compares two aging processes, and design for the most efficient process. The effect of ionic composition on wettability alteration was studied by analysing oil recoveries due to SI of formation water (FW), synthetic seawater (SSW) or modified versions of synthetic seawater at 96°C . The ionic composition of SSW was altered by increasing the magnesium (Mg2+) and sulfate (SO2−4) ion concentrations. Three different modified synthetic sea waters; one with two times sulfate concentration and four times magnesium concentration (SSW-2S4Mg), a second water with two times sulfate concentration and eight times magnesium concentration (SSW-2S8Mg), and finally a low salinity water where the NaCl concentration is reduced to 10% of the SSW concentration (0.1-NaCl-SSW). For reproducibility of results, two cores were used in each run of SI experiment. Contact angle measurements conducted at room temperature on polished rock chips aged both at 25°C (room temperature) and at 96°C were also done using the same set of brines to supplement results of spontaneous imbibition. Zeta potential measurements were conducted on Angola 8μm rock particles suspended in each of the test brines to study the rock-brine interface at 25°C and 70°C. An improved SI rig that allows an uninterrupted SI process was set up and worked smoothly without leakages, pressure build up and water boiling. From SI experiment, improved oil recoveries of 6-10% with SSW after FW, showed that SSW is an EOR fluid in limestone cores. Recoveries of 4-6% and 4-10% with SSW-2S4Mg and SSW-2S8Mg, respectively, showed that enriching SSW with Mg2+and SO2−4ions improves the water wetting state in limestone cores and causes more spontaneous imbibition. The experiment with Ainsa cores gave a recovery of 5% with 0.1-NaCl-SSW after SSW showed the impact of selective dilution. Additional recovery of 13% with SSW-2S4Mg confirmed that reducing the NaCl content in SSW improves the activity of potential determining ions in the wettability alteration process in limestone cores. This was also confirmed with contact angles on water wet samples after aging in 0.1-NaCl-SSW for 3 days Different aging methods were studied by aging two Ainsa cores with either dynamic or static aging. For this comparison, a new experimental set up for dynamic aging was designed and built. This setup could handle high temperatures and pressures below 35 bars. Spontaneous imbibition results showed that dynamic aging is a better wettability alteration process than static aging. A recovery of 12% was recorded in the core aged dynamically and 4% for the statically aged when SSW was introduced in a tertiary mode

This experimental study investigates the osmosis and the spontaneous emulsification as oil mobilization mechanisms during the low salinity water flooding by measuring the connate water expansion area in an oil-wet microfluidic system. Two types of synthetical oil, heptane and dodecane, and different salinity brines are chosen to use in the experiments. Meanwhile, surfactants are added into the oil phase to calculate the water transportation rate due to the spontaneous emulsification, comparing with the water transportation rate due to the osmosis. Dynamic light scattering and pendant drop experiments were conducted with the same fluids to study the spontaneous emulsification process. The HSW expansion due to the osmosis was observed at the microfluidic experiments with both heptane and dodecane under a salinity gradient. The water transportation rate for the osmosis is as high as the rate for the spontaneous emulsification with enough amounts of surfactants added into the heptane. Insufficient surfactants added may inhibit the water transportation in the synthetic oil. The dodecane shows weaker water transportability in the same condition. It is still hard to give any conclusion on the effect of the oil viscosity and water solubility.