Real Rock Samples Research Articles

Convection-diffusion-reaction of CO2-enriched brine in porous media: A pore-scale study

CO2-enriched brine interaction with reservoir minerals and the subsequent mineral trapping of CO2 alter the morphology of pore structure. Such changes in the pore space modify the storage capacity of reservoirs and increase the long-term security of CO2 storage. The extent of pore space modification depends on the relative weight of advection, diffusion and reaction mechanisms. We present a general framework for a direct simulation of reactive transport in digitized reservoir rock samples based on a pore-scale modeling in two-dimensional (2D) and three-dimensional (3D) pore-throat networks. We examine the impact of transport properties such as Péclet (Pe) and Damköhler (Da) numbers, on the petrophysical properties and dissolution of mineral in pore space. We implement marker-based watershed segmentation to extract pore networks of 3D micro-CT (Computerized Tomography) scan images. The extracted network is used to simulate the reactive solute transport and dissolution on real rock samples. This approach enables us to study reaction of CO2-enriched brine with reservoir rock samples, which is vital in predicting long-term security of CO2 storage. We implement our approach to study CO2 injection in samples from the Cranfield site, Mississippi, U.S.A. We show that for small PeDa numbers, the concentration and dissolution patterns are more uniform.

Reservoir-on-a-Chip Technology Opens a New Window Into Oilfield Chemistry

With its ability to replicate little slivers of reservoir rocks, microfluidics is giving the oil and gas industry a new way to capture images of interactions between chemicals and hydrocarbons. The biggest advantage this emerging technology holds over more established research tools is that it can capture the images at all. “You actually see what it looks like when the oil, water, and chemistry all interact, and that means we are making direct measurements of the performance characteristics,” explained Stuart Kinnear, the chief executive officer of Interface Fluidics. The Edmonton, Alberta-based startup of just 3 years is generating increasing interest among operators and suppliers that want independent reviews of whether particular production-enhancing chemicals will work inside a reservoir as advertised. The work places it amid a small group of firms trying to take microfluidics from its native home in the biomedical sector and into the oil field. Interface Fluidics’ innovation is a type of microfluidic chip that is etched from a postage-stamp-sized strip of silicon and glass to form what it calls a “reservoir analogue.” Depending on the inputs, such as data obtained from rock samples or even industry literature, a blank chip can in a matter of a few hours be turned into a tiny duplicate of a porous sandstone from Alberta or the nanodarcy pathways of the Permian Basin’s Wolfcamp Shale. So far, more than 20 different types of formations have been replicated for projects involving heavy-oil extraction, hydraulic fracturing fluid analysis, and enhanced oil recovery (EOR) for shale. “We can also copy-and-paste to make a hundred or a thousand copies if you wanted to,” added Kinnear, highlighting another advantage that microfluidics offers over relying solely on analysis of real rock samples: repeatability. Thanks to the chip-making process, “you know the only thing you are changing run to run is the chemistry.” To simulate reservoir-like conditions, the chips are heated, pressurized, and loaded with samples of the crude and water from the look-alike’s actual field. Videos taken as chemicals are introduced reveal how the medley of fluids mobilize around the artificial pore structures and get oil flowing, or not. Kinnear described this element as the technology’s “killer app.” Because each chip is transparent on one side, a microscope-mounted camera can be used to document experiments with high resolution. Prized by first-adopters, the recordings explain what drives flow behavior, e.g., phase trapping, wettability modification, solids deposition, or emulsion. First Adopters See Wide Applicability For at least one chemical maker, that window into porosity has become a critical tool for validating its own emerging technology, a new line of nanosurfactants tailored for shale reservoirs. “The visual aspect is something we’ve never had before, and that really helps us understand what’s going on,” said Bill O’Neil, the research director at ChemTerra Innovation, the chemical subsidiary of Calgary-based service provider Trican Well Service. Its pilot with Interface Fluidics, details of which were published in March (SPE 189780), resulted in the company moving forward with a significantly larger study that is still underway.

A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

A numerical method is formulated for the solution of the advective Cahn–Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation describes phase separation of an immiscible binary mixture at constant temperature in the presence of a conservation constraint and dissipation of free energy. Porous media / pore-scale problems specifically entail images of rocks in which the solid matrix and pore spaces are fully resolved. The interior penalty discontinuous Galerkin method is used for the spatial discretization of the CH equation in mixed form, while a semi-implicit convex–concave splitting is utilized for temporal discretization. The spatial approximation order is arbitrary, while it reduces to a finite volume scheme for the choice of element-wise constants. The resulting nonlinear systems of equations are reduced using the Schur complement and solved via inexact Newton’s method. The numerical scheme is first validated using numerical convergence tests and then applied to a number of fundamental problems for validation and numerical experimentation purposes including the case of degenerate mobility. First-order physical applicability and robustness of the numerical method are shown in a breakthrough scenario on a voxel set obtained from a micro-CT scan of a real sandstone rock sample.

Complex dynamics of drill-strings: Theory and experiments

We investigate complex drill-string dynamics in a downhole drilling where strong nonlinear interactions between various types of vibration take place. First, we present a low dimensional model of the downhole drilling where a drill-bit cutting a rock formation has a strong coupling between torsional and axial oscillations. The model can be used to study drilling stability as an example results are given. Then we introduce a new experimental rig developed by the Centre for Applied Dynamics Research at the University of Aberdeen, capable of reproducing all major types of drill-string vibration. One of the most important features of this versatile experimental rig is the fact that commercial drill-bits, employed in the drilling industry, and real rock-samples are used. The rig operate in different configurations, which enables the experimental study of various phenomena, such as stick-slip oscillations, whirling and drill-bit bounce. It also allows to determine mechanical characteristics of the drill-bits, which are used to calibrate mathematical models.

Suppression of Drill-String Stick-Slip Vibration

We investigate experimentally and numerically suppression of drill-string torsional vibration while drilling by using a sliding mode control. The experiments are conducted on the novel experimental drilling rig developed at the University of Aberdeen [1] and using PDC commercial drill-bits and real rock-samples. A mathematical model of the experimental setup which takes into account the dynamics of the drill-string and the driving motor, is proposed. Then a sliding mode control method is employed to suppress stick-slip oscillations. The experimental and numerical results considering a time delay of the actuator are in a close agreement. Stick-slip vibration is eliminated and significant reduction in vibration amplitude has been observed when using the controller.

Helical Buckling of Drill-Strings

This paper presents experimental and numerical investigations of the complex drill-string vibration, with particular attention to the helical buckling of drill-strings and its influence on the system dynamics. The analysis is conducted using a novel experimental drilling rig, capable of exhibiting of all major types of drill-string vibration, including torsional, axial and lateral modes, which utilizes real industrial drill-bits and rock samples. A good qualitative and quantitative agreement between the experiments and numerical model is demonstrated.

Real rock-microfluidic flow cell: A test bed for real-time in situ analysis of flow, transport, and reaction in a subsurface reactive transport environment

Physical, chemical, and biological interactions between groundwater and sedimentary rock directly control the fundamental subsurface properties such as porosity, permeability, and flow. This is true for a variety of subsurface scenarios, ranging from shallow groundwater aquifers to deeply buried hydrocarbon reservoirs. Microfluidic flow cells are now commonly being used to study these processes at the pore scale in simplified pore structures meant to mimic subsurface reservoirs. However, these micromodels are typically fabricated from glass, silicon, or polydimethylsiloxane (PDMS), and are therefore incapable of replicating the geochemical reactivity and complex three-dimensional pore networks present in subsurface lithologies. To address these limitations, we developed a new microfluidic experimental test bed, herein called the Real Rock-Microfluidic Flow Cell (RR-MFC). A porous 500μm-thick real rock sample of the Clair Group sandstone from a subsurface hydrocarbon reservoir of the North Sea was prepared and mounted inside a PDMS microfluidic channel, creating a dynamic flow-through experimental platform for real-time tracking of subsurface reactive transport. Transmitted and reflected microscopy, cathodoluminescence microscopy, Raman spectroscopy, and confocal laser microscopy techniques were used to (1) determine the mineralogy, geochemistry, and pore networks within the sandstone inserted in the RR-MFC, (2) analyze non-reactive tracer breakthrough in two- and (depth-limited) three-dimensions, and (3) characterize multiphase flow. The RR-MFC is the first microfluidic experimental platform that allows direct visualization of flow and transport in the pore space of a real subsurface reservoir rock sample, and holds potential to advance our understandings of reactive transport and other subsurface processes relevant to pollutant transport and cleanup in groundwater, as well as energy recovery.

Modeling of Solute Transport in a 3D Rough-Walled Fracture\u2013Matrix System

Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.

Klinkenberg slippage effect in the permeability computations of shale gas by the pore-scale simulations

The prediction of permeability (i.e., apparent permeability) for the shale gas is challenging due to the Klinkenberg slippage effect that depends on the pore size and gas pressure. A recent Monte Carlo molecular simulation method (i.e., DSBGK method) is employed to accurately compute the permeability by the pore-scale simulations at different pressures. The computed results of a benchmark problem proposed here are used to verify the accuracy of the simple Klinkenberg correlation model, which relates the permeability to the intrinsic permeability (i.e., liquid permeability) and pressure. The verification shows that the Klinkenberg correlation model as a data fitting formula is appropriate for the industry applications since the relative error is small in the whole range of the flow regime as long as it has been calibrated for each particular rock sample at the two ends with low and high pressures, respectively, by determining the model parameters using accurate permeability data that can be obtained by the scheme presented herein. This conclusion is consistent with the experimental observations of real rock samples by Klinkenberg as shown in Appendix.

Modeling Fluid’s Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks

We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces.

Performance improvement of ionic surfactant flooding in carbonate rock samples by use of nanoparticles

Various surfactants have been used in upstream petroleum processes like chemical flooding. Ultimately, the performance of these surfactants depends on their ability to reduce the interfacial tension between oil and water. The surfactant concentration in the aqueous solution decreases owing to the loss of the surfactant on the rock surface in the injection process. The main objective of this paper is to inhibit the surfactant loss by means of adding nanoparticles. Sodium dodecyl sulfate and silica nanoparticles were used as ionic surfactant and nanoparticles in our experiments, respectively. AEROSIL® 816 and AEROSIL® 200 are hydrophobic and hydrophilic nanoparticles. To determine the adsorption loss of the surfactant onto rock samples, a conductivity approach was used. Real carbonate rock samples were used as the solid phase in adsorption experiments. It should be noted that the rock samples were water wet. This paper describes how equilibrium adsorption was investigated by examining adsorption behavior in a system of carbonate sample (solid phase) and surfactant solution (aqueous phase). The initial surfactant and nanoparticle concentrations were 500–5000 and 500–2000 ppm, respectively. The rate of surfactant losses was extremely dependent on the concentration of the surfactant in the system, and the adsorption of the surfactant decreased with an increase in the nanoparticle concentration. Also, the hydrophilic nanoparticles are more effective than the hydrophobic nanoparticles.

Torsional vibrations of helically buckled drill-strings: experiments and FE modelling

This paper presents investigations of a complex drill-string vibrations on a novel experimental rig, developed by the Centre for Applied Dynamics Research at the University of Aberdeen. The rig is capable of exhibiting of all major types of drill-string vibrations, including torsional, axial and lateral modes. The importance of this work lies in the fact, that the experimental rig utilizes real industrial drill-bits and rock samples, which after careful identification of Torque On Bit (TOB) speed curves, allows to use an equivalent friction model to accommodate for both frictional and cutting components of the bit-rock interactions. Moreover, the proposed Finite Element model, after a careful calibration, is capable of replicating experimental results, for the prebuckled configuration of the drill-string. This allows us to observe the effect of winding and unwinding of the helical deformation during stick-slip motion.

Assumptions of the analytical solution for solute transport in a fracture–matrix system

This study focuses on numerical modeling of fluid flow and solute transport in rough-walled rock fractures and fracture-matrix systems, with the main aim to investigate the impacts of fracture surface roughness on flow and transport processes in rock fractures. Both 2D and 3D fracture models were built from laser-scanned surface tomography of a real granite rock sample, to consider realistic features of surface tomography and potential asperity contacts. The flow was simulated by directly solving the Navier-Stokes equations (NSE) and the transport was modeled by solving the advection-dispersion equation (ADE) in the entire domain of fracture-matrix system, including matrix diffusion process. Such direct simulations provided detailed flow and concentration fields for quantitatively analysis of flow and transport behavior. The detailed analysis of surface roughness decomposition, complex flow patterns (i.e., channeling, transverse and eddy flows), effective advective flow apertures, effective transmissivity, effective dispersivity, residence time, transport resistance and specific surface area demonstrated significant impacts of realistic fracture surface roughness on fluid flow and solute transport processes in rock fractures. The results show that the surface roughness and shear displacement caused asperity contacts significantly enhance nonlinearity and complexity of flow and transport processes in rough-walled fractures and fracture-matrix systems. The surface roughness also causes invasion flows in intersected fractures which enhance solute mixing at fracture intersections. Therefore, the fracture surface roughness is an important source of uncertainty in application of such simplified models like cubic law (CL) for fluid flow and analytical solutions for solute transport in rock fractures. The research conducted advances our understanding of realistic flow and transport processes in natural fractured rocks. The results are useful for model validation/extension, uncertainty analysis/quantification and laboratory experiments design in the context of various applications related to fracture flow and transport.

Study of interrelation between electromagnetic radiation and rock strength

The paper presents the study of the electromagnetic radiation of real rock samples under acoustic impact. The test samples are made of kerns from the iron ore mine with different petrophysical features and strength. The study has shown that the electromagnetic radiation parameters are related to the sample strength. However, this dependence is not observed for samples with magnetite that can be due to individual structural-textural features and quartz inclusions.

Statistical scaling of geometric characteristics in stochastically generated pore microstructures

We analyze the statistical scaling of structural attributes of virtual porous microstructures that are stochastically generated by thresholding Gaussian random fields. Characterization of the extent at which randomly generated pore spaces can be considered as representative of a particular rock sample depends on the metrics employed to compare the virtual sample against its physical counterpart. Typically, comparisons against features and/patterns of geometric observables, e.g., porosity and specific surface area, flow-related macroscopic parameters, e.g., permeability, or autocorrelation functions are used to assess the representativeness of a virtual sample, and thereby the quality of the generation method. Here, we rely on manifestations of statistical scaling of geometric observables which were recently observed in real millimeter scale rock samples [13] as additional relevant metrics by which to characterize a virtual sample. We explore the statistical scaling of two geometric observables, namely porosity (ϕ) and specific surface area (SSA), of porous microstructures generated using the method of Smolarkiewicz and Winter [42] and Hyman and Winter [22]. Our results suggest that the method can produce virtual pore space samples displaying the symptoms of statistical scaling observed in real rock samples. Order q sample structure functions (statistical moments of absolute increments) of ϕ and SSA scale as a power of the separation distance (lag) over a range of lags, and extended self-similarity (linear relationship between log structure functions of successive orders) appears to be an intrinsic property of the generated media. The width of the range of lags where power-law scaling is observed and the Hurst coefficient associated with the variables we consider can be controlled by the generation parameters of the method.

Multifractal analysis of the pore space of real and simulated sedimentary rocks

It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock, among which its transport properties are often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study, we performed multifractal analysis of pore distribution on simulated sedimentary rocks using the relaxed bidisperse ballistic deposition model (RBBDM). The RBBDM can generate a 3-D structure of sedimentary rocks of variable porosity by tuning the fraction p of particles of two different sizes. We also performed multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40 per cent) while the other is a reefal carbonate of low porosity, around 7 per cent. 2-D sections of X-ray microtomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show multifractal character. The results from analysis of real rock agree quite well with the simulated structure of low porosity. The simulated rock of high porosity showed a weak multifractal nature though the real rock sample of similar porosity was found to be strongly multifractal. We propose a ‘structure parameter’ ξ which is a function of porosity and the generalized dimensions, and controls the transport properties of the rock.

Test Design and Sample Preparation Procedure for Experimental Investigation of Hydraulic Fracturing Interaction Modes

Hydraulic fracturing is a complex operation which is influenced by several factors including the formation properties, state of stresses in the field, injecting fluid and pumping rate. Before carrying out the expensive fracturing operation in the field, it would be useful to understand the effect of various parameters by conducting physical experiments in the laboratory. Also, laboratory experiments are valuable for validating numerical simulations. For this purpose, laboratory experiments may be conducted on synthetically made samples to study the effect of various parameters before using real rock samples, which may not be readily available. To simulate the real stress conditions in the field, experiments need to be conducted on cube-shaped samples on which three independent stresses can be applied. The hydro-mechanical properties of a sample required for modelling purposes and the design of a scaled hydraulic fracturing test in the laboratory can be estimated by performing various laboratory experiments on cylindrical plugs. The results of laboratory experiments are scaled to field operation by applying scaling laws. In this paper, the steps to prepare a cube-shaped mortar sample are explained. This follows a review of the sample set-up procedure in a true tri-axial stress cell for hydraulic fracturing experiments. Also, the minimum tests on cylindrical plugs required to estimate the hydro-mechanical properties of the rock sample are explained. To simulate the interaction mode when a hydraulic fracture approaches an interface in the laboratory, the procedure for producing samples with parallel artificial fracture planes is explained in this paper. The in-fill material and the angle of fracture planes were changed in different samples to investigate the effect of interface cohesion and the angle of approach on the interaction mechanism.

Fractal geometry of sedimentary rocks: simulation in 3-D using a Relaxed Bidisperse Ballistic Deposition Model

Several studies, both theoretical and experimental, show that sedimentary rocks have a fractal pore-grain interface. In this paper a computer simulated 3-D sedimentary rock structure generated by the Relaxed Ballistic Bidisperse Deposition Model (RBBDM), is investigated to characterize the micro structure of its pores. The pore volume and the rock-pore interface show the same fractal dimension indicating that the pore volume is a fractal. The two point density correlation is computed for the pore space and the results compare favourably with the range reported from experiments. An array of 2-D X-ray tomography micrograph sections of a real sedimentary rock, an oolitic limestone (pure calcite) from the Mondeville formation of Middle Jurassic age (Paris Basin, France), was used to generate a 3-D bitmap. The 3-D real rock sample generated in this manner, was analysed for similar studies as the simulated structure. The results were compared with those obtained from simulation. The simulation results agree qualitatively with the real rock sample. Diffusion through the connected pore space of the simulated structure was studied using a random walk algorithm and the results compared with the similar simulation study done on the 3-D oolitic limestone specimen. In both cases diffusion was found to be anomalous indicating that the sedimentary rock has a fractal geometry. The favourable comparability of results between the simulated and real rock supports the usefulness of the model of sedimentary rock generation which can be applicable to transport phenomena.

Fractal pore structure of sedimentary rocks: Simulation in 2-d using a relaxed bidisperse ballistic deposition model

Abstract Several studies, both theoretical and experimental, show that sedimentary rocks have fractal pore–grain interface. The real rocks are 3-d structures with highly tortuous and often fractal pore spaces. Before attempting simulation of this daunting geometry, we present here, as a preliminary study, a simpler 2-d version. In this paper, a computer simulated 2-d sedimentary rock structure is generated by the relaxed bidisperse ballistic deposition model. Grains of two different sizes are dropped ballistically on a linear substrate. By changing the fraction of the two types of particles, the porosity of the rock structure can be tuned. The structure undergoes compaction through the relaxation of possible unstable overhangs. The micro structure of the pore space is investigated. The pore mass and the rock–pore interface show a fractal behaviour with the same fractal dimension indicating that the pore volume is a fractal. Our simulation results indicate that the process of compaction of grains during the deposition process seems to erase the dependency of the fractal dimension on the grain size distribution. The two point density correlation is measured for the pore space. It shows anisotropy which is an outcome of the growth rule. X-ray tomography of two-dimensional sections of real sedimentary rocks obtained from Mallorca Island is subjected to the same study and the results compared with those obtained from simulation. The simulation results agree qualitatively with the real rock sample. We also study diffusion on the pore space. Diffusion is found to be anomalous as is expected in fractal spaces. It also bears the signature of anisotropy of the structure. Diffusion studies on the real rock sample could not yield conclusive results as the system size is not large enough.

Hydromechanical study of rock–mortar interfaces

Hydromechanical compression tests have been performed on rock–mortar interfaces representing the contact between a host rock and a concrete bulkhead within an underground nuclear waste repository. The rock used in the tests is a Toarcian argillite. Most published studies concerning rock–concrete interfaces involve concrete–concrete contacts in which rock replicas are used instead of real rock samples. As a result, the effect of rock features, such as bedding planes and changes of the rock interface zone, on the hydromechanical behaviour of the interface cannot be investigated. The tests discussed in this paper demonstrate that the mechanical response is not affected when changing the parameters of the samples even not mismatching both walls. On the contrary, an initial monitored lateral displacement modifies the hydromechanical behaviour by limiting the interface ability to be hydraulically closed. The latter ability has been quantified by a simple evolution law and the difference of behaviour between the two kinds of samples has been confirmed. The analysis led to determine the hydraulic aperture shows that the values obtained are much lower to the classical values available in the literature. Finally, the application of the experimental results to the confinement by a bulkhead showed the localization of the flow within the interface.