In this study, we have extended and applied the diffuse source upscaling methodology to sandstone and carbonate pore network models in order to evaluate their effective transmissibility and permeability. The proposed method allows us to find transmissibility values for sub-volumes of the pore network during the transition from transient to pseudo steady state flow. The pore network models utilize a lattice grid construction, consisting of nodes and bonds that connect the nodes. The Eikonal equation is solved on the lattice using Dijkstra's method to obtain the diffusive time of flight, which is then used to model the transition from transient to pseudo steady state flow. The solution uses the concept of a transient drainage volume, which increases with time as pressure propagates into the nodes of the pore network. The diffuse source upscaling approach allows us to calculate the transmissibility of the drainage volume as it increases with time. The calculated results can be compared to the analytical results, where the sample is assumed to be internally homogeneous. A synthetic model was created to illustrate how the calculated lattice model and the analytic reference results compare for a homogeneous model. The comparison of the carbonate analytical and calculated results showed that there exists a high degree of internal heterogeneity while the more homogeneous sandstone model showed a close agreement with the synthetic model. For both samples, the late time pseudo steady state permeability showed a good correspondence with other permeability evaluations. The diffuse source method has more directional information available than the steady state method. Hence, the new method of analysis can be viewed as an extension of pseudo steady state concepts of permeability to transient flow, with increased spatial resolution corresponding to the transient drainage volume. Instead of obtaining only the steady state transmissibility from a pore network model, the diffuse source approach provides us with the ability to better characterize the internal heterogeneity of a model and to explain the wide range of permeability values obtained by other approaches.
Shale formations exhibit multi-scale geological features such as nanopores in formation matrix and fractures at multiple length scales. Accurate prediction of relative permeability and capillary pressure are vital in numerical simulations of shale reservoirs. The multi-scale geological features of shale formations present great challenges for traditional experimental approach. Compared to nanopores in formation matrix, fractures, especially connected fractures, have much more significant impact on multiphase flows. Traditional flow models like Darcy's law are not valid for modeling fluid flow in fracture space nor in nanopores. In this work, we apply multiphase lattice Boltzmann simulation for unsteady-state waterflooding process in highly fractured samples to study the effects of fracture connectivity, wetting preference, and gravitional forces.
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 23-25 July 2018. The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by anyone other than the author without the written consent of URTeC is prohibited.
ABSTRACT: The mechanical behaviors of intact and jointed Blanco Mera granite are studied using the lattice-spring-based synthetic rock mass (LS-SRM) modeling approach. Both intact and jointed granite specimens are characterized for peak compressive strengths and elastic moduli under unconfined and confined conditions. Three (1+2) and five (2+3) planar joints are introduced in the intact specimens to investigate the mechanical behavior of jointed rock masses. Itasca’s SRMTools is used for the numerical modeling. The LS-SRM approach has advantages over other discrete element model (DEM)-based SRM modeling approaches in terms of model construction, model calibration, and computation efficiency. Because the LS-SRM models can incorporate non-planar joints, mechanical responses of jointed granite with non-planar joints are also investigated. The numerical modeling results agree reasonably well with the laboratory test results. Modeling results of confined compression of jointed rock models with planar joints shows a degradation in both strength and deformation modulus with the increase in joint density. Similar trend is observed in jointed rock models with non-planar joints.
ABSTRACT: The nano-indentation technique was applied to microporous carbonates from the Easter Parisian Basin made of nearly 100% calcite. Room-dried, small, irregular pieces, 5mm thick and with a polished surface of about 1 cm2 are used. Then, the distribution function and the linear auto-correlation of the indentation modulus are derived from these data.
The numerical analysis consists in generating random three dimensional media with a local indentation modulus M(x) which has the same statistical properties as the measured ones. This is achieved via a non linear transformation of normal correlated Gaussian fields. Then, the elasticity equation with variable Lamé coefficients is solved by a code based on lattice springs. The elastic velocities are derived and compared to the measured ones.
Elastic and mechanical properties of rocks are classically obtained in the laboratory on core plugs whose diameter is 1’’ to 1.5’’ and length up to about 3’’. This includes P- and S-wave velocities at ultrasonic frequency, where Young’s, bulk and shear moduli are derived knowing the bulk density of the sample, and moduli directly deduced from strain-stress curves. However intact core plugs are not always available, either because of the presence of fractures or because of the pore consolidation state of the samples (e.g. poorly consolidated sandstones, mudstones, etc.). It is thus interesting to be able to extract elastic and/or anelastic parameters from small fragments of rocks.
There have been some attempts to use some methods that, unlike techniques such as Scanning Electron Microscopy (SEM) or optical microscopy that only give a qualitative description of the microstructure, provide a quantitative description. (Prasad, 2001) used acoustic microscopy (Scanning Acoustic Microscopy SAM and Acoustic Sounding AS) whose basic principle is almost identical to that of reflection seismology to compare seismic properties of two sandstones with their cementation strength inferred from acoustic microscopy. (Rabe et al., 1996) and (Prasad et al., 2002) used atomic force microscopy to measure Young’s moduli of rocks.
Han, Yanhui (Aramco Services Company: Aramco Research Center) | Detournay, Christine (Itasca Consulting Group) | Cundall, Peter (Itasca Consulting Group) | Abousleiman, Younane (University of Oklahoma)
The tensile strength characteristics and related strain-softening/hardening laws were derived from laboratory tests on nano-cantilever beams of kerogen rich shales (KRS) at nominal low, medium and high values of kerogen content and implemented as a user-defined spring model in XSite (a lattice code developed by Itasca based on the discrete element method). The brittleness of the shale samples in the nano-scale experiments were more pronounced in samples with lower values of kerogen content. The macroscopic toughness, and tensile strength properties (assuming the material has no structural defect) were obtained by performing direct, self-similar notched tension tests on microscopic samples with low, medium and high kerogen contents in the lattice code. The notched tests were characterized by two dimensionless parameters, i.e., the ratio of initial crack size over sample width, and the crack resolution in the lattice (the ratio of initial crack size over the lattice resolution). With the first ratio and lattice resolution fixed, extensive parametric studies were performed to generate log-log plots of the critical tensile stress versus the crack resolution in the lattice. The macroscopic tensile strength of the simulated KRS material was estimated from the horizontal plateau obtained at low crack resolution values in the plots. The toughness corresponding to the condition of LEFM (linear elastic fracture mechanics) was measured from the segment observed at high values of crack resolution in the logarithm plots where the slope was -½. Some interesting phenomena were observed in the simulations, e.g., the extent of the process zone near crack tips appeared to remain constant in the tests at nominal low kerogen content; the value of crack resolution beyond which LEFM applies increases as the kerogen content increases (which is consistent with the lower brittleness, or higher plasticity level, at high kerogen content). Using the calibrated macroscopic toughness, fluid injection tests were simulated in meterscale numerical models at uniform nominal kerogen content.
ABSTRACT: The mechanical behavior of Zhenping marble is studied using the lattice-spring-based synthetic rock mass (LS-SRM) modeling approach. Mechanical response of the rock is assessed using stress–strain relations under unconfined and confined compressions. ITASCA's SRMTools is used for the numerical modeling. The LS-SRM approach has advantages over bonded-particle-based and bonded-block-based SRM modeling approaches in terms of model construction, model calibration, and computation efficiency. Calibration of the mechanical properties of Zhenping marble is performed using the laboratory test results. In addition, a parametric study is performed to discern the sensitivity of the lattice model parameters on the macroscopic mechanical properties of rock. Stress–strain curves are affected by confining pressure and the post-peak response exhibits a typical brittle-ductile transition with plastic deformation at higher confinements. The numerical modeling results demonstrate the capability to reasonably capture the macroscopic properties of Zhenping marble such as elastic deformation modulus, crack initiation stress, tensile strength, and strength envelope, all of which are very close to the laboratory test results. The results of this study illustrate the usefulness of the LS-SRM approach in modeling mechanical properties of hard rocks.
The application of numerical modeling in the determination of mechanical properties of rock mass is widely accepted due to the ability to reproduce test results at low cost compared with laboratory and in-situ tests. Numerical modeling is preferred over laboratory and in-situ tests because of the inconvenience and logistic issues related to these physical test procedures. Numerical modeling techniques can be categorized into continuum and discontinuum methods (Jing, 2003). In rock mass modeling, the discontinuum approach is favored over the continuum approach because of its ability to explicitly represent discontinuities and capture failure process and large displacements caused by block translation, rotation, and detachment (fracture opening). Over the years, several DEM (Discrete Element Method) codes have been used to study the strength and deformation properties of both intact and jointed rocks. ITASCA's grain-based model, bonded particle models (BPM) in PFC and bonded block models (BBM) in 3DEC are widely used. Although numerous studies were conducted in 2D, 3D modeling is required to solve most rock engineering problems.
Sezgin, Jean-Gabriel (AIST-Kyushu University Hydrogen Materials Laboratory (HydroMate)) | Fjær, Hallvard G. (Institute for Energy Technology) | Matsunaga, Hisao (Kyushu University) | Yamabe, Junichiro (AIST-Kyushu University Hydrogen Materials Laboratory (HydroMate), Kyushu University) | Olden, Vigdis (SINTEF)
Diffusion measurements and thermal desorption measurements have been performed on a X70 pipeline steel, in as received and normalized and quenched condition, after being hydrogen charged for 200 h at 100 MPa hydrogen gas pressure and 85°C. Numerical simulations based on the assumption of thermodynamic equilibrium were performed, aiming to compare the trapping energies when fitting to the TDS spectra. TDS experiments revealed a reversible trap site with activation energy of 26.2 kJ.mol−1. Irreversible trap sites with an activation energy of >100 kJ.mol−1 were observed from both as-received and heat-treated condition. In contrast, a reversible trap site with an activation energy of 49.2 kJ.mol−1 was observed only from the heat-treated condition. The numerical modelling based on the assumption of equilibrium between hydrogen in traps and hydrogen in lattice is seen to provide a good fit to the experimental data.
Subsea oil and gas structural steel pipelines are exposed to hydrogen at the steel surface due to cathodic protection towards corrosion. Hydrogen reduces the fracture toughness in the base metal as well as in welded joints, which may be critical for the structural integrity of the pipeline. As atomic hydrogen enters the steel it occupies lattice sites and traps, as dislocations, grain boundaries and precipitates, often categorized as reversible and irreversible traps according to their trapping energy.
To be able to build predictive models for the fracture susceptibility of pipelines under operation conditions, knowledge of the amount of diffusible hydrogen and trapped hydrogen that may contribute to fracture, are vital information. Thus, knowledge of the trapping energies is essential.
In the present work, results from Thermal Desorption Spectrometry (TDS) measurements of X70 structural steel will be presented. As-received steel and heat-treated (normalized and quenched) steel, representative of the coarse grain heat affected zone of a welded joint, are investigated. Finally, the measured trapping energies, diffusivity and hydrogen concentration are discussed and compared to a numerical model, where the trapping energies are assessed.
Acid bullheading is a well-known treatment for removing downhole scale and formation damage in oil and gas fields. The treatment is performed by using a controlled percentage of hydrogen chloride, and is normally operated under restricted wellhead pressure for health, safety, and environment (HSE) and well integrity purposes. These constraints sometimes prevent the treatment to be more effective in removing formation damage and improving injectivity and/or productivity of oil and gas wells. The present work is related to a fundamental study of fluid invasion in different types of formation with regard to the designed acid bullheading setups. The results are compared and analyzed based on a numerical investigation for the same geometrical and dynamical parameters to assess the efficiency of the fluid invasion designed process. The new treatment design utilizes the concept of cyclic pressure by fluctuating the injection velocity. In this paper, a mathematical formulation of fluid flow invasion in a porous medium is presented using a lattice Boltzmann numerical analysis. This method uses a mesoscopic approach to solve the flow problem instead of using Navier-Stokes equations and giving good numerical accuracy. It mimics different formation porosities, injection velocities, and procedures over time. A qualitative comparison between constant and variable injection velocities was performed under a fixed period of time. The new simulation code visually demonstrates the growth of fluid invasion in the investigated domains and highlights clear differences between the two cases of continuous and cyclic injections. This approach presents a new design in matrix stimulation that could effectively optimize oil and gas treatment operations.
Oil and gas wells are normally treated after drilling to remove mud cake buildup around the formation. They are also treated after a period of production to remove scale or any hydrocarbon precipitations such as asphalt or bitumen formation at the vicinity of the borehole. A common treatment practice to remove formation damage is the acid bullheading procedure (Mitchell et al., 2003). The treatment involves a mixture of chemicals that are used to remove formation damage by forcibly pumping the fluid from the wellhead at restricted rate/pressure to prevent completion damage and be able to reach higher penetration depth. The acid concentration is controlled by percentage to avoid completion degradation problem and maintain HSE minimum requirements. In the matrix acidizing, the scale of interaction between the fluid invasion and pore spaces can be investigated at micro-scale. A proper design methodology should be used to assess the effectiveness of the overall treatment. Normally, the design of the treatment job involves basic field assessments and mainly relies on the offsetting wells experience (Sun et al., 2014). This paper provides qualitative analysis of fluid flow invasion in porous medium using a particle based approach - Lattice Boltzmann Method (LBM) (Qian et al., 1992). The method has been widely used to simulate the fluid dynamic at mesoscopic scale. It has been extended to simulate and analyze multi-physics such as the evolution of thermal, chemical, and fluid interactions (Scuui, 2001). It simplifies the complex geometrical structure such as the void spaces in the rock and solves it in an arbitrary lattice domain (dimensionless domain). The method has been extensively used in simulating micro-scale phenomenon and validated against experimental works (Wongcharoen and Huang, 2014). In the present work, constant and variable injection velocities in different formation types are analyzed. Fluid flow invasion and progression are observed in low, medium, and high porosity geometrical domain.
The present study is devoted to the flow peoperties of a vortex shedding system behind a bluff body that has a crescent cross-section, facing downstream of the flow. The investigation is conducted numerically using a lattice Boltzmann method. As a benchmark validation, the studied system was compared to the system of vortices formed behind the classical case of a circular cylinder for the same flow configuration and dynamic conditions, while varying the Reynolds number. The flow simulations have revealed that the crescent body affected substantially the shedding mechanism with remarkable differences when compared to the classical cylindrical case. There was a clear decrease in the shedding frequency with the crescent body that is beneficial when using this system as a metering tool.
The vortex shedding flow system had, and still has, a lot of interest from researchers in fluid dynamics due to its many applications for flow metering purposes, for studies of vortical flows or as a benchmark case for numerical methods (Tuann and Olson, 1978; Loc, 1980; Coutanceau & Defaye, 1991; Lakshmipathy, 2004; Reich et al., 2005). The Von-Karman vortex system, known as vortex shedding, occurs when a flow passes around a bluff body, classically cylindrical. To investigate different aspects of the vortex shedding, bluff bodies with different shapes were studied both experimentally and numerically.
The flow behind a circular cylinder is classicaly supposed symmetric at low Reynolds numbers in the range of 70 to 100. When Reynolds number increases, the flow begins separating just at the downstream edge of the cylinder and forms an alternating system of vortices with a constant shedding frequency. This phenomenon has been used as means to measure flow rates with a high accuracy due to its low cost and low maintenance, and being not sensitive to physical properties of the fluid flows measured. Therefore, this metering method has been used in several industries to measure flow rates of liquids, gases and steam flows over a large interval of Reynolds numbers. From the fundamental point of view, this flow system was investigated numerically by many authors. One of first authors was Payne (1958) who studied this flow system for Reynolds numbers below 100 and characterized in details the shedding system in this flow rates range.