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Book Experimental Investigation of Supercritical CO2 Trapping Mechanisms at the Intermediate Laboratory Scale in Well defined Heterogeneous Porous Media

Download or read book Experimental Investigation of Supercritical CO2 Trapping Mechanisms at the Intermediate Laboratory Scale in Well defined Heterogeneous Porous Media written by and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heterogeneous nature of typical sedimentary formations can play a major role in the propagation of the CO2 plume, eventually dampening the accumulation of mobile phase underneath the caprock. From core flooding experiments, it is also known that contrasts in capillary threshold pressure due to different pore size can affect the flow paths of the invading and displaced fluids and consequently influence the build- up of non-wetting phase (NWP) at interfaces between geological facies. The full characterization of the geologic variability at all relevant scales and the ability to make observations on the spatial and temporal distribution of the migration and trapping of supercritical CO2 is not feasible from a practical perspective. To provide insight into the impact of well-defined heterogeneous systems on the flow dynamics and trapping efficiency of supercritical CO2 under drainage and imbibition conditions, we present an experimental investigation at the meter scale conducted in synthetic sand reservoirs packed in a quasi-two-dimensional flow-cell. Two immiscible displacement experiments have been performed to observe the preferential entrapment of NWP in simple heterogeneous porous media. The experiments consisted of an injection, a fluid redistribution, and a forced imbibition stages conducted in an uncorrelated permeability field and a homogeneous base case scenario. We adopted x-ray attenuation analysis as a non-destructive technique that allows a precise measurement of phase saturations throughout the entire flow domain. By comparing a homogeneous and a heterogeneous scenario we have identified some important effects that can be attributed to capillary barriers, such as dampened plume advancement, higher non-wetting phase saturations, larger contact area between the injected and displaced phases, and a larger range of non-wetting phase saturations.

Book Intermediate Scale Laboratory Testing to Understand Mechanisms of Capillary and Dissolution Trapping During Injection and Post  Injection of CO2 in Heterogeneous Geological Formations

Download or read book Intermediate Scale Laboratory Testing to Understand Mechanisms of Capillary and Dissolution Trapping During Injection and Post Injection of CO2 in Heterogeneous Geological Formations written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Carbon Capture and Storage (CCS) represents a technology aimed to reduce atmospheric loading of CO2 from power plants and heavy industries by injecting it into deep geological formations, such as saline aquifers. A number of trapping mechanisms contribute to effective and secure storage of the injected CO2 in supercritical fluid phase (scCO2) in the formation over the long term. The primary trapping mechanisms are structural, residual, dissolution and mineralization. Knowledge gaps exist on how the heterogeneity of the formation manifested at all scales from the pore to the site scales affects trapping and parameterization of contributing mechanisms in models. An experimental and modeling study was conducted to fill these knowledge gaps. Experimental investigation of fundamental processes and mechanisms in field settings is not possible as it is not feasible to fully characterize the geologic heterogeneity at all relevant scales and gathering data on migration, trapping and dissolution of scCO2. Laboratory experiments using scCO2 under ambient conditions are also not feasible as it is technically challenging and cost prohibitive to develop large, two- or three-dimensional test systems with controlled high pressures to keep the scCO2 as a liquid. Hence, an innovative approach that used surrogate fluids in place of scCO2 and formation brine in multi-scale, synthetic aquifers test systems ranging in scales from centimeter to meter scale developed used. New modeling algorithms were developed to capture the processes controlled by the formation heterogeneity, and they were tested using the data from the laboratory test systems. The results and findings are expected to contribute toward better conceptual models, future improvements to DOE numerical codes, more accurate assessment of storage capacities, and optimized placement strategies. This report presents the experimental and modeling methods and research results.

Book Quantitative Characterization and Engineering Application of Pores and Fractures of Different Scales in Unconventional Reservoirs     Volume II

Download or read book Quantitative Characterization and Engineering Application of Pores and Fractures of Different Scales in Unconventional Reservoirs Volume II written by Wenlong Ding and published by Frontiers Media SA. This book was released on 2023-04-05 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Study of Trapping Mechanisms of Supercritical Carbon Dioxide in Deep Heterogeneous Geological Formations Through Intermediate scale Testing and Modeling

Download or read book Study of Trapping Mechanisms of Supercritical Carbon Dioxide in Deep Heterogeneous Geological Formations Through Intermediate scale Testing and Modeling written by Luca Trevisan and published by . This book was released on 2015 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Final Report of  A Detailed Study of the Physical Mechanisms Controlling CO2 Brine Capillary Trapping in the Subsurface   University of Arizona  DE SC0006696

Download or read book Final Report of A Detailed Study of the Physical Mechanisms Controlling CO2 Brine Capillary Trapping in the Subsurface University of Arizona DE SC0006696 written by and published by . This book was released on 2016 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carbon capture and storage (CCS) of carbon dioxide emissions generated by production or combustion of fossil fuels is a technologically viable means to reduce the build-up of CO2 in the atmosphere and oceans. Using advantages of scale and location, CCS is particularly suitable for large point sources near ubiquitous deep saline aquifers, depleted gas reservoirs, or at production reservoirs for enhanced oil recovery (EOR). In the BES-funded research project, Oregon State University (OSU) carried out capillary trapping experiments with proxy fluids that mimic the properties of the scCO2/brine system under ambient temperatures and pressures, and successfully developed a unique and novel x-ray compatible, high-pressure, elevated temperature setup to study the scCO2/brine system under challenging reservoir conditions. Both methodologies were applied to a variety of porous media, including synthetic (glass bead) and geologic (Bentheimer sandstone) materials. The University of Arizona (UA) developed pore-scale lattice Boltzmann (LB) models which are able to handle the experimental conditions for proxy fluids, as well as the scCO2/brine system, that are capable of simulating permeability in volumes of tens of millions of fluid elements. We reached the following summary findings (main institute indicated): 1. (OSU/UA) To understand capillary trapping in a multiphase fluid-porous medium system, the system must be analyzed from a pore-scale force balance perspective; trapping can be enhanced by manipulating wetting and nonwetting phase fluid properties. 2. (OSU) Pore-scale fluid connectivity and topology has a clear and direct effect on nonwetting phase capillary trapping efficiency. 3. (OSU) Rock type and flow regime also have a pronounced effects on capillary trapping. 4. (OSU/UA) There is a predictable relationship between NWP connectivity and NWP saturation, which allows for development of injection strategies that optimize trapping. The commonly used Land model (Land, 1968) does not predict amount of trapped NWP accurately. 5. (UA) There are ambiguities regarding the segmentation of large-volume gray-scale CT data into pore-volumes suitable for pore-scale modeling. Simulated permeabilities vary by three orders of magnitude and do not resemble observed values very well. Small-volume synchrotron-based CT data (such as produced by OSU) does not suffer significantly from segmentation ambiguities. 6. (UA) A standard properly parameterized Shan-Chen model LB model is useful for simulating porous media with proxy fluids as well as the scCO2/brine system and produces results that are consistent with tomographic observations. 7. (UA) A LB model with fluid-interactions defined by a (modified) Peng-Robinson Equation of State is able to handle the scCO2/brine system with variable solid phase wettability. This model is numerically stable at temperatures between 0 and 250 °C and pressures between 3 and 50 MPa, and produces appropriate densities above the critical point of CO2 and exhibits three-phase separation below. Based on above findings OSU and UA have proposed continued experimentation and pore-scale modeling of the scCO2/brine system. The reported research has extensively covered capillary trapping using proxy fluids, but due to limited beam-time availability we were unable to apply our high-pressure CO2 setup to sufficient variation in fluid properties, and initial scCO2 connectivity. New data will also allow us to test, calibrate and apply our LB models to reservoir conditions beyond those that are currently feasible experimentally. Such experiments and simulations will also allow us to provide information how suitable proxy fluids are for the scCO2/brine system. We believe it would be worthwhile to pursue the following new research questions: 1. What are the fundamental differences in the physics underlying capillary trapping at ambient vs. supercritical conditions? 2. Do newly developed pore-scale trapping interactions and relations ...

Book Investigation of Buoyant Plumes in a Quasi 2D Domain

Download or read book Investigation of Buoyant Plumes in a Quasi 2D Domain written by Yuhao Sun and published by . This book was released on 2014 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leakage of stored bulk phase CO2 is one risk for sequestration in deep saline aquifers. As the less dense CO2 migrates upward within a storage formation or in layers above the formation, the security of its storage depends upon the trapping mechanisms that counteract the migration. The trapping mechanism motivating this research is local capillary trapping (LCT), which occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer with spatially heterogeneous petrophysical properties. When a CO2 plume rising by buoyancy encounters a region where capillary entry pressure is locally larger than average, CO2 accumulates beneath the region. One benefit of LCT, applied specifically to CO2 sequestration and storage, is that saturation of stored CO2 phase is larger than the saturation for other permanent trapping mechanisms. Another potential benefit is security: CO2 that occupies local capillary traps remains there, even if the overlying formation that provides primary containment were to be compromised and allow leakage. Most work on LCT has involved numerical simulation (Saadatpoor 2010, Ganesh 2012); the research work presented here is a step toward understanding local capillary trapping at the bench scale. An apparatus and set of fluids are described which allow examining the extent of local capillary trapping, i.e. buoyant nonwetting phase immobilization beneath small-scale capillary barriers, which can be expected in typical heterogeneous storage formation. The bench scale environment analogous to CO2 and brine in a saline aquifer is created in a quasi-two dimensional experimental apparatus with dimension of 63 cm by 63 cm by 5 cm, which allows for observation of plume migration with physically representative properties but at experimentally convenient ambient conditions. A surrogate fluid pair is developed to mimic the density, viscosity and interfacial tension relationship found at pressure and temperature typical of storage aquifers. Porous media heterogeneity, pressure boundary conditions, migration modes of uprising nonwetting phase, and presence of fracture/breach in the capillary barrier are studied in series of experiments for their influences on LCT. A variety of heterogeneous porous media made of a range of sizes of loosely packed silica beads are used to validate and test the persistence of local capillary trapping mechanism. By adjusting the boundary conditions (fluid levels in reservoirs attached to top and to bottom ports of the apparatus), the capillary pressure gradient across the domain was manipulated. Experiments were conducted with and without the presence of fracture/potential leakage pathway in the capillary seal. The trapped buoyant phase remained secure beneath the local capillary barriers, as long as the effective capillary pressure exerted by the trapped phase (proportional to column height of the phase) is smaller than the capillary entry pressure of the barrier. The local capillary trapping mechanism remained persistent even under forced imbibition, in which a significantly higher hydraulic potential gradient, and therefore a larger gradient in capillary pressure, was applied to the system. The column height of buoyant fluid that remained beneath the local capillary barrier was smaller by a factor corresponding to the increase in capillary pressure gradient. Mimicking a breach of the caprock by opening valves at the top of the apparatus allowed buoyant mobile phase held beneath the valves to escape, but buoyant phase held in local traps at saturations above residual, and therefore potentially mobile, was undisturbed. This work provides systematic validation of a novel concept, namely the long-term security of CO2 that fills local (small-scale) capillary traps in heterogeneous storage formations. Results from this work reveal the first ever unequivocal experimental evidence on persistence of local capillary trapping mechanism. Attempts to quantify the nonwetting phase saturation and extent of LCT persistence serve as the initial steps to potentially reduce the risks associated with long-term storage security.

Book Experimental Study of Multiphase Flow in Porous Media during CO2 Geo Sequestration Processes

Download or read book Experimental Study of Multiphase Flow in Porous Media during CO2 Geo Sequestration Processes written by Ali Saeedi and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been numerous computer-based simulation studies carried out on the subject of CO2 geo-sequestration. However, the amount of experimental data available in the literature on this topic, especially with regards to multiphase flow characteristics of fluid-rock systems during such processes, is very limited. This research was carried out with the aim of providing a better understanding of the multiphase fluid flow characteristics of fluid-rock systems during the geo-sequestration process. The ultimate goal of this research was to experimentally evaluate the change in a number of multiphase flow characteristics of the system over time caused by the potential chemical and physical/mechanical processes occurring during deep CO2 disposal. In order to achieve this goal the effects of cyclic/alternating CO2-brine flooding, flow direction, existence of residual hydrocarbon (natural gas) and change in the reservoir stress field on the system’s multiphase flow behaviour were investigated. Until completion of this study there were no experimental data published in the literature addressing the above mentioned issues and the results obtained, and published within this thesis were the first of their kind.

Book An Investigation Into the Pore scale Mechanisms of Capillary Trapping

Download or read book An Investigation Into the Pore scale Mechanisms of Capillary Trapping written by Anna L. Herring and published by . This book was released on 2015 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geologic CO2 sequestration is a climate change mitigation strategy that prevents CO2 emissions to the atmosphere by capturing CO2 gasses from large point source emissions streams and then pressurizing and pumping the supercritical-state CO2 into underground geologic storage reservoirs. Once underground, CO2 is prevented from buoyant migration to the surface by various trapping mechanisms, one of which is capillary trapping. Capillary trapping is a secure trapping mechanism that immobilizes CO2 on relatively short timescales; accurate prediction and optimization of capillary trapping of CO2 is crucial to ensure the safety and success of a sequestration operation. The research comprising this dissertation utilizes x-ray computed microtomography (x-ray CMT) to allow for three-dimensional (3D) investigation of the main factors influencing nonwetting phase capillary trapping from a pore-scale in-situ perspective. Results from ambient- and supercritical-condition experiments are presented that provide insight as to the controls on capillary trapping during multiphase flow in porous media. The presented findings may be used to help design injection strategies that optimize capillary trapping of CO2 during sequestration operations and to help develop more accurate predictive transport models.

Book Negative Emissions Technologies and Reliable Sequestration

Download or read book Negative Emissions Technologies and Reliable Sequestration written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-04-08 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: To achieve goals for climate and economic growth, "negative emissions technologies" (NETs) that remove and sequester carbon dioxide from the air will need to play a significant role in mitigating climate change. Unlike carbon capture and storage technologies that remove carbon dioxide emissions directly from large point sources such as coal power plants, NETs remove carbon dioxide directly from the atmosphere or enhance natural carbon sinks. Storing the carbon dioxide from NETs has the same impact on the atmosphere and climate as simultaneously preventing an equal amount of carbon dioxide from being emitted. Recent analyses found that deploying NETs may be less expensive and less disruptive than reducing some emissions, such as a substantial portion of agricultural and land-use emissions and some transportation emissions. In 2015, the National Academies published Climate Intervention: Carbon Dioxide Removal and Reliable Sequestration, which described and initially assessed NETs and sequestration technologies. This report acknowledged the relative paucity of research on NETs and recommended development of a research agenda that covers all aspects of NETs from fundamental science to full-scale deployment. To address this need, Negative Emissions Technologies and Reliable Sequestration: A Research Agenda assesses the benefits, risks, and "sustainable scale potential" for NETs and sequestration. This report also defines the essential components of a research and development program, including its estimated costs and potential impact.

Book Geologic Carbon Sequestration

Download or read book Geologic Carbon Sequestration written by V. Vishal and published by Springer. This book was released on 2016-05-11 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exclusive compilation written by eminent experts from more than ten countries, outlines the processes and methods for geologic sequestration in different sinks. It discusses and highlights the details of individual storage types, including recent advances in the science and technology of carbon storage. The topic is of immense interest to geoscientists, reservoir engineers, environmentalists and researchers from the scientific and industrial communities working on the methodologies for carbon dioxide storage. Increasing concentrations of anthropogenic carbon dioxide in the atmosphere are often held responsible for the rising temperature of the globe. Geologic sequestration prevents atmospheric release of the waste greenhouse gases by storing them underground for geologically significant periods of time. The book addresses the need for an understanding of carbon reservoir characteristics and behavior. Other book volumes on carbon capture, utilization and storage (CCUS) attempt to cover the entire process of CCUS, but the topic of geologic sequestration is not discussed in detail. This book focuses on the recent trends and up-to-date information on different storage rock types, ranging from deep saline aquifers to coal to basaltic formations.

Book Modeling Supercritical CO2 Injection in Heterogeneous Porous Media

Download or read book Modeling Supercritical CO2 Injection in Heterogeneous Porous Media written by and published by . This book was released on 2003 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the physical processes that occur during the sequestration of CO2 in brine-bearing geologic formations using TOUGH2. An equation of state package that treats a two-phase (liquid, gas), three-component (water, salt, and CO2) system is employed. CO2 is injected in a supercritical state that has a much lower density and viscosity than the liquid brine it displaces. In situ, the supercritical CO2 forms a gas-like phase, and also partially dissolves in the aqueous phase. Chemical reactions between CO2 and rock minerals that could potentially contribute to mineral trapping of CO2 are not included. The geological setting considered is a fluvial/deltaic formation that is strongly heterogeneous, making preferential flow a significant effect, especially when coupled with the strong buoyancy forces acting on the gas-like CO2 plume. Key model development concerns include vertical and lateral grid resolution, grid orientation effects, and the choice of characteristic curves.

Book Quantifying CO2 Capillary Heterogeneity Trapping Through Experiments  Data Analysis  and Simulation

Download or read book Quantifying CO2 Capillary Heterogeneity Trapping Through Experiments Data Analysis and Simulation written by Hailun Ni and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: CO2 geologic storage is an integral part of the climate change solutions in that it allows society to transition toward carbon neutral energy while still relying on fossil fuels. Both the primary and secondary trapping mechanisms immobilize the injected CO2 in the reservoir and keep it securely trapped. This work focuses on one such secondary trapping mechanism, residual trapping, which is caused by capillary forces induced by natural geological heterogeneities both at the pore scale and the mesoscale (millimeter scale). To differentiate between residual trapping at the two different scales, we call the former pore-scale residual trapping and the latter capillary heterogeneity trapping. The mechanisms and the various factors affecting pore-scale residual trapping have been extensively studied previously. However, only a handful of studies have examined the role mesoscale heterogeneity plays in capillary heterogeneity trapping. This work mainly focuses on predicting, identifying, and quantifying the CO2 capillary heterogeneity trapping potential of geological formations. We first use coreflooding experiments to investigate which parameter best represents the degree of mesoscale heterogeneity in the context of residual trapping in order to predict the amount of CO2 capillary heterogeneity trapping with an empirical relationship. Then, we use statistical analysis of the data to examine the effects of mesoscale heterogeneity on capillary dominated flow behaviors and to identify and visualize CO2 capillary heterogeneity trapping behavior in sandstone core samples. Finally, we use an improved percolation model to simulate and quantify the effects of mesoscale heterogeneity on residual trapping and the extent of such effects as compared to the pore-scale trapping mechanism. The data analysis results have confirmed that post-imbibition CO2 capillary heterogeneity trapping indeed occurs upstream of capillary barriers. Furthermore, it can also occur within the capillary barriers themselves. Both experiments and simulations have shown that CO2 capillary heterogeneity trapping increases with the degree of mesoscale heterogeneity. Macroscopic percolation simulation results have shown that the capillary heterogeneity trapping contribution can be quite large for heterogeneous rocks with good mesoscale capillary barriers. Experimental results show that the variance in the drainage CO2 saturation fields created under capillary dominated flow conditions can best capture the degree of mesoscale heterogeneity in terms of predicting CO2 capillary heterogeneity trapping.

Book Local Capillary Trapping in Geological Storage of Carbon Dioxide  CO2

Download or read book Local Capillary Trapping in Geological Storage of Carbon Dioxide CO2 written by Ehsan Saadatpoor and published by . This book was released on 2017 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the injection of CO2 into a subsurface formation, storage mechanisms help immobilize the CO2. Injection strategies that promote the movement of CO2 during the post-injection period can increase immobilization by mechanisms of dissolution and residual phase trapping. This book argues that the heterogeneity intrinsic to sedimentary rocks gives rise to another category of trapping called "local capillary trapping." The study presented in this book evaluates local capillary trapping, its effectiveness to add an element of increased capacity and containment security in CO2 storage, and assesses the amount and extent of local capillary trapping expected to occur in typical storage formations.

Book Capillary Flow in an Interior Corner

Download or read book Capillary Flow in an Interior Corner written by Mark Milton Weislogel and published by . This book was released on 1996 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Geological Carbon Storage

    Book Details:
  • Author : Stéphanie Vialle
  • Publisher : John Wiley & Sons
  • Release : 2018-11-15
  • ISBN : 1119118670
  • Pages : 372 pages

Download or read book Geological Carbon Storage written by Stéphanie Vialle and published by John Wiley & Sons. This book was released on 2018-11-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geological Carbon Storage Subsurface Seals and Caprock Integrity Seals and caprocks are an essential component of subsurface hydrogeological systems, guiding the movement and entrapment of hydrocarbon and other fluids. Geological Carbon Storage: Subsurface Seals and Caprock Integrity offers a survey of the wealth of recent scientific work on caprock integrity with a focus on the geological controls of permanent and safe carbon dioxide storage, and the commercial deployment of geological carbon storage. Volume highlights include: Low-permeability rock characterization from the pore scale to the core scale Flow and transport properties of low-permeability rocks Fundamentals of fracture generation, self-healing, and permeability Coupled geochemical, transport and geomechanical processes in caprock Analysis of caprock behavior from natural analogues Geochemical and geophysical monitoring techniques of caprock failure and integrity Potential environmental impacts of carbon dioxide migration on groundwater resources Carbon dioxide leakage mitigation and remediation techniques Geological Carbon Storage: Subsurface Seals and Caprock Integrity is an invaluable resource for geoscientists from academic and research institutions with interests in energy and environment-related problems, as well as professionals in the field.

Book Observations of Buoyant Plumes in Countercurrent Displacement

Download or read book Observations of Buoyant Plumes in Countercurrent Displacement written by Angelica Maria Hernandez and published by . This book was released on 2011 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leakage of stored bulk phase CO2 is of particular risk to sequestration in deep saline aquifers due to the fact that when injected into typical saline aquifers, the CO2 rich gas phase has lesser density than the aqueous phase resulting in buoyancy driven flow of the fluids. As the CO2 migrates upward, the security of its storage depends upon the trapping mechanisms that counteract the migration. While there are a variety of trapping mechanisms the mechanism serving as motivation for this research is local capillary trapping. Local capillary trapping occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer (Saadatpoor, 2009). When the rising CO2 plume encounters a region where capillary entry pressure is locally larger than average, CO2 accumulates beneath the region. While research is continued by means of numerical simulation, research at the bench scale is needed to validate the conclusions made from simulation work. Presented is the development of a bench scale experiment whose objective is to assess local capillary trapping. The initial step in accomplishing this objective is to understand the fluid dynamics of CO2 and brine in a saline aquifer which is categorized as two phase immiscible buoyancy driven displacement. Parameters influencing this displacement include density, viscosity, wettability and heterogeneity. A bench scale environment created to be analogous to CO2 and brine in a saline aquifer is created in a quasi-two dimensional experimental apparatus, which allows for observation of plume migration at ambient conditions. A fluid pair analogous to supercritical CO2 and brine is developed to mimic the density and viscosity relationship found at pressure and temperature typical of storage aquifers. The influences of viscosity ratio, density differences, porous medium wettability and heterogeneity are observed in series of experimental sequences. Three different fluid pairs with different viscosity ratios and density differences are used to assess density and viscosity influences. Porous media of varying grain size and wettability are used to assess the influence of heterogeneity and wettability. Results are qualitatively consistent with theoretical results and those from previous works.