Grant S. Bromhal

PORE-LEVEL MODELING OF IMMISCIBLE DRAINAGE: VALIDATION IN THE INVASION PERCOLATION AND DLA LIMITS

Motivated by a wide-range of applications from ground water remediation to carbon dioxide sequestration and by difficulties in reconciling experiments with previous modeling, we have developed a pore-level model of two-phase flow in porous media. We have attempted to make our model as physical and as reliable as possible, incorporating both capillary effects and viscous effects. After a detailed discussion of the model, we validate it in the very different limits of zero capillary number and zero-viscosity ratio. Invasion percolation (IP) models the flow in the limit of zero capillary number; results from our model show detailed agreement with results from IP, for small capillary numbers. Diffusion limited aggregation (DLA) models the flow in the limit of zero-viscosity ratio; flow patterns from our model have the same fractal dimension as patterns from DLA for small viscosity ratios.

Probabilistic Design of a Near-Surface CO2 Leak Detection System

A methodology is developed for predicting the performance of near-surface CO(2) leak detection systems at geologic sequestration sites. The methodology integrates site characterization and modeling to predict the statistical properties of natural CO(2) fluxes, the transport of CO(2) from potential subsurface leakage points, and the detection of CO(2) surface fluxes by the monitoring network. The probability of leak detection is computed as the probability that the leakage signal is sufficient to increase the total flux beyond a statistically determined threshold. The methodology is illustrated for a highly idealized site monitored with CO(2) accumulation chamber measurements taken on a uniform grid. The TOUGH2 code is used to predict the spatial profile of surface CO(2) fluxes resulting from different leakage rates and different soil permeabilities. A response surface is fit to the TOUGH2 results to allow interpolation across a continuous range of values of permeability and leakage rate. The spatial distribution of leakage probability is assumed uniform in this application. Nonlinear, nonmonotonic relationships of network performance to soil permeability and network density are evident. In general, dense networks (with ∼10-20 m between monitors) are required to ensure a moderate to high probability of leak detection.

Spatial distribution of avalanches in invasion percolation: their role in fingering

For two decades, invasion percolation (IP) has provided a simple model of ‘drainage’ where a non-wetting fluid is injected into a porous media saturated with a wetting fluid, in the limit where capillary forces dominate and viscous forces are negligible. IP produces a characteristic fingering with a fractal dimension close to that of ordinary critical percolation. Avalanches (also called ‘bursts’ or ‘Haines jumps’) have been observed. In this paper, we focus on the practical issues relating to the causes of the fingering and of the low saturations of injected fluid. We show that the saturation and the average position of the injected fluid exhibit standard fractal scaling behavior. However, the fractional flow of the injected fluid does not allow an average analysis because of the noise arising from the avalanches, even for the million site systems investigated in this paper. In studying the spatial distribution of these avalanches, we find a size cutoff depending upon the position of the avalanches; this is characteristic of the finite size of the system and signals that the systems have not achieved self-organized criticality. Furthermore, we show that the average size of these avalanches, 〈sa〉, increases with their average distance, 〈x〉, from the outlet as 〈sa〉≈〈x〉1.1. As a result, larger avalanches will tend to occur at the end of longer fingers causing preferential growth of the long fingers at the expense of the shorter fingers.

Uncertainty Analysis of a CO2 Sequestration Project Using Surrogate Reservoir Modeling Technique

While CO2 Capture and Sequestration (CCS) is considered a part of the solution to overcoming the ever increasing level of CO2 in the atmosphere, one must be sure that significant new hazards are not created by the CO2 injection process. The risks involved in different stages of a CO2 sequestration project are related to geological and operational uncertainties. This paper presents the application of a grid-based Surrogate Reservoir Model (SRM) to a real case CO2 sequestration project in which CO2 were injected into a depleted gas reservoir. An SRM is a customized model that accurately mimics reservoir simulation behavior by using Artificial Intelligence & Data Mining techniques. Initial steps for developing the SRM included constructing a reservoir simulation model with a commercial software, history matching the model with available field data and then running the model under different operational scenarios or/and different geological realizations. The process was followed by extracting some static and dynamic data from a handful of simulation runs to construct a spatio-temporal database that is representative of the process being modeled. Finally, the SRM was trained, calibrated, and validated. The most widely used Quantitative Risk Analysis (QRA) techniques, such as Monte Carlo simulation, require thousands of simulation runs to effectively perform the uncertainty analysis and subsequently risk assessment of a project. Performing a comprehensive risk analysis that requires several thousands of simulation runs becomes impractical when the time required for a single simulation run (especially in a geologically complex reservoir) exceeds only a few minutes. Making use of surrogate reservoir models (SRMs) can make this process practical since SRM runs can be performed in minutes. Using this Surrogate Reservoir Model enables us to predict the pressure and CO2 distribution throughout the reservoir with a reasonable accuracy in seconds. Consequently, application of SRM in analyzing the uncertainty associated with reservoir characteristics and operational constraints of the CO2 sequestration project is presented.

Grid-Based Surrogate Reservoir Modeling (SRM) for Fast Track Analysis of Numerical Reservoir Simulation Models at the Gridblock Level

Developing proxy models has a long history in our industry. Proxy models provide fast approximated solutions that substitute large numerical simulation models. They serve specific useful purposes such as assisted history matching and production/injection optimization. Most common proxy models are either reduced models or response surfaces. While the former accomplishes the run-time speed by grossly approximating the problem the latter accomplishes it by grossly approximating the solution space. Nevertheless, they are routinely developed and used in order to generate fast solutions to changes in the input space. Regardless of the type of model simplifications that is used, these conventional proxy models can only provide, at best, responses at the well locations, i.e. pressure or rate profiles at the well. In this paper we present application of a new approach to building proxy models. This method has one major difference with the traditional proxy models. It has the capability of replicating the results of the numerical simulation models, away from the wellbores. The method is called Grid-Based Surrogate Reservoir Model (SRM) since it is has the unique capability of being able to replicate the pressure and saturation distribution throughout the reservoir at the grid block level, and at each time step, with reasonable accuracy. Grid-Based SRM performs this task at high speed, when compared with conventional numerical simulators such as those currently in use (commercial and in-house) in our industry. To demonstrate the capabilities of Grid-Based SRM, its application to three reservoir simulation models are presented. Fist is a giant oil field in the Middle East with a large number of producers, second, to a CO2 sequestration project in Australia, and finally to a numerical simulation study of potential carbon storage site in the United States. The numerical reservoir simulation models are developed using two of the most commonly used commercial simulators 1 . Two of the models presented in this manuscript are consisted of hundreds of thousands of grid blocks and one includes close to a million cells. The Grid-based SRM that learns and replicates the fluid flow through these reservoirs can open new doors in reservoir modeling by providing the means for extended study of reservoir behavior with minimal computational cost. Surrogate Reservoir Modeling (SRM) is

Effects of Matrix Shrinkage and Swelling on the Economics of Enhanced-Coalbed-Methane Production and CO2 Sequestration in Coal

In this work, the Palmer-Mansoori model for coal shrinkage and permeability increases during primary methane production was rewritten to also account for coal swelling caused by CO{sub 2} sorption. The generalized model was added to a compositional, dual porosity coalbed-methane reservoir simulator for primary (CBM) and ECBM production. A standard five-spot of vertical wells and representative coal properties for Appalachian coals was used. Simulations and sensitivity analyses were performed with the modified simulator for nine different parameters, including coal seam and operational parameters and economic criteria. The coal properties and operating parameters that were varied included Youngs modulus, Poissons ratio, cleat porosity, and injection pressure. The economic variables included CH{sub 4}, price, Col Cost, CO{sub 2} credit, water disposal cost, and interest rate. Net-present value (NPV) analyses of the simulation results included profits resulting from CH{sub 4}, production and potential incentives for sequestered CO{sub 2}, This work shows that for some coal seams, the combination of compressibility, cleat porosity, and shrinkage/swelling of the coal may have a significant impact on project economics.

Ground-penetrating radar survey and tracer observations at the West Pearl Queen carbon sequestration pilot site, New Mexico

The potential for leakage of injected CO2 at carbon sequestration sites is a significant concern in the design and deployment of long-term carbon sequestration efforts. Effective and reliable monitoring of near-surface environments in the vicinity of these sites is essential to ensure the viability of sequestration activities as well as long-term public and environmental safety. Identification of geologic features (such as faults, fracture zones, and solution enhanced joints that might facilitate release of injected CO2 back into the atmosphere) is a key step in this process. This study reports on near-surface geologic and geophysical characterization efforts conducted at the Department of Energy National Energy Technology Laboratory (NETL) West Pearl Queen carbon sequestration pilot site in southeastern New Mexico, USA, and their use for uncovering possible mechanisms associated with escape of small amounts of perfluorocarbon tracers injected with the CO2.

Top-down, intelligent reservoir modelling of oil and gas producing shale reservoirs: case studies

Producing hydrocarbon from shale plays has attracted much attention in recent years. Advances in horizontal drilling and multi-stage hydraulic fracturing have made shale reservoirs a focal point for many operators. Our understanding of the complexities associated with the flow mechanism in shale has not kept up with our interest in shale formations. We present the application of a new reservoir modelling approach to history matching, forecasting and predicting hydrocarbon production from shale reservoirs, where instead of imposing our understanding on the reservoir model, we allow the production history, well log, and hydraulic fracturing data to force their will on our model. By carefully listening to the data, we developed a data-driven model and history match the production process and validate our model (using blind production history). Examples of three case studies in Lower Huron and New Albany shale formations (gas producing) and Bakken shale (oil producing) are presented in this article.

Pattern Recognition and Data-Driven Analytics for Fast and Accurate Replication of Complex Numerical Reservoir Models at the Grid Block Level

Reservoir simulation models are used extensively to model complex physics associated with fluid flow in porous media. Such models are usually large with high computational cost. The size and computational footprint of these models make it impractical to perform comprehensive studies which involve thousands of simulation runs. Uncertainty analysis associated with the geological model and field development planning are good examples of such studies. In order to address this problem, efforts have been made to develop proxy models which can be used as a substitute for a complex reservoir simulation model in order to reproduce the outputs of the reservoir models in short periods of time (seconds). In this study, by using artificial intelligence techniques a Grid-Based Surrogate Reservoir Model (SRMG) is developed. Gridbased SRM is a replica of the complex reservoir simulation models that is trained, calibrated and validated to accurately reproduce grid block level results. This technology is applied to a CO2 sequestration project in Australia. This paper presents the development of the reservoir simulation model and the Grid-based SRM. The SRM is able to generate pressure and gas saturation at the grid block level. The results demonstrate that this technique is capable of generating the reservoir simulation output very accurately within seconds.

Darcy Flow in a Wavy Channel Filled with a Porous Medium

Flow in channels bounded by wavy or corrugated walls is of interest in both technological and geological contexts. This paper presents an analytical solution for the steady Darcy flow of an incompressible fluid through a homogeneous, isotropic porous medium filling a channel bounded by symmetric wavy walls. This packed channel may represent an idealized packed fracture, a situation which is of interest as a potential pathway for the leakage of carbon dioxide from a geological sequestration site. The channel walls change from parallel planes, to small amplitude sine waves, to large amplitude nonsinusoidal waves as certain parameters are increased. The direction of gravity is arbitrary. A plot of piezometric head against distance in the direction of mean flow changes from a straight line for parallel planes to a series of steeply sloping sections in the reaches of small aperture alternating with nearly constant sections in the large aperture bulges. Expressions are given for the stream function, specific discharge, piezometric head, and pressure.