Browsing by Subject "Scale-up"
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Item Reservoir modeling accounting for scale-up of heterogeneity and transport processes(2009-12) Leung, Juliana Yuk Wing; Srinivasan, SanjayReservoir heterogeneities exhibit a wide range of length scales, and their interaction with various transport mechanisms control the overall performance of subsurface flow and transport processes. Modeling these processes at large-scales requires proper scale-up of both heterogeneity and the underlying transport mechanisms. This research demonstrates a new reservoir modeling procedure to systematically quantify the scaling characteristics of transport processes by accounting for sub-scale heterogeneities and their interaction with various transport mechanisms based on the volume averaging approach. Although treatments of transport problems with the volume averaging technique have been published in the past, application to real geological systems exhibiting complex heterogeneity is lacking. A novel procedure, where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a small sub-volume of the reservoir, can be integrated with the volume averaging technique to provide effective description of transport at the coarse scale. In a volume averaging procedure, scaled up equations describing solute transport in single-phase flow are developed. Scaling characteristics of effective transport coefficient corresponding to different reservoir heterogeneity correlation lengths as well as different transport mechanisms including convection, dispersion, and diffusion are studied. The method is subsequently extended to describe transport in multiphase systems to study scaling characteristics of processes involving adsorption and inter-phase transport. Key conclusions drawn from this dissertation show that 1) variance of reservoir properties and flow responses generally decrease with scale; 2) scaling of recovery processes can be described by the scaling of effective mass transfer coefficient (Keff); in particular, mean and variance of Keff decrease with length scale, similar in the fashion of recovery statistics (e.g., variances in tracer breakthrough time and recovery); 3) the scaling of Keff depends on the underlying heterogeneity and is influenced by the dominant transport mechanisms. To show the versatility of the approach for studying scale-up of other transport mechanisms, it is also applied to derive scaled up formulations of non-Newtonian polymer flow to investigate the scaling characteristics of the apparent viscosity and effective shear rate in porous media.Item Scale-up methodology for chemical flooding(2010-12) Koyassan Veedu, Faiz; Delshad, Mojdeh; Pope, Gary A.Accurate simulation of chemical flooding requires a detailed understanding of numerous complex mechanisms and model parameters where grid size has a substantial impact upon results. In this research we show the effect of grid size on parameters such as phase behavior, interfacial tension, surfactant dilution and salinity gradient for chemical flooding of a very heterogeneous oil reservoir. The effective propagation of the surfactant slug in the reservoir is of paramount importance and the salinity gradient is a key factor in ensuring the process effectiveness. The larger the grid block size, the greater the surfactant dilution, which in turn erroneously reduces the effectiveness of the process indicated with low simulated oil recoveries. We show that the salinity gradient is not adequately captured by coarse grid simulations of heterogeneous reservoirs and this leads to performance predictions with lower recovery compared to fine grid simulations. Due to the highly coupled, nonlinear interactions of the many chemical and physical processes involved in chemical flooding, it is better to use fine-grid simulations rather than coarse grids with upscaled physical properties whenever feasible. However, the upscaling methodology for chemical flooding presented in this work accounts approximately for some of the more important effects, as demonstrated by comparison of fine grid and coarse grid results and is very different than the way other enhanced oil recovery methods are upscaled. This is a step towards making better performance predictions of chemical flooding for large field projects where it is not currently feasible to perform the large number of simulations required to properly consider different designs, optimization, risk and uncertainty using fine-grid simulations.Item Scale-up of dispersion for simulation of miscible displacements(2013-05) Adepoju, Olaoluwa Opeoluwa; Lake, Larry W.; Johns, Russell T.Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements.Item Scale-up of reactive processes in heterogeneous media(2014-12) Singh, Harpreet, active 21st century; Srinivasan, SanjayPhysical and chemical heterogeneities cause the porous media transport parameters to vary with scale, and between these two types of heterogeneities geological heterogeneity is considered to be the most important source of scale-dependence of transport parameters. Subsurface processes associated with chemical alterations result in changing reservoir properties with interlinked spatial and temporal scale, and there is uncertainty in the evolution of those properties and the chemical processes. This dissertation provides a framework and procedures to quantify the spatiotemporal scaling characteristics of reservoir attributes and transport processes in heterogeneous media accounting for chemical alterations in the reservoir. Conventional flow scaling groups were used to assess their applicability in scaling of recovery and Mixing Zone Length (MZL) in presence of chemical reactivity and permeability heterogeneity through numerical simulations of CO₂ injection. It was found out that these scaling groups are not adequate enough to capture the scaling of recovery and transport parameters in the combined presence of chemical reactivity and physical heterogeneity. In this illustrative example, MZL was investigated as a function of spatial scale, temporal scale, multi-scale heterogeneity, and chemical reactivity; key conclusions are that 1) the scaling characteristics of MZL distinctly differ for low permeability and high permeability media, 2) heterogeneous media with spatial arrangements of both high and low permeability regions exhibit scaling characteristics of both high and low permeability media, 3) reactions affect scaling characteristics of MZL in heterogeneous media, 4) a simple rescaling can combine various MZL curves by merging them into a single MZL curve irrespective of the correlation length of heterogeneity, and 5) estimates of MZL (and consequently predictions of oil recovery) will fluctuate corresponding to displacements in a permeable medium whose lateral length is smaller than the correlation length of geological formation. We illustrate and extend the procedure of estimating Representative Elementary Volume (REV) to include temporal scale by coupling it with spatial scale. The current practice is to perform spatial averaging of attributes and account for residual variability by calibration and history matching. This results in poor predictions of future reservoir performance. The proposed semi-analytical technique to scale-up in both space and time provides guidance for selection of spatial and temporal discretizations that takes into account the uncertainties due to sub-processes. Finally, a probabilistic particle tracking (PT) approach is proposed to scale-up flow and transport of diffusion-reaction (DR) processes while addressing multi-scale and multi-physics nature of DR mechanisms and also maintaining consistent reservoir heterogeneity at different levels of scales. This multi-scale modeling uses a hierarchical approach which is based on passing the macroscopic subsurface heterogeneity down to the finer scales and then returning more accurate reactive flow response. This PT method can quantify the impact of reservoir heterogeneity and its uncertainties on statistical properties such as reaction surface area and MZL, at various scales.