Micro-scale modeling of formation damage
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Loss of formation permeability often occurs during drilling, produced water re-injection, perforation, and CO₂ injection for subsurface storage. Formation permeability loss might significantly decrease wells' productivity/injectivity, or affect the stability of the subsurface CO₂ storage unit. Permeability damage during drilling or produced water re-injection is in part due to solid particle entrapment in the formation. Permeability damage following perforation or CO₂ injection is known to be, in part, due to grain crushing as a result of changes in the local stress regime. In this dissertation we study both permeability damage mechanisms - particle entrapment and grain crushing - through a micro-scale modeling approach. In order to study the first permeability damage mechanism, i.e. solid particle entrapment, this dissertation provides a novel workflow for micro-scale modeling of particle entrapment due to straining in porous media based on first principles. The novelty of the presented workflow is its flexibility of modeling different types of porous media using their pore space geometry in the form of microscopic images. The presented approach is the first method that does not impose pore-grain surface restrictions on pore and throat bodies, such as being a cylinder, plane or a sphere. The procedure includes discrete element method (DEM) simulation of the interactions between the suspended particles and porous medium. We further extend the workflow to upscale the micro-scale simulation results thus enabling the prediction of solid deposition profiles on a core scale. Lastly, we use the micro-scale modeling procedure to study proppant transport in rough-walled fractures. Results of modeling particulate flow through an individual pore show that suspension velocity is the major parameter controlling particle straining in tight and wide pores. We also find that vibrating the pore improves particulate flow by preventing particle bridging across the pore. This phenomenon might be the microscopic mechanism that has caused earthquakes (larger than magnitude 3) to enhance the production from asphaltene-damaged reservoirs. Next we study the particle straining in a microscopic sample of disordered sphere pack. Unlike individual pores, this sample is more representative and the simulation allows the computation of upscaling parameters. We find, however, that the suspended particles have a wide distribution of individual velocities and are not permanently trapped. Thus for upscaling we explore using classical rate of entrapment as well as rate of accumulation (the latter not having any assumption on particle velocity within the volume). We compare the results derived by the deep bed filtration (DBF) model with the results obtained by the general material balance formulation for modeling particle removal by straining and obtain a better match for the latter for a specific experimental study in monosized sphere pack. Results of the study indicate that for the DBF model the correlation between the suspension concentration and the rate of particle entrapment in a clean bed is linear; however for the general material balance equation the rate of particle accumulation has a power-law correlation with the suspension concentration. Finally we conduct a study on proppant flow in rough walled fractures. Findings of this study show a slight decline in the fracture conductivity with time. In addition, the obtained proppant accumulation rates show that the proppant front movement clearly deviates from the piston-like displacement and the proppant fronts slow over time. Due to the similarity of proppant transport in rough fractures with a wide distribution of apertures and particle straining in porous media, we recommend a similar continuum scale modeling formulation. This approach captures proppant accumulation behind the front unlike current continuum models. We then shift focus to the mechanical behavior of weakly consolidated sandstone during CO₂ injection into brine-laden formations. We adopt a bonded agglomerate approach to simulate the behavior of sandstone and investigate the extents of grain crushing when sandstone samples are loaded under different conditions. We define two sets of bonds in the system: intra-grain bonds, which bond together the sub-grain particles to form agglomerates that are proxy models for crushable sand grains; and inter-grain bonds, which bond those agglomerates together to form a consolidated sandstone sample with crushable grains. The bonded DEM models the bonds between pairs of particles as brittle elastic beams. The mechanical properties of the bonds are obtained by calibrating the model against experimental studies on loading of single sand grains and sandstone samples. The calibrated model successfully predicts the different breakage patterns in individual quartz and feldspar grains under compressive loading. Finally we model the weakening effect of CO₂ on sandstone. DEM has been extensively used for micro-scale modeling of grain crushing in unconsolidated media by introducing agglomerate grains, alas its extension for sandstones has been lacking. We evaluate bonded DEM for this purpose and present a preliminary study of the effects of numerical chemical alteration due to CO₂ on grain crushing and permeability. We implement the weakening effect by reducing bonds' size and strength. Reducing intra-grain bond size and strength has a weakening effect on sand grains and reducing inter-grain bond size and strength weakens the cement. Next, we load the weakened and unaltered samples under hydrostatic pressure and record their mechanical response and permeability change due to compaction. The studied unaltered and cement-weakened samples show minimal amount of grain crushing. The sample with weakened cement and grain, loses up to 6% of its intra-grain bonds as a result of hydrostatic loading up to 40 MPa. The permeability change in this sample is mainly due to porosity loss due to compaction. Parallelization of the method (currently unavailable) will allow for more extensive study of grain crushing and damaged zones in sandstones in a wide variety of scenarios.