A network model for capture of suspended particles and droplets in porous media
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Produced water presents economical and environmental challenges to oil producers. Downhole separation technology is able to separate oil or gas from produced fluid in downhole environment and injects waste water into deeper formations, thus saving energy and reducing waste emission. More than 120 downhole separation systems have been installed worldwide, but only about 60% of the installations achieved success. Most of the failures were due to the injectivity decline under the invasion of impurities in the injected water, such as suspended particles and oil droplets. A reliable model is needed to predict the reaction of reservoir permeability under the invasion of such impurities and serves as a tool to screen appropriate formations for downhole separator installations.Previous experimental studies on particle-induced permeability damage reveal that high particle concentration, low fluid velocity, large particle size lead to more severe damage. The damage mechanisms are attributed to surface interception, bridging and size exclusion of particles in porous media. While for droplets, the resultant permeability decline is mostly due to surface interception. Empirical correlations with key parameters determined by core flooding data are widely applied to the simulation of permeability decline under invasion of particles and droplets. These correlations are developed based on characteristics of certain rocks and fluids, thus their applications are very restricted.A more scientific method is to model the flow and capture of particulates at pore level. Reservoir rocks are porous media composed of pores of various sizes. Pore network models employ certain assumptions to imitate real porous media, and have been proved realistic in simulating fluid flow in porous media. In this study, a 2-dimensional square network model is used to simulate capture of particles and droplets in porous media. Pore bodies are represented by globes and pore throats are imitated with capillary tubes. The flow rates in the network are obtained by simultaneously solving mass balance equations at each pore body. The network model is tuned to match the porosity and permeability of a certain rock and serves as the infrastructure where the capture process takes place.Particles are categorized as Brownian and non-Brownian particles according to size. For Brownian particles, diffusion is dominant and Fick’s law is applied to each pore inside the network to obtain deposition rate. For non-Brownian particles, their trajectories are mainly governed by gravity and drag force acting on them. Besides, the size of each particle is compared with the size of the pore where it is captured to determine the damage mechanism. For particles much smaller than the pore size, surface deposition is dominant and the permeability decline is gradual. For particles with sizes comparable to pore size, bridging and clogging are dominant and the permeability decline is much more severe.Unlike particles, droplets can not be captured on top of each other. Accordingly, a captureequilibrium theory is proposed. Once the pore surface is covered by droplets, equilibrium is reached and droplets flow freely through porous media without being captured. The simulation on capture of oil droplets reveals that the surface wettability has significant influence on the resultant permeability damage. Most natural reservoirs are neutrally or oil wet. It is thus recommended to apply these surface conditions to future simulations.The proposed model is validated with test data and reasonably good agreements are obtained. This new mechanistic model provides more insights into the capture process and greatly reduces the dependence on core flooding data.
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