The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

The original publication can be found at www.springerlink.comDeep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.Alvarez, A. C., Hime, G., Marchesin, D., Bedrikovetski, P

Transport of Explosive Residue Surrogates in Saturated Porous Media

Department of Defense operational ranges may become contaminated by particles of explosives residues (ER) as a result of low-order detonations of munitions. The goal of this study was to determine the extent to which particles of ER could migrate through columns of sandy sediment, representing model aquifer materials. Transport experiments were conducted in saturated columns (2 × 20 cm) packed with different grain sizes of clean sand or glass beads. Fine particles (approximately 2 to 50 μm) of 2,6-dinitrotoluene (DNT) were used as a surrogate for ER. DNT particles were applied to the top 1 cm of sand or beads in the columns, and the columns were subsequently leached with artificial groundwater solutions. DNT migration occurred as both dissolved and particulate phases. Concentration differences between unfiltered and filtered samples indicate that particulate DNT accounted for up to 41% of the mass recovered in effluent samples. Proportionally, more particulate than dissolved DNT was recovered in effluent solutions from columns with larger grain sizes, while total concentrations of DNT in effluent were inversely related to grain size. Of the total DNT mass applied to the uppermost layer of the column, <3% was recovered in the effluent with the bulk remaining in the top 2 cm of the column. Our results suggest there is some potential for subsurface migration of ER particles and that most of the particles will be retained over relatively short transport distances

Impact of kaolinite clay particles on the filtration of cryptosporidium-sized microspheres

Granular filtration remains a key barrier for Cryptosporidium removal in water treatment plants without UV irradiation. To assess the impact of clay particles in source water on Cryptosporidium removal efficiency by granular filtration, this study investigated the co-transport of Cryptosporidium-sized microspheres and kaolinite particles in sand columns. To investigate the influence of clay load on microsphere transport and deposition, varying influent kaolinite concentrations (0–106particles/mL) and microsphere concentrations (102–106microspheres/mL) were tested. The spatial distribution of retained microspheres was examined subsequent to experiments via filter coring. Results demonstrate that increasing the influent microsphere concentration impaired filter performance due to a blocking mechanism whereby previously retained particles repel incoming particles. In contrast, when the particulate load was dominated by kaolinite (for an equivalent particulate load), filter performance improved as a result of filter ripening whereby previously deposited particles act as additional collectors. Thus, microsphere-kaolinite interactions proved to be favorable although both particles possessed negative zeta potentials in the tested conditions. This study demonstrates that granular filter performance is vulnerable to peak events of microbial contamination. Conversely, Cryptosporidium-sized microsphere removal by granular filtration is enhanced in the presence of kaolinite in source water.</jats:p