caa a22 4500 463162544 CHVBK 20180406164752.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s11242-006-9082-3 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9082-3 The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media [Elektronische Daten] [Amaury Alvarez, Gustavo Hime, Dan Marchesin, Pavel Bedrikovetsky] Deep 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. Springer Science+Business Media, Inc., 2007 Deep bed filtration nationallicence Suspension transport nationallicence Porous media nationallicence Inverse problem nationallicence Tikhonov regularization nationallicence Formation damage nationallicence System of convection-reaction equations nationallicence Alvarez Amaury Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut Hime Gustavo Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut Marchesin Dan Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut Bedrikovetsky Pavel Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut Transport in Porous Media Springer Netherlands 70/1(2007-10-01), 43-62 0169-3913 70:1<43 2007 70 11242 https://doi.org/10.1007/s11242-006-9082-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9082-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alvarez Amaury Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Hime Gustavo Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Marchesin Dan Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Bedrikovetsky Pavel Fluid Dynamics, IMPA - Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22.460-320, Jardim Botánico, Rio de Janeiro, Brazil aut NATIONALLICENCE 773 0- Transport in Porous Media Springer Netherlands 70/1(2007-10-01), 43-62 0169-3913 70:1<43 2007 70 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer