Exact solution for 1D deep bed filtration with particle capture by advection and dispersion

Author(s):  
L.I. Kuzmina ◽  
Yu.V. Osipov
Author(s):  
Liudmila Kuzmina ◽  
Yuri Osipov

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution


SPE Journal ◽  
2009 ◽  
Vol 14 (03) ◽  
pp. 477-487 ◽  
Author(s):  
Rafael G. Guedes ◽  
Firas A.H. Al-Abduwani ◽  
Pavel Bedrikovetsky ◽  
Peter K. Currie

Summary Severe injectivity decline during seawater injection and produced-water reinjection is a serious problem in offshore waterflood projects. The permeability impairment occurs because of the capture of particles from injected water by the rock, both internally in the pores and externally in a filter cake. The reliable modeling-based prediction of injectivity decline is important for injected-water-treatment design and management (injection of seawater or produced water, water filtering, etc.). The classical deep-bed filtration model includes a single overall description of particle capture. During laboratory or field data interpretation using this model, it is usually assumed that several simultaneously occurring capture mechanisms are represented in the model by a single overall mechanism. The filtration coefficient, obtained by fitting the model to the laboratory or field data, represents the total kinetics of the particle capture. The purpose of this study is to justify this approach of using an aggregated single filtration coefficient. A multiple-retention deep-bed filtration model needs to describe several simultaneous capture mechanisms. The kinetics of the different capture mechanisms can differ from one another by several orders of magnitude. This greatly affects the particle propagation in natural reservoirs and the resulting formation damage. In this study, a model for deep-bed filtration taking into account multiple particle-retention mechanisms is discussed. It is proven that the multicapture model can be reduced to a single-capture-mechanism deep-bed filtration model. The method for determination of the capture kinetics for all individual capture processes from the breakthrough curve is discussed. As an example, the complete characterization of filtration with monolayer and multilayer deposition of iron oxide colloids is performed using particle-breakthrough curves from coreflooding.


Author(s):  
Ludmila I. Kuzmina ◽  
Yuri V. Osipov

Filtration of the suspension in a porous medium with a geometric particle capture mechanism is con-sidered. The porous medium has an initial deposit unevenly distributed across the filter. The nonlinear model of deep bed filtration suggests that the porosity and permeability of the porous medium depend on the deposit. The asymptotics of the movable boundary of the two phases is determined. The asymptotic solution of the problem is constructed and calculated near the filter inlet.


1996 ◽  
Vol 53 (4) ◽  
pp. R3028-R3031 ◽  
Author(s):  
Claude Ghidaglia ◽  
Lucilla de Arcangelis ◽  
John Hinch ◽  
Élisabeth Guazzelli

2020 ◽  
Vol 80 (5) ◽  
pp. 2120-2143
Author(s):  
Vladimir E. Nazaikinskii ◽  
Pavel G. Bedrikovetsky ◽  
Liudmila I. Kuzmina ◽  
Yuri V. Osipov

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Z. You ◽  
P. Bedrikovetsky ◽  
L. Kuzmina

Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For monodispersed suspension and transport in porous media with distributed pore sizes, the microstochastic model allows for upscaling and the exact solution is derived for the obtained macroscale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores.


1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov

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