An optimal viscosity profile in the secondary oil recovery

Carasso, C.; Paşa, Gelu

doi:10.1051/m2an/1998320202111

Cited by 15 publications

(37 citation statements)

References 5 publications

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“…In a mobil system of coordinates, moving with the velocity U of water far upstream, the intermediate region is [1] and [3]. The total amount C of polymer is:…”

Section: The Model Of Gorell and Homsymentioning

confidence: 99%

“…Carasso and Pasa, [1], obtain formula for an optimal viscosity in PS, and an upper estimation for the growth constant, in terms of J.l(0) -the limit value of the viscosity in PS on the PS -oil interface. The above Strum-Liouville problem is discretizated by using the finite-difference method.…”

Section: The Estimation Of the Growth Constantmentioning

confidence: 99%

“…We consider the viscosity profile (1). Then the relations (2), (6), (8) give us the growth constant (), the injection length L and the total amount C of polymer C in terms of p,(0).…”

Section: A New Optimal Profile In Terms Of Jl(o)mentioning

confidence: 99%

See 2 more Smart Citations

The Control of Saffman-Taylor Instability

Paşa

2003

Analysis and Optimization of Differential Systems

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“…In a mobil system of coordinates, moving with the velocity U of water far upstream, the intermediate region is [1] and [3]. The total amount C of polymer is:…”

Section: The Model Of Gorell and Homsymentioning

confidence: 99%

Section: The Estimation Of the Growth Constantmentioning

confidence: 99%

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The Control of Saffman-Taylor Instability

Paşa

2003

Analysis and Optimization of Differential Systems

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“…The viscosity in the mixture is the parameter of the problem, used to improve the interfaces stability. The details concerning the mechanical model are given in [1], [2], [6], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

“…A formula for an optimal viscosity in the mixture is given in [1]. The characteristic values are estimated in terms of the unknown viscosity in the mixture, by using a finite-difference approximation and the Greschgorin's theorem.…”

Section: Introductionmentioning

confidence: 99%

Estimations for the characteristic values of a Sturm-Liouville problem

Paşa

2002

Z. angew. Math. Phys.

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We consider a particular Sturm-Liouville problem, with boundary conditions containing the characteristic values. This problem governs the stability of the interfaces in oil recovery, by using the Hele-Shaw model of a homogeneous porous medium. We obtain estimations of the approximative characteristic values, by using a finite-difference approximation and the Gerschgorin's localization theorem. We obtain estimations of the exact characteristic values by using the Rayleigh's quotient of the initial problem. The upper limit of the approximative characteristic values is (in general) greater than the lower limit of the exact characteristic values. The same upper limit is given by the two methods, for a particular value of a parameter of the problem. This value gives us a large improvement of the stability. A previous convergence result is confirmed. Mathematics Subject Classification (2000). 34B24, 34L15, 76S05.

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A Class of Viscosity Profiles for Oil Displacement in Porous Media or Hele-Shaw Cell

Paşa

Titaud²

2005

Transp Porous Med

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This paper is devoted to the study of the stability of oil displacement in porous media. Results are applied to the secondary oil recovery process: the oil contained in a porous medium is obtained by pushing it with a second fluid (usually water). As in Saffman and Taylor (1958) and Gorell and Homsy (1983) the porous medium will be modelized by a HeleShaw cell. If the second fluid is less viscous, the fingering phenomenon appears, first studied by Saffman and Taylor (1959). In order to minimize this instability, we consider, as in Gorell and Homsy (1983), an intermediate polymer-solute region (i.r.), with a variable viscosity l, between water and oil. This viscosity increases from water to oil. The linear stability of the interfaces is governed by a Sturm-Liouville problem which contains eigenvalues in the boundary conditions. Its characteristic values are the growth constants of the perturbations. The stability can be improved by choosing a ''minimizing'' viscosity profile l which gives us an arbitrary small positive growth constant. In this paper, we suggest a class of minimizing profiles. This main result is obtained by considering the Rayleigh quotient to estimate -without any discretization -the characteristic values of the above Sturm-Liouville problem. A finitedifference procedure and Gerschgorin's localization theorem were used by Carasso and Pas¸a (1998) to solve the above problem. A formula of an exponential viscosity profile in (i.r.) was obtained. The new class of minimizing viscosity profiles described in this paper includes linear and exponential profiles. The corresponding total amount of polymer and the (i.r.) length are estimated in terms of the limit value of l on the (i.r.) -oil interface. Our results are compared with the previous theoretical viscosity profiles. We show that the linear case is more favorable compared with the exponential profile. We give lower estimates of the total amount of polymer and of the (i.r.) length for a given improvement of the stability , compared with the SaffmanTaylor case.

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An optimal viscosity profile in the secondary oil recovery

Cited by 15 publications

References 5 publications

The Control of Saffman-Taylor Instability

The Control of Saffman-Taylor Instability

Estimations for the characteristic values of a Sturm-Liouville problem

A Class of Viscosity Profiles for Oil Displacement in Porous Media or Hele-Shaw Cell

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