Unsteady filtration of the oil-CO$_2$ flow in a homogeneous reservoir under different temperature and pressure conditions

A. V. Radaev ; S. P. Plohotnikov ; F. Kh. Tazyukov ; A. N. Sabirzyanov ; I. T. Salimyanov

Matematičeskoe modelirovanie, Tome 33 (2021) no. 2, pp. 109-124.

Résumé

An experimental stand has been developed to study the hydrodynamics of the "oil-supercritical CO$_2$" flow in a homogeneous porous terrigenous medium at pressures up to 25 MPa and temperatures up to 473K. The experimental stand makes it possible to measure the solubility of carbon dioxide in oil and oil in carbon dioxide during non-stationary filtration of the oil-supercritical CO$_2$ system in a low-permeability homogeneous porous medium in a dynamic mode. The study of the solubility of the model low-viscosity oil when displacing it from the model of a terrigenous homogeneous oil reservoir, the study of the dynamic viscosity of the liquid substance "oil-supercritical CO$_2$". Based on the obtained experimental data on the thermophysical properties of the systems "oil-supercritical CO$_2$", a mathematical model of the process of unsteady filtration of the flow "oil-supercritical CO$_2$" in a low-permeability homogeneous porous medium has been developed. The problem was solved numerically by the finite difference method. In the process of sampling, a scheme was used implicit in pressure and explicit in saturation (the socalled IMPES method). Namely, for each moment of time, the pressure was calculated from a system of linear equations, while the saturation was taken from the previous time layer. Then the saturation was recalculated explicitly using the found pressures. When discretizing the derivative for adjacent nodes, the permeability is taken from the node in which the pressure is higher (that is, the “upstream” scheme was used). The convergence of the solution was controlled by performing numerical experiments on condensed grids. The developed mathematical model made it possible to calculate the values of the displacement coefficient of real oil. The mechanisms of increased oil recovery from permeable and low-permeability porous media have been identified.

Détail

Keywords: supercritical fluid, low-permeability porous medium, non-stationary multicomponent filtration, relative phase permeability.
Mots-clés : oil displacement coefficient

Bibliographie

[1] R. KH. Muslimov, “Puti sovershenstvovaniia modelirovaniia protscessov razvedki i razrabotki mestorozhdenii s trudnoizvlekaemymi zapasami nefti”, Mater. Mezhd. nauchno-prakt. konferentsii «Modelirovanie geologicheskogo stroyeniia i protsessov razrabotki – osnova uspeshnogo osvoyeniia neftyanykh i neftegazovykh mestorozhdenii» 2018, Izdatelstvo Slovo, Kazan, 2018

[2] KH. Aziz, E. Settari, Matematicheskoe modelirovanie plastovyh sistem, Nedra, M., 1982, 407 pp.

[3] G. I. Barenblatt, V. M. Entov, V. M. Ryzhik, Teoriia nestatsionarnoi filtratsii zhidkosti i gaza, Nedra, M., 1972, 288 pp.

[4] A. V. Radaev, “Vliyanie termobaricheskikh, fiziko-khimicheskikh i geologicheskikh uslovii na vytesnenie vysokovyazkoi nefti iz odnorodnykh plastov s ispolzovaniyem sverkhkriticheskogo CO$_2$”, Vestnik Kazanskogo tekhnologicheskogo universiteta, 2010, no. 2, 254–256

[5] A. V. Radaev, “Vliyanie termobaricheskikh usloviy v odnorodnom plaste na vytesnenie malovyazkoi nefti sverkhkriticheskim dioksidom ugleroda”, Sverkhkriticheskie flyuidy: Teoriia i praktika, 4:3 (2009), 7–15

[6] A. V. Radaev, “Eksperimentalnaia ustanovka dlia issledovaniia protsessa vytesneniia nefti pri termobaricheskikh usloviyakh realnykh plastov s ispolzovaniem sverkhkriticheskikh flyuidnykh sistem”, Vestnik Kazanskogo tekhnol. universiteta, 2009, no. 3, 96–102

[7] A. V. Radayev, Termodinamika protsessa vytesneniia trudnoizvlekayemoi nefti sverkhkriticheskim dioksidom ugleroda, avtoreferat dissertatsii ... kand. tekhn. nauk, Kazan, 2010

[8] GOST 14249 89. Sosudy i apparaty vysokogo davleniia. Normy i metody rascheta na prochnost, M., 55 pp.

[9] F. N. Shamsetdinov, “Eksperimentalnaia ustanovka dlya issledovaniia viazkosti gazonasyshchennykh zhidkikh uglevodorodov pri davleniyakh do 50 MPa”, Vestnik Kazanskogo tekhnologicheskogo universiteta, 16:18 (2013), 112–114

[10] A. V. Radaev, “Matematicheskaia model protsessa nestatsionarnoi filtratsii sistemy «neft–sverkhkriticheskii CO$_2$» v odnorodnom plaste v shirokom intervale izmeneniia temperatur i davlenii”, Vestnik Kazanskogo gosudar. tekhn. univers. im. Tupoleva, 2019, no. 3, 26–29

[11] A. I. Brusilovskii, Fazovye prevrashcheniia pri razrabotke mestorozhdenii nefti i gaza, Graal, M., 2002, 575 pp.

[12] I. I. Duniushkin, I. T. Mishenko, E. I. Yeliseeva, Raschety fiziko khimicheskikh svoistv plastovoi i promyslovoi nefti i vody, Izdatelstvo FGUP «Neft i gaz» RGU nefti i gaza im. I.M. Gubkina, M., 2004, 448 pp.

[13] I. F. Golubev, Viazkost gazov i gazovykh smesei, Spravochnoe rukovodstvo, GIFML, M., 1959, 375 pp.

[14] A. V. Radaev, “Vliyanie termobaricheskikh uslovii v odnorodnom plaste na vytesnenie malovyazkoi nefti sverkhkriticheskim dioksidom ugleroda”, Sverkhkriticheskie flyuidy: Teoriya i praktika, 4:3 (2009), 7–15

[15] Gabriela B. Savioli, M. Susana Bidner, “Simulation of the oil and gas flow toward a well – A stability analysis”, Journal of Petroleum Science and Engineering, 48 (2005), 53–69 | DOI

[16] TU-09.10.12.190-073-02069639-2016. Issledovanie protsessa vytesneniia nefti iz nasypnykh i karbonatnykh modelei plasta sverkhkriticheskimi flyuidnymi sistemami, 2016, 25 pp.