Plane-radial model for water gas displacement by water
UDC: 622.279:681.5
DOI: 10.33285/1999-6934-2023-4(136)-45-51
Authors:
TOLPAEV VLADIMIR A.
1,2,
AKHMEDOV KURBAN S.1,
LOSKUTOV KIRILL R.1,
GAZALIEV ISLAM R.3
1 Gazprom VNIIGAZ, Stavropol, Russia
2 North-Caucasus Federal University, Stavropol, Russia
3 Gazprom transgaz Makhachkala, Makhachkala, Russia
Keywords: gas, water, well, reservoir pressure, bottomhole pressure, drawdown, flow rate, gas-water contact, watering time
Annotation:
A new method of presenting the topic "Plane-radial gas displacement by water" is proposed for students who do not have partial differential equations in their mathematical training program as well as fundamental concepts of vector analysis. Plane-radial filtration of water and gas by dynamic viscosities μw and μg is considered subordinating to the linear Darcy law. The new method relies only on the methods of differential and integral calculus of functions of one real variable and does not use the methods for differential calculus of several variables functions. The proposed method is based on replacing the well-known classical boundary condition at the gas-water contact, a new condition, which implies the equality of the pore volume occupied by the moving water front to the pore volume occupied by natural gas before displacement, thus significantly simplifying all mathematical calculations. An approximate and, at the same time, sufficiently accurate analytical solution of the differential equation on the movement of gas-water contact boundary is given. In the approximate solution, rather slowly varying functions ln(R/RGWC) and ln(RGWC/rc) are replaced by constant average values. An example of a calculation-graphical student task on the plane-radial gas displacement by water is presented. To consolidate the topic, students are offered typical tasks with individual input data in each variant (pressure on the supply circuit and bottomhole pressure in the well, radius of the supply circuit, initial gas-water contact radius, reservoir thickness, its porosity, permeability, coefficients of dynamic viscosity of gas and water under reservoir conditions, well radius). It is required to calculate: 1) the approximate value of the pressure on the gas-water contact, taken constant; 2) flow-rate of a gas well at the initial moment of time and at the moment of watering; 3) watering time of a gas producing well operating in the mode of water-reciprocating gas displacement; 4) building of graphs of changes of the gas-water contact radius and the dependence of the normalized flow rate of a gas well on time. The above-mentioned conditions make acceptable the proposed method of presenting the topic "plane-radial water displacement of gas" for students of oil and gas specialties 21.05.02 "Applied Geology".
Bibliography:
1. Basniev K.S., Kochina I.N., Maksimov V.M. Podzemnaya gidromekhanika: ucheb. dlya vuzov. – M.: Nedra, 1993. – 416 s.
2. Evdokimova V.A., Kochina I.N. Sbornik zadach po podzemnoy gidravlike: ucheb. posobie dlya vuzov. – M.: Al'yans, 2007. – 168 s.
3. Shchelkachev V.N., Lapuk B.B. Podzemnaya gidravlika. – Izhevsk: NITs "Regulyarnaya i khaoticheskaya dinamika", 2001. – 736 s.
4. GOST 30319.1-96. Mezhgosudarstvennyy standart. Gaz prirodnyy. Metody rascheta fizicheskikh svoystv. Opredelenie fizicheskikh svoystv prirodnogo gaza, ego komponentov i produktov ego pererabotki. – Vved. 1997–07–01. – M.: Izd-vo standartov, 1997. – III, 16 s.
5. Svid. 2016613006 o gos. registratsii programmy dlya EVM. Raschet znacheniy dinamicheskoy vyazkosti v zadannykh diapazonakh izmeneniy termobaricheskikh parametrov dlya uglevodorodnykh gazovykh smesey / V.A. Tolpaev, R.A. Ryskalenko, S.A. Gogoleva; pravoobladatel' OAO "SevKavNIPIgaz". – № 2016610343; zayavl. 20.01.2016; zaregistr. 15.03.2016; opubl. 20.04.2016.
6. Tablitsy fizicheskikh velichin: sprav. / pod red. akad. I.K. Kikoina. – M.: Atomizdat, 1976. – 1008 s.
7. Mustafaeva G.R., Mustafaeva S.R. Opredelenie vodonasyshchennosti neftyanykh plastov // Oborudovanie i tekhnologii dlya neftegazovogo kompleksa. – 2022. – № 3(129). – S. 40–44. – DOI: 10.33285/1999-6934-2022-3(129)-40-44
8. Abdullin A.F., Dolgikh M.Yu., Makarov D.V. Uvelichenie effektivnosti sistemy podderzhaniya plastovogo davleniya putem primeneniya radial'nogo vskrytiya plasta na primere mestorozhdeniya Zapadnoy Sibiri // Oborudovanie i tekhnologii dlya neftegazovogo kompleksa. – 2022. – № 6(132). – S. 56–62. – DOI: 10.33285/1999-6934-2022-6(132)-56-62
Back to issue