title: ÐÐ¾Ð´ÐµÐ»Ñ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ñ, Ð¾Ð±Ð¾ÑÑÐ´Ð¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð£Ð­Ð¦Ð, ÑÐ°Ð±Ð¾ÑÐ°ÑÑÐµÐ¹ Ð² Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¾Ð¼ ÑÐµÐ¶Ð¸Ð¼Ðµ ÑÐºÑÐ¿Ð»ÑÐ°ÑÐ°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ°Ð·Ð½Ð¾Ð³Ð¾ ÑÐ»ÑÐ¸Ð´Ð°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: The model of a ESP well operating in a periodic mode for multi-phase fluid
Creators: name: ÐÑÐ°ÐµÐ²Ð°, Ð¡Ð°Ð±Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÐÐµÑÑÑÐ½ÑÐµ Ð¸ Ð³Ð°Ð·Ð¾Ð²ÑÐµ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ñ
ÐÐ°ÑÐ¾ÑÑ ÑÐµÐ½ÑÑÐ¾Ð±ÐµÐ¶Ð½ÑÐµ
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ
ÑÐ¶Ð¸Ð¼Ð°ÐµÐ¼ÑÐ¹ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ°Ð·Ð½ÑÐ¹ ÑÐ»ÑÐ¸Ð´
Ð³Ð°Ð·Ð¾Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ½Ð°Ñ ÑÐ¼ÐµÑÑ Ð² Ð½ÐºÑ
dynamic of pressure at the pump intake level
compressible multi-phase fluid
gas-liquid mixture in tubing

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ñ, Ð¾Ð±Ð¾ÑÑÐ´Ð¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð£Ð­Ð¦Ð, ÑÐ°Ð±Ð¾ÑÐ°ÑÑÐµÐ¹ Ð² Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¾Ð¼ ÑÐµÐ¶Ð¸Ð¼Ðµ ÑÐºÑÐ¿Ð»ÑÐ°ÑÐ°ÑÐ¸Ð¸. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÑÑÐ¸ Ð²Ð¸Ð´Ð° ÑÐ»ÑÐ¸Ð´Ð°: Ð½ÐµÑÐ¶Ð¸Ð¼Ð°ÐµÐ¼ÑÐ¹ Ð¾Ð´Ð½Ð¾ÑÐ°Ð·Ð½ÑÐ¹, ÑÐ¶Ð¸Ð¼Ð°ÐµÐ¼ÑÐ¹ Ð¾Ð´Ð½Ð¾ÑÐ°Ð·Ð½ÑÐ¹, ÑÐ¶Ð¸Ð¼Ð°ÐµÐ¼ÑÐ¹ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ°Ð·Ð½ÑÐ¹. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð¾Ð¿Ð¸ÑÑÐ²Ð°Ð»Ð°ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°, ÑÐ¾ÑÑÐ¾ÑÐ²ÑÐ°Ñ Ð¸Ð· Ð¿Ð»Ð°ÑÑÐ° ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¾ÑÐ¼Ñ, Ð²ÑÐºÑÑÑÐ¾Ð³Ð¾ Ð² ÑÐµÐ½ÑÑÐµ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¼ÐµÑÐ°Ð½Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ð¾Ð¹. ÐÐ·ÑÑÐ°Ð»ÑÑ Ð¿Ð»Ð°ÑÑ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð², Ñ Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½ÑÐ¼ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸ÐµÐ¼ Ð½Ð° ÐºÐ¾Ð½ÑÑÑÐµ Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ. ÐÐ»Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¾Ð¿Ð¸ÑÑÐ²Ð°Ð»ÑÑ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ Ð±Ð°Ð»Ð°Ð½Ñ Ð¸ Ð±Ð°Ð»Ð°Ð½Ñ Ð¼Ð°ÑÑÐ¾Ð²ÑÑ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð² Ð½Ð° Ð³Ð»ÑÐ±Ð¸Ð½Ðµ Ð¿ÑÐ¸ÐµÐ¼Ð° Ð½Ð°ÑÐ¾ÑÐ°. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐ¸Ñ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¹ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ Ð±ÑÑÐµÑÐ½Ð¾Ðµ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð¸ ÑÐ°ÑÑÐ¾ÑÐ° ÑÐ°Ð±Ð¾ÑÑ Ð½Ð°ÑÐ¾ÑÐ°. ÐÐ»Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð²ÑÐµÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹, Ð±ÑÐ» ÑÐ½Ð°ÑÐ°Ð»Ð° ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½ Ð¿ÑÐ¸ÑÐ¾Ðº ÑÐ»ÑÐ¸Ð´Ð° Ð¸Ð· Ð¿Ð»Ð°ÑÑÐ°. ÐÐµÐ±Ð¸Ñ Ð¸Ð· Ð¿Ð»Ð°ÑÑÐ° Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑ Ð¸Ð· ÑÐµÐ±Ñ ÑÑÐ½ÐºÑÐ¸Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð¾Ñ Ð·Ð°Ð±Ð¾Ð¹Ð½Ð¾Ð³Ð¾ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð² ÑÐ²Ð¾Ñ Ð¾ÑÐµÑÐµÐ´Ñ Ð·Ð°Ð±Ð¾Ð¹Ð½Ð¾Ðµ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð¾Ñ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ. ÐÐ°Ð»ÐµÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÐ»ÑÐ¸Ð´Ð° Ð² ÐÐÐ¢, Ð³Ð´Ðµ Ð´ÐµÐ±Ð¸Ñ ÑÐ²Ð»ÑÐµÑÑÑ ÑÑÐ½ÐºÑÐ¸ÐµÐ¹ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ, ÑÐ°ÑÑÐ¾ÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð½Ð°ÑÐ¾ÑÐ°, Ð±ÑÑÐµÑÐ½Ð¾Ð³Ð¾ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ Ð´ÐµÐ±Ð¸ÑÐ° Ð¸Ð· Ð¿Ð»Ð°ÑÑÐ°. ÐÐ²Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÐ»ÑÐ¸Ð´Ð° Ð² Ð·Ð°ÑÑÑÐ±Ð½Ð¾Ð¼ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÐµÑÑÑ ÑÐµÑÐµÐ· ÐµÐ³Ð¾ Ð¿Ð»Ð¾ÑÐ°Ð´Ñ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ»ÑÐ¸Ð´Ð° Ð¸ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÑÐ¾Ð²Ð½Ñ Ð²Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¸Ð· ÑÑÐ¼Ð¼Ñ Ð¼Ð°ÑÑÐ¾Ð²ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ Ð¿ÐµÑÐ²Ð°Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½Ð°Ñ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ Ð¿Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð° ÑÐµÑÐµÐ· Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½ÑÑ ÑÑÐ¼Ð¼Ñ Ð¼Ð°ÑÑÐ¾Ð²ÑÑ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð² Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ Ð²ÑÐ¾ÑÐ°Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½Ð°Ñ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ Ð¿Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸. ÐÐ»Ñ Ð²Ð¾ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð¸Ñ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑÑÑ ÑÐ°Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ðµ Ð² ÑÑÐ´ Ð¢ÐµÐ¹Ð»Ð¾ÑÐ°. Ð¢Ð°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼, Ð±ÑÐ»Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÐµÑ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÑ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð½Ð° Ð¿ÑÐ¸ÐµÐ¼Ðµ Ð½Ð°ÑÐ¾ÑÐ°, ÑÐµÑÐµÐ· ÐºÐ¾ÑÐ¾ÑÑÑ Ð²ÑÑÐ¸ÑÐ»ÑÑÑÑÑ Ð²ÑÐµ Ð¾ÑÑÐ°Ð»ÑÐ½ÑÐµ Ð¿Ð¾ÐºÐ°Ð·Ð°ÑÐµÐ»Ð¸ ÑÐ°Ð±Ð¾ÑÑ ÑÐºÐ²Ð°Ð¶Ð¸Ð½Ñ. ÐÐ»Ñ Ð¿Ð¾Ð´ÑÐ²ÐµÑÐ¶Ð´ÐµÐ½Ð¸Ñ ÑÐ¸Ð·Ð¸ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð° Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ°.
description: In this paper, a model of a ESP well operating in a periodic mode is considered. Three types of fluid are considered: incompressible single-phase, compressible single-phase, compressible multi-phase. In the course of the work, a system was described that consisted of a reservoir of a cylindrical shape, opened in the center by a vertical mechanized well. A formation of finite dimensions was considered, with a constant pressure on the supply circuit. To build a mathematical model, the material balance and the balance of mass flows at the pump intake depth were described. Buffer pressure and pump frequency were used as control actions. To determine all the parameters of the governing equations, the fluid flow from the reservoir was first described (in fact, this is the flow rate that is in the production string). The flow rate from the reservoir is a function that depends on the bottomhole pressure and time, in turn, the bottomhole pressure depends on the intake pressure. Next, the flow of fluid in the tubing is considered, where the flow rate is a function of the intake pressure, pump frequency, buffer pressure and flow rate from the reservoir. Fluid movement in the annulus is described in terms of the cross-sectional area of the annulus, changes in fluid density and dynamic level over time. As a result, the first derivative of the intake pressure with respect to time is determined from the sum of mass flows, and the second derivative of the intake pressure with respect to time is determined through the derivative of the sum of mass flows. Next, we reconstruct the intake pressure function using a Taylor series expansion. Thus, a model of a periodic well was obtained, which described the dynamics of pressure at the pump intake level, through which all other well performance indicators were calculated. An analytical check was made to confirm the physicality of the model.