Development of oil and gas fields using horizontal wells with multi-stage hydraulic fracturing, multilateral wells and multi-branch wells is a high-priority direction of advancement for the oil and gas industry (F. N. Nughaimish et al, 2005; Bazitov M. V. et al, 2015; Chellappan S. K, et al, 2016; Al-Gamber et al, 2013; Bone R. E. et al., 2016; Ayokunle, A. T. et al., 2016; Abdulazeem A. et al., 2016; Hoang S. et al., 2008; Gritchina V. et al., 2016; Bogachev K. et al., 2016). Operation of such wells is affected not only by geological conditions, but also by bottomhole design features and position of wellbores with respect to reservoir boundaries. Existing numeric and analytical models do not allow for the consideration of many geological and technological factors.

This publication describes a mathematical model of fluid inflow to a multilateral well with arbitrary geometric parameters. Solving the problem of determining multilateral well inflow involves a solution describing variation of pressure in a reservoir caused by a linear source. The solution makes it possible to simulate behavior of a random-geometry well by dividing the entire length of its wellbores into linear intervals and placing linear sources within them. The mathematical model features a capability to consider effects caused by formation boundaries (impermeable, constant pressure, or mixed type) and by finite and infinite conductivity fractures. The model also makes it possible to calculate inflow to a multilateral well penetrating several reservoirs with different physical characteristics, as well as determine mean reservoir pressure dynamics in each reservoir. As a result, we have developed a computation module for determination of fluid flow into a multilateral well. The module has been tested on several problems, with results compared against a commercial simulator. We have also compared results with actual field data for multilateral wells. As a consequence, we were able to establish that the error of solution was less than 10%. The approach we have developed can be used to determine fluid production trends for wells with different completion types, including multifractured horizontal and fishbone wells.

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