Physical and mathematical modeling of cyclic steam stimulation for oil reservoirs

Abstract

This article discusses the construction of a physical and mathematical model of the steam cycle effect on oil reservoirs. Existing models require calculations in hydrodynamic simulators or significantly simplify the description of the motion of the heat front. Within the framework of the proposed model, a number of assumptions are introduced regarding the movement of the thermal interface between the heated oil located in the bottomhole zone and the oil whose temperature is equal to the initial one. It is assumed that this boundary has the form of a straight line in a rectangular coordinate system. Moreover, at the initial moment of time, the straight line is determined by two points: the value of the maximum power taken on the vertical axis, directed downward, and the maximum radius of heating on the horizontal axis. In the future, these parameters are reduced. It is assumed that over time, the interface between the “cold” and heated oil shifts parallel to its initial position with a decrease in the parameters that determine it. This approach to describing the displacement over time of this boundary is proposed for the first time. The purpose of the article is to determine the flow rate of the well in the case of steam-thermal treatment of the formation, taking into account the size of the heated zone. In particular, the coolant injection cycle time and the characteristic time of the steam and thermal impregnation for the proposed model are determined. The physical processes considered during the construction of this model are described by conservation laws. The calculation of the area in which the heated oil will be located takes into account parameters such as flow rate and heat content of the coolant, reservoir thickness and thermal properties of the surrounding rocks. The article discusses the issues related to the relevance of the application of the methodology of vapor-cyclical effects on oil reservoirs. The result of the developed model is the dependence of the oil production rate on time for the cyclic treatment of bottom-hole zones of wells. The proposed method allows us to analyze the development efficiency depending on the main technological parameters. Such calculations allow you to choose the most optimal development strategy, and therefore, increase oil recovery.