A Comprehensive Mathematical Model for Predicting Thermophysical Properties of Superheated Steam in Horizontal Injection Wells Considering Phase Change

Abstract

Abstract Superheated-steam injection in horizontal wells is a complex process, involving not only mass and heat transfer, but also phase change. The objectives of this work are to establish a comprehensive mathematical model for predicting thermophysical properties (i.e. mass flow rate, fluid pressure, the degree of superheat and steam quality) and to analyze the performance of superheated-steam injection in horizontal wells. In this study, using mass and momentum balance to a differential control volume of a horizontal wellbore, we present governing equations for mass flow rate and pressure drop, respectively. More importantly, phase change behavior of superheated steam is taken into account. Then, implicit equations for both the degree of superheat and steam quality are further derived based on energy balance in the wellbore. Next, the above equations are coupled and solved iteratively for each segment and a calculation flowchart is provided. Finally, the effects of the degree of superheat, injection rate, injection pressure, reservoir permeability and oil viscosity on the profiles of the above thermophysical properties are analyzed in detail. The results indicate that for a given degree of superheat, the mass flow rate drops faster after superheated steam is cooled to wet steam, but in the same position of the horizontal wellbore, the mass flow rate increases with the degree of superheat. Secondly, we show that enhancing the injection rate maybe a good method to ensure that the toe section of the horizontal well can also be heated effectively, more importantly, the higher the injection rate is, the longer the distance from the phase change point to the heel-position of the horizontal well is, and after phase change occurs, the lower the injection rate is, the faster the steam quality drops. Thirdly, it is found that both the mass flow rate and the degree of superheat in the same position of the horizontal wellbore decrease with injection pressure. Finally, the paper further reveals that when the reservoir permeability is high or the oil viscosity is low, the mass flow rate and the degree of superheat decline rapidly. Superheated-steam injection in horizontal wells has not been widely reported in the literature. The comprehensive mathematical model proposed in this paper, which is supported by the measured field data, can be adopted to predict the thermophysical properties and to analyze the performance of superheated-steam injection in horizontal wells. In our study, we also consider the phase change behavior of superheated steam that possibly occurs in practice.