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Thermodynamic model of steam injection pipeline considering the effect of time and phase change

Zhao Xuan, Niu Chengcheng, Wang Jun, Zhu Xiuxing

Journal of Power Technologies

2019

Vol. 99, nr 2

123--130

Thermodynamic parameters in heavy oil thermal recovery wells form the basis for evaluating the thermal efficiency of steam injection. However, various factors in wellbores affect the variation law of thermodynamic parameters, hindering attempts to make an accurate description of them. A thermodynamic model of wellbores is proposed in this study which factors in the effects of time and phase change with a view to: (i) improving the accuracy of thermodynamic parameter analysis, and (ii) identifying the main factors and rules that govern thermal efficiency. With the time factor considered, the transient conduction function of a coupled wellbore-formation was established, and the heat loss during steam injection was analyzed. Meanwhile, a wellbore pressure gradient equation was established using the Beggs-Brill model with consideration of the influence of phase transformation in wellbore. Steam pressure, which varies with flow pattern, was also analyzed. The accuracy of the proposed model was verified by comparing the results of the analysis with the test data. Taking this approach, the influence of steam injection parameters on thermal efficiency was studied. The results demonstrate that the relative error of the pressure analysis result of proposed model is 1.06% and the relative error of temperature is 0.24%. The main factor affecting thermal efficiency is water in the annulus of the wellbore, followed by the steam injection rate. The thermal efficiency of the wellbore is about 80% when the water depth in the annulus is 300 m. An increase in the injection rate or extension of the injection time can improve thermal efficiency, whereas an increase in steam injection pressure reduces thermal efficiency. The proposed method provides good prospects for optimizing high efficiency steam injection parameters of heavy oil thermal recovery wells.

The modified XFEM for solving problems of a phase change with natural convection

Stąpór Paweł

Archive of Mechanical Engineering

2019

Vol. LXVI, nr 3

273--294

This paper presents an extended finite element method applied to solve phase change problems taking into account natural convection in the liquid phase. It is assumed that the transition from one state to another, e.g., during the solidification of pure metals, is discontinuous and that the physical properties of the phases vary across the interface. According to the classical Stefan condition, the location, topology and rate of the interface changes are determined by the jump in the heat flux. The incompressible Navier–Stokes equations with the Boussinesq approximation of the natural convection flow are solved for the liquid phase. The no-slip condition for velocity and the melting/freezing condition for temperature are imposed on the interface using penalty method. The fractional four-step method is employed for analysing conjugate heat transfer and unsteady viscous flow. The phase interface is tracked by the level set method defined on the same finite element mesh. A new combination of extended basis functions is proposed to approximate the discontinuity in the derivative of the temperature, velocity and the pressure fields. The single-mesh approach is demonstrated using three two-dimensional benchmark problems. The results are compared with the numerical and experimental data obtained by other authors.