A Unified Model for Predicting Flowing Temperature Distribution in Wellbores and Pipelines

Abstract

Summary This paper presents a general and unified equation for flowing temperature prediction that is applicable for the entire range of inclination angles. The equation degenerates into Ramey's equations for ideal gas or incompressible liquid and into the Coulter and Bardon equation, with the appropriate assumptions. This work also proposes an approximate method for calculating the Joule-Thomson coefficient for black-oil models. Introduction Flowing temperature distribution often is predicted with different methods for pipelines and wellbores. The Ramey method usually is used for predicting wellbore temperature distribution. This method rigorously incorporates the complex process of transient heat transfer between the wellbore and the reservoir. Ramey's method, however, is limited to either ideal gas or incompressible liquid flow. The Coulter and Bardon equation commonly is used for pipeline temperature prediction. A more rigorous thermodynamic behavior of the flowing fluid is taken into account, incorporating the Joule-Thomson coefficient. Although the Coulter and Bardon equation originally was derived for gas flow, it also is used for single-phase liquid or two-phase flow. This equation is limited, however, by the assumptions of steady-state heat transfer with a constant-temperature environment and horizontal flow.

Comprehensive Design and Manufacturing Solutions for Sand Control and Tooling towards Enhanced Oil Recovery

“…The first is the comprehensive model which separates the flow pattern and pressure gradient to get a prediction of the fluid movement in the well [34]. The second is a unified model which combines flow pattern and pressure gradient to determine a prediction of fluid flow in a well [35].…”

“…FCDs are used to provide zonal isolation of flow in and out of targeted formations within a reservoir by providing the ability to selectively open or close steam ports in the injection and production zones [70], [71]. In conjunction with sand screen liners, they provide sand control, steaming control, and production vacuuming coherently for the SAGD wells [24], [35]. The design of FCDs is focused on improving the performance of the tool in controlling the steam distribution in the reservoir, minimizing pressure drop across the tools, and improving the reliability of the devices over their lifespan.…”

“…The second is a unified model which combines flow pattern and pressure gradient to determine a prediction of fluid flow in a well [7]. Multiphase flow is a type of flow that often results in liquid carry over in the gas phase and gas entrainment (including natural gas and steam) in the liquid phase [32], [35]. Currently, the method of determining the behavior of multiphase flow is by experimental means, therefore this program also pay great emphasis on experimental aspects of the SAGD flow controls.…”

The heat and mass transfer characteristics of superheated steam in horizontal wells with toe-point injection technique

“…Ejiogu and Fiori (1987) and Tortike and Farouq Ali (1989) presented empirical formulas for calculating steam thermophysical properties. Sagar et al (1991) proposed a simplified model for predicting temperature distribution of saturated steam along the vertical wellbores based on the Coulter-Bardon equation, and Alves et al (1992) developed a new model describing the relationships between enthalpy and pressure in wellbores. Bahonar et al (2010Bahonar et al ( , 2011 took vertical heat transfer into consideration and proposed their numerical model which was later compared with previous models.…”

Effect analysis of non-condensable gases on superheated steam flow in vertical single-tubing steam injection pipes based on the real gas equation of state and the transient heat transfer model in formation

“…Both analytical and numerical solutions were obtained of thermal fluid flow in wellbores. Alves et al (1992) and Hasan and Kabir (1994) presented two rigorous models for estimating temperature and steam quality in wellbores by solving the continuity, energy and momentum balance equations simultaneously. Then, huge amount of works were done by Kabir 1996, 2012;Hasan et al 2009) and Kabir et al (1996) on heat conduction rate in radial direction and flow models in wellbores under various injection conditions, which laid a solid foundation for following studies on multiphase flow, coupling effect of wellbore/formation and Joule-Thomson effect, etc.…”