Application of a New Fully-Coupled Thermal Multiphase Wellbore Flow Model

Abstract

Thermal recovery processes are widely applied for the production of heavy oil and oil sands. Thermal reservoir simulation models, however, often lack a comprehensive well modeling capability. Such a capability is required to capture the detailed thermal effects that occur in the wellbore. These effects can be important as they impact wellbore pressure and temperature and thus production and injection. We recently developed a fully-coupled black-oil thermal multiphase wellbore flow model and implemented it into Stanford's General Purpose Research Simulator (GPRS). The model computes pressure, temperature, and oil, water and gas phase fractions along the wellbore as a function of time and includes treatments for slip between fluid phases, heat losses to the reservoir, and general variations of fluid properties with temperature and pressure. The purpose of this paper is to validate and test the coupled wellbore-reservoir model for challenging and realistic cases. The thermal wellbore model is first validated through comparison to field data for three-phase flow in a long well with both vertical and inclined sections. Close agreement between the model and field data is obtained. Complex wells containing multiple branches are then simulated, including a steam-water case with vaporization and condensation. The general conclusion from this work is that the new model is capable of simulating a wide variety of complex coupled reservoir-wellbore phenomena. Introduction Thermal recovery processes such as steam flooding, steam assisted gravity drainage (SAGD), and downhole electrical heating are essential for the production of heavy oil and oil sands, and they are also under investigation for the in situ upgrading of oil shales. Under any of these recovery processes, a key to efficient reservoir management and process optimization is the ability to perform accurate reservoir simulations. Although the current generation of flow simulators is able to model thermal effects within the reservoir, the wellbore flow models linked with these simulators often lack comprehensive thermal capabilities. This may limit simulation accuracy for many cases. Thus, there is a need for the development, validation and testing of comprehensive thermal wellbore flow models that are coupled to reservoir simulators. This is the overall goal of the work described in this paper. Over the last few decades, there have been many analytical and numerical models presented for nonisothermal wellbore flow. This literature is reviewed in detail by Livescu et al. (2008) so our discussion here will be brief. The analytical models include, among others, those of Ramey (1962), Satter (1965), Hasan and Kabir (1994, 1999, 2002, 2007) and Livescu et al. (2008). These models are useful in many contexts though they typically include many simplifications, such as assuming steady state flow or neglecting spatially varying inflow, which render them unsuitable for use in general simulators. Numerical models are much more general as they potentially allow for transient effects, spatial variability, slip between phases, general property variation, etc. Such models have been developed by Farouq Ali (1981), Farouq Ali and Abou-Kassem (1989), Stone et al. (1989, 2002), Holmes et al. (1998), Pourafshary et al. (2007) and Livescu et al. (2008). These models entail one-dimensional (axial) representations of the wellbore and include coupled conservation equations for multiple components (e.g., oil, water and gas), an energy equation, and a pressure drop relationship. Flow from the reservoir into the wellbore (in the case of a production well) provides source terms for the wellbore flow model. Previous formulations have been developed for both black-oil models (Stone et al., 1989; Livescu et al., 2008) and fully compositional models (Stone, 2002; Pourafshary et al., 2007).

Two Issues in Wellbore Heat Flow Modelling Along With the Prediction of Casing Temperature in the Steam Injection Wells

“…The total pressure drop inside the wellbore tubing is attributed to four major effects: hydrostatic, frictional, acceleration (kinetic) and unsteady-state and can be expressed as [ (Beggs and Brill (36) , Ali (16) , Hasan and Kabir (28) , Hasan et al (29) , Hasan et al (37) , Livescu et al (38,39) , Hasan and Kabir (30) , Hasan et al (31) , Livescu et al (33) and Livescu et al (32) ]: The temperature rise of the cement and tubular material may be taken to be a fraction of the rise in the fluid temperature at any time [Hasan and Kabir (28) and Hasan et al (29) ]. In this case, the thermal storage parameter, C T , represents the capacity of the wellbore to store or release heat as a multiple of the fluid mass and fluid heat capacity.…”

Two Issues in Wellbore Heat Flow Modeling along with the Prediction of Casing Temperature in the Steam Injection Wells

“…The total pressure drop inside the wellbore tubing are attributed to the four major effects: hydrostatic, frictional, acceleration (kinetic), and unsteady-state and can be expressed as (Beggs and Brill 1973;Farouq Ali 1981;Hasan and Kabir 2002;Hasan et al 2005;Hasan et al 2007;Livescu et al 2008aLivescu et al , 2008bLivescu et al 2009;Livescu et al 2010…”

“…The energy balance equation for multi-phase flow inside the tubing can be expressed as (Farouq Ali 1981;Hasan and Kabir 2002;Hasan et al 2005;Livescu et al 2008aLivescu et al , 2008bLivescu et al 2009;Livescu et al 2010) ( ) ( )…”

An explicit finite difference model for prediction of wellbore pressure and temperature distribution in CO2 geological sequestration

“…However, some key parameters are regarded as constant and only consider the partial coupling between pressure (flow) and temperature (thermal) in the above analytical models. Then, Livescu et al 27,28 proposed a new full coupling numerical model by using the DFM, which has a higher computational accuracy. Later, to grasp the slip between phases and to better handle unsteady flow, Shi et al 29 introduced the drift-flux model (DFM) to describe the wellbore flow.…”