T2Well—An integrated wellbore–reservoir simulator
Introduction
At its most basic level, management of subsurface fluid resources involves a system comprising the wellbore and the target reservoir. As discrete pathways through geologic formations, boreholes and wells are critical to the success of many water, energy, and environmental management operations (e.g., geologic carbon sequestration, oil and gas production, waste water disposal, compressed air energy storage, geothermal energy production, and subsurface remediation). Unlike flow in the reservoir, flow in a wellbore cannot be simply described by Darcy's Law; instead, full momentum equations have to be used. Many stand-alone simulators for two-phase flow in wellbores with various levels of sophistication have been developed independently of the many reservoir simulators, even though the flow processes in wellbores and in reservoirs are often strongly coupled in reality. For example, Lu and Connell (2008) proposed a quasi-steady numerical approach that included two-phase flow of CO2 and used a productivity index approach to couple the wellbore to the reservoir. Lindeberg (2011) included transient effects of two-phase CO2 flows in the well without coupling to the reservoir. Remoroza et al. (2011) developed an approach for geothermal applications that coupled the wellbore flow with the reservoir but assumed steady-state and single-phase flow in the well. Hadgu et al. (1995) developed a similar approach for geothermal applications using the dynamic production index method. Livescu et al. (2009) developed a fully coupled wellbore–reservoir flow simulators for oil/gas industry applications using a simplified correction term to account for the transient flow effects in the wellbore.
The main difficulties for simulating wellbore–reservoir flow as an integrated system are: (1) different governing equations apply to the wellbore and the reservoir that need to be solved efficiently in a uniform framework; (2) the significant contrast in temporal and spatial scale between the wellbore and the reservoir that results in a very challenging set of stiff partial differential equations; and (3) other complexities (e.g., dry-out) that are caused by the interactions between the wellbore and the reservoir. This paper presents a new approach for simulating non-isothermal, two-phase, and multi-components flow in wellbore–reservoir systems. The new model (T2Well) solves for flow and transport in the wellbore and reservoir together as an integrated system using the Newton–Raphson method in TOUGH2 even though flow in the well and reservoir sub-domains is controlled by entirely different physics, specifically two-phase viscous flow in the wellbore and two-phase porous media flow in the reservoir. A novel hybrid implicit scheme is used to solve the transient momentum equation in the wellbore with the Drift-Flux-Model, which makes it possible to seamlessly couple flow in the wellbore (under a wide range of flow regimes, e.g., bubbly, slug, churn, annular) with Darcy flow in the reservoir without using approximations such as those discussed above (e.g., quasi-steady state, single phase flow, or productivity index, etc.).
Section snippets
Theory
We treat the wellbore–reservoir flow problem as an integrated system in which the wellbore and reservoir are two different sub-domains where flow is controlled by the appropriate governing eq. (1D two-phase momentum equation for the wellbore, and 3D multiphase Darcy's Law for the reservoir). As a result, the governing equations for the flow processes in wellbore–reservoir system are an extended set of those used by standard TOUGH2 (Table 1). As shown in Table 1, the major differences in
Implementation
The component mass- and energy-balance equations of Table 1 are discretized in space using the conventional integrated finite-difference scheme of TOUGH2 for both the wellbore and the reservoir. Apart from the special treatment of the momentum equation in the wellbore (discussed below), time discretization is carried out using a backward, first-order, fully implicit finite-difference scheme. In the framework of TOUGH2, the discretized mass and energy conservation equations are written in terms
Verification against an analytical solution of steady-state two-phase flow
To verify the T2Well code, we first compare the numerical model against an analytical solution considering a wellbore only (Pan et al., 2011a). We consider an idealized problem of steady-state, isothermal, two-phase (air and water) flow through a vertical wellbore of 1000 m length. The parameters of the problem are given in Table 2. Thermophysical properties of this air–water system is described by TOUGH2 module EOS3.
The T2Well/EOS3 problem is run as a transient problem with adaptive time
Conclusions
We have developed a new modeling approach that can simulate nonisothermal, two-phase, and multi-component flow in wellbores connected to reservoirs as an integrated system within the framework of TOUGH2. The new model has been verified against an analytical solution and validated against field data measured during a CO2 production test. As demonstrated in the example applications, the code can be used to analyze many practical problems in various fields assuming appropriate EOS modules are
Acknowledgment
The authors also thank Christine Doughty (LBNL) for an internal review that helped to improve the paper. This work was supported, in part, by the CO2 Capture Project (CCP) of the Joint Industry Program (JIP), by the National Risk Assessment Partnership (NRAP) through the Assistant Secretary for Fossil Energy, Office of Sequestration, Hydrogen, and Clean Coal Fuels, through the National Energy Technology Laboratory, and by Lawrence Berkeley National Laboratory under U.S. Department of Energy
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