A Generalized Wellbore and Surface Facility Model, Fully Coupled to a Reservoir Simulator
- B.K. Coats (Landmark Graphics) | G.C. Fleming (Landmark Graphics) | J.W. Watts (Landmark Graphics) | M. Rame (Landmark Graphics) | G.S. Shiralkar (BP)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2004
- Document Type
- Journal Paper
- 132 - 142
- 2004. Society of Petroleum Engineers
- 4.3.4 Scale, 5.5 Reservoir Simulation, 2.2.2 Perforating, 4.1.2 Separation and Treating, 5.5.8 History Matching, 5.6.9 Production Forecasting, 5.5.1 Simulator Development, 3.3.6 Integrated Modeling, 5.5.5 Evaluation of uncertainties, 4.1.5 Processing Equipment, 2.3 Completion Monitoring Systems/Intelligent Wells, 4.2 Pipelines, Flowlines and Risers, 5.3.9 Steam Assisted Gravity Drainage, 5.1.5 Geologic Modeling, 1.6 Drilling Operations, 1.7.5 Well Control
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The formulation of a black-oil or compositional fully coupled surface and subsurface simulator is described. It is based on replacing the well model in a conventional reservoir simulator with a generalized network model of the wells and facilities. This allows for representation of complex wellbore geometry and downhole equipment. The method avoids the inefficiencies and/or inaccuracies of other coupled models, in which wells and facilities are treated as separate domains or in which the global system is not solved simultaneously. Example cases demonstrate the performance of the model for cases with simple and segmented wellbores (with and without facilities).
Introduction and Background
The objective of our work is to develop an integrated reservoir and facility simulator that is as efficient and general as possible. This involves many technologies. This paper focuses on the primary aspect of our new model that differentiates it from previous work, specifically the manner in which domain decomposition is applies to simulation of the coupled system of reservoirs, wells, and facilities.
Conventional Well Model.
A basic example of domain decomposition is the well model in a reservoir simulator. A simple representation of a reservoir simulator is shown in Fig. 1. In the well model, within each simulator Newton iteration, each well is decoupled from the reservoir through reservoir boundary conditions consisting of fixed current iterate values of the perforated grid-cell variables. Well rates and pressures are determined subject to the well boundary conditions, which apply at the boundary with the facilities. At the end of each simulator Newton iteration, the reservoir and well equations are solved simultaneously. Most current reservoir models implicitly represent well rates in terms of an additional variable (to the primary reservoir cell variables), well bottomhole pressure. Conventional well models treat the wellbore as a mixed tank, but many include methods for explicit inclusion of pressure losses caused by friction and acceleration through various approximations and assumptions.
Modeling of Advanced Wells.
The advent in recent years of horizontal- and multilateral-well drilling technology and of complex wellbore configurations resulting from implementation of intelligent completion systems has resulted in the development of increasingly sophisticated well models for use in reservoir simulation. The complex geometries, increased lengths of perforated intervals, and potential presence of downhole-flow-control devices in these wells, along with the need to more accurately model low-potential recovery methods such as steam-assisted gravity drainage, have resulted in the requirement of a much more detailed representation of wellbore composition, rate, and pressure distributions than is possible in conventional well models.
Stone et al.1 presented a three-phase, thermal, segmented wellbore casing and tubing model implicitly coupled to a thermal dead-oil reservoir model for improved simulation of steam-assisted gravity drainage with dual horizontal wells. Reservoir mass and energy balances; segmented wellbore energy, momentum, and mass balances; and the perforation-rate equations were solved simultaneously through Newton iteration. Capacitance was represented in the wellbore control volumes, and simultaneous annular/tubular flow was modeled for a given wellstream. The authors found that simulator timestep size was impractically limited for field-scale problems when wellbore conditions were changing rapidly. More recently, Holmes et al.2 presented a black-oil model with an implicit configurable segmented wellbore. Four primary variables were included for each wellbore segment - a weighted total flow rate, weighted fractional flows of water and gas, and pressure. The corresponding equations were three component mass balances and a hydraulics relationship for each segment (representing pressure drop caused by gravity, friction, and acceleration) through correlations or hydraulics tables. The pressure equation for the segment terminating at the well's datum depth was replaced with the limiting boundary condition - either a rate constraint, a bottomhole pressure constraint, or, for wells on tubinghead pressure control, a hydraulics relationship for the tubing represented by hydraulics tables. Tables also could be used for pressure drops across flow-control devices. Stone et al.3 then extended this work to compositional and thermal applications. We note that these advanced wellbore models are very similar to the network models of facilities.
Coupled Surface/Subsurface Models.
In reservoir models, flow in the reservoir and flow between the reservoir and wellbores is decoupled (either bottomhole or at the wellheads) from flow through the remainder of the production and injection facilities by specifying pressure and/or rate constraints for each well. If individual-well rates and pressures are known from production history, then the decoupled reservoir/well model is sufficient to match historic reservoir behavior by specifying and matching the observed boundary conditions as a function of time. However, when used in predictive mode for reservoirs with gathering and distribution networks, the proper decoupled well boundary conditions are in general variable in time and dependent on reservoir behavior, equipment performance, production strategy, hydraulics relationships, and pressure, rate, and source composition constraints that may be applied within the surface network. When production is controlled in the surface facilities, it is in general necessary (or at least desirable) to include the facilities in a full-field model to predict how the otherwise specified boundary conditions will vary in time.
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