The extension of a previously reported well model to compositional and thermal applications is discussed. This multisegment, multibranching wellbore model has been fully coupled to a commercial reservoir simulator that can operate in black-oil, compositional, or thermal modes. In this paper, the discussion will focus on thermal, heavy-oil applications in which simulation requires a better representation of the wellbore geometry and the physics of fluid flow and heat transfer.


Gravity-drainage processes with possible steam (SAGD) or gas vapor (VAPEX) assistance and other recovery technologies often require the use of long horizontal wells with flow in an inner tubing and outer annulus.1–3

Thermal studies that simulate horizontal wells have been discussed by many authors. Recovery techniques include cyclicsteam projects,4–10 dual-well SAGD,11 and single-well SAGD.12 In these studies, the oils are heavy (970 to 1014 kg/m3; 14 to 8°API), with viscosities ranging from 2,000 cp at 32°C in California fields up to 1,000,000 cp at 12°C for oils found at the UTF project13 in the Athabasca tar sands deposit. These studies have, for the most part, used the conventional wellbore line source/sink model available in any thermal simulator.

Simulation technology for horizontal wells has improved dramatically since the late 1980s. At this time, Stone et al.14 described a horizontal well model that featured a mechanistic multiphase fluid-flow model in the wellbore and allowed flow simultaneously in an inner tubing and outer annulus. This was designed to handle simulations in the near-wellbore region of a dual-well SAGD process and, because of the more detailed flow regime map, could not handle larger-scale simulations for stability reasons. Also during this time period, Long et al.15 carried out the Seventh SPE Comparative Solution Project concerning the modeling of horizontal wells in reservoir simulation. A variety of methods was used by the participants to model the inflow into the horizontal well model. These included the use of an inflow performance relationship (IPR) with a separate well model or direct coupling by modeling the well as part of the grid. Similarly, there were various wellbore hydraulics models ranging from a constant-pressure line sink to friction pressure-drop relations or simple functional fits of published holdup correlations. All of these horizontal well models were designed to run robustly and stably in large-scale field simulations. However, some were limited in their ability to calculate a multiphase pressure drop, others in not allowing the wellbore model geometry to correspond to the engineering design of the well rather than to the simulation grid. Some methods allowed multiphase pressure drops with explicit updates or other approximations.

Recently, Tan et al.16 have described a fully coupled discretized thermal wellbore model with the ability to simulate flow in casing/annulus wellbore cells. Estimates of the relative flow rates are made based on phase saturations and straight-line relative permeability curves. These estimates are passed to a subroutine that calculates flow rates from the correlated Beggs et al.17 measurements. Wellbore cells are connected to reservoir cells.

A multisegment well model that can simulate flow in advanced wells was discussed by Holmes et al.18,19 This model, implemented in a commercial black-oil simulator, is able to determine the local flowing conditions (the flow rate and pressure of each fluid) throughout the well. It allows for pressure losses along the wellbore and across any flow-control devices. In addition to being fully implicitly coupled, with crossflow modeling and the standard group control facilities, horizontal wells, multilateral wells, and "smart" wells containing flow-control devices can also be modeled. The trajectory is not constrained by the simulation grid. For example, the wellbore may run outside the grid or across layers. Properties and geometry can be updated at any time in the simulation.

In this paper, we first describe the implementation and enhancements to the implicit multisegment well model discussed in Ref. 18 that allow this model to run in compositional and thermal modes. In these modes, the equation of state (EOS) or thermal K-value treatment of the fluid pressure/volume/temperature (PVT) is extended to the wellbore flow. Phase volumes are computed in each segment and are then used to calculate the multiphase pressure drop. In thermal mode, an enhancement allows the definition of heat transfer coefficients, which permit heat loss to the reservoir, to another segment, or to the overburden. Another enhancement allows individual segments to inject or produce fluids, which permits the direct modeling of gas lift, downhole water pumps, or circulating wells, available in any mode. It is important in compositional, and especially thermal, wellbore simulations to provide an accurate initial estimate of the well solution; otherwise, there can be convergence problems. A method for predicting the initial state within the well is also shown later.

We then present four case studies. Each case study has been set up from published engineering analyses of fields in western Canada and California, U.S.A. The well model used in these studies is considerably more detailed than that in the original published simulation work. Not only are the wellbore hydraulics more accurately modeled with multiphase flow models, but the geometry of the wells is also specified in more detail. Wellbore geometry includes the ability to run the well outside the simulation grid, allowing the modeling of heat loss from a steam-injection well to the formation, between the surface and the simulation grid. Also, an undulating well trajectory can be specified and is demonstrated in one of the studies. Fluid flow down an inner tubing and back along an outer completed annulus is demonstrated in three of the studies, in which heat transfer occurs between the inner tubing and the outer annulus and between the annulus and the formation. Two of these studies contain a segment at the heel of a horizontal annulus that removes fluids to an external sink, allowing part of the circulating fluids to return to the surface while the remainder are injected, produced, or stored in the wellbore. Where possible, differences are shown between the multisegment model and a standard line source/sink model that demonstrate the effects of modeling the improved wellbore physics.

Description of the Multisegment Well Model

The multisegment well model reported by Holmes et al.18 was originally implemented in a black-oil simulator. It uses four main variables: a total fluid-flow rate through the segment, weighted fractional flows of both water and gas, and pressure in the segment.

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