A Numerical Model Coupling Reservoir and Horizontal Well-Flow Dynamics: Transient Behavior of Single-Phase Liquid and Gas Flow
- Ronaldo Vicente (Petrobras) | Cem Sarica (U. of Tulsa) | Turgay Ertekin (Pennsylvania State U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2002
- Document Type
- Journal Paper
- 70 - 77
- 2002. Society of Petroleum Engineers
- 6.5.2 Water use, produced water discharge and disposal, 5.5.1 Simulator Development, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.3.2 Multiphase Flow, 5.5 Reservoir Simulation, 1.6 Drilling Operations, 2.2.2 Perforating, 2 Well Completion, 4.6 Natural Gas, 3.3.1 Production Logging, 5.4.6 Thermal Methods, 2.4.3 Sand/Solids Control, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.6.8 Well Performance Monitoring, Inflow Performance, 5.2 Reservoir Fluid Dynamics, 1.14 Casing and Cementing, 4.1.2 Separation and Treating, 5.6.4 Drillstem/Well Testing, 3.2.5 Produced Sand / Solids Management and Control
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A fully implicit, 3D simulator with local refinement around the wellbore is developed to solve reservoir and horizontal well flow equations simultaneously for single-phase liquid and gas cases. The model consists of conservation of mass and Darcy's law in the reservoir, and mass and momentum conservation in the wellbore for isothermal conditions. The coupling requirements are satisfied by preserving the continuity of pressure and mass balance at the sandface. The proposed simulator is tested against and verified with the results obtained from a commercial code ECLIPSE-100, and available public domain simulators and semianalytical models.
The model can be used to simulate the transient pressure and flow rate behavior of both the reservoir and the horizontal wellbore. Traditional decoupling of the wellbore transients from the reservoir transients does not capture the horizontal well pressure and flow rate transients at early times because the interaction between the reservoir and wellbore is inherently neglected. Simulation runs with the proposed model reveal the actual characteristics of horizontal wellbore storage and unloading, as well as flow pattern determination during transient well testing using pressure derivative curves. The effects of permeability, formation thickness, well length, and fluid compressibility are also studied.
With the recent developments in drilling technology, horizontal well drilling and completions have found widespread application and have become an attractive and well-established alternative in field development. Indeed, because of their successful performance in increasing productivity, adding new reserves and improving the overall cost-effectiveness of field operations, horizontal wells are no longer a special application in many fields, but actually a routine in both new and mature developments.1 When compared with conventional vertical or deviated wells, horizontal wells increase productivity significantly by enhancing the reservoir contact area and creating smaller drawdown. Therefore, horizontal wells are ideally suited for reservoirs with low permeability, high anisotropy, thin layers, and natural fractures, or in reservoirs experiencing gas or water coning and sand production problems. In addition, horizontal wells can be more effective in enhanced oil recovery projects, such as steam injection, by improving the inflow treatment performance, and in offshore environments by drilling several horizontal wells from a central platform.
Although a number of numerical and analytical tools have been developed to investigate the flow behavior and predict the performance of horizontal wells, several issues that can significantly affect performance predictions have not been addressed properly. One of these issues is the indiscriminate use of steady-state or pseudosteady-state models when transient conditions prevail. In such cases, the former models are inappropriate and lead to erroneous predictions.2 Thuren et al.3 have presented that a reservoir can operate completely under transient conditions during the entire water injection operation.
Another issue is the improper treatment of wellbore flow and reservoir-wellbore interaction. The earlier studies assuming constant pressure along the horizontal wellbore treated the horizontal well as an infinite-conductivity medium. However, as discussed by Ozkan et al.,4 the infinite-conductivity idealization is applicable only in low-productivity systems in which the pressure losses in the wellbore are negligible compared to the pressure decreases encountered in a drawdown. Utilizing a simplified steady-state wellbore model, they also showed that the pressure losses in the wellbore affect the productivity of a horizontal well significantly when the wellbore pressure losses and the drawdown have similar orders of magnitude. Furthermore, unlike the results obtained with the infinite-conductivity assumption, the flux distribution along the wellbore has been shown to be asymmetric, with a greater amount of fluid entering near the downstream end of the wellbore. Therefore, especially for high flow rates, the wellbore hydraulics can play an important role in the production behavior of a horizontal well, and they should not be neglected.
Several researchers have attempted to include wellbore hydraulics in horizontal well performance studies, and a review of the literature reveals a variety of methods addressing the inflow performance and wellbore hydraulics calculations. In 1989, Dikken5 presented a model coupling a homogeneous reservoir to a horizontal well for steady-state and single-phase flow using a material balance relationship across the boundary. Blasius' equation was applied for computing pressure losses in turbulent flow case. By introducing a constant productivity index along the wellbore, the problem was solved analytically for an infinitely long horizontal well and numerically for a finite length well.
Several studies attempting to quantify the productivity properly and to predict the performance of horizontal wells more realistically came after Dikken's pioneering work. Novy6 proposed a generalized model by developing equations in cylindrical coordinates, assuming single-phase (liquid or gas) and steady-state flow conditions. The flow model was formulated as a boundary value problem, and a solution was obtained by implementing a numerical finite-difference scheme. Landman7 extended Dikken's model, describing the specific productivity of the well as a function of the permeability of the formation and the perforation density. Ozkan et al.4 presented a rigorous semianalytical model that couples wellbore and reservoir fluid flow and incorporates the effect of laminar and turbulent flow regimes in the wellbore. However, transient conditions in the horizontal wellbore were not considered.
Suzuki8 presented a finite-conductivity solution of horizontal well for pressure-transient behavior using a semianalytical method. Although the model includes the wellbore-transient behavior, it assumes incompressible fluid flow in the wellbore. Dickstein et al.,9 based on a system of conservation equations, proposed a fully implicit numerical model with local grid refinement around the wellbore to solve the coupled horizontal well-reservoir flow system for single-phase slightly compressible fluids.
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