Summary
A coupled reservoir-geomechanics model is developed to simulate the enhanced production phenomena in both heavy-oil reservoirs (northwestern Canada) and conventional oil reservoirs (i.e., North Sea). The model is developed and implemented numerically by fully coupling an extended geomechanics model to a two-phase reservoir flow model. Both the enhanced production and the ranges of the enhanced zone are calculated, and the effects of solid production on oil recovery are analyzed. Field data for solid production and enhanced oil production, collected from about 40 wells in the Frog Lake area (Lloydminster, Canada), are used to validate the model for the cumulative sand and oil production. Our studies indicate that the enhanced oil production is mainly contributed (1) by the reservoir porosity and permeability improvement after a large amount of sand is produced, (2) by higher mobility of the fluid caused by the movement of the sand particles, and (3) by foamy oil flow. A relative permeability reduction after a certain period of production may result in a pressure-gradient increase, which can promote further sand flow. This process can further improve the absolute permeability and the overall sand/fluid slurry production. Our numerical results simulate the fact that sand production can reach up to 40% of total fluid production at the early production period and decline to a minimum level after the peak, generating a high-mobility zone with a negative skin near the wellbore. Such an improvement reduces the near-well pressure gradient so that the sanding potential is weakened, and it permits an easier path for the viscous oil to flow into the well. Our studies also suggest that the residual formation cement is a key factor for controlling the cumulative sand production, a crucial factor that determines the success of a cold production operation and improved well completion.
Introduction
Field results from many heavy-oil reservoirs in northwestern Canada, such as Lindbergh and Frog Lake in the Lloydminster fields, suggest that primary recovery is governed mainly by the processes of sand production and foamy-oil flow.1–3 To manage production in such reservoirs, the challenge we face is optimizing production so that sand production is under control. For decades, industries have developed various highly effective tools for sand control. In practice, however, sand control often results in reduced oil flow or no production at all, particularly in heavy-oil reservoirs. For example, it has been observed that an average oil production of only 0.0 to 1.5 m3/d can be achieved in a well in which no sand production is allowed, while 7 to 15 m3/d oil may be produced with sand production.4 A significant improvement in production also has been reported by allowing a certain amount of sand produced before gravel packing in the high-rate production well in conventional reservoirs.5 It seems that sanding corresponds to a high oil production in these reservoirs, as sand production either increases the reservoir mobility or allows the development of highly permeable zones such as channels (wormholes).1 Encouraging sand production to enhance oil production, on the other hand, increases oil production costs owing to environmental problems. Consequently, neither trying to eliminate the sand production completely nor letting sand be produced freely, we attempt to develop a quantified model linking sand rate and reservoir enhancement so that we can forecast the economic outcome of such an operation. The investigation of sand production has been extensive, but it has been limited primarily to the areas of incipience of sand production and control. Sand arching and production initiation from a cavity simulating a perforating tunnel were studied, and a critical flow rate before sanding was found for single-phase steady-state flow.6 Such a study was extended to gas reservoirs, in which the gas density is a function of pressure,7 and to those formations subject to nonhydrostatic loading.8,9 Studying the enhanced production and the cumulative sand production, a series of simplified models for massive sand production have been developed.10,11 Similar models based on a coupled classic geomechanics model were also proposed thereafter.12,13 Because these aforementioned sand-production models are somewhat restricted by the fact that they are simplified by analytical methods, and in reality reservoir formations are much more complex (i.e. nonlinear behaviors), a numerical model coupling a multiphase transient fluid flow to elastoplastic geomechanical deformation is thus developed in this article; its purpose is to simulate these major nonlinear effects. According to the proposed model, a corresponding plastic yielding zone (or a disturbed zone) propagates into reservoir formation because of the transient fluid pressure diffusion, and the corresponding effective stresses change near a wellbore. A possible absolute permeability change inside the yielding zone is also considered, as dilatant deformation developed may enhance the permeability in the plastic zone. As a primary unknown, saturation is assumed to change with the induced pore-pressure change. The relative permeability is updated by the saturation, which in turn changes the response of the pore pressure and the skeleton deformation.
A continuum mechanics approach is used in our calculation. Rather than characterizing each random wormhole proposed,1,4,5 we impose a homogeneous medium with an average permeability to make the numerical solutions manageable. The wormholes or geomechanical dilatation zone can be represented by a higher-permeability region in the plastic yielding zone owing to porosity enhancement,1 and solid flow is considered as a continuous moving phase along the transient fluid flow. Alternatively, a sand erosion model was introduced, and the geomechanics coupling to a single-phase flow was presented previously.14,15
Analysis of Characteristics of Damping Valve Based on High-Order Discrete Scheme