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A Multi-Timestep Domain Decomposition Method Applied to Polymer Flooding
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVII, Sep 2020, Volume 2020, p.1 - 16
Abstract
Summary
Waterflooding has been commonly used for secondary oil recovery. However, it is well known that the efficiency of oil recovery decreases when the mobility ratio is large, or the reservoir is highly heterogeneous. In these scenarios, the polymer flooding technique arises as an efficient alternative to increase the production curves. The injection of a high viscosity polymer solution reduces the mobility ratio, improving the displacement and sweep efficiency. On the other hand, mechanical retention and adsorption phenomena give rise to formation damage close to the injection wells resulting in injectivity loss. In this context, our main goal is to construct a new computational model based on domain decomposition methods capable of coupling the phenomena in different spatial and time scales during the polymer flooding. From the mathematical point of view, we consider the polymer solution a pseudo-plastic flow with the hydrodynamic model given by a non-linear Darcy’s Law where the injected fluid viscosity depends on the shear rate as suggested by the Carreau’s Law. Furthermore, the polymer movement is quantified making use of a convection-diffusion-reaction transport equation where the non-linear reactive part is due to mechanical retention and adsorption. The studied model takes formation damage into account considering that porosity and permeability depend on the retained polymer concentrations mechanically retained or adsorbed. From the computational point of view, the non-linear mathematical model is discretized making use of the finite element method together with a staggered algorithm and the Newton-Raphson method. The kinetic law for mechanical retention is post-processed by the Runge-Kutta method. It is important to highlight that polymer may accumulate in the neighborhood of the injection well on a fast time scale causing injectivity loss. Contrary to the rest of the reservoir, where large time steps and a coarse spatial mesh can be used, on the neighborhood of the injection wells small time steps and a fine spatial mesh are sometimes required. In this context, we propose the application of domain decomposition techniques to couple the near-well/reservoir domains with accuracy and lower computational cost. To this end, we apply a multi-time step domain decomposition method to couple retention and adsorption near well phenomena with polymer transport in the reservoir. Finally, we propose some numerical simulations to show the efficiency of the domain decomposition as well as to quantify injectivity during polymer flooding.
- 30 Sep 2020