Daqing Oilfield has successfully achieved the largest scale chemical flooding industrial application in the world, the annual oil production by chemical flooding has been more than 10 million tons for 20 years. The reservoir numerical simulation technology has played an important role to ensure better oil recovery effect for chemical flooding. With the continuous expansion of chemical flooding application scale in Daqing Oilfield, the reservoir numerical simulation for chemical flooding has ever encountered a series of new challenges need to be resolved, such as mathematical characterization of oil displacement process for chemical flooding, computation speed and simulation accuracy, etc.
This paper focuses on the existing difficulties in the reservoir numerical simulation for chemical flooding, developing a series of novel techniques for chemical flooding numerical simulation suitable for large scale field application of chemical flooding. Firstly, based on the new cognation of chemical flooding theory in recent years, a chemical flooding mathematical model has been developed in order to simulate the complex oil recovery process mechanism of chemical flooding more accurately, the aspect of oil displacement mechanism description, in addition to the mobility control and capillary desaturation processes, but also adds oil displacement model for chemical flooding which includes: polymer elasticity improves microscopic oil displacement efficiency, the multiple molecular weight polymers process mechanism, compound synergistic effect of chemical flooding process with low surfactant concentration, multi-surfactant compound effect, chemical competitive adsorption, reservoir wettability altering, alkali corrosion and scaling. Secondly, based on operator splitting, potential characteristics, and multi-grid method, a fast solution scheme with high stability for complex mathematical model of chemical flooding has been developed, increasing the computation speed to a large extent. Thirdly, a series of numerical simulation parameters measuring experiments have been carried out, obtaining the accurate parameters for chemical flooding numerical simulation. Finally, based on Ensemble Kalman filter algorithm, a data assimilation method has been constructed, increasing numerical simulation history matching accuracy for chemical flooding.
The established reservoir numerical simulation novel method for chemical flooding has been successfully applied to chemical flooding projects in Daqing Oilfield, and an application case of the chemical flooding project in Daqing Oilfield is given in this paper, the numerical simulation results for chemical flooding demonstrate that established reservoir numerical simulation technology increases both the computation speed and simulation accuracy.

A more efficient formulation of the undrained split iterative coupling scheme is derived for solving the coupled fluid flow and geomechanics problem. In the standard undrained split scheme, the mechanics problem is solved first then followed by the fluid flow problem within every iterative coupling iteration (Mikelic et al. 2013). The scheme will not advance to the next timestep until the current iterative coupling iteration is converged. In this work, we will exploit the inherent parallel-in-time nature of the mechanics solve only (Borregales et al. 2018), which leads to a partially parallel in time scheme. This is a natural extension of the multirate (i.e. multiple timestep sizes) formulation of the undrained split iterative coupling scheme (Kundan et al. 2016, Almani et al. 2019) in which the fluid flow problem takes a sequence of fine timesteps within one relatively coarser geomechanics timestep. However, in the proposed approach, the fluid flow problem takes a sequence of fine timesteps, and the mechanics problem assumes the same sequence of fine timesteps, which are solved in parallel within one coupled iteration. In this work, a rigorous theoretical investigation of the proposed algorithm is carried out and the convergence analysis is established for heterogeneous poro-elastic media. The approach has shown to be contractive, and the localized contraction estimates are determined, and compared against the standard multirate undrained split scheme. This new formulation uses the same timestep size for both fluid flow and geomechanics without sacrificing the computational efficiency of the multirate scheme. Moreover, it will result in a more accurate solution due to the fact that both fluid flow and geomechanics share the same timestep size. This is the first time in literature the convergence of a partially parallel in time formulation of the undrained split iterative coupling scheme is established.

[1] Mikelic A., and Wheeler M. F. Convergence of iterative coupling for coupled flow and geomechanics. Computational Geosciences. 2013; 17(3):455-461.
[2] Kumar K., Almani T., Singh G., and Wheeler M.F. Multirate undrained splitting for coupled flow and geomechanics in porous media, Springer International Publishing, Cham 2016; pp. 431–440.
[3] Almani T., Manea A., Kumar K., and Dogru A. Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media”. Computational Geomechanics, 2019.
[4] Borregales M., Kumar K., Radu F. A., Rodrigo C., and Gaspar FJ. A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model. Comput Math Appl. 2018; 77(6):1466-1478.

In this study we introduce a new method of numerical simulations of fluid flows, in which a certain property of each individual volume (e.g., shear viscosity) depends on the time elapsed since this particular volume entered the flow domain (so-called residence time). In oilfield services applications such fluids are used for well cementing (cement slurry) and hydraulic fracturing (water-based fluids containing cross-linked polymer molecules). Novelty of the method is that it uses a purely Eulerian approach for fluid flow description instead of Lagrangian approaches typically used in existing numerical studies to resolve tracking of individual fluid volumes.
The method is based on representing the fluid as a mixture of fictitious fluids, which are being transformed to each other according to a certain time-variation law. By changing the properties of introduced fluids, it is possible to adjust the property of their mixture to any arbitrary residence time dynamics. The suggested method is applicable to numerical schemes that are stable with respect to small perturbations to time-dependent parameters. Multiple implementation strategies are available depending upon the base mathematical model describing fluid flow. To avoid links with particular governing equations describing the flow and numerical schemes, only general mathematical problem formulation is provided. This also allows for extension of the method to other fields of studies.
Verification of the developed numerical algorithm is carried out for two flow configurations, namely, 1D flow of incompressible fluid with a constant velocity and time-dependent shear viscosity and transport of proppant in a cross-linked polymer fluid through an open hydraulic fracture described using 2D aperture-averaged model. First case demonstrates that even for fluids with unrealistic dependence of material properties on residence time, the proposed method provides accurate results using reasonable number of fictitious fluids. On the basis of second case we show the effect of residual time-dependent fluid rheology on proppant transport as compared to time-dependent rheology (so that in the whole flow domain the rheology parameters are similar at each time instant) and illustrate the necessity to resolve residence-time dependencies of carried fluid properties for accurate proppant placement predictions.
Finally, we discuss new algorithm’s advantages, limitations as well as time- and memory- asymptotics.
The proposed method can be used to develop effective numerical algorithms for simulations of various processes accompanying oil field development including well cementing and hydraulic fracturing of hydrocarbon-bearing formations, in which fluid properties depend on residence time and require tracking of material volumes.