Physics-informed neural networks (PINNs) are an emerging technology in the scientific computing domain. Contrary to data-driven methods, PINNs have been shown to be able to approximate and generalize well a wide range of partial differential equations (PDEs) by imbedding the underlying physical laws describing the PDE. PINNs, however, can struggle with the modeling of hyperbolic conservation laws that develop shocks, and a classic example of this is the Buckley–Leverett problem for fluid flow in porous media. In this work, we explore specialized neural network architectures for modeling the Buckley–Leverett shock front. We present extensions of the standard multilayer perceptron (MLP) that are inspired by the attention mechanism. The attention-based model was, compared to the multilayer perceptron model, and the results show that the attention-based architecture is more robust in solving the hyperbolic Buckley–Leverett problem, more data-efficient, and more accurate. Moreover, by utilizing distance functions, we can obtain truly data-free solutions to the Buckley–Leverett problem. In this approach, the initial and boundary conditions (I/BCs) are imposed in a hard manner as opposed to a soft manner, where labeled data are provided on the I/BCs. This allows us to use a substantially smaller NN to approximate the solution to the PDE.

Low salinity waterflooding (LSW) has shown promising results in terms of increasing oil recovery at laboratory scale. In this work, we study the LSW effect, at laboratory scale, and provide a basis for quantifying the effect at field scale by extracting reliable relative permeability curves. These were achieved by experimental and numerical interpretation of laboratory core studies. Carbonate rock samples were used to conduct secondary and tertiary unsteady-state coreflooding experiments at reservoir conditions. A mathematical model was developed as a research tool to interpret and further validate the physical plausibility of the coreflooding experiments. At core scale and a typical field rate of ~1 ft/day, low salinity water (LS) resulted in not only ~20% higher oil recovery compared to formation water (FW) but also recovered oil sooner. LS water also showed capability of reducing the residual oil saturation when flooded in tertiary mode. The greater oil recovery caused by LSW can be attributed to altering the wettability of the rock to less oil-wet as confirmed by the numerically extracted relative permeability curves.

Low salinity polymer (LSP) flooding is getting more attention due to its potential of enhancing both displacement and sweep efficiencies. Modeling LSP flooding is challenging due to the complicated physical processes and the sensitivity of polymers to brine salinity. In this study, a coupled numerical model has been implemented to allow investigating the polymer-brine-rock geochemical interactions associated with LSP flooding along with the flow dynamics. MRST was coupled with the geochemical software IPhreeqc. The effects of polymer were captured by considering Todd-Longstaff mixing model, inaccessible pore volume, permeability reduction, polymer adsorption as well as salinity and shear rate effects on polymer viscosity. Regarding geochemistry, the presence of polymer in the aqueous phase was considered by adding a new solution specie and related chemical reactions to PHREEQC database files. Thus, allowing for modeling the geochemical interactions related to the presence of polymer. Coupling the two simulators was successfully performed, verified, and validated through several case studies. The coupled MRST-IPhreeqc simulator allows for modeling a wide variety of geochemical reactions including aqueous, mineral precipitation/dissolution, and ion exchange reactions. Capturing these reactions allows for real time tracking of the aqueous phase salinity and its effect on polymer rheological properties. The coupled simulator was verified against PHREEQC for a realistic reactive transport scenario. Furthermore, the coupled simulator was validated through history matching a single-phase LSP coreflood from the literature. This paper provides an insight into the geochemical interactions between partially hydrolyzed polyacrylamide (HPAM) and aqueous solution chemistry (salinity and hardness), and their related effect on polymer viscosity. This work is also considered as a base for future two-phase polymer solution and oil interactions, and their related effect on oil recovery.