# Using Low Salinity Waterflooding to Improve Oil Recovery in Naturally Fractured Reservoirs
## 3 Setup of Numerical Models
### Single Matrix Block Models  
Most often, the dual-porosity model is employed to simulate the fluid flow behaviour in naturally fractured reservoirs [1; 33; 37; 38]. The model assumes two solution nodes in every gridblock with distinct properties that represent the matrix medium and fractures, respectively. The flow occurs between the gridblocks in the reservoir model through the fracture nodes only. Meanwhile, matrix nodes can solely exchange the fluid locally to the corresponding fracture node within the gridblock. Previous works have demonstrated that the dual-porosity model tends to overestimate the fluid exchange between the matrix and fractures and, hence, overestimate the matrix recovery (e.g., [1; 39]). In contrast, fine-scale modelling can provide an accurate prediction of the fluid exchange rate between the matrix and fractures. Therefore, it is necessary to assess the impact of the low salinity waterflooding using both modelling scales.  
A single matrix block with the dimensions \(5\) ft \(\times\) 8 ft \(\times\) 12 ft was used to construct two models to evaluate the effect of the low salinity waterflooding on the matrix recovery. The first model represents a discretised matrix scheme, with a 1 ft resolution in the \(x_{\text{-}}\), \(y_{\text{-}}\), and z-direction, respectively, with a total number of 480 cells in the simulation model. Meanwhile, the surrounding fractures have also been represented explicitly at the grid boundary in a discretised form, as illustrated in Figure 5A. The fine-scale model can be simulated using a single-porosity model. In the second model, the matrix and fractures were modelled in a dual-porosity scheme with two cells only, one for the matrix and the second for fractures, as shown in Figure 5B. The second model can be simulated using the dual-porosity model.  
The single block model in Figure 5B represents the smaller element in the dual-porosity model. The dimensions of the matrix blocks are determined through fracture intensities, which determine their sizes, hence, oil recovery [40; 41]. This model depicts the fluid flow behaviour using the dual-porosity model, which can be linked to the intermediate scale model or a full-field scale model. On the other hand, the fine-scale model can mimic the recovery mechanisms more precisely. It has the ability to capture the transient effect and saturation front, which the dual-porosity model has often failed to do.  
In conventional waterflooding, it has been frequently observed that the injected water breaks through in the producers due to the high permeability of fractures leaving a significant amount of oil behind in the matrix cells. Similarly, the injected low salinity brine sweeps the oil from fractures much faster than sweeping the oil from the matrix cells. Then, a fluid exchange process occurs due to capillary imbibition, gravity drainage, and viscous forces. These conditions were mimicked by assuming fractures to be fully saturated with the injected low salinity brine. Meanwhile, the matrix is saturated with oil at connate formation water saturation. A straight-line relative permeability was assigned to fractures, and a relative permeability set of a fractured formation, as illustrated in Figure 1,  
Figure 5: An illustration of the single matrix block model. (**A**) A discretised matrix block (fine-scale model), which can be simulated using a single-porosity model, after [PERSON] et al. [2]. (**B**) Single block model, which can be simulated using the dual-porosity model.  
has been used for the matrix. A prediction of 10 years was carried out to obtain the fluid exchange between the matrix and fractures under a low salinity waterflooding scheme. Further model input data and details can be found in [PERSON] et al. [2].