Using Low Salinity Waterﬂooding to Improve Oil Recovery in Naturally Fractured Reservoirs

: Low salinity waterﬂooding is an e ﬀ ective technique to accelerate and boost oil recovery. The impact of this technique has been investigated widely in laboratories for various scales and rock typing, most of which have demonstrated a potential improvement in oil recovery. This improvement has been attributed to several chemical and physical interactions that led to a change in the wettability to become more water-wet, as well as a reduction in the residual oil saturation. Meanwhile, it is rare to ﬁnd a discussion in the literature about the e ﬃ ciency of low salinity ﬂooding in naturally fractured reservoirs. Therefore, in this work, we investigate the potential advantages of this method in fractured reservoirs using numerical simulations. A new approach to estimate the weighting factor using a tracer model has been proposed to determine the brine salinity and, hence, its properties in the mixing region. We have also used the relative permeability curves as a proxy for any physical and chemical mechanisms which are not represented explicitly in the model. The simulation outcomes highlighted the advantage of low salinity waterﬂooding in fractured reservoirs. An increment in oil recovery by 10.7% to 13% of Stock Tank Oil Initially In Place (STOIIP) was obtained using the dual- and single-porosity model, respectively. Therefore, the low salinity waterﬂooding technique represents a promising low-cost, e ﬀ ective method in fractured reservoirs.


Introduction
Carbonate reservoirs in the Middle East hold a significant proportion of remaining conventional oil reserves, most of which are classified as naturally fractured [1,2]. These reservoirs are well known for their low recoveries compared with their counterpart clastic unfractured reservoirs [3]. Most of these reservoirs have already produced for several decades using natural depletion mechanisms or undergone secondary conventional waterflooding projects. However, developing fractured reservoirs requires an affordable technique that is able to sweep the oil and improve recoveries, as well as controlling the early breakthrough of water that is often observed in conventional waterflooding. It is often the case that enhanced oil recovery techniques are not feasible due to the high cost of such projects.
Low salinity waterflooding is a promising low-cost technique to increase oil recovery. Experimental outcomes have proven a significant improvement in oil recovery when low salinity waterflooding schemes were applied [4]. During low salinity waterflooding, multiple recovery mechanisms have been attributed to be responsible for the increment in oil recoveries, such as cation exchange [5,6], an increase in the pH [7][8][9], changes of the charges at the rock surfaces [10], wettability alteration [11][12][13][14],

1.
A new weighting factor has been proposed based on a 1D tracer model.

2.
The results of reported coreflood experiments were utilised to generate the relative permeability sets of the flooded regions by low salinity brine.

3.
Various scales were employed to demonstrate the impact of the low salinity waterflooding in fractured reservoirs as well as to highlight the influence of the dual-porosity model on the simulation outcome.
Initially, we collected and evaluated the published results of coreflood experiments to conclude a range of change to the system wettability (in the form of saturation exponents) and the residual oil saturation (e.g., the published results of [20,21,23,25,26]). Then, we proposed a new approach to determine the weighting factor using a tracer model, which can improve the simulation accuracy in the mixing zone. On the other hand, it is challenging to model the chemical interactions that have been proposed to occur during low salinity water flooding at sector or field scales accurately. Therefore, we utilised the relative permeability curves as a proxy for any chemical and physical interactions that have not been represented explicitly in the simulation model. The generated sets of relative permeability Table 1. An illustration of the brine properties using an increment step of 20% in the normalised salinity. The table is based on a maximum salinity of 100,000 ppm and a minimum of 3000 ppm, using a linear formula and the conditions of the Qamchuqa reservoir. This table (except Columns 1 and 2) is utilised in the simulation model to calculate the brine properties in the mixing region. In the later work, both water and brine will be used interchangeably for the injected water or formation water, and they have the same meaning and the term low salinity has been shortened in the figures to LoSal for simplicity. However, the above-explained methodology has demonstrated the following points:

The Relative Permeability of the Flooded Regions by Low Salinity Brine
The results of the published laboratory experiments have been collected and analysed to calculate a percentage of change in the parameters of the relative permeability. The estimated rate of change in each variable due to the impact of the low salinity brine is summarised in Table 2. The listed percentages of change were used to generate three sets of the relative permeability to address the uncertainty in the laboratory results using Corey Equations (1) and (2). The calculated flow curves of the regions flooded by the low salinity brine exhibited a shift to the right (i.e., towards a more water-wet state), as illustrated in Figure 1.
(1) k rw_altered = (k rw_a ) S or S w − S wc 1 − S wc − S or_a n w_a (2) where: k ro_altered , k rw_altered Relative permeability of oil and water, respectively, for the region flooded by low salinity. k ro at S wc Oil relative permeability at connate water saturation. k rw_a at S or Water relative permeability at residual oil saturation after low salinity waterflooding. S w , S wc Water saturation and connate water saturation.

S or_a
Residual oil saturation of the flooded region by low salinity. n o_a , n w_a Saturation exponents of oil and water.
The units of the above parameters are fraction except for the saturation exponents which are dimensionless. Table 2. Quantitative summary of the impact of the low salinity on the oil recovery through relative permeability parameters which was calculated from the published results of [20,21,23,25,26]. The Minimum and Maximum parameter values were computed from the references' results while the average was obtained arithmetically.  Table 2. Quantitative summary of the impact of the low salinity on the oil recovery through relative permeability parameters which was calculated from the published results of [20,21,23,25,26]. The Minimum and Maximum parameter values were computed from the references' results while the average was obtained arithmetically. (1) where: kro_altered, krw_altered Relative permeability of oil and water, respectively, for the region flooded by low salinity.

kro at Swc
Oil relative permeability at connate water saturation. krw_a at Sor Water relative permeability at residual oil saturation after low salinity waterflooding.

Sw, Swc
Water saturation and connate water saturation.

Sor_a
Residual oil saturation of the flooded region by low salinity. no_a, nw_a Saturation exponents of oil and water. The units of the above parameters are fraction except for the saturation exponents which are dimensionless. Figure 1. The generated relative permeability sets for a fractured formation using the calculated ranges in Table 2 for the saturation exponents and saturation endpoints. The black curves represent the original relative permeability set, while the coloured curves represent the relative permeability of the flooded region by low salinity brine for three levels of alterations.

Determination of Weighting Factor (WF)
The weighting factor plays a significant role in determining the salinity of the brine mixture, hence, its properties, as illustrated in Table 1. It controls the dilution process or blending between the high salinity and the injected low salinity water in the mixing zone. Al-Ibadi [24,27] has referred to a linear relationship of the weighting factor, as shown in Equation (3): Figure 1. The generated relative permeability sets for a fractured formation using the calculated ranges in Table 2 for the saturation exponents and saturation endpoints. The black curves represent the original relative permeability set, while the coloured curves represent the relative permeability of the flooded region by low salinity brine for three levels of alterations.

Determination of Weighting Factor (WF)
The weighting factor plays a significant role in determining the salinity of the brine mixture, hence, its properties, as illustrated in Table 1. It controls the dilution process or blending between the Appl. Sci. 2020, 10, 4211 5 of 21 high salinity and the injected low salinity water in the mixing zone. Al-Ibadi [24,27] has referred to a linear relationship of the weighting factor, as shown in Equation (3): where: WF Weighting factor, fraction SC mix Brine mixture salinity, ppm. SC LoSal Injected brine salinity, ppm. SC maxeff Maximum effective salinity, ppm.
This linear relationship might be valid when the differences between the minimum salinity and the maximum effective salinity ranges are not very high. However, in a significant salinity contrast, an exponential relationship is more appropriate to represent the salinity increment in the mixing zone. This contrast is applicable in the case of formation water in the petroleum reservoirs, where its salinity can be as high as 200,000 ppm or more (e.g., Nahr Umr reservoir in Iraq has a formation water salinity of 200,000 ppm [28]). In contrast, the salinity of the injected fluid is several thousands of ppm.
In this paper, we present an approach to estimate the weighting factor using a one-dimensional model. The model simulated a highly idealised fractional flow displacement process of Buckley-Leverett. The dimensions of the model were (1000 ft × 25 ft × 50 ft) with 5 ft resolution in the x-direction. A relative permeability set and capillary pressure data of a fractured formation were used along with a proper fluid model to initialise the simulation model. The model represents an immiscible oil-water system and comprises an injector and a producer at the grid ends. A steady-state displacement was designed using controlled surface rates for both production and injection.
A conventional water injection scenario was simulated using a tracer concentration of 3000 for the injected water and a tracer of 100,000 for the formation water. Meanwhile, both injected water and formation water have the same high salinity. The results of the tracer model are illustrated through the profile of tracer concentration in Figure 2A and the profile of water saturation in Figure 2B. The mixing region of the tracer concentration during water injection occurred in a limited interval in the mixing zone. Meanwhile, high and low tracer concentrations were dominant at both sides of the mixing interval within the mixing zone region.
Appl. Sci. 2020, 10, x 5 of 21 where: WF Weighting factor, fraction SCmix Brine mixture salinity, ppm. SCLoSal Injected brine salinity, ppm. SCmaxeff Maximum effective salinity, ppm. This linear relationship might be valid when the differences between the minimum salinity and the maximum effective salinity ranges are not very high. However, in a significant salinity contrast, an exponential relationship is more appropriate to represent the salinity increment in the mixing zone. This contrast is applicable in the case of formation water in the petroleum reservoirs, where its salinity can be as high as 200,000 ppm or more (e.g., Nahr Umr reservoir in Iraq has a formation water salinity of 200,000 ppm [28]). In contrast, the salinity of the injected fluid is several thousands of ppm.
In this paper, we present an approach to estimate the weighting factor using a one-dimensional model. The model simulated a highly idealised fractional flow displacement process of Buckley-Leverett. The dimensions of the model were (1000 ft × 25 ft × 50 ft) with 5 ft resolution in the xdirection. A relative permeability set and capillary pressure data of a fractured formation were used along with a proper fluid model to initialise the simulation model. The model represents an immiscible oil-water system and comprises an injector and a producer at the grid ends. A steadystate displacement was designed using controlled surface rates for both production and injection.
A conventional water injection scenario was simulated using a tracer concentration of 3000 for the injected water and a tracer of 100,000 for the formation water. Meanwhile, both injected water and formation water have the same high salinity. The results of the tracer model are illustrated through the profile of tracer concentration in Figure 2A and the profile of water saturation in Figure  2B. The mixing region of the tracer concentration during water injection occurred in a limited interval in the mixing zone. Meanwhile, high and low tracer concentrations were dominant at both sides of the mixing interval within the mixing zone region. A significant width of the tracers' mixing zone was indicated by the simulation result, as illustrated in Figure 2. The width of the mixing zone depends on the petrophysical properties of the medium, as well as on the flow properties of the existing fluids. Moreover, physical phenomena can also influence the width of the mixing region, such as the dispersion effect that tends to spread the Appl. Sci. 2020, 10, 4211 6 of 21 A significant width of the tracers' mixing zone was indicated by the simulation result, as illustrated in Figure 2. The width of the mixing zone depends on the petrophysical properties of the medium, as well as on the flow properties of the existing fluids. Moreover, physical phenomena can also influence the width of the mixing region, such as the dispersion effect that tends to spread the injected waterfront out. Therefore, a normalised distance was used to represent the change in the tracer concentration, as illustrated in Figure 3.
Appl. Sci. 2020, 10, x 6 of 21 injected waterfront out. Therefore, a normalised distance was used to represent the change in the tracer concentration, as illustrated in Figure 3. In Figure 3, the tracer concentration curve contained two dominant intervals (Region 1 and Region 3) of approximately 23% of the normalised distance for each region of low and high tracer concentration. The change in the tracer concentration in these regions is minimal. However, a significant change occurs between 23% and 77% in the dimensionless distance, as the tracer concentration exponentially raises in Region 2. Therefore, regardless of the interval width of the mixing zone, the dilution of the solute tracer concentration has the illustrated shape in Figure 3. Likewise, the mixing zone during low salinity brine injection is expected to have the same pattern. Therefore, the obtained mixing curve pattern of the tracers can be utilised to conclude a weighting factor formula.
The estimated weighting factor formula, which was based on the tracer simulation results, has employed the normalised salinity (NS) to obtain a general form, as shown in Equation (4). Meanwhile, the normalised brine salinity can be calculated using Equation (5). A comparison between the linear weighting factor normally used and the current work of the exponential weighting factor has been illustrated in Figure 4. The linear approach uses Equation (3), while the proposed weighting factor formula is given in Equation (4). The outcome of the simulated tracer model was validated using the analytical solution of the fractional flow, as explained in the Appendix.  In Figure 3, the tracer concentration curve contained two dominant intervals (Region 1 and Region 3) of approximately 23% of the normalised distance for each region of low and high tracer concentration. The change in the tracer concentration in these regions is minimal. However, a significant change occurs between 23% and 77% in the dimensionless distance, as the tracer concentration exponentially raises in Region 2. Therefore, regardless of the interval width of the mixing zone, the dilution of the solute tracer concentration has the illustrated shape in Figure 3. Likewise, the mixing zone during low salinity brine injection is expected to have the same pattern. Therefore, the obtained mixing curve pattern of the tracers can be utilised to conclude a weighting factor formula.
The estimated weighting factor formula, which was based on the tracer simulation results, has employed the normalised salinity (NS) to obtain a general form, as shown in Equation (4). Meanwhile, the normalised brine salinity can be calculated using Equation (5). A comparison between the linear weighting factor normally used and the current work of the exponential weighting factor has been illustrated in Figure 4. The linear approach uses Equation (3), while the proposed weighting factor formula is given in Equation (4). The outcome of the simulated tracer model was validated using the analytical solution of the fractional flow, as explained in the Appendix A.

Relative Permeability and Capillary Pressure of the Mixing Zone
At the current stage of work, two sets of relative permeability were defined to represent the region of high salinity formation water and the region flooded by low salinity injected brine, as illustrated in Region 3 and Region 1 in Figure 3, respectively. Moreover, the proposed weighting factor formula was used to determine the flow curves in the mixing zone, which controls the brine mixture properties and fluid mobility. Therefore, estimating the relative permeability curves in the mixing region, as illustrated by Region 2 in Figure 3, required the two previously discussed relative permeability sets, using the following Equations [29][30][31]: Similarly, the capillary pressure in the mixing region (Pcow_Mixing zone) can be computed using the capillary pressure curves of the low salinity waterflooding region (Pcow LoSal ) and the high salinity region (Pcow HighSal ) of the formation water, as explained in Equation (8)

Setup of Numerical Models
Fine-scale modelling has been used widely to investigate various problems of recovery mechanisms and flow behaviour in both conventional and fractured reservoirs (e.g., [1, [32][33][34]). These models help to obtain an accurate result by avoiding the common simulation issues and artefacts such as upscaling problems and numerical convergence errors that frequently occurred at the reservoir scale modelling and simulation [3,35,36]. However, the detailed representation in the finescale model cannot be applied for the full field-scale due to the insufficient computational power resources and the simulation cost. Therefore, multiple scales were utilised in the current workflow to demonstrate the impact of low salinity waterflooding at each level, besides highlighting the upscaling challenges of the fine-scale model result into a larger scale, such as sector modelling or full-field modelling.
The impact of the low salinity waterflooding on the matrix recovery using the new proposed weighting factor formula has been evaluated using our previous fine-scale model and the Qamchuqa reservoir model. The details of both models can be found in Aljuboori et al. [2], where a linear relationship of the weighting factor has been used in their simulation. Meanwhile, we utilised the exponential weighting factor formula in the current workflow, and then we compared the results.  (4). The weighting factor value of one represents the beginning if the low salinity in the mixing zone. Meanwhile, a zero-weighting factor value represents the end of the mixing zone with high salinity concentration.

Relative Permeability and Capillary Pressure of the Mixing Zone
At the current stage of work, two sets of relative permeability were defined to represent the region of high salinity formation water and the region flooded by low salinity injected brine, as illustrated in Region 3 and Region 1 in Figure 3, respectively. Moreover, the proposed weighting factor formula was used to determine the flow curves in the mixing zone, which controls the brine mixture properties and fluid mobility. Therefore, estimating the relative permeability curves in the mixing region, as illustrated by Region 2 in Figure 3, required the two previously discussed relative permeability sets, using the following Equations [29][30][31]: Similarly, the capillary pressure in the mixing region (P cow_Mixing zone ) can be computed using the capillary pressure curves of the low salinity waterflooding region (P cow LoSal ) and the high salinity region (P cow HighSal ) of the formation water, as explained in Equation (8)

Setup of Numerical Models
Fine-scale modelling has been used widely to investigate various problems of recovery mechanisms and flow behaviour in both conventional and fractured reservoirs (e.g., [1, [32][33][34]). These models help to obtain an accurate result by avoiding the common simulation issues and artefacts such as upscaling problems and numerical convergence errors that frequently occurred at the reservoir scale modelling and simulation [3,35,36]. However, the detailed representation in the fine-scale model cannot be applied for the full field-scale due to the insufficient computational power resources and the simulation cost. Therefore, multiple scales were utilised in the current workflow to demonstrate the impact of low salinity waterflooding at each level, besides highlighting the upscaling challenges of the fine-scale model result into a larger scale, such as sector modelling or full-field modelling.
The impact of the low salinity waterflooding on the matrix recovery using the new proposed weighting factor formula has been evaluated using our previous fine-scale model and the Qamchuqa reservoir model. The details of both models can be found in Aljuboori et al. [2], where a linear relationship of the weighting factor has been used in their simulation. Meanwhile, we utilised the exponential weighting factor formula in the current workflow, and then we compared the results.

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 × 8 ft × 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-, y-, 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. relationship of the weighting factor has been used in their simulation. Meanwhile, we utilised the exponential weighting factor formula in the current workflow, and then we compared the results.

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 × 8 ft × 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-, y-, 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 4A. 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 4B. The second model can be simulated using the dualporosity model. The single block model in Figure 4B 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 dualporosity 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 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, 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 Aljuboori et al. [2]. Two recovery cases were simulated to evaluate the matrix recovery. The first model was designed to mimic the water advancement in fractures due to their high permeability leaving the matrix oil trapped behind, as shown in Figure 6A. In this case, it has been assumed that fractures were flooded with low salinity brine, while the matrix saturated with oil and connate formation water. Then, a fluid exchange process occurs under static conditions between the matrix and fractures due to capillary, gravity, and viscous forces. In the second case, the model comprises an injector and a producer located at the opposite corners of the grid, as illustrated in Figure 6B. In this case, fractures were assumed to be fully saturated with oil, while the matrix blocks saturated with oil and connate water. The low salinity brine was injected at a variable rate to maintain a constant bottom hole pressure, and the producer was opened to flow from the first layer only. The same prediction scenario of 10 years of the fine-scale model was adapted for simulating the above-discussed cases. The intermediate scale models have two objectives: (1) validate the simulation outcome of the single block model by comparing their results.

Intermediate Scale Modelling
(2) illustrate the differences between the injection scenario and the flooded scenario of the low salinity brine, which cannot be performed using the illustrated single block model in Figure 5B.
Appl. Sci. 2020, 10, x 9 of 21 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, 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 Aljuboori et al. [2].

Intermediate Scale Modelling
An intermediate scale model was constructed to simulate the low salinity waterflooding using the same properties of the fine-scale model. The dimensions of the model are 200 ft × 200 ft × 60 ft with a gridblock resolution of 40 ft × 40 ft × 12 ft, and a total number of 250 cells for both matrix and fractures. Moreover, average matrix properties were used to identify the impact of low salinity injection water on oil recovery without heterogeneity effect. Appropriate fluid properties and relative permeability sets of Upper Qamchuqa formation were used to initialise the simulation model. The matrix block dimension in this model is the same as the dimension of the fine-scale model of the previous section (i.e., 5 ft × 8 ft × 12 ft) to allow for performance comparison. Two recovery cases were simulated to evaluate the matrix recovery. The first model was designed to mimic the water advancement in fractures due to their high permeability leaving the matrix oil trapped behind, as shown in Figure 5A. In this case, it has been assumed that fractures were flooded with low salinity brine, while the matrix saturated with oil and connate formation water. Then, a fluid exchange process occurs under static conditions between the matrix and fractures due to capillary, gravity, and viscous forces. In the second case, the model comprises an injector and a producer located at the opposite corners of the grid, as illustrated in Figure 5B. In this case, fractures were assumed to be fully saturated with oil, while the matrix blocks saturated with oil and connate water. The low salinity brine was injected at a variable rate to maintain a constant bottom hole pressure, and the producer was opened to flow from the first layer only. The same prediction scenario of 10 years of the fine-scale model was adapted for simulating the above-discussed cases. The intermediate scale models have two objectives: (1) validate the simulation outcome of the single block model by comparing their results. (2) illustrate the differences between the injection scenario and the flooded scenario of the low salinity brine, which cannot be performed using the illustrated single block model in Figure 4B.

Field Scale Modelling -The Qamchuqa Reservoir
The Qamchuqa reservoir is one of the producing reservoirs of the Jambur field, which is located in the north of Iraq. The reservoir consists of two thick-bedded limestone formations with an average thickness of approximately 600 m in total; further geological description of the Qamchuqa reservoir can be found in Aljuboori et al. [1]. The history matching project has been carried out on the reservoir for four decades of production history, where consistent matching results were achieved for most of the producers [2]. Even recently, in 2020, the production of the Qamchuqa reservoir has continued

Field Scale Modelling-The Qamchuqa Reservoir
The Qamchuqa reservoir is one of the producing reservoirs of the Jambur field, which is located in the north of Iraq. The reservoir consists of two thick-bedded limestone formations with an average thickness of approximately 600 m in total; further geological description of the Qamchuqa reservoir can be found in Aljuboori et al. [1]. The history matching project has been carried out on the reservoir for four decades of production history, where consistent matching results were achieved for most of the producers [2]. Even recently, in 2020, the production of the Qamchuqa reservoir has continued using natural driving mechanisms, which resulted in a considerable pressure drop of (≈1200 psi) in the reservoir to the end of 2015 [2]. Therefore, the low salinity technique represents a competitive, affordable recovery method to support the reservoir pressure and to improve the sweep efficiency from the matrix medium as well as to sustain the production from the Qamchuqa reservoir. As highlighted previously, the same model of the Qamchuqa reservoir, which has been discussed in details in our previous work of Aljuboori et al. [2], has been used to assess the performance differences utilising linear relationship and exponential approach of the weighting factor. The same low salinity water injection scenario of 14 years was performed by injecting 45,000 STB/D through six injection wells. Furthermore, the salinity of the injected brine is 3000 ppm, where both injected brine salinity and the reservoir salinity represented as total dissolved solids (TDS) in the simulation model using ECLIPSE black oil simulator.

Results and Discussion
Before we delve into the results and discussions, it is essential to give a glimpse of the impact of low salinity brine injection on the fractional flow of the water phase and how this can increase the oil recovery. The generated relative permeability sets of the regions flooded by low salinity have been used to evaluate the fractional flow of water, as illustrated in Figure 7A. The calculated fractional flow profile demonstrated a systematic shifting towards the higher water saturation with preserving its shape during the change increment in wettability. This shift can improve the displacement of oil, which leads to a significant improvement in oil recovery and delay the water breakthrough remarkably. This example illustrates that the water breakthrough time has been slowed down considerably. At the maximum change in relative permeability, the water breakthrough has slowed down to 2613 days compared with 1777 days using the high salinity brine injection scenario (i.e., breakthrough time delayed by 47%), as indicated by the red and black colour in Figure 7B, respectively.
Appl. Sci. 2020, 10, x 10 of 21 from the matrix medium as well as to sustain the production from the Qamchuqa reservoir. As highlighted previously, the same model of the Qamchuqa reservoir, which has been discussed in details in our previous work of Aljuboori et al. [2], has been used to assess the performance differences utilising linear relationship and exponential approach of the weighting factor. The same low salinity water injection scenario of 14 years was performed by injecting 45,000 STB/D through six injection wells. Furthermore, the salinity of the injected brine is 3000 ppm, where both injected brine salinity and the reservoir salinity represented as total dissolved solids (TDS) in the simulation model using ECLIPSE black oil simulator.

Results and Discussion
Before we delve into the results and discussions, it is essential to give a glimpse of the impact of low salinity brine injection on the fractional flow of the water phase and how this can increase the oil recovery. The generated relative permeability sets of the regions flooded by low salinity have been used to evaluate the fractional flow of water, as illustrated in Figure 7A. The calculated fractional flow profile demonstrated a systematic shifting towards the higher water saturation with preserving its shape during the change increment in wettability. This shift can improve the displacement of oil, which leads to a significant improvement in oil recovery and delay the water breakthrough remarkably. This example illustrates that the water breakthrough time has been slowed down considerably. At the maximum change in relative permeability, the water breakthrough has slowed down to 2613 days compared with 1777 days using the high salinity brine injection scenario (i.e., breakthrough time delayed by 47%), as indicated by the red and black colour in Figure 7B, respectively.

Single Matrix Block Model
An exponential weighting factor was used to simulate the low salinity waterflooding scenario, and the outcome was compared with the same model using a linear weighting factor. The results of the two weighting factor approaches were almost similar with a marginal difference of 0.1%, 0.2%, and 0.7% of the ultimate oil recovery for the minimum, average, and maximum alteration, respectively. However, the improvement in the oil recovery of the fine-scale model due to the impact of low salinity waterflooding is 2.3%, 7.5%, and 13% of STOIIP for the earlier mentioned alteration degree, respectively, as illustrated in Figure 8. These incremental percentages were calculated based on the result of the high salinity waterflooding scenario. In this fine-scale model, the single-porosity model was used in the simulation. Meanwhile, the same matrix block has been modelled using the

Single Matrix Block Model
An exponential weighting factor was used to simulate the low salinity waterflooding scenario, and the outcome was compared with the same model using a linear weighting factor. The results of the two weighting factor approaches were almost similar with a marginal difference of 0.1%, 0.2%, and 0.7% of the ultimate oil recovery for the minimum, average, and maximum alteration, respectively. However, the improvement in the oil recovery of the fine-scale model due to the impact of low salinity waterflooding is 2.3%, 7.5%, and 13% of STOIIP for the earlier mentioned alteration degree, respectively, as illustrated in Figure 8. These incremental percentages were calculated based on the result of the high salinity waterflooding scenario. In this fine-scale model, the single-porosity model was used in the simulation. Meanwhile, the same matrix block has been modelled using the dual-porosity model. The increment in oil recovery for the single block model using the dual-porosity option is 1.5%, 6.7%, and 10.7% of STOIIP for the minimum, average, and maximum cases, respectively, compared with the high salinity waterflooding scenario. The results of the above scenarios were compared to highlight the outcome differences, as illustrated in Figure 9 and summarised in Table 3.
Appl. Sci. 2020, 10, x 11 of 21 dual-porosity model. The increment in oil recovery for the single block model using the dual-porosity option is 1.5%, 6.7%, and 10.7% of STOIIP for the minimum, average, and maximum cases, respectively, compared with the high salinity waterflooding scenario. The results of the above scenarios were compared to highlight the outcome differences, as illustrated in Figure 9 and summarised in Table 3.   The highlighted differences in the above table confirm the tendency of the dual-porosity model to overestimate the predicted oil recovery, the recovery speed, and the saturation profile, as dual-porosity model. The increment in oil recovery for the single block model using the dual-porosity option is 1.5%, 6.7%, and 10.7% of STOIIP for the minimum, average, and maximum cases, respectively, compared with the high salinity waterflooding scenario. The results of the above scenarios were compared to highlight the outcome differences, as illustrated in Figure 9 and summarised in Table 3.   The highlighted differences in the above table confirm the tendency of the dual-porosity model to overestimate the predicted oil recovery, the recovery speed, and the saturation profile, as Figure 9. A comparison of oil recoveries of the fine-scale model (solid lines) and the single block model (dashed lines) using an exponential weighting factor for various levels of relative permeability alterations (minimum, average, and maximum), in addition to high salinity waterflooding scenario. Table 3. Simulation results of fine-scale and single block models using single and dual-porosity models, respectively, highlighting the recovery differences between their performance.

Scenario
Fine The highlighted differences in the above table confirm the tendency of the dual-porosity model to overestimate the predicted oil recovery, the recovery speed, and the saturation profile, as concluded by [1,39]. Furthermore, the recovery speed and saturation front were significantly higher compared with the fine-scale modelling, as shown in Figure 9. The optimistic oil recovery of the dual-porosity model resulted from an exaggeration in the fluid exchange rate between the matrix and fractures. Moreover, the total height of the matrix block in the dual-porosity model (i.e., 12 ft) contributed to the oil exchange rate in the transfer rate calculations. Meanwhile, the height of a single cell in the fine-scale model (i.e., 1 ft based on the model resolution) has used in the fluid exchange calculations, which has a lower contribution. Moreover, the advancement of the low salinity waterfront took a longer time to sweep the same equivalent volume of the corresponding matrix block of the dual-porosity model. Figure 10 illustrates the saturation profile of the low salinity water phase in the fine-scale model and the single block model after 10 days. A single saturation value was computed for the matrix cell in the dual-porosity model, as illustrated in Figure 10A. Meanwhile, every cell in the fine-scale model show variations in saturation, see Figure 10B. Furthermore, the total exposed volume of the matrix for the fluid exchange with fractures are 480 ft 3 , and 300 ft 3 for the dual-porosity model and the fine-scale model, respectively, which affected the matrix recovery in the early time. Therefore, the dual-porosity model exhibited a higher oil recovery due to the larger matrix volume exposed to the fluid exchange with fractures. The dominant force of the capillary pressure can be identified in Figure 10B, where the fluid transfer occurs in all directions of the matrix blocks.
Appl. Sci. 2020, 10, x 12 of 21 concluded by [1,39]. Furthermore, the recovery speed and saturation front were significantly higher compared with the fine-scale modelling, as shown in Figure 9. The optimistic oil recovery of the dualporosity model resulted from an exaggeration in the fluid exchange rate between the matrix and fractures. Moreover, the total height of the matrix block in the dual-porosity model (i.e., 12 ft) contributed to the oil exchange rate in the transfer rate calculations. Meanwhile, the height of a single cell in the fine-scale model (i.e., 1 ft based on the model resolution) has used in the fluid exchange calculations, which has a lower contribution. Moreover, the advancement of the low salinity waterfront took a longer time to sweep the same equivalent volume of the corresponding matrix block of the dual-porosity model. Figure 10 illustrates the saturation profile of the low salinity water phase in the fine-scale model and the single block model after 10 days. A single saturation value was computed for the matrix cell in the dual-porosity model, as illustrated in Figure 10A. Meanwhile, every cell in the fine-scale model show variations in saturation, see Figure 10B. Furthermore, the total exposed volume of the matrix for the fluid exchange with fractures are 480 ft 3 , and 300 ft 3 for the dualporosity model and the fine-scale model, respectively, which affected the matrix recovery in the early time. Therefore, the dual-porosity model exhibited a higher oil recovery due to the larger matrix volume exposed to the fluid exchange with fractures. The dominant force of the capillary pressure can be identified in Figure 10B, where the fluid transfer occurs in all directions of the matrix blocks.

Intermediate Scale Modelling
As stated earlier, these models were designed for comparison and validation purposes. The model simulated a low salinity waterflooding scenario. The results of this case were compared with the results of the single block model to validate the findings of the single block model against the intermediate scale model under the same condition using the dual-porosity solver. The simulation outcomes show almost identical oil recovery despite the differences in the scale of the two models, as shown in Figure 11.
On the other hand, the oil recoveries of both intermediate models (i.e., Case A and Case B in Figure 6) were compared to assess the matrix recovery under the sweep process by the injected low salinity brine scenario and the flooded scenario when the fluid exchange occurred under static condition. The three levels of uncertainty in the change to the relative permeability due to the impact of low salinity brine were simulated to evaluate oil recovery under the above-explained conditions. The simulation results indicate faster oil recovery in the flooded case compared with the injection case as all matrix blocks were in contact with the low salinity brine that filled fractures. Meanwhile, in the injection case, the matrix blocks were in contact with the oil in fractures. Then, the injected low

Intermediate Scale Modelling
As stated earlier, these models were designed for comparison and validation purposes. The model simulated a low salinity waterflooding scenario. The results of this case were compared with the results of the single block model to validate the findings of the single block model against the intermediate scale model under the same condition using the dual-porosity solver. The simulation outcomes show almost identical oil recovery despite the differences in the scale of the two models, as shown in Figure 11.
On the other hand, the oil recoveries of both intermediate models (i.e., Case A and Case B in Figure 6) were compared to assess the matrix recovery under the sweep process by the injected low salinity brine scenario and the flooded scenario when the fluid exchange occurred under static condition. The three levels of uncertainty in the change to the relative permeability due to the impact of low salinity brine were simulated to evaluate oil recovery under the above-explained conditions. The simulation results indicate faster oil recovery in the flooded case compared with the injection case as all matrix blocks were in contact with the low salinity brine that filled fractures. Meanwhile, in the injection case, the matrix blocks were in contact with the oil in fractures. Then, the injected low salinity brine displace the oil from fractures and become in contact with additional matrix blocks as the low salinity waterfront advanced. The simulation results are illustrated in Figure 12.
Appl. Sci. 2020, 10, x 13 of 21 salinity brine displace the oil from fractures and become in contact with additional matrix blocks as the low salinity waterfront advanced. The simulation results are illustrated in Figure 12.

Full Field Scale Modelling
A low salinity injection scenario has carried out in the north region of the Qamchuqa reservoir using six injection wells to sweep the oil towards the nearby producers, see Figure 13. The proposed locations of the injectors were designed to evaluate the impact of high salinity and low salinity brine injection scenarios on the performance of the Qamchuqa reservoir. Therefore, this injection design does not represent an optimal scenario of a secondary recovery project to develop the reservoir. Appl. Sci. 2020, 10, x 13 of 21 salinity brine displace the oil from fractures and become in contact with additional matrix blocks as the low salinity waterfront advanced. The simulation results are illustrated in Figure 12.

Full Field Scale Modelling
A low salinity injection scenario has carried out in the north region of the Qamchuqa reservoir using six injection wells to sweep the oil towards the nearby producers, see Figure 13. The proposed locations of the injectors were designed to evaluate the impact of high salinity and low salinity brine injection scenarios on the performance of the Qamchuqa reservoir. Therefore, this injection design does not represent an optimal scenario of a secondary recovery project to develop the reservoir.

Full Field Scale Modelling
A low salinity injection scenario has carried out in the north region of the Qamchuqa reservoir using six injection wells to sweep the oil towards the nearby producers, see Figure 13. The proposed locations of the injectors were designed to evaluate the impact of high salinity and low salinity brine injection scenarios on the performance of the Qamchuqa reservoir. Therefore, this injection design does not represent an optimal scenario of a secondary recovery project to develop the reservoir.
The dual-porosity model was used to simulate the effect of change in wettability on the performance of the Qamchuqa reservoir under a low salinity recovery scheme and included the exponential weighting factor. A secondary recovery mode of low salinity brine injection was carried out for 14 years. The uncertainty in the change to the Qamchuqa reservoir wettability has been addressed by using three levels of alteration to the relative permeability (minimum, average, and maximum).
Initially, the low salinity waterflooding scenarios gave a similar performance to the high salinity brine injection in the first six years of injection. Then, the change in wettability started to take effect and could be seen at the producers. This helped maintain the oil productivity for an extra two and a half years at a rate of 38,000 STB/D compared to an average rate of 32,500 STB/D for the high salinity waterflooding. Meanwhile, the oil flow rate maintained its high rate of 32,500 STB/D to the end of the prediction scenario of year 14 compared with 25,000 STB/D for the high salinity brine injection. At the same time, a reduction in the field water cut by 32.5% was also observed, as the injected low salinity brine exchanged with the oil in the matrix blocks. This process led to a reduced volume of injected water reaching the producer (i.e., less water cut) and increased oil production, as illustrated in Figure 14. The dual-porosity model was used to simulate the effect of change in wettability on the performance of the Qamchuqa reservoir under a low salinity recovery scheme and included the exponential weighting factor. A secondary recovery mode of low salinity brine injection was carried out for 14 years. The uncertainty in the change to the Qamchuqa reservoir wettability has been addressed by using three levels of alteration to the relative permeability (minimum, average, and maximum).
Initially, the low salinity waterflooding scenarios gave a similar performance to the high salinity brine injection in the first six years of injection. Then, the change in wettability started to take effect and could be seen at the producers. This helped maintain the oil productivity for an extra two and a half years at a rate of 38,000 STB/D compared to an average rate of 32,500 STB/D for the high salinity waterflooding. Meanwhile, the oil flow rate maintained its high rate of 32,500 STB/D to the end of the prediction scenario of year 14 compared with 25,000 STB/D for the high salinity brine injection. At the same time, a reduction in the field water cut by 32.5% was also observed, as the injected low salinity brine exchanged with the oil in the matrix blocks. This process led to a reduced volume of injected water reaching the producer (i.e., less water cut) and increased oil production, as illustrated in Figure 14.

Upper Qamchuqa Formation
Lower Qamchuqa Formation  The dual-porosity model was used to simulate the effect of change in wettability on the performance of the Qamchuqa reservoir under a low salinity recovery scheme and included the exponential weighting factor. A secondary recovery mode of low salinity brine injection was carried out for 14 years. The uncertainty in the change to the Qamchuqa reservoir wettability has been addressed by using three levels of alteration to the relative permeability (minimum, average, and maximum).
Initially, the low salinity waterflooding scenarios gave a similar performance to the high salinity brine injection in the first six years of injection. Then, the change in wettability started to take effect and could be seen at the producers. This helped maintain the oil productivity for an extra two and a half years at a rate of 38,000 STB/D compared to an average rate of 32,500 STB/D for the high salinity waterflooding. Meanwhile, the oil flow rate maintained its high rate of 32,500 STB/D to the end of the prediction scenario of year 14 compared with 25,000 STB/D for the high salinity brine injection. At the same time, a reduction in the field water cut by 32.5% was also observed, as the injected low salinity brine exchanged with the oil in the matrix blocks. This process led to a reduced volume of injected water reaching the producer (i.e., less water cut) and increased oil production, as illustrated in Figure 14. Upper Qamchuqa Formation Lower Qamchuqa Formation Figure 14. Comparison of the waterflooding scenarios using high salinity and low salinity schemes in the Qamchuqa reservoir, using the exponential weighting factor.
We can conclude from the above behaviour that the impact of the change in wettability required a longer time to sense its influence at the reservoir scale (six years were needed to show a significant effect on the Qamchuqa reservoir). Moreover, other impacts of the low salinity water injection on reservoir behaviour such as pressure maintenance. Pressure maintenance, in turn, has controlled the gas cusping in the producers; hence, preserving the drive mechanism energy of the dissolved gas or the gas cap in the Qamchuqa reservoir as well as less technical problems at the surface facilities due to excessive gas flow rate (e.g., field Gas-Oil Ratio (GOR) in Figure 15). That enabled the reduction of the workover cost, as most of the reported workover operations in the Qamchuqa reservoir were carried out due to the gas coning.
We can conclude from the above behaviour that the impact of the change in wettability required a longer time to sense its influence at the reservoir scale (six years were needed to show a significant effect on the Qamchuqa reservoir). Moreover, other impacts of the low salinity water injection on reservoir behaviour such as pressure maintenance. Pressure maintenance, in turn, has controlled the gas cusping in the producers; hence, preserving the drive mechanism energy of the dissolved gas or the gas cap in the Qamchuqa reservoir as well as less technical problems at the surface facilities due to excessive gas flow rate (e.g., field Gas-Oil Ratio (GOR) in Figure 15). That enabled the reduction of the workover cost, as most of the reported workover operations in the Qamchuqa reservoir were carried out due to the gas coning. Figure 15. Comparison of the pressure support to the Qamchuqa reservoir during high salinity and low salinity waterflooding, where a similar impact was observed for both flooding schemes on the reservoir subsurface pressure and the produced gas-oil ratio. The natural depletion was provided for comparison.
The advantage of low salinity brine injection is the ability to initiate a chemical reaction that changes reservoir wettability to be more water-wet. This reduces the mobility of the water phase in the flooded regions of the reservoir. Furthermore, this chemical interaction between the low salinity brine, crude oil, and the rock can also lead to a reduction in the residual oil saturation by displacing the oil from the small pore throats and rock surfaces towards the larger pores. As a result, the mobility of the oil phase increases in the flooded regions, which enhances the overall sweep efficiency compared with the conventional high salinity waterflooding. Moreover, the conventional water injection scenario often leads to an early water breakthrough.
Despite the positive simulation results of the Qamchuqa reservoir, an intensive evaluation program is necessary to determine the effective brine composition, and to assess the effect of the clay content, the composition of the crude oil, pH, and rock characteristics on the performance of the low salinity injection, as well as to reduce the uncertainty and to execute this technique effectively. Eventually, a significant improvement in the sweep efficiency and reservoir performance may require a longer time frame to observe its impact and to confirm the observed results of laboratory experiments.
It is worth mentioning that additional uncertainty due to the existence of bitumen in the Qamchuqa reservoir can impact the performance of the low salinity waterflooding significantly. Therefore, it is important to study the bitumen characteristics, its distribution, and how that can impact on the fluid flow in the Qamchuqa reservoir. The negative role of the bitumen might nullify the expected improvement in the oil recovery using a low salinity water injection scenario as the bitumen occasionally behaves like a flow barrier between the aquifer and the oil zone if it existed as a uniform layer. However, the bitumen may have less impact if it exists as scattered patches. Figure 15. Comparison of the pressure support to the Qamchuqa reservoir during high salinity and low salinity waterflooding, where a similar impact was observed for both flooding schemes on the reservoir subsurface pressure and the produced gas-oil ratio. The natural depletion was provided for comparison.

Conclusion
The advantage of low salinity brine injection is the ability to initiate a chemical reaction that changes reservoir wettability to be more water-wet. This reduces the mobility of the water phase in the flooded regions of the reservoir. Furthermore, this chemical interaction between the low salinity brine, crude oil, and the rock can also lead to a reduction in the residual oil saturation by displacing the oil from the small pore throats and rock surfaces towards the larger pores. As a result, the mobility of the oil phase increases in the flooded regions, which enhances the overall sweep efficiency compared with the conventional high salinity waterflooding. Moreover, the conventional water injection scenario often leads to an early water breakthrough.
Despite the positive simulation results of the Qamchuqa reservoir, an intensive evaluation program is necessary to determine the effective brine composition, and to assess the effect of the clay content, the composition of the crude oil, pH, and rock characteristics on the performance of the low salinity injection, as well as to reduce the uncertainty and to execute this technique effectively. Eventually, a significant improvement in the sweep efficiency and reservoir performance may require a longer time frame to observe its impact and to confirm the observed results of laboratory experiments.
It is worth mentioning that additional uncertainty due to the existence of bitumen in the Qamchuqa reservoir can impact the performance of the low salinity waterflooding significantly. Therefore, it is important to study the bitumen characteristics, its distribution, and how that can impact on the fluid flow in the Qamchuqa reservoir. The negative role of the bitumen might nullify the expected improvement in the oil recovery using a low salinity water injection scenario as the bitumen occasionally behaves like a flow barrier between the aquifer and the oil zone if it existed as a uniform layer. However, the bitumen may have less impact if it exists as scattered patches.

1.
A new proposed approach of calculating the weighting factor in the mixing area has been presented to improve the simulation accuracy of the low salinity waterflooding. The weighting factor determines the salinity of the brine mixture, hence its properties, as well as it controls the fluid mobility through the calculated relative permeability in the mixing region. The impact of the exponential weighting factor might become significant in the small-scale modelling, which can be useful for modelling and simulation the laboratory coreflood experiments.

2.
The results of the coreflood experiments have been integrated into the reservoir simulation to assess the improvement in the oil recovery due to the change in wettability to a more water-wet state. The current work highlighted the critical role of the laboratory results that should be performed carefully. Furthermore, the uncertainty in the reported coreflood results has been addressed by computing three levels of change to the relative permeability and simulate each level independently to evaluate their recoveries.

3.
The remarkable delay in the water breakthrough can enhance the reservoir productivity and extend the production periods of the producers. However, accurate representation of the relative permeability in the mixing region between the high salinity set to the low salinity set is essential to avoid an overestimation of the sweep efficiency. 4.
The relative permeability was successfully used as a proxy to simulate the physical and chemical interaction which have not been modelled explicitly in the simulation model during low salinity waterflooding. The relative permeability emulated the observed change in wettability and the reduction in the residual oil saturation, which enables to simulate the impact of the low salinity waterflooding flawlessly. 5.
The study illustrated that there is an opportunity to increase oil recovery from the matrix using low salinity waterflooding even with a minor change in the relative permeability. This sensitive role to the generated relative permeability required accurate experimental results, which are essential for simulating the low salinity waterflooding scenario effectively and avoid any modelling or experimental artefact. 6.
The accelerated recovery during low salinity waterflooding encourages a switch from the current conventional waterflooding projects to achieve a higher recovery within a reduced time frame. However, for a full field case, a longer time is required to observe the improvements as the low salinity brine required time to flood the reservoir rock and alter its wettability and reduce the residual oil saturation. Moreover, the fine-scale simulation demonstrated a precise estimation of oil recovery, and it should be used as a reference solution to calibrate the outcomes of the dual-porosity model and avoid any misestimation of the reservoir performance. Acknowledgments: The authors would like to express their deepest gratitude to Universiti Teknologi PETRONAS for providing the required software license and creating the necessary working environment. The authors would also like to thank the Ministry of Oil of Iraq and the management of North Oil Company for their permission to use their data in this work.

Conflicts of Interest:
The authors certify that they have no affiliations with or involvement in any organisation or entity with any financial interest.

Appendix A
In this Appendix, we present the analytical solution for the proposed approach of estimating the weighting factor in the mixing zone of the low salinity waterflooding scheme using 1D model. The model has already been discussed, where the simulation results illustrated by using saturation profiles of both tracers and water. Then, the weighting factor equation has been concluded based on the results of the tracer simulation model.
Initially, the water front of the 1D model has been calculated analytically using the Buckley-Leverett theory to validate the simulation results. The fractional flow of the injected water can be determined analytically using the following equation [42,43]: where the relative permeability ratio in Equation (9) can be replaced with the exponential function of the plotted relationship between the water saturation and relative permeability ratio for the straight-line section, as illustrated in Figure A1A and expressed in Equation (10), where both a and b coefficients can be calculated [43]: k ro k rw = ae bS w Then, Equation (10) is substituted into Equation (9) to obtain: A tangent line was plotted from the initial water saturation to the maximum point in the water cut (f w ) curve, as demonstrated in Figure A1B to calculate the saturation of the leading waterfront, as well as to determine the distance from the injector at the required time. An example is given in Figure A1C to illustrate the water saturation, the leading front, and the distance from the injector after 462 days. Moreover, this analytical solution was compared with the 1D tracer simulation scenario, which is illustrated in Figure 2. The analytical solution had a sharp waterfront at a distance of 260 ft from the injector. Meanwhile, the result of the numerical simulation exhibited a gradual mixing in the waterfront with an average equal or slightly higher than the analytical solution frontal distance. The distance from the injection point can be estimated using Equation (12), where the (df w /dS w ) can be calculated using the derivative form of Equation (11).
Al-Ibadi [24] has illustrated that the high salinity water moving ahead to form the waterfront followed by low salinity water. The conclusion is the same even when the injected water has the same salinity as the formation of water, as illustrated in Figure A1D. In this example, both injected water and formation water have the same salinity while a tracer concentration of 3000 has used for the injected water compared with 100,000 for formation water. The simulation results demonstrated that a mixing zone of the tracer has formed, which starts with the maximum concentration in the waterfront and ends with the minimum concentration at a closer distance to the injection point. This conclusion is further illustrated using an overlapping plot of the subfigures shown in Figure A1C,D, as shown in Figure A2. In this plot, the leading frontal (i.e., beginning of the mixing zone) located at 305 ft from the injector and ending at 40 ft. Moreover, the mixing region of the brine mixture was situated within a 265 ft interval, which begins with the SC LoSal and ends with the SC Maxeff to the right. Therefore, the width of the mixing interval that starts altering the reservoir wettability and reduces the residual oil saturation depends on the weighting factor and the brine mixture salinity in this interval that determines the rate of change.
Appl. Sci. 2020, 10 Al-Ibadi [24] has illustrated that the high salinity water moving ahead to form the waterfront followed by low salinity water. The conclusion is the same even when the injected water has the same salinity as the formation of water, as illustrated in Figure A1D. In this example, both injected water and formation water have the same salinity while a tracer concentration of 3000 has used for the injected water compared with 100,000 for formation water. The simulation results demonstrated that a mixing zone of the tracer has formed, which starts with the maximum concentration in the waterfront and ends with the minimum concentration at a closer distance to the injection point. This conclusion is further illustrated using an overlapping plot of the subfigures shown in Figure A1C,D, as shown in Figure A2. In this plot, the leading frontal (i.e., beginning of the mixing zone) located at 305 ft from the injector and ending at 40 ft. Moreover, the mixing region of the brine mixture was situated within a 265 ft interval, which begins with the SCLoSal and ends with the SCMaxeff to the right. Therefore, the width of the mixing interval that starts altering the reservoir wettability and reduces the residual oil saturation depends on the weighting factor and the brine mixture salinity in this interval that determines the rate of change.