Brine with Total Dissolved Solids (TDS) of 4.0 g/l is used as make-up water for diluted polymer solutions. Brine composition is described in Table 1. Brine was filtered through 0.2 μm filter size by applying 2.0 Bar of Nitrogen gas pressure in order to avoid any undissolved component.

Two synthetic high molecular weight hydrolyzed polyacrylamides (HPAM) polymers and one bio-polymer are used in this work. Polymer solutions are prepared at three concentrations 500 ppm, 1000 ppm and 1500 ppm. The preparation procedure used is the one adopted by Hincapie and Ganzer, [20] . A detailed description of polymers is provided in Table 2. Diluted polymer solutions are filtered using a membrane filter with a size of 1.2 µm (pre-sheared solutions) and 5 µm (non-sheared solutions). Purpose of pre-shearing of polymer solution is well documented by Hincapie, [15] , Hincapie and Ganzer, [20] . It attempts to evaluate polymer stability, injectivity and viscoelastic properties. Shearing is performed by injecting polymer solutions through shearing device with the principle of flow through small nozzles, proposed by Hincapie and Ganzer, [20] . The shearing is done by applying 30 bar pressure with the purpose of degrading the macromolecules of the polymer without affecting polymer’s yield viscosity. This approach is expected will reduce potential injectivity problems as pointed by Hincapie and Ganzer, [20] .

Bentheimer core plugs are used in this work, with an average length and diameter of 60 mm and 30 mm, respectively. Core plugs were dried by placing them in an oven at 60˚C for at least 5 days. Porosity was measured using a Micromeritics 1340 pycnometer and permeability using a Gas Permeameter. Brine was injected at five different injection rates (0.5. 1.0, 2.0. 5.0, and 10.0 ml/min) to measure brine permeability. Table 3 provides a summary of the core plugs.

Quartz sand with grain size range of 63 - 80 µm screened was selected for sand-pack experiments. Average length and diameter of sand packs was same as those of core plugs. Porosity of sand-packs is measured through mass balance and volume balance method while permeability calculation is done using Darcy’s law by brine injection. Apart from that, stainless steel capillary tube (CT) of 0.5 mm ID and 3 m length is used to investigate impact of no converging-di- verging geometry on polymer solution.

Figure 3 provides a schematic representation of the core-flood setup [15] . It consists of a two-syringe injection pump connected in a multi-flow arrangement (infusion/withdrawal) and controlled by irreversible check valves. The core plug is placed in a core holder that receives confining pressure, applied using a positive displacement hand pump. A rubber sleeve is used to secure the core plug inside the core holder. We used a pressure transmitter to gather pressure data. The confining pressure was kept constant at 30bar to guarantee radial flow. Once calibrated, the pressure transducer measured the pressure difference between the holder’s inlet and exit ports, with the data recorded on a computer.

Single-phase sand pack experiments were performed with an essentially similar setup as the one shown in Figure 3. The experiment started with the preparation of the sand; placing it into the cell and previously weighing the dry mass of

the sand pack. The sand pack was subsequently saturated with CO2 prior to brine injection. This was to remove air bubbles and thus avoid air bubbles effect. After sufficient brine had been injected into the sand pack, permeability was determined. The procedures undertaken to perform the sand pack experiments were similar to those described for core plug experiments.

A CT (capillary tube) with an internal diameter of 0.5 mm and length 2.5 m was shaped into a helical structure as shown in Figure 4. Results from this approach are compared with results of core flooding and sand-pack injection. Experimental components e.g. Pressure measurement device and injection pump are the same as discussed in previous sections.

Viscoelastic phenomenon of polymer can be observed by drawing a similar scheme to that proposed by Heemskerk et al. [14] , Hincapie, R., [15] , Tahir et al., [21] ; where the measured pressure drop during polymer flooding experiments is plotted against interstitial velocity.

Heemskerk’s work described shear thinning behavior for a slope below 45˚, shear thickening for a slope greater than 45˚, and a Newtonian response for a slope of precisely 45˚. The results presented here are in exceptionally good agreement with those reported by Heemskerk et al. [14] , Hincapie, [15] , Tahir

et al., [21] . Figure 5 illustrates the following clearly observed behaviors of HPAM polymer solutions (pre-sheared and non-sheared): a characteristic slope for a Newtonian response at 45˚, shear thinning below 45˚, and shear thickening behavior above 45˚.

A typical plot to represent the pressure response is one where pressure response is related to injection flow rates or interstitial velocity [15] [21] . The overall approach taken in this work is reported in Figure 6(a) for the Bentheimer core plug and in Figure 6(b) for a sand pack experiment.

The plot considers the total pressure (∆P_T) obtained during the core flooding measurement and the pressures associated with shear (∆P_Sh), determined using Darcy’s law. These results enable determination of the pressure drop assumed to be by elongation (∆P_Elo). It would appear from Figure 6 that the calculated pressure drop only matched the experimental data at low interstitial velocity.

where,∆P_T = Total pressure obtained during the core flooding∆P_S = Determined using Darcy equation and Carreau-Yasuda flow curve fitted to rheometer data∆P_E = Pressure drop by elongation = ∆P_T − ∆P_S.4.3. Evaluation of Apparent Viscosity over Shear Rates for Sand Packs and CoresTypical plots to compare the matching between bulk viscosity and apparent

viscosity are shown in Figure 7. It is a common practice to present the data in such a way because it enables demonstrating the differences observed during the core flooding to data obtained in the rheometer. Figure 7(a) presents a comparison of the different approaches in the case of a hydrolyzed polyacrylamide (HPAM) solution. Approach 1 is based upon equation used for shear rate calculation proposed by Cannella et al., [7] , the approach 2 is taken from the equation proposed by Christopher and Middleman, [17] , the approach 3 is taken from Lee, [22] and the approach 4 is evaluated from the equation presented by Sheng, [23] . A summary of the shear rate correction coefficients is given in Table 4. Moreover, Figure 7(b) depicts the case for a biopolymer. Note that it is important to point out the differences of both plots. There was a tendency for the viscosity of the HPAM to increase at a certain apparent shear rate. This tendency

was not observed for the biopolymer. It is evident that these results demonstrate flow thickening or flow thinning in the porous media. This is pointed as a characteristic of flow in porous materials that is not observed in rheological measurements at similar rates. Similar observations have been presented previously by Cannella et al., [7] , Hejri et al., [24] , Teeuw and Hesselink, [25] . The results presented here are in good agreement with those reported in the literature.

Shear rates and apparent viscosity calculations using two different type of porous media (Bentheimer core and Quartz sand-pack) and CT are shown in Figure 8 for Hengfloc 63026 polymer solution. From Figure 8 it can be observed that the apparent viscosity and shear rates are calculated using the approach 1. As can be seen the core flooding and sand-pack data depicted an increased apparent viscosity due to the increment in pressure. This phenomenon has been previously observed as an onset. This is assumed to be related to stronger viscoelastic properties at higher shear rates. Unlike core flooding and sand packs, for the case of the CT experiments the only shear thinning behavior is observed. This is due to: 1) non-existence of pore size distribution (contrac- tions-expansions) in CT and 2) it is indeed a pipe flow (expected behavior). One

can argue that the apparent viscosity in sand-pack experiments is higher compared to the core flooding. This is explained by the variation in pore size distribution due to the sand grain size, as well as the differences in permeability and porosity, due to the low compaction.

Comparing shearing conditions of solutions given in Figure 9(a), sheared polymer showed lower bulk and apparent viscosity as related to non-sheared solutions over low shear rate values (1 s⁻¹). This was expected behavior as mechanical shearing break-downs the molecular chains of polymer to avoid injectivity problems. But at higher shear rates (100 s⁻¹), rheometer bulk viscosity for shear and non-sheared solution was almost same. At these higher shear rates, apparent viscosity for sheared solution was higher than non-sheared solution. This is because sheared polymers have less viscous forces as compare to non-sheared polymers. Thus less viscous forces will result more ease in flow and will result to dominance of turbulent pressure drop. This excessive pressure drop will contribute excessive apparent viscosity. But contribution of turbulence pressure drop at high injection rates need to be calculated [21] . Also in Figure 9(b) is the comparison of Flopaam 6035 S and Hengfloc 63026 1000 ppm non-sheared in a 4 g/l TDS brine solvent. Flopaam 6035S showed higher bulk and apparent viscosity as compare to Hengfloc 63026 solution. Reason could be difference in molecular structure and molecular weight of polymers (Table 2). Due to higher bulk and apparent viscosity, Flopaam 6035 S also showed injectivity issues as compare to Hengfloc 63026 in sand-packs.

The flow behaviour of an HPAM in a rheometer experiment compared to that in a core flooding experiment is commonly expressed as shown in Figure 10. Since the purpose in this work was to describe that onset or shear thickening, a different approach was chosen. Howe et al., [26] proposed a plotting approach from observations in microchannel that seem to be useful, as expressing the behaviour observed in core plugs. The suggested evaluation is based on plotting the normalized data obtained by taking the apparent viscosity (measured during core experiments) divided by bulk viscosity (rheometer) against the apparent shear rate. As reported by Howe et al., [26] , this manner of plotting is equivalent to plotting the measured pressure during core experiments divided by behaviour expected according to Darcy’s equation.

The results obtained for Flopaam 6035 S non-sheared and at different concentrations, are depicted in Figure 10(a). It is evident from the plot that at a certain shear rate the onset of elasticity occurs. This is consistent with results obtained by Howe et al., [26] and clearly indicates non-dependence of this onset on polymer concentration. This is contrary to the generally accepted assumption often made by the authors in petroleum related literature. For instance, it is assumed that elasticity in porous media depends strongly on the linear viscoelasticity (the one observed in small amplitude oscillatory SAOS measurements). As reported by Hincapie et al., [27] , SAOS can provide an insight only on whether a polymer might be elastic or inelastic, but it fails to predict the behaviour under flow. A similar trend was observed for pre-sheared solutions Figure 10(b).

Comparing Figure 10(a) and Figure 10(b) shows that an early onset seemed to occur for the non-sheared solutions. Quantitatively the ratio of apparent viscosity and bulk viscosity above 50% was found to be around 30 s⁻¹, where the onset started for the non-sheared solutions and around 70 s⁻¹ for the pre-sheared solutions. This was determined by observing the deviation of the ratio from the unity.

Additional support can be given to the results obtained in this work by considering the Weissenberg number. The Weissenberg number is described as a measure of the degree of nonlinearity or that degree to which normal stresses manifest during the flow [28] . For simplicity it can be considered as the product of the relaxation time (of the fluid) and the characteristic shear rate of the flow. In other words relaxation times obtained in Small Amplitude Oscillatory Shear (SAOS) multiplied by the apparent shear rate determined for each measurement. It can be observed in Figure 11 that the onset corresponded to the elastic properties of the polymer solutions. It could be inferred then, as reported by Hincapie, [15] , Howe et al., [26] that flow instabilities are related to elastic turbulence.