Study on polymer mechanical degradation in core plugs versus in capillary tubes

Polymer flooding has been recognized as an effective technology to improve oil recovery. While synthetic polymers have been widely used in this process, mechanical degradation tends to occur at near-wellbore regions where flow rate is high. In this paper, we evaluated the polymer mechanical degradation in both core samples and capillary tubes. Results showed that the degradation tended to be severer when the polymer solution flowing through tighter core samples or through capillary tubes with smaller diameter. After mechanical degradation, the polymer average molecular weight was lower and its distribution became wider, indicating the irreversible fragmentation of polymer molecules. The critical shear rate, beyond which evident polymer degradation occurred, tended to be lower for sandstone cores than that for carbonate cores in the same permeability range. On the other hand, the critical shear rates obtained from capillary tubes were significantly higher than those from the core samples. Correlations between the polymer degradation in core samples and in capillary tubes were established, which can be used to estimate the polymer mechanical degradation in reservoir rocks from the more convenient measurement using capillary tubes. This study provides a robust technique for polymer evaluation, and the results are also helpful for better understanding of the polymer flow in porous media.

Keywords Polymer · Mechanical degradation · Capillary tube · Carbonate core · Sandstone core · Critical shear rate

Introduction
Water soluble polymer has been widely used in chemical flooding processes for improving oil production. The main function of polymer is to make injection water more viscous to increase the macroscopic sweep efficiency of the flooding (Saboorian-Jooybari et al. 2016;Gao 2016). In chemical flooding, there are two main groups of polymers: synthetic polymers and biopolymers such as xanthan gum (Han et al. 2013;Wang et al. 2006;Kamal et al. 2015;Chen et al. 2021, Husna et al. 2022. The synthetic polymers included polyacrylamides, hydrolyzed polyacrylamides, sulfonated polyacrylamides, and associative polyacrylamides. They were used in most field applications due to their excellent performances and relatively low cost. The stability of polymer in aqueous solutions is the most concerned problem in the application (Han et al. 2014;Zhang et al. 2019;Kolawole et al. 2021). These synthetic polymer molecules possess flexible chain structures, which are more or less sensitive to mechanical shear (Sorbie 1991;Chen 2019). Owing to the chemical structures of the polymers, they experience different degrees of mechanical degradation in the surface injection facility and near-wellbore formations during the injection (Littmann et al. 1992;Puls et al. 2016). Mechanical degradation means that fluid stresses become large enough to fragment polymer molecules, resulting in an irreversible loss of viscosity and resistance factor. This happens when a polymer solution is flows at high flow rate through a porous medium or a constriction (Seright 1983), as shown in Fig. 1. When subjected to extension, polymer chain can elongate drastically and break. Therefore, the mechanical degradation of polymer in solution is mainly studied in extensional flows rather than in shear flow (Dupas et al. 2012). The most obvious way to quantify the mechanical degradation is to compare the viscosity of polymer solution before and after a forced flow. There are mainly two methods to evaluate the mechanical degradation, flow in capillary tube and flow in porous media.
In the capillary tube method, polymer solution flows through a contraction by a capillary geometry, creating an extensional laminal flow (Dupas et al. 2013). Ghoniem et al. (1981) reported that the mechanical degradation occurred in the entrance region of the capillary. The macromolecules were stretched by the extensional forces to overcome the C-C bond strength. Zaitoun et al. (2011) conducted capillary shear tests for EOR polymers. The effects of polymer molecular weight, polymer structure, and brine salinity were investigated. The results were interpreted in terms of macromolecule chain rigidity. Dupas et al. (2012) reported that the critical extensional rate strongly depended on the concentration and flow regimes, and also on solvent quality. Dupas et al. (2013) conducted capillary degradation tests and measured the extensional and shear viscosities. The results showed that the degradation affected shear viscosity much less than viscous dissipation in rapid converging flow. Wei et al. (2016) confirmed the entrance effect when polymer converges into the capillary tube. The effects of shear rate, shear circles and salinity were also investigated. The degraded polymer viscosity recovering with time was observed. Divers et al. (2017) studied the effects of ions and functional monomers on mechanical degradation by the capillary shear. Asen et al. (2019) studied the degradation in capillaries with different diameters and concluded that degradation depended on the velocity at the capillary entrance rather than on the shear rate at the capillary wall.
During flow in porous media, polymer solutions show shear thickening behavior from moderate to high flow rates. This causes the increase in resistance factor with increasing flux (Seright et al. 2011). However, at even higher flow rates, polymer degradation can occur. Seright (1983) reported that polymer solution showed an "entrance pressure drop" upon crossing the sandface when flowing through cores at high flow rate. Polymer mechanical degradation occurred mainly in the inlet face region. Martin (1986) studied polymer degradation in carbonate cores and found low permeability cores exhibited severer mechanical degradation. The heterogeneous nature of carbonate cores presented difficulties for the prediction of polymer degradation. Seright et al. (2008) studied the injectivity characteristics of polyacrylamide polymers. Results showed that the polymer solutions presented pseudo dilatant behavior at moderate to high fluxes. The onset of mechanical degradation occurred at a flux of 14 ft/d in 573 md Berea sandstone. Dupas et al. (2013) reported that extensional viscosity decreased more than the shear viscosity, resulting in much less resistance in porous media even at no shear viscosity loss. Brakstad and Rosenkilde (2016) proposed a physically based model for calculating polymer In most of previous works, only one of the two methods, either by capillary tube or by core plug, was used to evaluate the polymer degradation. For method using core plugs, only sandstone core plugs were used. In this work, we used both capillary tubes and core plugs to evaluate the mechanical degradation of polymers. The effects of core permeability, core length, and rock lithology including sandstone and carbonate, as well as capillary diameter were investigated. The molecular distributions of the sheared samples by capillary tubes and cores were measured and compared. The correlation between the degradation results by these two methods was explored to assist the operation of the polymer injections.
The paper is structured as follows. First, the experimental section is set up, including the experimental material and methods. Then in the results and discussion, the mechanical degradation results in capillary tube and core plugs were compared and investigated. The correlation between the two methods was developed. Lastly, it is presented with the summary and conclusions.

Brines
A synthetic high salinity water (HSW) was used to prepare the polymer solutions. The total dissolved salt (TDS) was 57,670 mg/L. Synthetic connate water with 213,734 mg/L TDS was used to saturate the core plugs. Table 1 shows the ion compositions of the brines.

Polymer
The polymer was a sulfonated polyacrylamide with a molecular weight of 14 million g/mol and hydrolysis degree of 4.2%.

Core plugs
Both carbonate and sandstone core plugs were used in the tests. The permeabilities ranged from 40 to 490 md. Table 2 gives the information of the core plugs.

Test procedure of mechanical degradation in cores
AFS-300 Coreflooding System, Core Lab, USA, was used in the core degradation test. Figure 2 gives the diagram sketch of core flooding system.
The test procedure is shown in the following flow chart (Fig. 3).

Test procedure of mechanical degradation in capillary tubes
Mechanical degradation in capillary tubes followed similar procedure of the tests in cores. The 2000 mg/L polymer solution was injected into the capillary tubes at different flow rates by the Coreflooding System. The effluent was collected after the polymer injection of at least 50 mL.

Viscosity measurement
The viscosity of the polymer solution was measured by TA Rheometer. The tests were at steady state with shear rate varied from 1 to 100 s −1 . The results gave the fluid viscosity as a function of shear rate.

Molecular weight distribution measurement
An Agilent 1260 gel permeation chromatography (GPC) system coupled with a refractive index detector (RID) and a light scattering detector (LS) was used for the determination of molecular weight distribution of polymer samples (Hou et al. 2020a, b). The column is PL auqagel-OH column (Mw range 1000 to > 10,000,000). Mobile phase was NaH 2 PO 4 solution with CH 3 COONH 4 and formamide. The dn/dc value was measured on Wyatt Optilab refractometer and turns out to be 0.163. The temperature of column and detector were both set at 45ºC to minimize the adsorption of polymers on the column.

Mechanical degradation in cores
Five mechanical degradation tests were conducted using carbonate and sandstone core plugs with different permeabilities and lengths. To calculate the shear rates in porous media, different equations were proposed. In this work, the model by Cannella et al. (1988) was used to estimate the equivalent shear rates at different flow rates, as Eqs. (1) and (2).
where K (mPa s n ) and n (dimensionless) are the consistency index and the component that are obtained by fitting the viscosity-shear rate curve, u p is the Darcy velocity of the polymer containing water phase in m/s, k is the average permeability in m 2 , k rw is the water phase relative permeability, S w is water saturation in fractional, φ is core porosity, ∞ is the viscosity at infinite shear rate in mPa s, and C is an empirical constant. Test the voscosity and molecular distribuiton of the effluent A general opinion is that the mechanical degradation comes from the extension but not shearing of the flow (Seright 1983). The elongation rate in a porous media was defined as the ratio between the interstitial flow rate and the average grain diameter (Southwick and Manke 1988), which was close to the shear rate equation. In the following discussion, the shear rate was used to interpret the degradation results.

Polymer viscosity after mechanical degradation
The viscosities of the polymer samples after flow through core samples at different flow rates were measured for evaluating the mechanical degradations. Figure 4 shows the relative viscosity (viscosity/viscosity initial ) for the sheared polymer samples after flowing through the five core plugs. The results indicate that the relative viscosity decreased with increasing flow rate. In low permeability cores (C59 and S39), the relative viscosity reduction was faster than that in moderate permeability cores (C31, S08 and S30). This also suggests that the polymer degradation in cores relies primarily on the core permeability rather than the lithology.
On the other hand, the viscosity loss of polymer solution after flowing through the cores can be calculated by Eq. 3.
where µ after is the viscosity of the sample after flow through the core in mPa s, µ before is the viscosity of the initial sample before injection in mPa s. Figure 5 shows the viscosity loss results of the polymer solutions after flow through the two carbonate core samples, C31 and C59. The viscosity of the effluent polymer solution after flowing through core C31 (3) Viscosity loss = after − before before ⋅ 100, did not show significant decrease at flow rates below 20 mL/ min. A noticeable decrease in viscosity happened at flow rate of 20 mL/min, which is corresponding to a shear rate of 4402.06 s −1 . For the effluent from the test on core 59, the viscosity decrease occurred at the flow rate 2 ml/min, corresponding to a shear rate of 1122.21 s −1 . At the same shear rate, polymer viscosity loss was higher for the effluent from core C59 than that from core C31. The permeability of core C31 and core C59 were 390 md and 60 md, respectively. The less permeable core produced more severe mechanical degradation to the polymer solution. To confirm the results, the polymer mechanical degradation was conducted on two sandstone core samples, S08 and S39, with similar permeability ranges. Figure 6 shows that similar to the tests on the carbonate cores, there were critical shear rates above which the effluent polymer viscosity started to decrease. The polymer solution lost more viscosity after flowing through the lower permeability core sample of S39 than that after flowing through the higher permeability core.
In field injection, the polymer solution flows through the wellbore radially to the reservoir. The flow rate is much higher at the regions near the wellbore than in the deep reservoir. When passing through convergent and divergent pores in the porous media at high flow rate, the abrupt flow rate change will produce an extension dominated flow. The polymer chain can be stretched without fully adjusting the conformation in align with the flow field. Above a critical extensional strain rate, the polymer chain is ruptured to smaller chains. Not like the viscosity change due to the shear thinning in rheometer, the mechanical degradation results in the permanent viscosity loss and affects negatively to the performance in the deep reservoir.
Two sandstone core plugs with similar permeability but different length was used to study the effect of core length on the polymer mechanical degradation. Figure 7 shows the  1 3 viscosity loss of polymer in the two core plugs. Although the critical shear rates varied slightly, the two viscosity loss curves almost overlapped after the critical shear rates. This indicates that the length of the core has limited effect on the polymer degradation. This confirmed the general conclusion that polymer degraded only at the rock surface or the first section of the rock (Seright 1983;Jouenne et al. 2017). The degradation occurred at the entrance of the flow constriction which induces the elongation stress to the polymer molecular. The similar stretch in the deep core cannot produce further rapture to the broken molecular chains. Asen et al.
(2019) observed there was degradation taking placing even after 20 m in cores by a novel experimental set-up. However, the degradation was associated with high pressure gradient which at field scale was not realistic. The effect of core lithology on the viscosity loss is shown in Fig. 8. The two core plugs were in same length and slightly different permeabilities. The critical shear rate of carbonate core C31 was higher than the sandstone core S10. This indicated that the carbonate core had less mechanical degradation capacity than the sandstone core at relatively low shear rate. When shear rate was above 4000 s −1 , the polymer viscosity loss became larger in the carbonate core than in the sandstone core. As well illustrated in the literature, carbonate reservoir was inherently more heterogeneous than sandstone reservoir due to the susceptible mineralogy, complex deposition and diagenetic processes, and fracturing. Even in the core scale, there was micro fractures or large pores, which had more contributions to the flux. The extension or shearing to the polymer chains was much lower in these large flow channels. This maybe the reason of higher critical flow rate in carbonates. Given that the permeability of carbonate core C31 was lower than the sandstone core S10, at high flow rate the polymer chains undertook server extension or shearing when flowing through sample C31, leading to greater viscosity loss.

Polymer injectivity and in situ rheology
The pressure difference between the inlet and outlet of the cores was recorded in the five mechanical degradation tests. A stabilized differential pressure was achieved at each flow rate. Using the pressure and flow rate data, the injectivity and injectivity loss of the polymer flow was calculated by the method of Han et al. (2012). The five tests showed similar a trend in the pressure gradient and injectivity. Figure 9 shows the results of Core C31 as an example. As pressure gradient increased with the flow rate, the injectivity decreased significantly under low shear rates up to 20 mL/min and then increased slowly as the flow rate increasing. This corresponds to the viscosity results in Fig. 4, in which the noticeable decrease in viscosity started at flow rate of 20 mL/min. The mechanical degradation of the polymer solutions made it easier to flow through the porous Sandstone S08 490 md Sandstone S10 450 md Fig. 7 Viscosity loss in the sandstone core S08 and S10 Carbonate C31 390 md Sandstone S10 450 md Fig. 8 Viscosity loss in the carbonate core C31 and sandstone core S10 media, thus increasing the injectivity. The transition point was consistent with the critical flow rate of mechanical degradation, which confirmed the viscosity loss due to the mechanical degradation. The other four tests showed similar results. Assuming the Darcy's Law holds in the flow rate range of the tests, the apparent resistant factor of polymer solution could be calculated by the stabilized differential pressure at each flow rate by Eq. 4.
where ARF is apparent resistant factor in mPa s, RRF is the residual resistant factor in dimensionless, µ a is apparent viscosity in mPa s, K core is permeability in d, A is sectional area of core plug in cm 2 , ΔP is pressure drop in atm, q is flow rate in mL/s, L is core length in cm.
As an example, the result of the apparent resistance factors from the test on core sample C31 is shown in Fig. 10 in comparison with the effluent polymer viscosities measured by rheometer. The apparent resistant factor first increased and then decreased with increasing flow rate. Polymer solution is non-Newtonian fluid. With the increase of flow rate, the polymer behavior in the porous media changed in four stages, apparent Newtonian flow, shear thinning, shear thickening and mechanical degradation (Ghoniem et al. 1981;Stavland et al. 2010). The increase of apparent resistant factor corresponded to the shear thickening stage, which caused by the elongation of the molecule above a critical shear rate. The decrease of apparent resistant factor corresponded to the mechanical degradation. Compared with the viscosity measured by rheometer in the blue line in Fig. 10, the apparent resistant factor was much higher. Considering that the residual resistance factor caused by polymer injection was limited, the high apparent resistant factor mainly came from the high apparent viscosity.
(4) ARF = RRF* a = K core AΔP qL The possible explanation was the viscoelastic and the turbulent energy dissipation at high flow rate.

Mechanical degradation in capillary tubes
According to Dupas et al. (2013), the equivalent shear rate by a capillary tube in terms of flow rate is calculated by Eq. 5.
where Q is the flow rate, m 3 /s; R is the inner radius of the capillary tube, m; γ is the equivalent shear rate, s −1 .
Because the characteristic average extensional rate at the entrance of the capillary is proportional to the shear rate, the capillary degradation results were interpreted by the shear rate.

Polymer viscosity after mechanical degradation
Three capillary mechanical degradation tests were conducted using capillary tubes with diameter of 0.12 mm, 0.254 mm and 0.508 mm. The viscosities of sheared samples by the three capillary tubes are plotted in Fig. 11. In the three tests, the viscosities of degraded samples below 200,000 s −1 did not show noticeable viscosity decrease. A relatively significant decrease in viscosities happened at an experiment shear rate of 200,000 s −1 , which indicated that a critical shear rate at 200,000 s −1 caused the polymer solution to lose large part of its viscosity.
Despite that the shear rate calculation took the tube inner diameters into account, the shear effects were different. The effects of capillary tube inner diameter on the  viscosity loss are shown in Fig. 12. We can see that under the same shear rate, the smaller the tube inner diameter, the stronger the shear effects. Although the shear rate was proportional to the extensional rate, it did not include the effect of the entrance abruption. For the smaller capillary tube, diameter difference at the entrance was larger, which produced higher elongation to the polymer chains. Consequently, the polymer lost more viscosity even at the same shear rate. However, the absolute difference was not so large. The degradation was still flow rate dominated.

Molecular weight distributions
The molecular weight distributions of the injected polymer sample and the degraded sample after flowing through porous media were measured by GPC. The results from the test using the 0.254 mm capillary tube are presented in Fig. 13 as an example. We can see that as the shear rate increased, the distribution showed a wider range of molecular weights, indicating that the long chains may have been cut into shorter chains during the degradation. The molecular distributions of degraded samples from core S08 are shown in Fig. 14. Unlike the results from the test using capillary tube, the distributions do not show a significant expansion in the range of the molecular weights. This could be caused by the malfunction of the GPC equipment. Puls et al. (2016) found the slight shift to the low molecular weight of the core sheared polymer sample. There was a general agreement that the polymer mechanical degradation was from the scission of the polymer chains. For the semi-dilute polymer solution, the degradation is governed by the entanglement network, and chain scission is random in laminar flow. Whereas in inertial flows, the chain degradation is mid-chain scission (Dupas et al. 2012). It seems that the degradation in current study was in the form of random scission, especially for the degradation in the cores.

Correlation between degradation in cores and capillary tubes
Both core plugs and capillary tubes could induce irreversible viscosity loss-mechanical degradation for polymer solution. Jouenne et al. (2017) conducted degradation test using different geometries and proposed an empirical normalization method to investigate a successive degradation event.
The results suggested that polymer mechanical degradation was path independent. So, any kinds of degrading geometry could represent the field degradation during injection. A possible inference was different geometries can be correlated with each other. Dejam (2018) setup a model to capture solute transport in a conduit (channel or tube) adjacent to a porous medium. Capillary tube could be considered as a basic element of the core plug. Core plug can be simplified to a bundle of capillary tubes connected in parallel and/or series. From this point of view, the core mechanical degradation could be correlated with the degradation in capillary tubes. Figure 15 presents the viscosity (at 6.81 s −1 ) results of the effluent samples from the mechanical degradation test using the 0.12 mm capillary tube. The relationship between the effluent viscosity and the capillary shear rate was fitted by an exponential equation, which is also shown in Fig. 15. Similarly, the effluent viscosity from the core degradation test is a function of the flow rate. A relationship between the core flow rate and the capillary shear rate could be established by achieving the same effluent viscosity. Figure 16 shows the estimated capillary shear rate (0.12-mm tube) as functions of the flow rate in core for the four core degradation tests. Results showed two groups of curves assorted by the permeability ranges, demonstrating different trends of polymer degradation in low permeability cores (C59 and S39) and in moderate permeability cores (C31 and S08). This was in consistence with the experimental results shown in Fig. 4. The cores having similar permeability demonstrated a very close relationship between the capillary shear rate and the flow rate in core. This indicates that the capillary degradation results could be used to estimate the core degradation with different core permeability for a certain polymer.
A mathematical correlation was developed based on the above relationship between the two test methods to explore an easy-to-operate method for estimating the polymer degradation in porous media, as in Eq. 6. The calculation results from this model are plotted as the lines in Fig. 16. Table 3 gives the inputs for the four core degradation tests.
The relationship can be enriched by additional more shear experiments and serve as a database of degradation curves for a specific polymer or rock.
in which, γ is the equivalent shear rate at certain flow rate in cores, s −1 , u is flow rate in cores, cc/min, γ max and γ min are the maximum and minimum equivalent shear rates, s −1 , and T is a scale factor.

Discussion
Polymer mechanical stability is an important factor to access and predict the performance of polymer flooding in reservoir. The tests using core samples are usually time consuming. The correlation between the degradation by capillary tubes and by core plugs provides an easy-to-operate way Flow rate, mL/min Fig. 16 Relationship between flow rate in core and corresponding shear rate in capillary at same effluent viscosity to evaluate the polymer mechanical degradation in porous media. By establishing a mapping between capillary tube and different permeability core plugs, the mechanical degradation at different flow rate can be predict. This mapping is also easy to be implemented in a simulator for an up-scaling simulation.
Physically, the mechanical degradation of polymer in core plug is much more complicated than that in capillary tubes. As long as the core plug is homogenous, there is a mathematical correlation between them. As the previous results showed that polymer viscosity loss caused by the degradation in carbonate cores was slightly different than that when flowing in the sandstones. The heterogeneity makes the mathematical mapping differently. One possible way to solve this problem is to setup a specific mapping using core plugs in same reservoir with similar heterogeneity.
All the tests in this work were performed at ambient condition. The oil reservoir is usually at high temperature and high-pressure conditions. To simulate this in the lab, a back-pressure regular is commonly used. There is a film in the regular. When the fluid pressure on one side of the film is larger than the pre-set pressure on the other side, the fluid is allowed to flow out. During this process, the fluid pressure dropped abruptly from pre-set pressure to ambient pressure, causing an additional degradation to the polymer. This is a great challenge to simulate the polymer degradation at high pressure condition. Both degradation in heterogeneous reservoir and at harsh reservoir conditions will be focused in further study.

Summary and conclusions
This work studied the mechanical degradation of polymer in capillary tubes and core samples. The effects of core permeability, core length, and rock lithology including sandstone and carbonate, as well as capillary diameter were investigated. The correlation between the mechanical degradation by these two methods was explored.
1. Polymer mechanical degradation in carbonate and sandstone cores showed critical shear rates beyond which significant viscosity loss took place. The critical shear rate was higher in carbonate cores than that in the sandstone cores in the same range of permeability. 2. Severer polymer mechanical degradation occurred in lower permeability cores, compared to that in higher permeability cores. 3. The core length had limited effect on the polymer mechanical degradation in terms of the critical shear rate and severity of the degradation. 4. The viscosity loss caused by the mechanical degradation improved the polymer injectivity in both carbonate and sandstone cores. 5. The critical shear rate was 200,000 s −1 for polymer degradation in the capillary tubes. Beyond the critical shear rate, the mechanical degradation appeared severe in smaller diameter capillary under the same shear rate. 6. The molecular weight distribution after mechanical degradation indicated the breaking of long molecular chains via random scission. 7. The polymer mechanical degradation occurred in capillary tubes can be correlated with that occurred in cores. This provides a convenient way to estimate the polymer mechanical degradation in reservoir rocks.
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