Journal of Colloid and Interface Science 234, 269–283 (2001) doi:10.1006/jcis.2000.7306, available online at http://www.idealibrary.com on

Unsteady-State Flow of Flexible Polymers in Porous Media Pacelli L. J. Zitha,∗,1 Guy Chauveteau,† and Liliane L´eger‡ ∗ Department of Applied Earth Sciences, Delft University of Technology, Mijnbouwstraat 120, 2628 RX Delft, The Netherlands; †Division Gisements, Institut Franc¸ais du P´etrole, 1 et 4 Avenue de Bois-Pr´eau, 92506 Rueil-Malmaison Cedex, France; and ‡Laboratoire de la Mati`ere Condens´ee, Coll`ege de France, 11, Place Marcellin Bethelot, 75231 Paris Cedex 05, France Received October 28, 1999; accepted October 30, 2000

In this paper we report an investigation of the unsteady-state flow of polymer solutions through granular porous media. The experiments were performed using high-molecular-weight nonionic and anionic polyacrylamides dissolved in water containing NaCl and model porous media obtained by packing silicon carbide (SiC) grains having a narrow grain size distribution. Before injection in porous media, the polymer solutions were carefully filtered according to a method that was proved to be efficient in removing any possibly remaining microgels. The SiC grain surface was passively oxidized by a controlled thermal treatment in order to obtain a surface partially covered by a thin silica layer having adsorption properties similar to those of quartzitic sand. By packing SiC grains of different sizes, porous media having identical adsorption properties and well-known pore throats sizes can be obtained with a good reproducibility. Parameters investigated include pore size, velocity gradient, polymer concentration, and adsorption energy. A striking unsteady-state flow behavior (pressure build-up at constant flow rate) is observed when three conditions are fulfilled: (a) the velocity gradient is larger than that known to be able to induce a coil–stretch transition, (b) the polymer adsorbs on the pore surfaces, and (c) the length of stretched macromolecules is larger than the effective pore throat diameter. When one of these conditions is not satisfied the flow remains steady. These observations are interpreted by a mechanism involving the adsorption and bridging across pore restrictions of elongated chains. We propose to refer to this peculiar mode of polymer adsorption as bridging adsorption. °C 2001 Academic Press Key Words: flexible polymers; polyacrylamides; elongation; adsorption; pore bridging; porous media; polymer filtration.

I. INTRODUCTION

Flexible polymers dissolved in (salted) water exhibit distinctive properties in porous media, allying a variety of physical features (complex rheology, adsorption, depletion near pore walls, permeability reduction, etc.) covering a broad range of usefulness. Fields where these properties are crucial include hydrocarbon recovery, water production and treatment, soil stabilization, filtration for separation, and purification in various laboratory

1 To whom correspondence should be addressed. E-mail: p.l.j.zitha@ ta.tudelft.nl. This author was affiliated with IFP during this study.

and industrial processes, to mention only a few. As a consequence great research efforts have been devoted in the past to investigating the characteristics of polymer flow-through porous media. As has been shown in several reviews (1–4), most previous studies have concerned either the influence of the velocity gradient in high-permeability media or the apparent viscosity in low-permeability media maintaining the velocity gradient sufficiently low. Studies devoted to pressure build-up phenomena in porous media are scarce in the literature and, to our knowledge, only Ref. (5) seems to have noted that pressure build-up occurs when the flow rate exceeds a certain onset value. In these early experiments, high-molecular-weight hydrolyzed polyacrylamide samples were injected by steps of increasing flow rates in low-permeability (small pores) granular porous media obtained by packing crushed quartz grains. At high flow rates, a slow pressure build-up was observed followed by a leveling off to a plateau. The plateau values increased with the flow rate and were always higher than the values that could be expected from viscosity measurements. However, when the experiments were performed the knowledge of the elongational and adsorption behavior was latent which hindered the interpretation of the results. At the same time, other authors (6, 7) showed that not only adsorption but also retention by mechanical means should be taken into account in the attempts to understand polymer flow in porous media. Several works (8, 9) showed later that polymer aggregates and microgels present in most commercial polymers could be at the origin of pressure build-up. This led to the development of a method of filtration with a low-velocity gradient to remove the microgels as described in Ref. (8). Since the behavior of polymer solutions at high flow rates is deemed crucial to control a large number of applications (reduction of water production in oil and gas recovery, industrial and laboratory filtration processes), the study reported below has been carried out. The purpose of this study was to investigate unsteady flows under well-controlled conditions in order to provide a reliable interpretation of this phenomenon. This is possible now mainly because a better understanding of the elongational flow and adsorption properties of flexible polymers in porous media has been achieved over the past two decades (3).

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The experiments consist of injecting nonionic and partially hydrolyzed polyacrylamide (PAM and HPAM) solutions in packs of calibrated silicon carbide (SiC) grains. Such linear flexible polymers are obtained by free-radical polymerization. The possible remaining microgels have been fully removed by extensive filtration of the solution through Millipore filters at very low deformation rates (8). Silicon carbide packs mimic natural sandstones while enabling a good reproducibility of both their pore size and their adsorption properties. The grain surfaces are partially coated with a thin layer of silica due to a thermal treatment designed to obtain a passive oxidation (see Section II.c and Ref. (10)). This paper is organized as follows. After a review of the literature concerning the microscopic aspects of polymer flow in porous media the experimental details are provided. The results are then given and discussed. The results are reported in four parts: (a) A series of experiments showing that unsteady flow is linked to polymer adsorption and high-velocity gradients is presented. The unsteady flow is interpreted as being the result of the adsorption of previously stretched chains across pore restrictions (bridging adsorption). (b) The determining parameters derived from this analysis are varied systematically to check whether their influence supports this interpretation. (c) The correlation between plugging level (increase of pressure drop) and polymer retention is established using an original method to determine how in-depth the polymer is retained inside a porous medium. (d) The irreversibility of bridging adsorption by varying flow rate is checked. Desorption occurs only when a strong desorbing agent is added to the flowing solvent (salted water). The conclusions of this study are then gathered. II. BACKGROUND

The excellent but dated review by Savins (1) emphasized that the rheology of polymer solutions in porous media flows was practically identical to that observed in pure shear flows despite the fact that polymer chains flowing in porous media are subjected to complex hydrodynamic stresses. However, this review concerned mainly experiments carried out with polymers having a size in solution negligible compared to that of pore restrictions, while several experimental results reported at that time had suggested complex retention phenomena. Subsequently, a survey of the studies of polymer flow through porous media in the petroleum literature by Willhite and Dominguez (2) stressed the significance of the adsorption of polymer chains onto pore walls. More recently, Chauveteau (3, 4) reviewed comprehensively the microscopic aspects associated with the rheology of the polymer solution focusing on depletion and adsorption phenomena on both macroscopic and pore levels. Those aspects are briefly reviewed below. We develop a simple picture of the microscopic aspects involved in polymer flow through porous media by considering two characteristic lengths, namely the chain end-to-end distance R (this is the Flory radius

RF for undeformed coils) and the effective or hydrodynamic pore diameter DP . Note that flow is characterized by the permeability k (an expression of the hydrodynamic conductivity) at the macroscopic level and by the effective or hydrodynamic pore diameter DP at the microscopic level; the pore diameter scales like the square root of the permeability for unconsolidated granular packs having the same porosity. a. Large pores. When DP À R (high permeability) polymer flow resistance does not depend on time (steady flow) at any constant velocity gradient, in accordance with the simple idea that there is neither flow-induced aggregation nor significant polymer–pore wall interactions. At low gradients the flow is Newtonian as observed by many authors (1–7). This Newtonian behavior means that thermal motion is dominant over hydrodynamic convection and therefore chains behave like statistical spherical coils without any significant deformation induced by hydrodynamic forces. At higher velocity gradients, the flow is shear-thinning as was shown in a number of studies (1–16). Shear thinning is observed when shear forces become predominant over Brownian forces, so that the coils are slightly elongated to become ellipsoids, thus reducing their size in the direction normal to flow. At even higher gradients, the flow was found to be strongly shear-thickening. This was interpreted by several workers by the predominance of the extensional stresses which can induce a coil-to-stretch transition (11–23). Such a transition was theoretically described by De Gennes (24, 25) as well as by Bird et al. (26). De Gennes predicted that the coil–stretch transition occurs when the elongation rate becomes larger than the reciprocal of the chain’s longest relaxation time. Moan et al. (15–17) showed that only shear thinning is observed in pure shear flows even at very high shear rates so that extensional stresses are needed to produce significant polymer stretching. In addition, Magueur et al. (17, 18), by using home-made periodically constricted capillaries, showed that the repetition of elementary extensions at short time intervals was able to produce very significant stretching, thus giving a convincing explanation of the shear thickening observed in porous media flows (18). Using ideas and experimental methods developed by James et al. (13, 14) it was shown that, in porous media, polymer elongation occurs mostly near the stagnation points behind the grains (3). This finding was in contrast with the earlier idea that elongation occurred at the converging zones upstream of the pore constrictions. Another important aspect was pointed out by James and Saringer (13). These authors showed that shear stresses occurring just before elongational stresses also reduce the critical elongation rate. This implies that during polymer flow through porous media, the coil–stretch transition can occur at much lower flow rates than the critical values obtained directly from the critical relaxation times of the chains. b. Small pores at low gradients. When R ∼ DP (but still DP > R) retention and sorption effects become obviously more significant. As already mentioned, the retention of microgels too large to pass through pore throats leads to a continuous increase

UNSTEADY-STATE FLOW OF FLEXIBLE POLYMERS

in flow resistance with time (3, 4, 8, 9). To prevent this artifact, a method consisting of filtering the solutions at very low gradients to remove the microgels was used to carry out several studies on polymer flow in small pores at low gradients (Newtonian limit). By using those solutions without microgels Chauveteau (27–30) showed that negative sorption (depletion layer effect) leads to a decrease of the polymer’s apparent viscosity as the pore size increases. These authors proposed a simple two-fluid flow model for the dependence of the apparent viscosity on pore dimension and polymer size and concentration, which is valid both in the absence and in the presence of an adsorbed layer. The twofluid model is consistent with the statistical approach of Aubert and Tirrell (31) who used elastic dumbbell models for polymer chains. These models retain the main features (e.g., concentration profile near the wall) of De Gennes (32) scaling theory for flexible chains near solid walls as well as of other models for the depletion effect presented in the comprehensive review of Kawaguchi and Takahashi (33). The thickness of the depleted layer was chosen to be equal to 1.24 times the radius of gyration in agreement with the theoretical work of Casassa et al. (34) using random walk chains as models for polymer chains. Casassa’s results were confirmed by Daoud et al. (35) and then by Adam and Delsanti (36) by small-angle neutron and light scattering experiments, respectively. Positive sorption (adsorption), on the other hand, gives rise to a polymer layer on pore walls. Since adsorbed chains are attached to the surface by a large number of segments they cannot be removed simultaneously so that adsorption seems irreversible for a long time (37–39). Therefore, the adsorbed layer reduces durably the permeability as was oberved by Gramain and Myard (39). Using a simple capillary bundle model, Bagassi et al. (37) showed that the pore diameter is reduced by nearly twice the viscometric radius of gyration. This indicates that a single layer adsorption occurs in agreement with the theoretical studies of De Gennes (32) among others (33). Hand and Williams (40) and Hikmet et al. (41) have suggested the occurrence of entanglement in the adsorption layer, forming multilayers for some specific polymer–surface couples. However, such entanglement processes can safely be disregarded in our experimental system. Below the origin of adsorption in silicon carbide is discussed. c. Adsorption energy and origin. Chauveteau et al. (2, 3, 42, 43) and Broseta and Medjahed (44) reported experimental investigations of the adsorption of high-molecular-weight neutral and anionic polyacrylamides from aqueous solution containing NaCl and CaCl2 at various ionic strengths onto both quartzitic sand and silicon carbide particle packs. These authors found that hydrogen bonds between carboxyl groups belonging to the polymer and the silanols on the pore surface play a negligible role in adsorption. The reason is seemingly that hydrogen bonds between silanols and water molecules have energy higher than or similar to that of hydrogen bonds between the carboxylates and silanols. This conclusion was derived from experimental results showing the following two features of nonionic polyacrylamide (PAM) adsorption: (a) the adsorption density of PAM

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does not vary with saline density, as shown by its insensitivity to pH and ionic strength, and (b) the adsorption density of PAM is identical on surfaces that do not bear any silanols, such as titania, carbonates, and basal surfaces of kaolinite and montmorillonite (4). As a result of the negligible role of silanols, it can be concluded that the adsorption of polyacrylamides onto siliceous surfaces is mainly driven by van der Waals forces and entropy. Indeed, the gain in entropy of water molecules displaced by polymer segments is higher than the loss of entropy of the polymer segments during adsorption. The main consequence of the above analysis is that adsorption energy on siliceous surfaces is weak. Under these conditions, the density of polymer segments in direct contact with the surface is low. The polymer segments in direct contact with the surface occupy only a very small fraction of the total available surface so that room remains available for additional adsorption. In contrast, Pefferkorn et al. (45, 46) found that the adsorption density of polyacrylamides on glass beads bearing grafted aluminol groups is much higher and mostly due to short-range hydrogen bond interactions between carboxyls and aluminols, even though van der Waals forces are present. Similar results were found for adsorption on the lateral surface of kaolinite where adsorption density is about 4 times higher than that on surfaces which do not bear aluminols (4). For anionic polymers such as HPAM long-range electrostatic interactions contribute to decrease adsorption energy at low ionic strength (42, 43). In the presence of salt (e.g., NaCl, KCl, CaCl2 ) the charges along polymer chains and on the surface are screened. Hence, the static adsorption properties of the electrically neutral PAM and the anionic HPAM at very high salinity are expected to be quite similar. At moderate salinities, however, the adsorption energy of HPAM is much lower than that of PAM. Adsorption can be determined by the depletion of polymer in a solution brought into contact with the solid grains (42, 46). This batch adsorption method represents only approximately the phenomena taking place in granular porous media. For this reason Broseta and Medjahed (44) among others (47) estimated adsorption in porous media from the delay of polymer front with respect to a nonadsorbing tracer. This method may be less accurate than the depletion technique due to the inaccessibility of a fraction of the solid surface accessible to the polymer. d. Nonadsorbing systems. Lecourtier et al. (43) and Broseta and Medjahed (44) showed that the adsorption of polyacrylamide can be strongly reduced when the SiC grains have been subjected to an active oxidation obtained by a thermal treatment at 700◦ C for over 15 h in the presence of air. Under these conditions the SiC surface becomes amorphous silica. This idea is consistent with the earlier studies by Griot and Kitchener (48) where polyacrylamides were shown to adsorb very little on amorphous silica previously hydrated. Chauveteau and coworkers (49) have found that another method to prevent the adsorption of PAM on SiC consists of adding Na2 HPO4 to the batch.

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TABLE 2 Properties of the Polymer Solutions

III. EXPERIMENTAL

1. Materials and Methods a. Polymer solutions. Most of the experiments were performed with a nonionic polyacrylamide (PAM), and the remaining ones with a partially hydrolyzed polyacrylamide (HPAM). Both polymers were manufactured by Rhone-Poulenc, and were provided as a clean white powder with about 10 to 15% hydration water (this water-to-polymer ratio varies with time, hydrolysis, and conditions of storage of the polymer). Polymer properties are summarized in Table 1. The weight-average molecular weight M¯ w of both polymers, and the degree of hydrolysis τ of HAPM, were reported in previous papers (15–18). M¯ w was determined by small-angle laser light scattering using a Chromatix KMX6 apparatus, and τ by potentiometric titration. The index of polydispersity ID was determined by a method of flow-dependent fractional separation (37). Polymer solutions in brine were prepared under gentle stirring and then filtered at low gradient to remove any microgels or microaggregates possibly present, using procedures previously described (see Section II.b and Ref. (8)). Brine solutions were filtered through cellulose acetate Millipore membranes with a pore diameter of 0.22 µm, and degassed under vacuum, to remove any dissolved gas. The properties of the polymer solutions are given in Table 2. Polymer concentrations were determined by total organic carbon (TOC) analysis, using a Dhormann 80 apparatus. The viscosities were determined with a Low Shear 30TM Couette viscometer, allowing measurements over a wide range of shear rates including very low ones (0.01–100 s−1 ). With the data given in Table 1, the degree of polymerization N and the contour length L c are respectively 1.5 × 105 and 40 µm for PAM. The values for HPAM are roughly the same. The properties of the polymer solutions, determined by viscometry, are given in Table 2. All data were obtained at 30.0 ± 0.1◦ C. For PAM the intrinsic viscosity [η]0 and the Huggins coefficient k 0 were estimated at 2350 ± 50 cm3 /g and 0.54 ± 0.05, respectively. The fact that k 0 is slightly larger than 0.4 indicates that water is a solvent of intermediate quality at 30◦ C; we use the term almost good solvent conditions for this situation. For the partially hydrolyzed polyacrylamide the intrinsic viscosity and the Huggins coefficient were available in previous papers (3, 4, 15–18) as a function of the salinity. At 20 g/l NaCl, [η]0 and k 0 are equal to 3750 ± 100 cm3 /g and 0.35 ± 0.05, respectively, and to 7100 ± 100 cm3 /g and 0.30 ± 0.05 at 5 g/l NaCl. Since k 0 < 0.4 for both salt concentrations it can be concluded that HPAM is under good solvent conditions. The decrease in inTABLE 1 Polymer Properties Polymer (code)

M¯ w (g/mol)

ID

Degree of hydrolysis (%)

PAM (AD10) HPAM (AD 37)

10–11 × 106 8–10 × 106

2.2–2.4 2.2–2.4