energies

Review An Overview on Polymer Retention in Porous Media

Sameer Al-Hajri * , Syed M. Mahmood * , Hesham Abdulelah and Saeed Akbari

Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak, Malaysia; [email protected] (H.A.); [email protected] (S.A.) * Correspondence: [email protected] (S.A.-H.); [email protected] (S.M.M.); Tel.: +60-111-667-5972 (S.A.-H.); Tel.: +60-5368-7103 (S.M.M.)


Received: 8 September 2018; Accepted: 8 October 2018; Published: 14 October 2018


Abstract: Polymer flooding is an important enhanced oil recovery technology introduced in field projects since the late 1960s. The key to a successful polymer flood project depends upon proper estimation of polymer retention. The aims of this paper are twofold. First, to show the mechanism of polymer flooding and how this mechanism is affected by polymer retention. Based on the literature, the mobility ratio significantly increases as a result of the interactions between the injected polymer molecules and the reservoir rock. Secondly, to provide a better understanding of the polymer retention, we discussed polymer retention types, mechanisms, factors promoting or inhibiting polymer retention, methods and modeling techniques used for estimating polymer retention.

Keywords: polymer flooding; polymer retention; mobility ratio

1. Introduction Implementing enhanced oil recovery (EOR) techniques has become more significant to recover more hydrocarbons, with the continuation of exploration and development of new oil reserves. Vladimir et al. indicated that the lifetime of a reservoir mostly consists of three phases [1]: primary recovery as oil is extracted by naturally driven mechanisms, secondary recovery with reservoir pressure maintaining techniques through water and gas injection, and enhanced oil recovery often called tertiary recovery with a wide range of advanced technologies [2]. In primary recovery and secondary recovery, only 20–40% of the potential oil can be extracted. It is possible to extract up to 30% of the original oil reserve in the well by the implementation of EOR techniques [1,3–5]. Furthermore, as of 2017, it has been estimated by the organization of the petroleum exporting countries that approximately 1.5 trillion barrels of proven crude oil remain in reservoirs globally. After the exhaustion of the applications of conventional recovery methods, enhanced oil recovery helps not only extract these reserves but also guarantees a continued supply of oil in the future [6]. EOR mechanisms broadly include chemical flooding, gas injection and thermal recovery. In chemical flooding, some chemicals such as polymers are added to the injected water to enhance the oil displacement ability. The ability of water to displace oil and increase production was first noticed in the Pithole city area of Pennsylvania in 1865 as an accidental water injection to the hydrocarbon zone [7]. In 1924, petroleum companies realized the problem of insufficient oil recovery by natural energy and the need to sweep more oil from reservoirs, and first five spot pattern water injection was first implemented in Bradford oil field, Pennsylvania [7,8]. More hydrocarbon was extracted using waterflooding techniques. However, in 1949, Muskat first indicated that waterflood performance would be affected by fluid mobility [9], which was an essential discovery that helped other researchers start studying new techniques for improving water mobility. Stiles, Dykstra, and Parsons used permeability and distribution capacity in waterflooding calculations, and the latter two researchers pointed out the effect of the mobility ratio and permeability variation on recovery [10,11]. The mobility ratio’s effect on water

Energies 2018, 11, 2751; doi:10.3390/en11102751 www.mdpi.com/journal/energies Energies 2018, 11, 2751 2 of 19 encroachment for a specific flood patter was also studied. Moreover, the mobility ratio impacts on injection and production histories in a five-spot waterflood were also investigated [12,13]. Furthermore, Dyes showed the effect of the mobility ratio on the production of oil after a breakthrough [14]. By 1962 Caudle, Witte and Barnes suggested that by increasing water viscosity, waterflood sweep efficiency can be improved [15,16]. In 1964, Pye and Sandiford conducted a fruitful study showing that adding a small amount of water-soluble the polymer can efficiently reduce the mobility of water used in waterflooding which in turn will reduce the mobility ratio thus improving sweep of oil [17,18]. Since then, studies were directed towards the polymer flooding efficiency, affecting factors, limitations, challenges, measurements and modeling techniques of polymer flooding.

1.1. Mechanism of Polymer Flooding It is not possible for oil and water to completely displace one another in a reservoir as oil and water are immiscible fluid [19,20]. Immiscibility of both fluids is reflected in the residual oil saturation and irreducible water in the relative permeability curve. As indicated by Mridul results, for a waterflood system, despite the injected quantity of water into the reservoir, the oil saturation is not reduced below the residual oil saturation [21]. Introducing the injected water with a water-soluble polymer will increase the water viscosity [20,22–27]. Moreover, the effective permeability of water in the swept zone can be reduced depending on the type and concentration of the polymer used [28–30]. Polymer flooding is an enhanced oil recovery process in which a specified polymer concentration (usually 200–1500 ppm) is added to the injected water. Polymer increases the viscosity of the injected solution and therefore preferably decreases the water to oil mobility ratio which results in improving the displacement efficiency of the injected displacing solution [31–33]. Polymer flooding does not significantly improve displacement (microscopic) efficiently because the change in capillary number (NC) is rather small. However, residual oil saturation can be reached more quickly and economically [34].

1.2. Mobility Ratio The mobility ratio concept is widely utilized in literature for describing the displacement process efficiency such as waterflooding displacement efficiency [7,35,36]. The mobility ratio provides measurements of the fluid’s relative movement for the displacement process. It is defined as the ratio of the mobility of the displacing fluid to the mobility of the displaced fluid [37]. The term mobility of a fluid is a measure of the ratio of the effective permeability of a particular fluid to its viscosity [21]. For a specific flood application, if the mobility ratio is higher than one, the flood is considered unstable, and viscous fingering is expected. In contrast, a flood is deemed to be stable for a mobility ratio of less than one and displacement is efficient [37]. The following equation defines the mobility ratio.

K K M = rw / ro (1) µw µo

It is important to mention here that mobility ratio is calculated before the breakthrough. From the equation Krw is considered the value at average water saturation behind the flood front in the water contacted portion of the reservoir. This means that polymer flooding application is more efficient if started at earlier stages of the reservoir, particularly before breakthrough. However, lots of polymer flood operations are initiated after water breakthrough [7,31]. As a result, to calculate the mobility ratio during polymer flooding, we use the equation:    Krp Kro Krw Mpo = λrp/λT = + (2) µp µo µw which defines the mobility ratio as the relative mobility of the polymer slug λrp to the total relative mobility of the oil water bank λT. In order to obtain these values, the relative permeability curves need to be measured on native state cores in the laboratory, whereas, the mobility of the polymer is usually Energies 2018, 11, 2751 3 of 19 determined at the residual oil saturation. Furthermore, just before the breakthrough, the relative mobility of the water Krw is assumed to be zero. µw During polymer flooding, the direction of the saturation changes. Therefore, the mobility ratio during polymer flooding for the same polymer concentration increases from a low to a maximum value in the medium saturation range [31]. Jewett and Schurz concluded that improvement in oil recovery using polymer flooding is mainly implemented for cases with waterflooding mobility ratio at a range of 1:10, and the oil recovery increment seems to fall off more quickly below a mobility ratio of one rather than a mobility ratio above ten [38]. The idea of using polymer flooding is to use a polymer that functions as a mobility control agent that will provide a better displacement and sweep efficiencies. It is estimated that the efficiency of Energies 2018, 11, x FOR PEER REVIEW 3 of 18 polymer flood is in the range of 0.7–1.75 lb polymer per bbl of incremental oil production [3]. Therefore, polymer89 flooding During target polymer is the flooding, oil saturation the direct aboveion of the the saturation residual changes. oil saturation Therefore, the [39 mobility–41]. Polymer ratio flooding 90 during polymer flooding for the same polymer concentration increases from a low to a maximum has shown91 tovalue besuccessful in the medium in saturation a variety range of types [31]. Jewett of reservoirs. and Schurz Moreover,concluded that comparing improvement to inother oil enhanced oil recovery92 techniques,recovery usingpolymer polymer flooding flooding is mainly is simpler implemented and efficientfor cases with [42 waterflooding,43]. However, mobility there ratio are significant interactions93 betweenat a range of the 1:10, injected and the oil polymer recovery increment molecules seems and to fall the off reservoir more quickly rock below [44 a –mobility46]. These ratio interactions 94 of one rather than a mobility ratio above ten [38]. may cause95 the polymerThe idea of to using be retainedpolymer flooding by the is to reservoir use a polymer rock that and functions may as cause a mobility a bank control of agent injection fluid to form wholly96 that or partiallywill provide denuded a better displacement of the polymer. and sweep The efficiencies. viscosity It is of estima thisted fluid that bankthe efficiency will be of much lower than the97 injected polymer polymer flood is solution. in the range Generally, of 0.7–1.75 lb this polymer will reduce per bbl of the incremental efficiency oil of production the polymer [3]. flood [47]. 98 Therefore, polymer flooding target is the oil saturation above the residual oil saturation [39–41]. This99 paperPolymer provides flooding has an shown overview to be successful of recent in a variety advances of types in of reservoirs. polymer Moreover, retention comparing in porous media. This overview100 to other consists enhanced of a oil discussion recovery techniques, on polymer polymer retention flooding is concept,simpler and the efficient three [42 mechanisms,43]. However, of polymer retention,101 factorsthere are influencing significant interactions polymer between retention, the injected methods polymer molecules used toand estimate the reservoir polymer rock [44–46 retention]. and 102 These interactions may cause the polymer to be retained by the reservoir rock and may cause a bank modelling103 techniquesof injection fluid for to polymer form wholly adsorption. or partially denuded Furthermore, of the polymer this. The paper viscosity shows of this fluid the bank advantages and technical104 issueswill be of much each lower of the than measuring the injected polymer methods. solution. Therefore, Generally, this this reviewwill reduce paper the efficiency intends of to provide a comprehensive105 the polymer reference flood for [47 researchers]. investigating polymer retention to enhance the understanding 106 This paper provides an overview of recent advances in polymer retention in porous media. This of polymer107 retentionoverview consists and its of relevancea discussion on to polymer retention flooding concept, projects. the three mechanisms of polymer 108 retention, factors influencing polymer retention, methods used to estimate polymer retention and 2. Polymer109 Retentionmodelling techniques for polymer adsorption. Furthermore, this paper shows the advantages and 110 technical issues of each of the measuring methods. Therefore, this review paper intends to provide a Polymer111 comprehensive retention has reference a major for impact researchers onthe investigating rate of polymer polymer propagation retention to enhance through the porous media during112 polymer understanding flooding, of andpolymer consequently, retention and its on relevance oil recovery to polymer [48 ,flooding49]. It hasprojects a substantial. effect in porous media113 on the2. transportPolymer Retention andperformance of polymer solution [50,51]. Consequently, high polymer retention can dramatically delay oil movement and recovery during polymer flooding. To illustrate 114 Polymer retention has a major impact on the rate of polymer propagation through porous media this behavior,115 during Green polymer and flooding, Willhite and (1998) consequently, showed on aoil delay recovery factor [48,49] ranging. It has a substantial from very effect low in retention of 10 µg/g116 to asporous high media as 200 on theµg/g transport as shown and performance in Figure of1 polymer. For one solution pore [50 volume,,51]. Consequently, at low high retention rates 117 and a polymerpolymer concentration retention can ofdramatically 2000 ppm, delay the oil delaymovement factor and recovery is approximately during polymer 0.03 flooding. (3%). To In the case of 118 illustrate this behavior, Green and Willhite (1998) showed a delay factor ranging from very low moderate119 polymerretention retentionof 10 µg/g to ofas high 100 asµ 200g/g µg/ andg as shown a polymer in Figure concentration 1. For one pore volume, of 1500 at low ppm, retention the delay factor is about120 0.35 rates (35%), and a which polymer meansconcentration that of 35% 2000 moreppm, the of d theelay factor polymer is approximately needs to 0.03 be (3%). injected In the for reaching 121 the targetedcase formation, of moderate compared polymer retention to the of 100 case µg/ withg and a no polymer polymer concentration retention. of 1500 With ppm, the very delay high polymer 122 factor is about 0.35 (35%), which means that 35% more of the polymer needs to be injected for reaching retention123 of 200the targetedµg/g andformation, above, compared polymer to the retention case with no might polymer have retention. a tremendous With very high impact polymer on the rates of oil displacement124 retention and of the200 µg/ economicg and above, feasibility polymer retention of polymer might have flooding. a tremendous impact on the rates of 125 oil displacement and the economic feasibility of polymer flooding.

126 127 Figure 1.FigurePolymer 1. Polymer bank bank delay delay factor factor caused caused by polymer by polymer retentio retentionn [52]. [52].

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128 FForor aa successfulsuccessful implementation implementation of of polymer polymer flooding, flooding polymer, polymer retention retention must mustbe evaluated be evaluated before 129 beforefield application. field application It is vital. It is tovital understand to understand and predictand predict the influencethe influence of retention of retention on on the the transport transport of 130 ofthe the polymer polymer solution solution to to have have a a proper proper design design of of field field scale scale projects projects [[5353].]. PolymerPolymer retentionretention has been 131 identifiedidentified as as one of the majormajor concernsconcerns inin thethe polymerpolymer floodingflooding operatingoperating process.process. Polymer retention 132 includesincludes a adsorption,dsorption, mechanical mechanical entrapment, entrapment, and and hydrodynamic hydrodynamic retention retention as shown as shown in F inigure Figure 2. 2.

133 Figure 2. Polymer retention mechanism in porous media [47]. 134 Figure 2. Polymer retention mechanism in porous media [47]. 2.1. Adsorption 135 2.1. Adsorption The interaction between the polymer molecules and the solid surface is referred to as 136 adsorptionThe interaction [54]. This between interaction the polymer makes the molecules molecules and of the the solid polymer surface bind is referred onto the to surface as adsorption of the solid[54]. 137 Thisrock largelyinteraction by physical makes the adsorption molecules (van of derthe Waal’spolymer and bind hydrogen onto the bonding) surface insteadof the solid of chemisorption, rock largely 138 bywhich physical means adsorption a full chemical (van bond der Waal between’s and the hydrogen polymer bonding) molecules instead and the of solid chemisorption, surface is unlikely which 139 meansto form a full [47]. chemical Therefore, bond molecules between the generally polymer are molecules adsorbed and onto the thesolid rock surface surface is unlikely by the to mean form of [47 an]. 140 Therefore,overall low molecules free energy generally as shown are adsorbed in Figure 3onto. The the low rock free surface energy by isthe formed mean of first an overall by an entropic low free 141 energycontribution, as shown as water in Figure molecules 3. The are low released free energy from is the formed polymer first solution by an entropic or rock surfacecontribution, due to as polymer water 142 moleculesadsorption, are this, released in turn, from will the cause polymer an increase solution in entropy or rock [ 55surface]. Reduction due to polymer of the bulk adsorption, polymer solution this, in 143 turn,concentration will cause by an adsorption increase in also entropy increases [55]. entropy.Reduction In of contrast, the bulk there polymer is an entropysolution lossconcentration that counters by 144 adsorptionthe previous also entropy increases gains, entropy resulting. In contrast from the, there loss of is thean configurationalentropy loss that freedom counters of the the previous polymer 145 entropywhen it is gains, adsorbed resulting on the from surface the [ loss56]. Enthalpyof the configurational also contributes freedom to the lowof the free polymer energy of when polymer it is 146 adsorbedadsorption, on that the occurssurface for [56 ionic]. Enthalpy polymers. also Thiscontribut contributiones to the islow due free to polymerenergy of electrostatic polymer adsorption, attraction 147 thator repulsion, occurs for depending ionic polymers. on the This surface contribution net ionic is charge. due to polymer electrostatic attraction or repulsion, 148 dependingPolymers on the are surface characterized net ionic by charge having. high molecular weights and long chains; these chains 149 containPolymers many polarare characterized groups, which by will having attach high to the molecular available weights polar points and long on thechains rock; these surface chains [48]. 150 containEssentially, many the polar polymer groups, occupies which thewill adsorptionattach to the sites avail ata theble polar rock surface,points on so the the rock larger surface available [48]. 151 Essentiallysurface area, the to the polymer polymer occup moleculeies the will adsorption have a higher sites level at the of adsorption. rock surface, Adsorption so the larger can beavailable severe, 152 surfaceas polymer area adsorptionto the polymer is irreversible molecule will [52 ,have57]. If a thehigher adsorbed level of polymer adsorption. occupies Adsorption a large can pore be volume, severe, 153 asit willpolymer be difficult adsorption to recover is irreversible a considerable [52,57 amount]. If the adsorbed of oil. Furthermore, polymer occupies the formation a large permeability pore volume, is 154 itdecreased, will be difficult leading to to recover a lower a recovery considerable factor. amount of oil. Furthermore, the formation permeability 155 is decreased, leading to a lower recovery factor.

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156 157156 Figure 3. Polymer adsorption in porous media [56]. 157 Figure 3.3. Polymer adsorption in porous media [56].]. 158 2.2. Mechanical Entrapment 2.2. Mechanical Entrapment 159158 2.2. MechanicalMechanical Entrapment entrapment has been studied by several researchers (Gogarty, Smith, Szabo, Mechanical entrapment has been studied by several researchers (Gogarty, Smith, Szabo, 160159 DominguezMechanical and Willhite)entrapment [58– 62 has]. P beenolymer studied molecules by severalare relatively researchers large in (Gogarty solution,. Entrapment Smith, Szabo, of Dominguez and Willhite) [58–62]. Polymer molecules are relatively large in solution. Entrapment of 161160 polymersDominguez occurs and Willhite)in porous [ media58–62] .as P olymerthe polymer molecules molecules are relatively are large large relative in solution to the size. Entrapment of the pores. of polymers occurs in porous media as the polymer molecules are large relative to the size of the pores. 162161 Severalpolymers mechanisms occurs in porous contribute media to asthe the net polymer effect termed molecules mechanical are large entrapment. relative to the Gogarty size of visualiz the pores.ed Several mechanisms contribute to the net effect termed mechanical entrapment. Gogarty visualized 163162 mechanicalSeveral mechanisms entrapment contribute as an end to result the net of effectplugged termed small mechanical pores by polymer entrapment. molecules Gogarty which visualiz are tooed mechanical entrapment as an end result of plugged small pores by polymer molecules which are 164163 largemechanical to enter entrapment them [58]. asWater an end and result salt molecules of plugged which small are pores considered by polymer to be molecules small in size which can are travel too too large to enter them [58]. Water and salt molecules which are considered to be small in size can 165164 throughlarge to enterporous them media [58]., Water but large and salt molecules molecules such which as are polymer considered molecules to be small will bein size trapped can travel and travel through porous media, but large molecules such as polymer molecules will be trapped and 166165 accumulatethrough porous in these media small, but pores. large Gogarty molecules determined such a sthat polymer there is molecules an effective will polymer be trapped molecular and accumulate in these small pores. Gogarty determined that there is an effective polymer molecular size, 167166 sizeaccumulate, for hydrolyzed in these smallpolyacrylamide pores. Gogarty molecules determined by filtering that there400 ppm is an of effective polymer polymer solution molecular through for hydrolyzed polyacrylamide molecules by filtering 400 ppm of polymer solution through different 168167 differentsize, for sizehydrolyzed of nuclep polyacrylamideore filters, Figure molecules 4 shows theby effectivefiltering size400 rangingppm of betweenpolymer 0.4solution and 2 µmthrough [58]. size of nuclepore filters, Figure4 shows the effective size ranging between 0.4 and 2 µm [58]. Smith’s 169168 Smithdifferent’s results size of were nuclep somehowore filters similar, Figure to 4 showsGogarty’s the effectiveresults. The size effective ranging betweensize of HPAM 0.4 and (M 2 µmolecular [58]. results were somehow6 similar to Gogarty’s results. The effective size of HPAM (Molecular weight = 170169 weightSmith’s = results 3 × 10 were) in 0.5 somehow% NaCl wassimilar in theto Gogarty’s range of 0.3results. to 1.0 The µm. effective According size to of the HPAM literature, (Molecular some 3 × 106) in 0.5% NaCl was in the range of 0.3 to 1.0 µm. According to the literature, some reported that 171170 reportedweight = that3 × 10adsorption6) in 0.5% mightNaCl wasbe t hein themajor range dominant of 0.3 to for 1.0 polymer µm. According retention to in the high literature, permeability some adsorption might be the major dominant for polymer retention in high permeability sands [63]. On the 172171 sandsreported [63 that]. On adsorption the other might hand be, mechanical the major dominant entrapment for ispolymer dominant retention in low in- permeabilityhigh permeability rock other hand, mechanical entrapment is dominant in low-permeability rock [60,61,63,64]. In contrast, 173172 [sands60,61, 63[63,64]. ]. On In contrast, the other Cohen hand ,and mechanical Christ suggested entrapment that isfor dominant a 5.6 Darcy in silica low-permeability pack, adsorption rock Cohen and Christ suggested that for a 5.6 Darcy silica pack, adsorption dominated 35.2% of the 174173 dominated[60,61,63,64 ] 35.2%. In contrast, of the Cohen polymer and retention, Christ suggested whereas thethat remainder for a 5.6 D retentionarcy silica was pack dominated, adsorption by polymer retention, whereas the remainder retention was dominated by mechanical entrapment [65]; 175174 mechanicaldominated entrapme 35.2% ofnt the[65 ]; polymer this can retention,be as a result whereas of high the heterogeneity. remainder retention It is worth was noting dominated that, forby this can be as a result of high heterogeneity. It is worth noting that, for better polymer flooding 176175 bettermechanical polymer entrapme floodingnt [65 perfo]; thisrmance can be as most a result of the of high current heterogeneity. polymer floods It is worth are implemented noting that, for in performance most of the current polymer floods are implemented in reservoirs with permeability 177176 reservoirsbetter polymer with permeability flooding perfo higherrmance than most 0.5 Darcy of the such current as Daqing polymer field floods with 800 are md; implemented Pelican lake: in higher than 0.5 Darcy such as Daqing field with 800 md; Pelican lake: with 1–3 Darcy; Mangala with 178177 withreservoirs 1–3 Darcy; with permeabilityMangala with higher approximately than 0.5 Darcy5 Darcy; such Marmul as Daqing with f15ield Darcy; with and800 Tambaredjomd; Pelican withlake: approximately 5 Darcy; Marmul with 15 Darcy; and Tambaredjo with a range of 4–12 Darcys. 179178 awith range 1– 3of Darcy; 4–12 D Mangalaarcys. with approximately 5 Darcy; Marmul with 15 Darcy; and Tambaredjo with 179 a range of 4–12 Darcys.

180 181180 FigureFigure 4 4.. PolymerPolymer filteration filteration with with different different size nuclepore filters filters [ 58].]. 181 Figure 4. Polymer filteration with different size nuclepore filters [58]. 182 2.3. Hydrodynamic Retention 182 2.3. Hydrodynamic Retention

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2.3. Hydrodynamic Retention Another type of polymer retention is hydrodynamic retention. Chauveteau and Kohler experimentally showed the effect of hydrodynamic retention while running an HPAM core flooding experiment. They noticed that polymer retention changed with the change in flow rates [66]. The idea came after observing that, after reaching steady state in a polymer retention experiment in a core, the retention level changed when a new value of the flow rate was adjusted [61,66,67]. In their experiment, as the flow rate increased from 3 cubic meters per day to 10.3 cubic meters per day, more polymer was lost in the porous media from the injected solution, as seen by a dip in the polymer effluent concentration. As the flow rate was lowered again to 3 cubic meters per day, the effluent polymer concentration rose above 400 ppm which was the input value, denoting a drop in the retained level. Hydrodynamic retention of the polymer is the least well defined and understood retention mechanism. The physical picture of the hydrodynamic retention mechanism is thought to be temporarily trapped in stagnant regions by hydrodynamic drag forces called osmotic forces. It may be possible for the polymer concentration in this region to exceed that of the injected fluid. If the flow stops, these polymer molecules may diffuse out of the stagnant region into the main flow channels, so when the flow is retrieved, they are produced as a peak in polymer concentration [47].

2.4. Inaccessible Pore Volume Inaccessible pore volume (IPV) has been widely reported in the literature [61,68–80] as a phenomenon that needs to be considered in polymer flooding applications. When the polymer molecular size is larger than some pores in a porous medium, the polymer molecules cannot flow through those pores. The volume of those pores that cannot be accessed by polymer molecules is called inaccessible pore volume (IPV) [47,70,81]. This IPV is occupied by water (brine) that contains no polymer, and this allows polymer concentration to be propagated through porous media more rapidly than water does [70]. IPV depends on the hydrodynamic size of the polymer in the solution, medium permeability, porosity, and pore size distribution and becomes more pronounced as molecular weight increases and the ratio of permeability to porosity (characteristic pore size) decreases. In extreme cases, IPV can be 30% of the total pore space [73].

2.5. A Combination of Adsorption and Inaccessible Pore Volume As mentioned in the previous section IPV reduces the volume of the porous media that the polymer flows through. Therefore, polymer adsorption can be decreased due to the presence of IPV since less polymer solution will be in contact with the rock surface than total pore volume. Dawson and Lantz (1972) first illustrated the effect of both polymer adsorption and IPV. Figure5 shows four possible scenarios for this effect as follows:

Scenario A: No retention nor IPV. The polymer will break through at 1 PV. Scenario B: No retention, IPV represents 0.25 PV of the total pore volume. The polymer will break through at 0.75 PV. Scenario C: Retention is 0.25 PV and no IPV. The polymer will break through at 1.25 PV. Scenario D: Retention is 0.2 PV, IPV is 0.25 PV. The polymer will break through at 0.95 PV.

In the case of no retention and no IPV, ideally, we expect the polymer to break out after injecting one PV of the polymer as shown in scenario A. Polymer bank emerges early as shown in scenario B in the case of the inaccessible pore volume and breakout curve will shift forward. On the contrary, the front edge will be affected and break out will be delayed by adsorption. Moreover, the back edge is not affected; hence, the polymer bank becomes smaller as shown in scenario C. the combination adsorption and IPV in porous media shifts the polymer bank forward and reduces the amount of the polymer at the effluent as a result of adsorption in the porous media as shown in Figure2 Scenario D. Energies 2018, 11, 2751 7 of 19 Energies 2018, 11, x FOR PEER REVIEW 7 of 18

227 Figure 5. Ideal breakout curves [70]. 228 Figure 5. Ideal breakout curves [70]. 2.6. Static Versus Dynamic Retention 229 2.6. Static Versus Dynamic Retention There are large differences between the level of static adsorption of polymers and dynamically 230 retainedThere level are in large a core differences or pack [ 82between] as shown the level in Table of static1. These adsorption differences of polymers are the result and dynamically of changes 231 inretained the specific level surface in a core area or ofpack consolidated [82] as shown and in unconsolidated Table 1. These packs differences and the are accessibility the result of of changes certain 232 portionsin the specific of the poresurface space. area These of consolidated differences and also unconsolidated depend on the extentpacks ofand mechanical the accessi retentionbility of thatcertain is 233 presentportions in of the the dynamic pore space. core floodThese experimentdifferences [also81,83 depend]. on the extent of mechanical retention that 234 is present in the dynamic core flood experiment [81,83]. Table 1. Comparison of polymer adsorption in static and dynamic test for three polymers at a polymer 235 concentrationTable 1. Comparison of 1500 mg/L.of polymer adsorption in static and dynamic test for three polymers at a polymer 236 concentration of 1500 mg/l. Polymer FP6040 DQ3500 KYPAM-2 Polymer FP6040 DQ3500 KYPAM-2 Static Test Static Test Adsorption amount µg/g 1492 876 1172 Adsorption amount µg/g Dynamic1492 Test 876 1172 Adsorption amount µg/gDynamic 196 Test 125 159 Adsorption amount µg/g 196 125 159

3. Factors Effecting Polymer Retention 237 3. Factors Effecting Polymer Retention 3.1. Polymer Type Effect 238 3.1. Polymer Type Effect In early studies by Szabo for dynamic polymer adsorption, it was shown that 2-acrylamido- 239 In early studies by Szabo for dynamic polymer adsorption, it was shown that 2-acrylamido- 2methyl propane sulfonate (AMPS) adsorption is lower than HPAM [60]. Broadly, xanthan adsorption 240 2methyl propane sulfonate (AMPS) adsorption is lower than HPAM [60]. Broadly, xanthan in porous media is much lower than that of HPAM and tends to show less sensitivity to the 241 adsorption in porous media is much lower than that of HPAM and tends to show less sensitivity to salinity/hardness conditions of the solvent [47,52]. In another study by Szabo, adsorption and 242 the salinity/hardness conditions of the solvent [47,52]. In another study by Szabo, adsorption and retention measurements in Berea cores were carried out on different types of polymers, including 243 retention measurements in Berea cores were carried out on different types of polymers, including AMPS polymers, HPAMs, a xanthan and other polymers. The range of measured retention was lower 244 AMPS polymers, HPAMs, a xanthan and other polymers. The range of measured retention was lower for the AMPS polymers (35–72 lb/AF) than for the HPAM polymers (88–196 lb/AF) in similar Berea 245 for the AMPS polymers (35–72 lb/AF) than for the HPAM polymers (88–196 lb/AF) in similar Berea cores (k = 0.328–0.679 Darcy) [60]. Figure6 shows more adsorption examples for different types of 246 cores (k = 0.328–0.679 Darcy) [60]. Figure 6 shows more adsorption examples for different types of polymers which illustrates the vast variation in adsorption as a function of the type of the polymer. 247 polymers which illustrates the vast variation in adsorption as a function of the type of the polymer.

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248 249 FigureFigure 6 6.. PolymerPolymer adsorption adsorption for for different different types of polymers [ 81].].

250 3.2. Molecular Weight Effect 251 Reported results co consideringnsidering the effect of molecular weight on polymer static adsorption for 252 sulfonated polyacrylamide polymers showed showed that that level of adsorption was increased by increasing 253 molecular weight [84,85].]. This is in accordance with theory since a polymer with a higher molecular 254 weight would form a thicker layer of the the polymerpolymer whenwhen adsorbed adsorbed on on a a surface surface [[8484].]. In dynamic dynamic 255 polymer adsorption studies, sometimes higher levels of adsorption were seen for higher molecular 256 weight polymers, but this adsorption level leveleded off off after a a specific specific value of of the molecular weight weight [ [8686]].. 257 However,However, dynamic adsorption in silica sand decreased with increasing molecular weight, although 258 the effect was was not not large.large. Studies Studies on on the the effect effect of molecular weight on retention of sulfonated sulfonated 259 polyacrylamide copolymerscopolymers studied studied by by Rashidi Rashidi (2009, (2009, 2011) 2011) led led to to the the conclusion conclusion that that by increasingby increasing the 260 molecularthe molecular weight weight of the of polymer, the polymer, less polymer less polymerwas retained was [ 83 retained,85]. The [83 observation,85]. The wasobservation explained was by 261 inaccessibleexplained by pore inaccessible volume pore concept; volume larger concept polymers; larger are polymers unable to are enter unable the smallerto enter poresthe smaller of the pores rock. 262 Lakatosof the rock. et al. Lakatos (1979) et found al. (1979) that found the level that of the HPAM level retentionof HPAM for retention a 500 ppm for a solution 500 ppm in solution the sandpack in the 263 decreasedsandpack decreased slightly with slightly increasing with increasing molecular molecular mass but decreasedmass but decreased even more even sharply more as sharply the degree as the of 264 hydrolysisdegree of hydrolysis increased [82increase]. Theyd considered[82]. They theconsidered degree of the hydrolysis degree of and hydrolysis the electrolyte and the concentration electrolyte 265 toconcentration have the most to have influence the most on molecular influence sizeon molecular (coil density) size (coil and hencedensity) the and adsorption hence the level. adsorp Intion this 266 respect,level. In theythis respect, noted that they the noted role ofthat the the molecular role of the mass molecular is very small.mass is very small. 3.3. Polymer Concentration Effect 267 3.3. Polymer Concentration Effect The adsorption amount dependence on the polymer concentration for a typical unhydrolyzed and 268 The adsorption amount dependence on the polymer concentration for a typical unhydrolyzed a partially hydrolyzed polyacrylamide shows similar behavior. Despite the considerable differences 269 and a partially hydrolyzed polyacrylamide shows similar behavior. Despite the considerable in the absolute values, it is characteristic that the adsorption increases with the increase in polymer 270 differences in the absolute values, it is characteristic that the adsorption increases with the increase concentration [52,79,87]. Zheng claimed that the Langmuir isotherm was applied to his results. 271 in polymer concentration [52,79,87]. Zheng claimed that the Langmuir isotherm was applied to his However, he only measured retention for 250 ppm, 750 ppm and 1500 ppm polymer solutions [87]. 272 results. However, he only measured retention for 250 ppm, 750 ppm and 1500 ppm polymer solutions Moreover, his results showed that the highest retention was at 1500 ppm, that is only less than 1.5 times 273 [87]. Moreover, his results showed that the highest retention was at 1500 ppm, that is only less than than that from the 250 ppm. Szabo measured retention by injecting polymer solution into a 1.2 Darcy 274 1.5 times than that from the 250 ppm. Szabo measured retention by injecting polymer solution into a unconsolidated core. Initially, polymer retention was 3.50 µg/g at 300 ppm; then by increasing polymer 275 1.2 Darcy unconsolidated core. Initially, polymer retention was 3.50 µg/g at 300 ppm; then by concentration to 600 ppm, retention was measured at 6 µg/g [60]. Another retention study by Huang 276 increasing polymer concentration to 600 ppm, retention was measured at 6 µg/g [60]. Another and Sorbie (1993) for Scleroglucan in Bollotini packed columns showed an increase from 8.21 µg/g to 277 retention study by Huang and Sorbie (1993) for Scleroglucan in Bollotini packed columns showed an 11.71 µg/g as the concentration rose from 50 to 200 ppm [79]. A summary of the results of the polymer 278 increase from 8.21 µg/g to 11.71 µg/g as the concentration rose from 50 to 200 ppm [79]. A summary concentration effect on adsorption is shown in Table2. 279 of the results of the polymer concentration effect on adsorption is shown in Table 2.

280 Table 2. Polymer retention dependency on polymer concentration.

Polymer Concentration Type of Retention Reference (ppm) Polymer (µg/g) 10–6000 HPAM 20–420 Zhang and Seright (2013) 20–1000 HPAM 21–30 Green and Willhite (1988)

Energies 2018, 11, 2751 9 of 19

Table 2. Polymer retention dependency on polymer concentration.

µ EnergiesPolymer 2018, 11 Concentration, x FOR PEER REVIEW (ppm) Type of Polymer Retention ( g/g) Reference 9 of 18 10–6000 HPAM 20–420 Zhang and Seright (2013) 20–1000250–1500 HPAM HPAM 40–58 21–30 GreenZheng and (2000) Willhite (1988) 250–150050–200 Scleroglucan HPAM 8.2–11.7 40–58 Huang and ZhengSorbie (2000)(1993) 50–200 Scleroglucan 8.2–11.7 Huang and Sorbie (1993) 281 Another study by Zhang and Seright (2014) for both static and dynamic retention on the polymer 282 concentrationAnother study effect by on Zhang adsorption and Seright concluded (2014) forthe both overall static behavior and dynamic of concentration retention on dependency. the polymer 283 concentrationThey concluded effect that ondifferent adsorption polymer concluded adsorption the behavior overall exists behavior in three of concentration regions dilute, dependency. semi-dilute 284 Theyand concentratedconcluded that regions different [51 polymer]. Polymer adsorption adsorption behavior has existsa small in three dependency regions dilute,in the semi-dilute dilute and 285 andconcentrated concentrated regions regions, whereas, [51]. polymer Polymer adsorption adsorption has hasa high a dependency small dependency on polymer in the concentration dilute and 286 concentratedin the semi-dilute regions, region whereas, as shown polymer in Figure adsorption 7. This has might a high be a dependency fruitful conclusion on polymer for the concentration adsorption 287 independency the semi-dilute on concentration region as shown as previous in Figure reports7. This showed might bea very a fruitful small conclusion increase in foradsorption the adsorption for low 288 dependencyand high polymer on concentration concentration as previous compared reports to polymer showed medium a very small concentration increase in between adsorption (500 for–2000) low 289 andppm. high polymer concentration compared to polymer medium concentration between (500–2000) ppm.

290

291 FigureFigure 7.7. Polymer adsorption in different concentration regions [[5151].]. 3.4. Rock Surface Effect 292 3.4. Rock Surface Effect The iron and clay content of the porous medium has a strong effect on retention. The HPAM 293 adsorptionThe iron level and on clay calcium content carbonate of the isporous significantly medium higher has a than strong adsorption effect on on retention the silica. surfaceThe HPAM [81]. 294 Higheradsorption adsorption level on mightcalcium be carbonate due to the is vigorous significantly interactions higher than between adsorption the carboxylate on the silica groups surface on [81 the]. 295 HPAMHigher andadsorption the surface mightCa be2+ due[59,64 to, 82the]. vigorou More experimentals interactions examples between on the iron carboxylate and clay groups content on effect the 2+ 296 areHPAM shown and in the Table surface3. 퐶푎 [59,64,82]. More experimental examples on iron and clay content effect 297 are shown in Table 3. Table 3. Polymer retention dependency on mineralogy. 298 Table 3. Polymer retention dependency on mineralogy. Mineral Polymer Type Retention (µg/g) Reference MineralKaolinite Polymer HPAM Type Retention 339–1217 (µg/g) Meister (1980)Reference [88] KaoliniteBaker dolomite HPAM 1.9–17.8339–1217 MeisterMeister (1980) (1980) [88] Baker dolomiteKaolinite XanthanHPAM 16,9001.9–17.8 HughesMeister (1990) (1980) KaoliniteSiderite Xanthan 15,60016,900 HughesHughes (1990) (1990) MontmorilloniteSiderite Xanthan CPAM 180,00015,600 ChiappaHughes (1999) (1990) Quartzite CPAM 610 Chiappa (1999) Montmorillonite CPAM 180,000 Chiappa (1999) Calcium carbonate HPAM 20–100 Szabo (1975) Quartzite CPAM 610 Chiappa (1999) Calcium carbonate HPAM 20–100 Szabo (1975) 3.5. Salinity Effect 299 3.5. SalinityIncreasing Effect the salinity concentration generally increases the level of polymer adsorption. 300 ManyIncreas physicaling the and salinity chemical concentration properties generally of the injected increase chemicals the level agents of polymer are affected adsorption by salinity,. Many 301 physical and chemical properties of the injected chemical agents are affected by salinity, like viscosity, 302 chemical activity, stability, and adsorption [12]. Charge type (positive, negative, or neutral) of the 303 rock surface is disturbed in the presence of salinity, which leads to different behavior of the rock 304 surface [12]. Smith (1970) showed that a low concentration of calcium ion 퐶푎2+ will promote HPAM 305 adsorption on silica, as the divalent ions compress/squeeze the size of the molecules of the flexible

Energies 2018, 11, 2751 10 of 19 like viscosity, chemical activity, stability, and adsorption [12]. Charge type (positive, negative, or neutral) of the rock surface is disturbed in the presence of salinity, which leads to different behavior of the rock surface [12]. Smith (1970) showed that a low concentration of calcium ion Ca2+ will promote HPAM adsorption on silica, as the divalent ions compress/squeeze the size of the molecules of the flexible HPAM and reduce the static repulsion between the silica surface and the polymer carboxyl group [59]. Smith results also showed that polymer retention increased from about 11 g/m2 at 1% NaCl to 60 g/m2 at 10% NaCl.

3.6. Hydrolysis Effect As the degree of hydrolysis increases, the level of HPAM retention in the sand pack decreases [82]. Adsorption decreases with hydrolysis until adsorption reaches a minimum. Minimum adsorption is because of the charge interaction between the carboxyl group on the polymer (negative charge) and the silica surface on the sand (negative charge). Therefore, an electrostatic repulsion occurs causing a decrease in adsorption.

3.7. Permeability Effect Polymer retention decreases with higher permeability. This is due to mechanical entrapment in a low permeability rock compared to that in a high permeability rock. Moreover, a high clay content in low permeability rocks is also another possible reason for higher retention. Table4 shows two types of rocks with a high dependency on permeability below 0.2 Darcy.

Table 4. Polymer retention dependency on polymer concentration.

Rock Type and Polymer Type Retention (µg/g) Reference Permeability Vosges sandstone 2100 md HPAM 155 Zaitoun and Kohler (1987) [89] Vosges sandstone 520 md HPAM 140 Zaitoun & Kohler (1987) Reservoir sandstone 137 md HPAM 12 Vela (1976) Reservoir sandstone 12 md HPAM 130 Vela (1976)

3.8. Wetting Phase Effect The wetting phase of the rock also affects polymer retention; in an oil-wet system, polymer retention of polyacrylamide at residual oil saturation will considerably decrease by factors of 2 to 5 compared to the retention if the core is 100% water-saturated [90]. However, in a water-wet system, the effect of residual oil saturation is less noticeable. For example, the retention with residual oil saturation of 0.2 is almost 7.5 µg/g compared to zero residual oil saturation with a retention of 10 µg/g.

3.9. Temperature Effect Adsorption decreases with temperature because of a combined physical and chemical reasons such as electrostatic repulsion, hydrophobicity, van der Waals forces and hydrogen bonds. For nonionic polymers, adsorption is more related to hydrogen bond, whereas adsorption is more related to electrostatic repulsion in ionic polymers. Increasing the temperature facilitates the hydrogen bond to break up, causing a decrease in polymer adsorption. Increasing temperature increases the negative charge on the rock surface, leading to higher electrostatic repulsion, so, the ionic polymer adsorption is reduced [81].

4. Polymer Retention Measurement Many factors need to be considered in polymer retention measurements which makes polymer retention measurement a very long and complicated process. A broad range of methods for calculating polymer retention in porous media was investigated by many researchers. We summarize these methods into three categories. Energies 2018, 11, 2751 11 of 19

4.1. Static Method Generally, static methods are used to measure polymer adsorption to estimate the effect of different parameters on polymer adsorption [85,91,92]. In this method, crushed sand is prepared, and a known concentration of polymer is added to the crushed core, then the polymer concentration is measured after separation of the polymer solution from the sand. Knowing the initial mass of the sand, polymerEnergies adoption2018, 11, x FOR is PEER calculated REVIEW by dividing the lost mass of the solution by the sand11 of 18 weight as shown in Equation (3). 342 Generally, static methods are usedq = toV measure(Co − Ce polymer)/W adsorption to estimate the effect of (3) 343 different parameters on polymer adsorption[85,91,92]. In this method, crushed sand is prepared, and where344 q isa theknown adsorption concentration concentration; of polymer is addedV is to the the volume crushed core, of the then polymer the polymer solution; concentrationCo is is the initial 345 polymer concentration;measured after separationCe is the of polymer the polymer concentration solution from afterthe sand. the Knowing static adsorption. the initial mass of the 346 sand, polymer adoption is calculated by dividing the lost mass of the solution by the sand weight as 347As mentionedshown in Equation in the (3) static. versus dynamic retention section, static and dynamic retention will give different results. Mostly, static results will be higher than dynamic results unless the dominant 푞 = 푉(퐶표 − 퐶푒)⁄푊 (3) retention mechanism is the mechanical entrapment in very low permeability cores. The static method 348 where q is the adsorption concentration; V is the volume of the polymer solution; Co is the initial relies349 on onlypolymer two concentration; polymer concentration Ce is the polymer measurements. concentration after the Therefore, static adsorption. errors in these measurements have350 an essentialAs mentioned impact onin the the static adsorption versus dynamic value. retention Moreover, section, to static make and the dynamic sand, retention the rock will needs to be pulverized,351 give which different exposes results. moreMostly, surface static results area will and be minerals higher than which dynamic might results not unless be availablethe dominant in the main rock.352 One retention more limitation mechanism in is using the mechanical the static entrapment test is that in very the low mechanical permeability entrapment cores. The static cannot method be measured. 353 relies on only two polymer concentration measurements. Therefore, errors in these measurements 354 4.2. Singlehave Polymer an essential Injection impact Method on the adsorption value. Moreover, to make the sand, the rock needs to be 355 pulverized, which exposes more surface area and minerals which might not be available in the main 356One ofrock. the One earliest more methods limitation in used using to the estimate static test polymer is that the retention mechanical in entrapmentporous media cannot was be based on 357 measured. the calculation of the remaining polymer concentration in porous media after measuring the effluent polymer358 [514.2.,63 Single,93]. Polymer Injection Method 359In this method,One of the the earliest polymer methods is injected used to estimate through polymer cores retention or sand in packs porous along media with was based a tracer. on Material balance360 calculationthe calculation is performedof the remaining for polymer the effluent concentration concentration in porous media profiles after in measuring to determine the effluent the retention level361 as shownpolymer in [ Equation51,63,93]. (4). 362 In this method, the polymer is injected through cores or sand packs along with a tracer. Material 363 balance calculation is performed for the effluent concentrationdCs profiles indC to determine the retention 364 level as shown in Equation− (4).∆φ VC + ∆DV = (1 − φ) + φp (4) dt dt 푑퐶푠 푑퐶 −∆ϕ푉퐶 + ∆퐷푉 = (1 − ϕ) + ϕ푝 (4) Polymer retention is calculated from the difference푑푡 between푑푡 the area under the curves of the polymer365 and tracerPolymer slug. retention Moreover, is calculated the inaccessiblefrom the difference pore between volume the (IPV) area under can be the estimated curves of the by the back edge366 area polymer between and the tracer two slug curves. Moreover, as shown the inaccessible in Figure pore8[70 volume]. (IPV) can be estimated by the back 367 edge area between the two curves as shown in Figure 8 [70]. It is difficult to retrieve the polymer from the porous media with the injection of a few pore volumes, 368 It is difficult to retrieve the polymer from the porous media with the injection of a few pore thus369 the amountvolumes of, thus the polymer the amount retained of the in polymer the porous retained media in the can porous be overestimated. media can be overestimated. Therefore an extended injection370 ofTherefore brine to an recover extended the injection polymer of brine is required to recover [ 48the]. polymer This is is a required result of [48 the]. This unfavorable is a result of displacement.the However,371 itunfavorable is important displacement. to indicate However, that a veryit is important low polymer to indicate concentration that a very low at polymer the effluent concentration will be associated 372 at the effluent will be associated with polymer detection errors which again will overestimate the with polymer detection errors which again will overestimate the amount of the retained polymer. 373 amount of the retained polymer.

374

Figure 8. Polymer retention measurement using a single polymer injection method. Energies 2018, 11, x FOR PEER REVIEW 12 of 18 Energies 2018, 11, 2751 12 of 19 375 Figure 8. Polymer retention measurement using a single polymer injection method.

376 4.3. Extended Injectivity Method 377 This method is the most used method in the literature to determine the polymer retention in 378 porous media [74,,94,,95].]. In this method, a polymer solution along with a tracer is injectedinjected intointo thethe 379 porous media.media. Injection continues until the polymer and tracer concentrations produced reach the 380 injected polymer polymer and and tracer tracer concentrations, concentrations, followed followed by extended by extended brine injectivity brine injectivity (~100) pore (~100) volumes pore 381 ofvolumes brine. Theof brine. mobile The polymer mobile and polymer tracer willand be tracer displaced will be from displaced porous media.from porous Finally, media. a second Finally, bank ofa 382 polymersecond bank and tracerof polymer solution and is tracer injected. solution Measurements is injected of. Measurements polymer retention of polymer and IPV retention (inaccessible andpore IPV 383 volume)(inaccessible use onlypore thevolume) front partuse only of the the break front out part curves of the from break the out two curves injected from slugs, the two which injected eliminates slugs, 384 thewhich problems eliminates associated the problems with the low associated concentration with the extended low concentration production and extended viscous fingering.production IPV and is 385 measuredviscous fingering. from the area IPV betweenis measured the second from polymer the area curve between and the the first/second second polymer tracer curve. curve Polymer and the 386 retentionfirst/second is measured tracer curve. from Polymer the area betweenretention the is measured first polymer from curve the andarea the between second thepolymer first polymer curve as 387 showncurve and in Figure the second9. polymer curve as shown in Figure 9.

388 389 Figure 9.9. Polymer retention measurement using extended injectivity method.

390 EquationEquation (5) shows the mathematical expressionexpression forfor polymerpolymer retentionretention andand IPVIPV calculation.calculation.   Cp퐶푝   퐶푡Ct   푃푉 PV R = 푅 = {[∑ [( ∗ ∆∗ PV∆PV)−− ( ∗∗∆∆PVPV)]] + IPV+ IPV} 퐶푝표Cpo∗ ∗ (5(5)) ∑ Cpo퐶푝표 퐶푡표Cto 푀푟 Mr

391 wherewhere RR isis the polymer retention in porous media; Cp and Cpo are the produced and injected polymer 392 consecutively; PV is the pore volume in the porous media; Ct and Cto are the produced and injected 393 tracer,tracer, respectively;respectively; IPVIPV isis thethe inaccessibleinaccessible porepore volumevolume MrMris is thethe massmass ofof thethe rock.rock.

394 4.4. Concentration ProfileProfile Method 395 Another method used to calculate polymer retention and IPV is by creating the breakout curves 396 in the same manner as in the the extended extended injectivity test for the first first and second polymer slug. According According 397 to HuhHuh (1990),(1990), The The dynamic dynamic retention retention can can be be determined determined by plottingby plotting the effluentthe effluent profile profile of a coreof a floodcore 398 experimentflood experiment [63]. With [63]. regardWith regard to the to theory the theory of diffuse of diffuse percolation, percolat whenion, awhen solution a solution flows throughflows through a core 399 ata corea constant at a constantvelocity, the velocity, point, where the point, the normalized where the concentration normalized concentration (Ce/Cinj) on the (Ce/Cinj) concentration on the 400 profileconcentration at any timeprofile is at 0.5 any [94 time,96]. is Retention 0.5 [94,96 and]. Retention IPV can and be directly IPV can measured be directly by measured reading by the reading values 401 correspondingthe values corresponding to the point to ofthe normalized point of normalized concentration concentration at 0.5 as shown at 0.5 as in shown Figure in 10 F.igure This method10. This 402 ismethod the least is the used least and used reported and reported in the literature. in the literature. However, However, it showed it showed comparatively comparatively identical identical results 403 withresults the with extended the extended injectivity injectivity test. The test. main The advantage main adv ofantage using of this using method this method is that IPV is that can IPV be directly can be 404 estimateddirectly estimated from the cutfrom off the value cut of off the value normalized of the normalized concentration concentration at 0.5 from the at second 0.5 from polymer the second slug 405 polymer slug without the need to plot the tracer curve using Equation (6). Retention is estimated

Energies 2018, 11, 2751 13 of 19 without the need to plot the tracer curve using Equation (6). Retention is estimated from the cut off value of the normalized concentration at 0.5 from the first and second polymer slug using Equation (7).

IPV = 1 − PV Ce (6) second slug Cinj =0.5

Retention = PV Ce − PV Ce (7) f irst slug Cinj =0.5 second slug Cinj =0.5

Figure 10. Polymer retention measurement using concentration profile method.

5. Modeling of Polymer Retention in Porous Media In polymer flooding, the polymer solution effectively reduces the displacing fluid mobility whereas the effective permeability of the reservoir is reduced by polymer retention [50]. Polymer retention simulation is primarily part of the polymer flood simulation that is extensively based on modeling parameters such as viscosity depending on polymer concentration, polymer solution shear thinning, shear degradation, permeability reduction, and polymer adsorption. Several simulators are being used to model polymer flooding processes such as Eclipse, CMG and UTCHEM. The imposed assumptions for flow equations development are equilibrium thermodynamic except for organic component dissolution and tracers, immobile solid phases, Fickian dispersion, slightly compressible fluids and soil, Darcy’s law and ideal mixing [95]. The boundary conditions are no dispersive flux and no flow across the impermeable boundaries. For a component k, the continuity of mass in combination with Darcy’s law is represented in terms of the overall volume of the component k per unit pore volume as shown in Equation (8).

  np ∂ ˇ − ∅Ckρk = ∇·[∑ ρk(Cklul − Dkl)] (8) ∂t l=1 where k is the component species index number (k for polymer = 4); l is the phase index number for water and oil (water = 1, oil = 2); O is the porosity; Cˇ k represents the overall concentration of the component k; ρk is the density of the component k; np is the number of the phases; Ckl is the component k concentration in phase l; ul is the phase l darcy velocity; and Dkl represents the dispersion tensor. Polymer retention in porous media results from adsorption of polymer molecules onto solid surfaces and trapping of the polymer within small pores. As mentioned in the previous sections, polymer retention slows the polymer breakout and depletes the polymer slug. To model polymer Energies 2018, 11, 2751 14 of 19 adsorption level, simulators use a Langmuir-type isotherm as shown in Equation (9) which mainly takes into account only the polymer concentration, salinity, and permeability.

    ap Cp − Cˆ p Cˆ p = minCp    (9) 1 + bp Cp − Cˆ p where Cp and Cpˆ is the injected and adsorbed polymer concentration, respectively. (Cp − Cpˆ ) represents the equilibrium concentration in the rock-polymer system. The minimum adsorption value is taken to ensure that the adsorption is no greater than the total polymer concentration. ap and bp are the fitting parameters. The parameter ap is calculated from Equation (10).
p = ap1 + ap2Csep (10) where Kre f and Csep is the reference permeability (at which adsorption parameters input are specified) and effective salinity respectively. The unit for ap is dimensionless. The effective salinity of the polymer adsorption Csep is defined by Equation (11).

C51 + (ßp − 1)C61 Csep = (11) C11 where C51, C61 and C11 are the anion, divalent, and water concentrations in the aqueous phase, respectively. ßp is the covalent coefficient. It is noteworthy to mention that the Langmuir model is an equilibrium relationship, and its application assumes polymer adsorption is instantaneous and reversible. When polymer adsorption is considered to be irreversible, the Langmuir model cannot be used directly as the polymer concentration is declining [81].

6. Scope of This Research This paper presents a complete review of polymer retention phenomenon with an aim to provide a comprehensive reference for researchers investigating polymer retention and field practitioner designing a polymer slug for their project:

• A discussion on the strength and limitation of polymer flooding and the mechanism of mobility ratio improvement was provided. • A review of the polymer retention phenomenon, highlighting its importance, was presented. • The factors influencing polymer adsorption, mechanical entrapment and hydrodynamic retention were identified. • The commonly used techniques for polymer retention measurements and their cons and pros viz’a viz other techniques were discussed. • The commonly used techniques for modeling were described.

7. Key Observation • The flow of polymer solutions through porous media is a complex phenomenon requiring an understanding of retention, flow capacity alteration, and inaccessible pore volume. Estimation of these factors is important for economic evaluation and slug design for a successful implementation of polymer flooding EOR. • Polymer retention is caused by adsorption on the surfaces, mechanical entrapment due to narrow passageways in porous media, and hydrodynamic entrapment due to high flow rates. • The retained polymer reduces the flow area, thus the flow capacity (permeability) of the porous media. The mobility of polymer is therefore reduced by both increased viscosity and reduced flow capacity. Energies 2018, 11, 2751 15 of 19

• Inaccessible pore volume allows the polymer to propagate through porous media more rapidly and reduces the amount of polymer retention. • Each measurement method has some limitations and cannot be relied upon solely. Therefore, a combination of at least two methods for static and dynamic measurements is often needed.

Author Contributions: Conceptualization, S.A.-H. and S.M.M.; Methodology, S.A.-H.; Software, H.A.; Validation, S.A.-H., S.M.M. and S.A.; Formal Analysis, S.A.-H.; Investigation, S.A.-H.; Resources, S.M.M.; Data Curation, H.A. and S.A.; Writing-Original Draft Preparation, S.A.-H.; Writing-Review & Editing, S.M.M.; Visualization, S.A.-H.; Supervision, S.M.M.; Project Administration, S.A.-H. and S.M.M.; Funding Acquisition, S.M.M. Funding: This research was funded by Universiti Teknologi PETRONAS and Yaysan UTP-Fundamental Research Grant (Cost Center 0153AA-E84). Acknowledgments: The authors wish to thank Universiti Teknologi PETRONAS for providing monetary support and an intellectual platform during this research. Conflicts of Interest: The authors declare no conflict of interest.

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