Transport and Plugging Behavior of Viscoelastic Suspensions in Fractured Tight Reservoirs

Abstract

Natural or hydraulic fractures in reservoirs can lead to conformance control issues and poor reservoir confinement, making fracture plugging an essential strategy for controlled fluid flow. This work has investigated the dynamics of solid particle transport and plugging behavior in fractured tight reservoirs using high- and low-permeability sand packs. Two distinct fluid systems have been studied, a polymer-solid suspension and a nanoparticle-viscoelastic surfactant suspension. Three key injection parameters were investigated: the viscosity of the carrier fluid, the concentration of the injected solids, and the particle size distribution of the solids. Results showed that using 0.5 wt % polymer concentration with 1 wt % solids can lead to 99% permeability reduction in ∼1000 Darcy sand packs. Increasing both concentrations leads to premature plugging and injectivity loss. Upscaling to 3-foot-long sand packs showed the ability of this system to plug larger fracture volumes uniformly along the length of the sand pack. For lower-permeability fractures ∼10 Darcy, it was necessary to reduce the particle size from 112 to 62.5 μm at the same 1 wt % concentration to maintain injectivity and achieve comparable plugging efficiency. Decreasing the particle size even further to the nanoscale resulted in deeper fracture penetration and 98% permeability reduction. For the nanoparticle-enhanced VES system, the absence of nanoparticles led to limited fracture plugging of 35%, but the addition of nanoparticles increased fracture permeability reduction to 99% in low-permeability fractures. High-permeability fractures showed up to 80% reduction of the permeability and an increase in the minimum pressure gradient for mobilization up to 35 psi at higher concentrations of VES and nanoparticles. This work highlights the ability of both of these systems to effectively plug fractures, with the extent of permeability reduction being subject to injection parameters such as carrier fluid viscosity, solids concentration, and solids particle size distribution that must be tailored to the fracture characteristics. These results provide valuable insight into conformance control, enabling a more efficient reservoir performance.

Introduction

Fracture plugging is an important aspect in subsurface engineering as it helps manage and optimize the productivity of naturally or hydraulically fractured reservoirs. Over time, fractures that helped enhance reservoir permeability and allow the flow of oil and gas become inefficient, whether because of proppant failure, , fines migration, undesired fluid invasion, or changes in reservoir pressure. In such cases, fracture plugging is employed to block those pathways, restore the integrity of the reservoir, and improve well injectivity. This process is essential for improving hydrocarbon recovery, reducing water cutoff, and providing uniform reservoir stimulation in multistage hydraulic fracturing operations. Depending on the specific reservoir conditions at hand, several materials and techniques have been developed to effectively plug fractures. One of the most common methods is the use of water-soluble polymer gel systems. These systems consist of a polymer mixed with a cross-linker to provide viscoelastic properties. The earliest attempts at creating an efficient gel plugging agent resulted in systems that do not have much of a buffer capacity, for example, the Cr­(VI)-HPAM system gelled at a pH of 4, while phenol-based gels formed at a pH of 9. After it was realized that reservoir lithology and permeability greatly impacted the performance of polymer gel systems, Cr­(III)-acetate and propionate systems were developed that were more controlled and predictable when injected. − These developments highlight an important advantage of polymer gel systems, which is their customizability in terms of gelation time, gelation strength, and gelation conditions (i.e., temperature, salinity). This allows the control of penetration depth and makes polymer gel systems suitable for both high- and low-permeability fractures. Although there have been polymer gel systems developed for high-temperature use, the main drawback of such systems remains their long-term thermal stability. − Another attractive method for fluid flow control is foam diversion. It involves the injection of a surfactant mixture and gas to create an in situ gas-in-water dispersion having a high apparent viscosity that can plug high-permeability thief zones. The efficacy of foam blocking has been shown in both laboratory scale and field scale. One clear benefit of this method is the reduction in the use of injection water, with the secondary benefit being the potential for geological carbon storage if hydrocarbon gas or CO₂ is used. It is possible to formulate a foaming surfactant mixture for a variety of reservoir conditions (i.e., pressure, temperature, salinity) even in the presence of oil. − One other important class of plugging systems is the use of solid particles. Material such as fiber or calcium carbonate can be used to create a physical barrier inside the fracture that prevents fluid communication. The advantage of such a system is the high mechanical strength provided by the solid particles, which can create a stable plug that can withstand harsh reservoir conditions. However, the very nature of this system makes it prone to particle settling during placement if the carrier fluid viscosity is too low, and shallow fracture penetration if the carrier fluid viscosity is too high. Finally, another class of non-Newtonian fluids used to control or limit the directional displacement in a reservoir is viscoelastic polymers. These differ from regular polymers in their response to deformation, where they exhibit both elastic solid-like and viscous fluid-like behavior. Viscoelastic shear measurements showed that both the elasticity and viscous moduli are higher for a viscoelastic polymer than for a single-network polymer. This contributed to a 20–30% increase in pressure gradient after water breakthrough in 1–2 mm fracture cores. This is attributed to the reversible nature of the viscoelastic network, which can be reassembled even after it has been broken through. It must be noted that viscoelastic polymers differ from viscoelastic surfactants (VES) in the way that their strength is achieved. For the former, viscoelastic behavior arises from the entanglement of long polymer chains, which recover once the deformation stress is removed. For the latter, amphiphilic molecules self-assemble and form worm-like micellar structures that behave like polymers, which leads to the viscoelastic behavior. Despite both of them being used in the context of enhanced oil recovery for decades, , the use of VES as a potential material for sealing integrity and CO₂ flow control has also recently been investigated through the use of surfactant mixtures that form CO₂-switchable worm-like micelles. When CO₂ is introduced to the surfactants, a pseudogemini structure is formed, resulting in higher apparent viscosity. When the CO₂ is then removed, the surfactant molecules return to their original state and the viscosity is recovered. − Nanoparticles, despite not being plugging agents themselves, can be added to such fluids to improve mechanical and thermal stability through enhanced cross-linking, which can lead to a high yield stress, thereby improving fracture blocking capacity. , Research into nanoparticle-enhanced VES systems has mainly focused on the addition of nanoparticles to improve hydraulic fracturing performance such as improved thermal stability, reduced fluid loss, and enhanced proppant transport. − However, the use of such a system for the purpose of long-fracture plugging has not yet been investigated. To that effect, the objective of the work presented here is to study the various factors that affect the plugging behavior of two suspension systems in both high (∼1000 D) and low (∼10 D) permeability sand packs: a polymer with solids system and a nanoparticle-enhanced VES system. Variables such as carrier fluid viscosity, solid particle size distribution (PSD), surfactant concentration, and solid concentration will be investigated to determine the maximum plugging distance in a sand pack.

Materials and Methods

Sand Pack

To simulate fractures of different permeabilities, a 1-foot-long sand pack was filled with crushed Berea sandstone. High-permeability fractures were mimicked using 8–12 mesh size grains (1.68–2.38 mm), while low-permeability fractures were mimicked using 100 mesh size grains (0.15 mm). The pack was filled with sand while simultaneously being attached to a shaker table to ensure homogeneous compaction and consolidation. The same shaking intensity was used for all packs to ensure consistency in the resultant pack permeability. To investigate material transport and plugging behavior in a longer medium, a 3-foot-long sand pack was used.

Plugging Solids

Two different solids were used in this work. To determine the particle size of these solids, a Mastersizer 3000+ from Malvern Panalytical was used. The instrument utilizes laser diffraction to measure particle sizes ranging from 0.1 to 1000 um. The dry sample is added to the deionized (DI) water circulation bath, and a laser beam passes through the dispersed particulate sample. The diffraction pattern is analyzed, and a particle size distribution is determined. The measurements were run six times, and an average distribution is obtained. The first solid, P1, is a proprietary mixture of cellulosic fibers and mineral granules with a density of 1.45 g/cm³. Two samples of P1 (P1A and P1B) with different particle sizes were used in this work. The respective particle size distributions of these samples measured using the laser particle analyzer are shown in Figure . The average particle sizes are 112 and 62.5 μm for P1A and P1B, respectively. The second solid, P2, consists of cellulose nanoparticles with a density of 1.51 g/cm³ and a highly uniform particle distribution centered at 70 nm. To make different plugging fluids for the sand pack flooding experiments described below, P1 is dispersed in either water or a polymer solution as the carrier fluid, while only VES is used as the carrier fluid for P2.

1.

Particle size distributions of (a) P1A and (b) P1B.

Brine

The synthetic brine used in this work was prepared by mixing 50,000 ppm of NaCl in DI water. This brine was used for the water-based injection and as the base fluid to which either polymer or VES was added.

Polymer

The polymer used in this work is a low-molecular-weight polyacrylamide polymer with a density of 0.75 g/cm³. The viscosity of this polymer in 50,000 ppm of NaCl brine was measured at 2 and 0.5 wt % at 25 °C, using an ARES-G2 rheometer from TA Instruments with the double gap concentric cylinder geometry. All measurements were repeated three times to be statistically representative. The results are shown in Figure . The measured baseline viscosity of the brine solution is about 0.8 cP at 25 °C. Adding 0.5 wt % polymer to this brine increased its viscosity to 1.5 cP, and a further viscosity increase to 6 cP could be obtained with 2 wt % polymer.

2.

Viscosities of brine and polymer solutions at 0.5 and 2 wt % polymer concentrations and 25 °C.

Viscoelastic Surfactant

An amidopropyl dimethyl betaine was used as the viscoelastic surfactant. The viscosity of this VES at 1, 2, and 4 wt % in 50,000 ppm of NaCl brine was measured with and without nanoparticle P2 and is shown in Figure .

3.

Viscosity of VES solutions (a) without nanoparticles and (b) with nanoparticles.

In the absence of nanoparticles, the VES solution showed shear-thinning behavior for all concentrations tested. The viscosity at 4 wt % VES (Figure a) starts at about 300 cP at a shear rate of 1 s^–1, decreasing to about 4 cP at the highest tested shear rate of 1000 s^–1. At 2 wt %, the viscosity started at 200 cP and decreased to 3 cP, while at 1 wt % it started at 130 cP and decreased to 2.6 cP. Adding nanoparticle P2 to these VES solutions increased the viscosity of all three solutions at all measured shear rates (Figure b). Specifically, adding 3 wt % nanoparticles to the 1 wt % VES solution increased the measured viscosity from 130 cP to around 2250 cP at a shear rate of 1 s^–1, and from 2.6 cP to around 6.5 cP at a shear rate of 1000 s^–1. Adding the same nanoparticle concentration to the 2 wt % VES solution increased the shear rate to 9775 and 20 cP at 1 s^–1 and 1000 s^–1 shear rates, respectively. Finally, the addition of 15 wt % nanoparticles to the 4 wt % VES solution led to a viscosity of 16100 cP at 1 s^–1 and 40 cP at 1000 s^–1. Since carrier fluid viscosity is a main parameter studied in this work, the concentrations for the VES and nanoparticles were chosen such that the resulting solutions have a wide range of viscosities at the shear rates encountered during the sand pack floods.

Similarly, viscoelastic properties such as the storage modulus G′ and the loss modulus G″ were measured using amplitude sweeps at a constant angular frequency of 10 rad/s in both the presence and absence of nanoparticles, and the results are shown in Figure .

4.

Storage and loss moduli for VES solutions at (a) 1 wt %, (b) 2 wt %, (c) 4 wt % (0) without nanoparticles and (1) with nanoparticles.

As can be seen in Figure (a)­(0)–(c)­(0), the viscoelastic behavior does not change significantly with the increasing concentration of VES. For all concentrations, the loss or damping factor, $\tan (\delta )=\frac{G^{″}}{G^{\prime }}$ , was less than one for oscillation strains up to 60% (i.e., the solution behaves like an elastic solid) while tan­(δ) was greater than one at strains greater than 60% (i.e., the solution behaves like a viscous liquid). This means that the VES solutions start behaving like a solid at low strains and then transition to a more liquid-like behavior at higher strains, indicating a breakdown of the molecular structure of the solution under increasing strain. This is consistent with the shear-thinning behavior observed in Figure . Adding nanoparticles to the VES maintains the general trends with oscillation strain (Figure (1)); however, the magnitude of the storage and loss moduli is increased by a factor of 10. The increase in viscosity, storage modulus, and loss modulus is a phenomenon observed frequently in the literature and is attributed to increased engagement in the presence of nanoparticles, leading to a more interconnected structure of micelles. ,,

Plugging Experiment

A schematic of the sand pack flooding setup is shown in Figure . The sand pack flood starts with measuring the porosity of the pack using the mass balance method. The dry unsaturated pack is first weighed, vacuumed, and then saturated with the 50,000 ppm of NaCl brine. The saturated weight is measured and the difference in mass divided by the density of the brine (1.02 g/cm³) is the pore volume (PV). The porosity is obtained by dividing the pore volume by the bulk volume of the pack. Pack permeability is measured using Darcy’s law by injecting brine at three constant rates and measuring the pressure drop across the pack.

5.

Sand pack flooding schematic.

The solid suspension is prepared at the desired conditions and added to a clear accumulator equipped with a top stirrer. The rotations per minute (RPM) of the stirrer are adjusted such that the solid particles are visibly being mixed. The mixture is injected into the sand pack at constant pressure using a compressed air source adjusted to 30 psi. The effluent is collected on a digital scale that reads continuous mass data in grams per second (g/s), allowing for the calculation of the mass flow rate during the plugging experiment. Solid suspension injection continues until at least 30 PVs have been injected or until production is nearly zero, whichever occurs first. Brine is then injected at the same constant pressure of 30 psi, and the mass effluent rate is determined. This allows for the calculation of the postplugging permeability, which will be converted to a permeability reduction percentage when compared to the original pack permeability. The pack and accumulators are emptied and cleaned after every experiment. The sand pack injection schemes for the polymer floods are shown in Table .

1. Sand Pack Injection Schemes for Polymer-Solid Systems.

flood	permeability (Darcy)	carrier fluid	polymer concentration (wt %)	solid concentration (wt %)	particle size (μm)/type	sand pack length (cm)
SP1	980	water		3	112/P1A	30
SP2	1270	water		1	112/P1A
SP3	830	polymer	2	3	112/P1A
SP4	830	polymer	0.5	1	112/P1A
SP5	2000	polymer	0.5	1	112/P1A	90
SP6	4	polymer	0.5	1	112/P1A	30
SP7	10	polymer	0.5	1	62.5/P1B
SP8	10	polymer	0.5	1	7 × 10–2/P2
SP9	14	polymer	0.5	1	7 × 10–2/P2	90

For the experiments with VES, a different injection strategy is performed. The VES solution is injected at a constant rate instead of constant pressure due to the apparent yield stress of the solution. A plug of only 1 PV of the solution is injected into the sand pack and is left for 1 h. Then, brine is injected at increasing increments of constant pressure to determine the minimum pressure gradient needed for mobilization. After breakthrough, brine is injected either in constant pressure or constant rate mode, depending on the permeability of the sand pack, and the postplugging permeability is measured. All VES experiments were conducted in a 1-foot-long centimeter sand pack. The sand pack injection schemes for the VES experiments are shown in Table .

2. Sand Pack Injection Schemes for VES-Solid Systems.

flood	permeability (Darcy)	VES concentration (wt %)	solid P2 concentration (wt %)
SP10	10	4	0
SP11	12	1	3
SP12	1070	2	3
SP13	1500	4	15

Results and Discussion

Table shows a summary of the results of the brine-solid, polymer-solid, and VES-solid flooding experiments, including the initial permeability (k _i ) and postplugging permeability reduction (i.e., percentage of initial permeability lost due to plugging).

3. Solid Injection Results for Different Carrier Fluids.

flood	k i	k i reduction (%)
water
SP1	980	99
SP2	1270	99
polymer
SP3	830
SP4	830	99
SP5	2000	99
SP6	4
SP7	10	97
SP8	10	98
SP9	14	99
VES
SP10	10	35
SP11	12	99
SP12	1070	77
SP13	1500	80

Brine-Solid Suspension

The measured pressure and effluent mass rate from plugging experiments SP1 and SP2 in high-permeability sand packs are shown in Figure . Both experiments maintained 30 psi throughout the injection. Both effluent mass rates show the same profile: a steeply decreasing slope until around 5 PVs injected, then a relatively constant rate until the pack is completely plugged and no more flow is collected from the outlet. Even though the sand pack permeability is slightly higher for SP2, the constant rate for SP2 was twice that for SP1 (about 0.5 g/sec). It is also noted that the injected suspension took about 38 PVs to completely plug the pack in SP1, whereas 55 PVs were needed for SP2 (i.e., a 45% increase in injected volume). Given that the sand pack is 1-foot-long, one PV injected can be approximated to be 1 foot injected if the pack is considered to be analogous to a high-permeability fracture. Therefore, comparing SP1 with 3 wt % solid concentration and SP2 with 1 wt % solid concentration, with similarly high permeabilities (∼1000 Darcy) and for the same particle size distribution, it can be said that lowering the solids concentration leads to a higher injection rate for the same injection pressure, as well as deeper penetration of solid particles into the fractures. The lower flow rate in SP1 could be attributed to the higher viscosity of the injected fluid at the higher solid concentration, while the increased penetration distance in SP2 could be attributed to the reduction of particle plugging at a lower concentration.

6.

Injection pressure and effluent mass rate for (a) SP1 and (b) SP2.

Increasing solid concentration has been shown to affect the injection pressure during constant rate injection in both numerical simulations as well as field cases. , This implies that for a constant injection pressure, a higher concentration would exhibit lower injection rates. The results also agree with previous experimental studies that showed fracture sealing time decreases with increasing concentration of irregular-shaped solid particles used for mitigating lost circulation during drilling. Therefore, the results from SP1 and SP2 floods suggest that reducing the solid concentration could lead to faster and deeper solid penetration, potentially resulting in a more uniform reduction of fracture permeability within a target fractured formation volume.

Polymer-Solid Suspension

High-Permeability Media

Figure shows the pressure data and effluent mass rate for floods in SP3 and SP4. The carrier fluid in SP3 has a viscosity of 6 cP at 2 wt % polymer concentration (Figure ), while the polymer concentration in SP4 was reduced to 0.5 wt % to obtain a lower viscosity of 1.5 cP. The mass effluent profile in SP3 shows a steep decline, reaching zero within 3.4 PVs injected. This almost immediate plugging behavior is consistent with the effect of the high carrier fluid viscosity mentioned earlier. The applied injection pressure of 30 psi was not sufficient to drive the 6 cP solid suspension through the high-permeability sand pack. Reducing the viscosity to 1.5 cP in SP4 showed a clear improvement in the transport of the solid suspension. There is the initial rapid decline in effluent mass rate as seen in Figure , but the injection volume reached 70 PVs of a 1-foot-long medium, which could be equivalent to 70 ft into a high-permeability, long fracture in the field. The constant mass flow rate was about 0.5 g/s, similar to that obtained in SP1, which used water as a carrier fluid and had a solid concentration of 3 wt %. Therefore, it can be concluded that reducing the carrier fluid viscosity by decreasing both the polymer and solid concentration allows a deeper placement of plugging solids in high-permeability fractures. However, comparing SP4 with 0.5 wt % polymer to SP2 with only water at the same solid concentration reveals that the viscosification of injected water with a polymer needs to be optimized to enhance solid penetration in the fractures without a rapid reduction of suspension injectivity. Previous experimental studies have shown that an increase in carrier fluid viscosity could improve solid particle mobility, such as increasing drag force, reducing particle settling velocity, and leading to more uniform particle placement. − However, there exists a threshold viscosity above which particle transport could be significantly impaired, , which could underlie the observation from the SP3 flood. It is evident that a polymer concentration of 0.5 wt % and a solid concentration of 1 wt % provide good solid particle mobility in high-permeability fractures under the flow conditions studied in this work.

7.

Injection pressure and effluent mass rate for (a) SP3 and (b) SP4.

It is noted that the experiments SP1 through SP4 simulated high-permeability fractures using a 1-foot-long sand pack. The observed transient behaviors of pore-scale processes (i.e., solid deposition and associated permeability reduction) over the injected pore volume may change with the simulated fracture length as the particle concentration and even average particle size could continuously change along the fracture during the suspension injection. To evaluate the scaling behavior of solid transport and plugging, a 3-foot-long sand pack was used for the suspension injection under the same experimental conditions as described in SP4. The resulting pressure and effluent mass rate for this experiment (SP5) are shown in Figure . The effluent mass rate stabilized around 0.5 g/s after around 12 PVs, which is the same rate as observed in SP4. Remarkably, the injected volume reached 49 PVs in this 3-foot-long sand pack. To determine if the entire pack is plugged or just the first foot from the inlet, sectional pressure drops were measured to determine the permeability of each foot in the pack. The original and postplugging permeabilities are shown in Table .

8.

Injection pressure and effluent mass rate for SP5.

4. Original and Postplugging Permeability of SP5.

section	original permeability	postplugging permeability	permeability reduction (%)
k 1	1784	7	99.6
k 2	2153	132	93.9
k 3	1824	140	92.3
k	2215	20	99

The entire pack showed a 99% reduction in permeability. Looking at the individual sections, section 1 shows the highest permeability reduction at 99.6%, while the reduction in section 3 is only slightly lower, at 92.3%. This indicates that indeed the first section shows the most solid retention, but section 3 still shows a dramatic permeability reduction. These results imply that the solid deposition is relatively uniform across the entire length of the sand pack, indicating pore lining and bridging as the main mechanism of permeability reduction at the injection conditions of 0.5 wt % polymer concentration and 1 wt % solids concentration. In other words, the carrier fluid viscosity and solid concentration could be simultaneously optimized to control the distribution of injected solid particles in a target fractured reservoir volume.

Low-Permeability Media

To study solid transport and plugging behavior in lower-permeability fractures, the average Berea sandstone grains were reduced to about 0.15 mm to obtain sand pack permeability between 4 and 14 D (Table ). The first suspension flood experiment with a 1-foot-long, low-permeability sand pack (SP6) used the same injection conditions as those for SP4 and SP5. The resulting pressure and mass effluent for this experiment are shown in Figure .

9.

Injection pressure and effluent mass rate for SP6.

During the injection at a constant pressure of 30 psi, no significant fluid production was observed. A further stepwise increase of the injection pressure to 50 and then 100 psi did not result in a significant fluid production uplift. The low sand pack permeability drastically reduced injectivity, making it extremely difficult to inject at the same conditions of 0.5 wt % polymer concentration and 1 wt % solids. To improve injectivity in the subsequent suspension injection experiments with the low-permeability sand pack, the carrier fluid viscosity and solids concentration were kept the same, but the average particle size was reduced from 112 to 62.5 μm (Figure ). The results of this experiment (SP7) are listed in Figure a.

10.

Injection pressure and effluent mass rate for (a) SP7 and (b) SP8.

As similarly observed in previous suspension floods in the high-permeability sand packs, the effluent mass rate drastically decreased over the first five injected PVs and then stabilized around 0.02 g/sec. The sand pack was completely plugged after only 12 PVs. Comparing with the suspension floods in the high-permeability sand packs at the same injection pressure of 30 psi indicates that the injectivity loss becomes severe for this range of medium permeability (sub 10 D), warranting the need for a further reduction of particle size to avoid premature plugging. For this purpose, the particle size was further reduced to submicrometer levels in the suspension flood experiment SP8, where the nanosized solid particles P2 were used. The results of this experiment are shown in Figure b. After the initial reduction, the effluent mass rate reached around 0.1 g/s and then slowly decreased to zero after more than 80 injected PVs. Such a remarkable improvement in plugging performance compared to SP7 shows the importance of solid particle size distribution (PSD) in long-fracture plugging as the fracture permeability decreases. A smaller solid PSD is needed for lower fracture permeabilities to result in effective plugging. This has been demonstrated both experimentally and via simulation. ,

To confirm the improved performance of the nanoparticle suspension in a longer medium, the experiment SP9 was conducted in a 3 ft sand pack under the same conditions as used in SP8, and the results are shown in Figure . Given the low permeability of the medium, a low effluent mass flow rate was also observed in this experiment (SP9). The average flow rate was about 0.02 g/sec, compared to 0.5 g/sec for the 3-foot-long high-permeability sand pack in SP5 at the same applied pressure drop.

11.

Injection pressure and effluent mass rate for SP9.

Furthermore, the smaller size of P2 (70 nm) compared to the size of P1A (112 μm) in SP5 results in a higher apparent viscosity of the carrier fluid at the same 0.5 wt % concentration. This is due to stronger interparticle forces exhibited by the nanoparticles’ high surface-to-volume ratio which increases electrostatic interactions. This added viscosity likely contributed to the uniformity of the plugging seen in SP9 as indicated by the sectional permeability reductions (Table ).

5. Original and Postplugging Permeability of SP9.

section	original permeability	postplugging permeability	permeability reduction (%)
k 1	12	0.01	99.9
k 2	15	0.03	99.8
k 3	15	0.01	99.9
k	14	0.01	99.9

Reducing the particle size in SP9 led to a plugging behavior similar to that in SP5. The results from these two experiments indicate that it is possible to obtain similar deposition and plugging behavior of solid particles in fractures with different permeabilities by adjusting the particle size distribution at fixed injection polymer and solid concentrations (e.g., 0.5 and 1 wt %, respectively, under the experimental conditions in this work).

VES-Solid Suspension

Low-Permeability Media

The viscoelastic behavior of an aqueous surfactant solution is governed by the dynamic entanglements of the surfactant worm-like micelles. The robustness of micelle breaking and reforming gives the solution its unique gel-like consistency, which can be customized to be used as a fluid diverting or plugging agent. Therefore, before investigating the ability of nanoparticle-enhanced VES suspensions to reduce fracture permeability, it is desired to evaluate the plugging behavior of the VES in the absence of nanoparticles. For this purpose, a sand pack flooding experiment (SP10) was conducted in which one PV of the VES solution at 4 wt % surfactant concentration was injected at a constant rate, followed by one h shut-in of the sand pack for the VES micelle structures to reform before brine injection began at varying applied pressure drops. It was found that the relationship between the measured effluent flow rate and the applied pressure is proportional as shown in Figure a and that the postplugging permeability to brine was around 6.5 Darcy, compared to the initial permeability of about 10 Darcy. This corresponds to a 35% reduction in permeability using only the VES solution in the absence of nanoparticles.

12.

Preplugging and postplugging pressure drops for (a) SP10 and (b) SP11.

It was observed from the rheological characterization of VES-nanoparticle suspensions (Figure ) that the interaction between VES and nanoparticles could significantly affect the viscoelastic properties of the suspensions (i.e., the storage modulus G′ and the loss modulus G″). To evaluate the impact of this effect on the plugging performance of VES, the VES-nanoparticle flooding experiment SP11 was conducted with 3 wt % nanoparticles under the same experimental conditions as described in SP10, except with a reduction of VES concentration to 1 wt %. After the VES slug was injected, the postplugging permeability was measured using constant rate brine injection, and the results are shown in Figure b. It is clear from the very high pressure drops encountered at much lower flow rates that the postplugging permeability is lower than the original permeability. In fact, it was determined to be around 0.01 Darcy compared to the original permeability of about 12 Darcy. This corresponds to a 99% reduction. These results show that it is possible to achieve highly efficient fracture plugging with the introduction of nanoparticles into the VES solution.

High-Permeability Media

In an attempt to achieve the same plugging performance in high-permeability sand packs, a higher concentration of VES and nanoparticles was used for this set of VES-solids experiments (SP12–SP13). The same injection strategy was adopted as in SP10-SP11, but the postplugging permeability was determined using constant-pressure brine injection as opposed to constant rate injection. The results of the postslug brine injection for SP12 with 2 wt % VES concentration and 3 wt % nanoparticles are shown in Figure a. Injecting brine at all pressures below 10 psi did not lead to any production from the sand pack. A breakthrough occurred at 10 psi after more than 26 min, at which point brine was being produced at a constant rate. This means that the minimum pressure gradient for mobilization at these conditions is around 10 psi.

13.

Injection pressure and effluent mass for SP12 (a) and SP13 (b).

Table shows the measured permeability at each injection pressure based on the effluent mass rate and the corresponding permeability reduction. Injecting at 10 psi resulted in a measured permeability of 150 Darcy, which corresponds to a 90% reduction relative to the original pack permeability. However, the effluent did show that the VES solution was still flowing at this injection pressure; therefore, the measured permeability is not the absolute permeability of the plugged pack. To ensure that rest of the mobile VES is removed, progressively higher injection pressures were chosen, until the effluent was clearly only brine. This first occurred at 15 psi, but to ensure that was the case, a higher injection pressure of 20 psi was tested as well. For both pressures, the measured permeability was 350 Darcy, corresponding to a 77% reduction in permeability.

6. Permeability Reductions for SP10 and SP11.

	low concentration (SP12)		high concentration (SP13)
injection pressure	permeability	reduction (%)	permeability	reduction (%)
2–8 psi
10 psi	150 Darcy	90
12 psi	330 Darcy	78
15 psi	350 Darcy	77
20 psi	350 Darcy	77
35 psi			44 Darcy	94
40 psi			64 Darcy	92
45 psi			76 Darcy	90
50 psi			92 Darcy	88
60 psi			128 Darcy	84
35 psi			164 Darcy	80

SP13 was conducted in the same way, but at higher concentrations of VES and nanoparticles −4 and 15 wt %, respectively, in an attempt to improve plugging efficiency above 77%. As can be seen from the pressure and effluent mass data in Figure b, no production occurred at any pressure below 35 psi. At 35 psi, brine production started at a constant rate, indicating that the minimum pressure gradient for mobilization is around 35 psi. This is higher than the 10 psi encountered in SP12, which can be attributed to the increased pseudocross-linking effect that the higher nanoparticle concentration has on the micelles, ,, as is supported by the rheological data shown in Figure , where the viscoelastic properties of the VES solution seemed to increase at higher concentrations. To determine the extent of permeability reduction, several injection pressures were used until the effluent was clear of any residual VES solution. After ensuring that 60 psi was enough to make the effluent clear, the injection pressure was decreased back down to 35 psi, and the permeability was determined to be around 164 Darcy, as shown in Table , which corresponds to a reduction of about 80%. These results show that the nanoparticle-enhanced VES system exhibits a minimum pressure gradient for mobilization that increases with higher concentrations of both VES and nanoparticles, and that even if it is exceeded, efficient plugging and permeability reduction could still be achieved.

Conclusions

This work investigated the dynamics of solid particle transport in relation to fracture plugging. The effects of fracture permeability, particle size distribution, and carrier fluid properties were investigated for polymer and VES systems. In the case of the polymer-solids system, it was found that a polymer concentration of 0.5 wt % and a solid concentration of 1 wt % allowed for deeper fracture penetration and uniform plugging, while excessive solid content or carrier fluid viscosity led to premature plugging or injectivity loss. These findings were observed in both ∼1000 Darcy high-permeability fractures and ∼10 Darcy low-permeability fractures. Upscaling 1-foot-long sand packs to 3-foot-long confirmed the ability of these injection conditions to maintain high plugging efficiency for larger fracture volumes, as evidenced by uniform solid deposition along the entire length of the sand pack, rather than localized plugging near the inlet. For lower-permeability fractures, it was necessary to reduce the plugging solid PSD by half from 112 to 62.5 μm, and even to submicron levels, to overcome injectivity loss and maintain significant permeability reduction in both 1-foot-long and 3-foot-long sand packs. This shows that for a given fracture permeability, it is possible to achieve highly efficient permeability reduction by adjusting the particle size distribution. For the nanoparticle-enhanced VES system, it was shown that the addition of nanoparticles significantly enhanced the fracture plugging efficiency compared to VES alone. This was demonstrated by an increase in the minimum pressure needed for mobilization from 15 to 35 psi and a slight permeability reduction increase from 77 to 80%. Higher fracture permeabilities required an increase in VES and nanoparticle concentrations but still showed up to 99% permeability reduction. This showcases the adaptability of this system for various fracture permeabilities. These results show the ability of both polymer-solids systems and VES-nanoparticles systems to effectively plug fractures, as long as key injection parameters such as polymer or VES concentration, solids concentration, and solid PSD are adjusted to suit the desired injectivity or fracture permeability. They also provide insight into field-scale applications of fracture plugging for reservoir conformance control.

The authors declare no competing financial interest.