Study of the Rheological Characteristics of Sediment-Gelling Compositions for Limiting Water Inflows

Abstract

In view of the poor knowledge of the applicability of sediment-gelling compositions (SGCs) in waterproofing the bottom-hole zone of wells, work in this area of research is one of the most promising in waterproofing today. The key goal of this work is to study the prospect of using SGCs for waterproofing as well as to calculate the rheological characteristics of the proposed SGCs depending on variations in the components of their composition (alkali and polymer). In the course of our studies, it was found that the key factors influencing the rheological characteristics of SGCs are not only the variation in the ratio in the composition of alkali and polymer but also the degree of salinity of the formation water, which must be taken into account when developing waterproofing. During this research, it was found that due to the absence of calcium and magnesium ions in fresh water, the proposed polymers have good solubility (the exponent in the rheological model is equal to or close to unity), which leads to an increase in the viscosity of solutions. The dependence of changes in the rheological constants of SGCs on such parameters as temperature and alkali concentration have been established. It was determined that an increase in the solution temperature leads to an increase in the rheological constant n from 0.8 to 0.92 (at a polymer concentration of 0.05 and a NaOH concentration of 0.1), while a variation in the NaOH alkali concentration from 0.1 to 0.75 leads to similar changes in one measured temperature range. The results obtained can be used in the future to evaluate the use of SGCs to create barrier waterproofing in the bottom-hole zone of wells during oil production.

1. Introduction

As is known, production wells are often completely flooded, while a significant part of the oil reserves still remain undeveloped. These features are inherent in various fields. Under these conditions, the most reliable way to increase oil recovery is to limit water inflow using modern technologies and chemicals [1,2]. In turn, for these methods to be effective, a waterproofing shield with a radius of a large length is required.

One of the technologies that enhances the efficiency of bottom-hole zone treatments by reducing the permeability of the washed zones of the bottom-hole formation and reducing the degree of its heterogeneity is the sediment-gelling composition—SGC. The action of such compositions is based on the creation of an insoluble sediment and polymer gel in the pore space of the bottom-hole formation zone, thereby blocking or reducing the permeability of water-washed intervals. Such technologies include the processing of the near-bottom-hole zone (NBHZ) with SGCs based on water-soluble polymers and alkalis. This technology is based on a reaction between two reagents in the reservoir, which, when mixed, interact with each other and reservoir water and form a precipitate and a gel in the near-wellbore region, preventing water from entering the well. A special case of this technology is the reaction of the polymer with formation water. In addition, as noted in the works [2,3], the efficiency of using SGCs based on water-soluble polymers and alkalis increases significantly due to the presence of a polymer that has flocculating properties, which makes it possible to bind the individual dispersed particles formed in the reservoir to themselves and to the rock of the reservoir, thereby further increasing the isolation effect.

However, the success of works on waterproofing with SGCs is still not high enough. It is possible to increase the effectiveness of water shutoff works due to a more reasonable choice of SGC for specific conditions of the treated wells [2].

As is known [3,4], the efficiency of NBHZ treatments with SGCs depends on their good selective filterability in zones with high water saturation, allowing for the creation of water-insulating barriers/shields in the desired direction and to a sufficient depth, and the controllability of the process of water-shedding of the flooded section of the reservoir according to the degree and duration of blockage and water-insulating properties of the formed screen [5], determined by the rheological and filtration characteristics of the SGC.

Currently, most of the world’s oil fields are at a late stage of development, which is characterized primarily by an increase in water cut and a decrease in oil production [5,6,7]. Well water cut is a serious and widespread problem in the oil industry, and it is the subject of numerous studies. In published works, researchers are trying to find out the causes of water manifestations and outline the sequence of studies to develop measures for their prevention and elimination. If we add the uncertainty of the conditions for modeling and decision making to the above, then the complexity of solving this problem becomes obvious. This explains the great attention of researchers on this problem. Like any other process that is a serious problem, watering also requires the establishment, proper understanding, and analysis of the causes of excess water supply [8]. To date, methods have been developed and proposed, according to which problems and their nature are determined using modern diagnostic methods, which make it possible to prevent and eliminate the source of excessive watering. Thus, in order to increase the efficiency of field development and reduce the cost of processing and disposal of produced water, it is necessary to control the process of water cut in production correctly and in a timely manner, with a preliminary study and the establishment of its causes [9,10].

For the successful application of technologies for limiting water inflows and methods for regulating the development process, which increase the effectiveness of measures to combat water cut, complex studies are required, including an analysis of the geological and physical conditions and the study of the rheological and filtration characteristics of the compositions used. The latter requires setting up, planning, and conducting experimental studies [11,12].

Thus, the presence of a number of problems associated with the high water content of the extracted products and the insufficient efficiency of water inflow limitation technologies indicates the relevance of this problem and necessitates the formulation and undertaking of studies to establish the causes of water ingress and to improve the technology and compositions of the systems used for waterproofing works. An increase in the efficiency of waterproofing works is possible with a thorough study and determination of the compliance of geological and technical conditions for the application of a particular technology, as well as through the study, improvement, and use of compositions with a relatively better insulating ability [13,14,15].

The scientific novelty of this work consists in the conducted experimental studies, during which the influence of polymer and alkali concentrations on the formation of the sedimentation mechanism was established and the dependences of the sediment volume as well as the rheological constants of sediment-gelling compositions on polymer and alkali concentrations were obtained.

2. Materials and Methods

To study the mechanism of precipitate formation in earlier works [2,4], SGCs based on polyacrylamide (PAA) and alkali-caustic soda (NaOH) were used. The concentration of PAA in SGCs varied within the range of 0.025–0.15, and NaOH within the range of 0.1–0.75%. SGCs were prepared by analogy with previous studies, in particular, according to [2,4], in fresh water.

Experiments to study the mechanisms of precipitation formation were carried out by conducting serial tests, implemented taking into account temperature variations as well as polymer and alkali concentrations. Temperature variations were carried out in the range from 30 to 80 °C; the choice of temperature range was determined by the ability to simulate the operating conditions of SGCs as closely as possible to real conditions. The variation in NaOH alkali concentration ranged from 0.1 to 0.75%, and the polymer concentration variation ranged from 0.025 to 0.15%. As a result of the experiments, dependences were obtained to evaluate the influence of the concentrations of polyacrylamide and alkali on the amount of precipitation. Based on the data obtained, the rheological characteristics of SGCs were calculated.

Calculations of rheological characteristics were carried out using methods of mathematical statistics as well as assessment of measurement errors and standard deviations. Based on the obtained dependencies, the flow pattern (Newtonian, dilatant, or pseudoplastic) of the proposed SGCs was determined depending on the conditions of temperature variation and polymer and alkali concentration.

The obtained results of the rheological characteristics of the proposed SGCs were compared with the results of experimental works [1,2,3,4,5,6,7,8,9,10,11,12,13], which made it possible to determine the optimal compositions for further research.

3. Results and Discussion

3.1. Investigation of the Mechanism of Sediment Formation in Sediment-Gelling Compositions

The purpose of this series of research was to study and evaluate the effect of the concentrations of polyacrylamide and alkali on the amount of precipitation. The amount of precipitate formed upon contact of the polymer and alkali was determined using a preweighed paper filter placed on a glass plate at the bottom of a 1 L beaker. An amount of 1 L of a polymer solution of a given concentration was poured into a beaker; then, a certain amount of NaOH was added to achieve the required alkali concentration. After holding the prepared composition for 48 h, the glass plate with the paper filter was removed from the beaker and placed in a drying cabinet, where it was dried at a temperature of 105 °C and then weighed again, and the amount of precipitate formed was determined by the difference in weights before and after it was placed in the beaker. The results obtained, expressed in milligrams per 1 L of solution, are presented in

Table 1. Dependence of the amount of precipitate formed on the concentrations of the polymer and alkali components of SGCs [1,2].

Alkali Concentration, %	PAA Concentration, %
	0.025	0.05	0.075	0.1	0.15
	Sediment Amount, mg/L
0.1	0.285	0.245	0.22	0.16	0.14
0.12	0.25	0.23	0.195	0.18	0.15
0.15	0.24	0.21	0.19	0.185	0.16
0.25	0.17	0.15	0.18	0.25	0.28
0.5	0.35	0.255	0.23	0.33	0.457
0.75	0.45	0.36	0.31	0.47	0.615

.

As can be seen from Table 1, at polymer concentrations in solution of 0.025–0.075%, an increase in alkali concentration from 0.1 to 0.25% leads to a decrease in sediment; with its further increase to 0.75%, an increase in the amount of sediment is observed. At polymer concentrations in the solution of 0.1–0.15%, with an increase in the concentration of alkali in the solution from 0.1 to 0.75%, only an increase in precipitation is observed. The results of these experimental studies were processed by us, using the methods of mathematical statistics. Moreover, partial dependences of the amount of sediment on the concentration of alkali were built at constant values of the PAA concentration given in the table. An analytical dependence of the amount of sediment on the concentration of alkali was established for different cases. Next, the dependence of the parameters of this expression on the PAA concentration was determined. Thus, we obtained the dependence of the amount of sediment on the concentrations of alkali and PAA in the following form:

$$v=f\left(k_{NaOH}, k_{PAA}\right),$$

(1)

Below are the results of the calculations. Figure 1 demonstrates graphs of the noted dependences of the volume of the precipitate on the concentration of alkali at constant concentrations of polyacrylamide. Approximations of each of the dependences shown in the figure were obtained by statistical processing. The most suitable in this case and common for all cases is the dependence in the form of a power law, expressed as follows:

$${V_{sed}=aC}_{NaOH}^b,$$

(2)

where parameter b depends on the concentration of polyacrylamide.

The values of parameter b depend on the concentration of polyacrylamide. This dependence is shown in Figure 2. An analytical approximation of this dependence was obtained and substituted into (1); thus, the dependence of the sediment volume on the concentrations of alkali and polyacrylamide was obtained in the following form (3):

$$V_{sed}=0.3289\cdot C_{NaOH}^{0.716\cdot e^{11.582\cdot C_{PAA}}}$$

(3)

Calculations were made according to this expression, and comparison with the actual experimental values showed their sufficient coincidence. The change in the amount of sediment upon contact of the polymer and alkali, depending on their concentration, is caused by the action of several factors. On the one hand, when alkali is introduced into the polymer solution, part of it interacts with polyvalent cations (Ca²⁺, Mg²⁺) contained in water, as a result of which the poorly soluble hydroxides of the Ca(OH)₂ type precipitate as a finely dispersed solid phase. The other part of the alkali, being adsorbed on polymer macromolecules, does not participate in the formation of a precipitate [1].

Therefore, at low concentrations of alkali (0.1–0.15%), with an increase in the concentration of the polymer in solution from 0.025 to 0.15%, a decrease in the amount of sediment is observed due to the increasing possibility that part of the alkali may be adsorbed on the polymer. The same mechanism also operates up to an alkali concentration of 0.25% at polymer concentrations in solution of 0.025–0.075%, with alkali and polymer, respectively, in the ranges of 0.5–0.75 and 0.025–0.075%. And at high concentrations of both reagents, the volume of the precipitate increases.

On the other hand, alkali facilitates the association of functional groups of the polymer into larger formations [1,3], as a result of which they can precipitate. At the same time, the polymer is able to bind the individual, formed, dispersed particles to each other and also lead to their precipitation. Therefore, with an increase in the concentration of both alkali and polymer above the indicated limits, all of the above mechanisms come into play. As a result, the amount of sediment increases both in the form of poorly soluble hydroxides and large polymer–alkaline aggregates.

Thus, the conducted studies have shown that by selecting the appropriate concentrations of polymer and alkali for each specific case of near-bottom-hole zone treatment, it is possible to control the amount of sediment formed and thereby increase the efficiency of limiting water inflows by SGCs.

3.2. Analysis of the Results of Studies Devoted to the Study of the Filtration Characteristics of Polymer Systems

In recent years, researchers have begun to pay serious attention to finding technological solutions to eliminate the consequences of water breakthrough through highly permeable interlayers of heterogeneous reservoirs while using the so-called flow-diverting technologies (FDT) [4,5,6,7,8]. Most of the functions of FDT are aimed at the formation of a water barrier by pumping the appropriate compositions into injection wells. As a result of this, the volume of water injection is redistributed, both in terms of thickness and area of the deposit, and the previously unexplored or poorly covered formation zones are connected to the development by waterflooding. It should be noted that a polymer solution plays one of the main roles in the mechanism of the formation of a water-insulating shield. In some of the studies carried out, the main focus of attention was the movement of compositions based on a PAA polymer solution of the brand “FP-307” and a chromium acetate cross-linker in a porous medium. One of the indicators that can be used to judge the change in their filtration characteristics when the formation is affected by water-soluble polymers is the residual resistance factor (R_res) [9], i.e., the ability of water-soluble polymers in contact with a porous medium, as a result of adsorption and physical blockage of small pores, to reduce its permeability. Therefore, knowledge of the filtration characteristics of a polymer solution makes it possible to determine the depth of its penetration into a porous medium, especially along the interlayers of a layered heterogeneous formation, the location of the water-insulating shield, and, consequently, the FDT efficiency.

To study the filtration characteristics of polymer systems, the papers [10,11] present the results of experimental studies to assess the filtration characteristics of polymer systems for use in the fields of Kazakhstan. When conducting studies [11] to assess the filtration characteristics of the CPS, an installation was used that consisted of two parallel-connected linear reservoir models, water boosters, a compressed air cylinder, a dosing pump, and pressure gauges. Linear reservoir models allow the modeling of a two-layer reservoir model with hydrodynamically noncommunicating interlayers. To create a two-layer reservoir model with interlayers of different permeabilities, quartz sand with a fraction of <0.1 mm and its mixture with marshallite were used. The design of a two-layer reservoir model allows the injection of fluid both jointly into high-permeability (k₁) and low-permeability (k₂) interlayers and separately into each interlayer, as well as its withdrawal from the interlayers separately. Experiments were carried out only in porous, water-saturated media. Two-layer reservoir models were saturated with waste formation water taken from the Karazhanbas field. The choice of permeability in the experiments is based on real, actual data on the Karazhanbas field, where the average reservoir permeability ranges from 1 to 15 µm² [10,11].

The studies carried out in the works of the authors [11] showed that when CPS is injected into a layered heterogeneous reservoir, the main part of it enters the high-permeability interlayer, and the higher the value of the permeability ratio, the more CPS enters the high-permeability interlayer. From this, it follows that CPS (based on polymer FP-307 (PAA) with chromium acetate as a cross-linker) creates an opportunity for effective control of the direction of filtration flows and the connection of low-permeability interlayers to work. The obtained results showed the possibility of conducting pilot tests of FDT based on a PAA polymer solution of the FP-307 brand and a chromium acetate cross-linker.

The analysis revealed the possibility of using this technology for a wide range of geological and physical conditions, especially for multilayer development objects, such as the Karazhanbas field. As the theoretical and experimental studies have shown, the highest efficiency of the technology is achieved when the ratio of the permeability of the layers is approximately 2 to 5. The increase in sweep efficiency occurs due to the involvement in the development of both low-permeability layers and areas with high filtration resistance, the so-called stagnant zones. To assess the technological efficiency and the possibility of using the flow-diverting technology, a set of laboratory experimental studies of the rheological characteristics of polymer solutions was carried out. During these studies, the dependencies of the viscosity of the cross-linked polymer system FP-307 (concentrations: 1–0.3%, 2–0.4%, 3–0.5%) on the shear rate in the injected water of the Karazhanbas field, the rheology (dependence of stress on shear rate) of the cross-linked polymer system FP307 with a marked concentration as well as the filtration of the cross-linked polymer systems used in diverting technologies in the fields of Kazakhstan were studied.

The authors of [15,16,17,18] studied the rheological properties of some developed polymer compositions. These polymeric compositions have been developed as water barriers and sand-reinforcing agents for oil and gas production wells. The influence of various factors on the rheology of compositions was studied, and their changes were evaluated in a wide range of temperatures (25–110 °C), shear rates (0–500 s⁻¹), saline solution percentages (0–15%), types of cross-linking agents and concentrations of (0–3%), and polymer concentrations (6–50%). It has been established that an increase in the shear rate from 0 s⁻¹ to 100 s⁻¹ leads to a decrease in shear and a decrease in the viscosity of dilute solutions (6–13%) from 25 cP to ~3 cP at 80 °C.

With regard to statistical analysis of the results of studies of the rheological characteristics of sediment-gelling compositions, as noted in [12], the main disadvantage of technologies using selective sediment-forming reagents is that they do not take into account the physical properties of the working fluids used, which leads to low water isolation of highly permeable aquifers [1] and insufficient impact on the low-permeability oil-bearing layer.

Therefore, to determine the injection rates of SGCs in NBHZ, the expected pressures and filtration conditions in porous media and knowledge of the rheological and filtration characteristics of SGCs is necessary. Our study of the rheological properties of SGCs depending on the concentrations of the polymer and alkali and the type of solvent was carried out on the rotational viscometer Reotest 2.1 according to the standard procedure, with thermostating at a temperature of 30 °C [1]. SGCs of the following composition were taken as samples for the study: ionomer “L” or technical PAA of ammonia purification with a molecular weight of 1.35 × 10⁶; sodium hydroxide (NaOH); and a solvent. The concentration of PAA and NaOH in the SGCs varied from 0.05 to 0.15% and from 0.1 to 0.75%, respectively, and the concentration of the ionomer “L” and NaOH changed from 0.075 to 1% and from 0.1 to 1%.

As solvents, similar to [1,2], distilled, fresh, sea, formation, and combined formation water were chosen, respectively.

On the basis of the experimental data obtained from the viscometer, the flow curves were plotted as a dependence of the shear stress (τ) on the shear rate ($\dot{\gamma }$). The parameters of this dependence were determined by the methods of mathematical statistics based on the processing of flow curves according to the power law of Ostwald–de Waele [9,13]. It is known that the media, which are characterized by flow curves passing through the origin, are called pseudoplastic, and their rheology is described by the Ostwald–de Waele power model. This model is expressed as follows:

$$\tau =k\times {\dot{\gamma }}^n,$$

(4)

where $\tau$ is the shear stress, Pa; k is the consistency coefficient, Pa∙sⁿ, where the shear rate gradient is s⁻¹; and n is the current index.

The parameters of these dependences, in turn, depend on the concentrations of the alkali and polymer as well as on the temperature. The data obtained are summarized in

Table 2. Dependence of the nature of the SGC flow on the concentrations of the polymer and alkali and on the temperature.

SGCs		Temperature, °C
Concentration, %		30		40		60		80
PAA	NaOH	Rheological Constants
		k	n	k	n	k	n	k	n
0.05	0.1	0.06	0.8284	0.036	0.8889	0.022	0.9136	0.016	0.9255
	0.12	0.037	0.8992	0.029	0.9059	0.022	0.9180	0.015	0.9350
	0.15	0.037	0.8953	0.024	0.9328	0.016	0.9645	0.009	0.9965
	0.25	0.03	0.9229	0.023	0.9409	0.017	0.9559	0.006	1.0000
	0.75	0.024	0.9575	0.017	0.9836	0.012	0.9849	0.008	1.0000
0.075	0.1	0.045	0.9006	0.029	0.9202	0.025	0.9153	0.007	0.9284
	0.12	0.08	0.9196	0.036	0.9116	0.026	0.9220	0.015	0.9630
	0.15	0.031	0.9695	0.025	0.9712	0.018	0.9721	0.013	0.9766
	0.25	0.031	0.9688	0.023	0.9802	0.015	1.0000	0.012	1.0000
	0.75	0.026	0.9814	0.018	1.0000	0.014	1.0000	0.008	1.0000

.

Figure 3 demonstrates plots of rheological constants versus alkali concentration (Figure 3a,b), polymer concentration (Figure 3c), and temperature (Figure 3d,e).

The coefficient “k” and the exponent “n” are constants characterizing the solution. “k” is a consistency indicator characterizing the pumpability of the solution, and “n” is an exponent indicating the degree of non-Newtonian characteristics. As the viscosity of the solution increases, “k” increases. As the viscosity decreases, “n” decreases [13].

It is known that at n = 1, the fluid is Newtonian, and as “n” decreases, the fluid becomes less viscous. In other words, the graph of shear stress versus shear rate is a straight line at n = 1, and as “n” decreases, the line curves more and more. As the bend in the curve increases, the rate of decrease in effective viscosity with increasing shear rate increases. Therefore, it can be said that the liquid becomes less viscous and thins out. When n > 1, the liquid behaves as a dilatant one, the viscosity of which increases with increasing shear rate and becomes thicker and more viscous.

As can be seen from Table 2, SGCs based on PAA and NaOH during viscometric flow exhibit pseudoplastic properties (n < 1), which weaken with a decrease in polymer concentration, with an increase in alkali concentration from 0.1 to 0.75% in SGCs, and at temperatures from 30 to 80 °C. For SGCs with 0.05% PAA, 0.25–0.75% alkali at 80 °C and for SGCs with 0.075% PAA, 0.75% alkali at 40 °C, 0.25–0.75% alkali at temperatures of 60 and 80 °C, a transition from pseudoplastic properties to Newtonian ones is observed. In this case, as already noted above, the media, which are characterized by flow curves passing through the origin of coordinates, are called pseudoplastic, and their rheology is described by the power-law model of Ostwald–de Waele. This model (4) is shown above.

During statistical analysis, averaged partial dependences of rheological constants on the concentrations of PAA, alkali, and temperature were built, their analytical approximations were found, and generalized dependences n (or k) = f(C_PAA,C_NaOH,t) were found using methods known from mathematical statistics. These parameters were determined by methods of mathematical statistics based on the processing of flow curves, as already noted, according to the Ostwald–de Waele power law [9,13]. The noted particular dependences are presented in graphical form in Figure 4 and

Table 3. Particular and generalized expressions for estimating the values of rheological constants.

	f(CPAA)	f(CNaOH)	f(t)	f(CPAA,CNaOH,t)
k	k = 0.0072$C_{PAA}^{-0.71}$	k = 0.02$C_{NaOH}^{-0.363}$	k = 5.1882t−1.328	$k=0.1837·C_{PAA}^{-0.598}·C_{NaOH}^{-0.306}·t^{-1.118}$
n	n = 1536 $C_{PAA}^{0.2016}$	n = 0.984$C_{NaOH}^{0.0561}$	n = 0.5872t0.1064	$n=1.0712·C_{PAA}^{0.1}·C_{NaOH}^{0.027}·t^{0.052}$

.

The dependences given in the table above were processed by statistical methods, with an assessment of the closeness of the relationship and adequacy according to the relevant criteria. A comparison of the calculated and experimental values, as well as statistical estimates, shows a fairly good agreement between the calculated and experimental values.

In [1,2,11], the rheological characteristics of SGCs based on the L ionomer and alkali were studied. Ionomers have unique physical properties, including electrical conductivity and viscosity—a rise in the viscosity of an ionomer solution with increasing temperature. Ionomers also have unique morphological properties because the nonpolar polymer backbone is energetically incompatible with polar ionic groups. As a result, the ionic groups in most ionomers will undergo microphase separation to form ion-rich domains. As can be seen from

Table 4. Dependence of the nature of the SGCs flow on the concentration of the polymer, alkali, and type of solvent.

Water	NaOH, %	Polymer Concentration,%
		Ionomer “L”
		0.075		0.15		0.5		1
		Rheological Constants
		k	n	k	n	k	n	k	n
fresh	0	0.006	0.8517	0.014	0.8156	0.101	0.7516	0.154	0.7686
	0.1	0.004	1.0000	0.0067	1.0000	0.206	0.7362	0.339	0.7848
	0.3	0.0035	1.0000	0.0058	1.0000	0.173	0.7192	0.253	0.7526
	0.5	0.0032	1.0000	0.0055	1.0000	0.17	0.7161	0.248	0.7284
	0.7	0.0024	1.0000	0.004	1.0000	0.168	0.714	0.217	0.7159
	1	0.002	1.0000	0.0033	1.0000	0.114	0.6955	0.206	0.6698
formation water	0	0.0016	1.0000	0.002	1.0000	0.006	1.0000	0.029	0.9332
	0.1	0.0017	1.0000	0.0021	1.0000	0.014	0.9409	0.051	0.8595
	0.3	0.002	1.0000	0.0026	1.0000	0.032	0.8628	0.087	0.8136
	0.5	0.0022	1.0000	0.0031	1.0000	0.038	0.8378	0.09	0.8084
	0.7	0.0024	1.0000	0.0035	1.0000	0.04	0.8324	0.151	0.7713
	1	0.0026	1.0000	0.0036	1.0000	0.068	0.7957	0.212	0.7799

, SGCs based on the L ionomer and alkali at low polymer concentrations of 0.075–0.15%, regardless of the concentration of alkali and the type of solvent, behave like Newtonian liquids. With a growth in the concentration of the ionomer “L” from 0.5% to 1%, SGCs behave like pseudoplastic fluids.

Moreover, with a growth in the concentration of alkali in SGCs, their pseudoplasticity increases, and the consistency coefficient for SGCs on fresh water decreases, while for SGCs on combined formation water, it increases. At all considered concentrations of the ionomer “L” (0.075–2.5%), its solutions in waters of various salinity in the absence of alkali behave like pseudoplastic liquids (see Table 4).

The results of these studies are shown in Table 4 and Figure 5. As is evident from the table and figure, SGCs based on the L ionomer and alkali at low polymer concentrations of 0.075–0.15%, regardless of the concentration of alkali and the type of solvent, behave like Newtonian liquids (the exponent in the rheological model is equal to 1 or close to it).

With a rise in the concentration of the ionomer “L” from 0.5% to 1%, SGCs behave like pseudoplastic fluids. Moreover, with an increase in the concentration of alkali in SGCs, their pseudoplasticity increases, and the consistency coefficient for SGCs on fresh water decreases; in contrast, for SGCs on combined formation water, it increases. At all considered concentrations of the ionomer “L” (0.075–2.5%), its solutions in waters of various salinity in the absence of alkali behave like pseudoplastic liquids (Table 4). In the noted works, “rheological curves” are given, expressing the dependence of shear stress on shear rate.

As can be seen from the comparison of the data given in Table 2 and Table 4, the concentration of sodium hydroxide leads to a weakening of the effect of the pseudoplastic properties of PAA-based SGCs and an increase for SGCs based on the “L” ionomer. Based on the results of the studies shown in Table 4, statistical processing was carried out and graphs were plotted, along with distributions of rheological constants in the plane and in space. Graphical dependences are presented in Figure 5. Figure 6 reveals the distributions of these parameters in a two- and three-dimensional image.

A comparative analysis of these results makes it possible to more clearly follow the change in rheological constants and the nature of the compositions used in the experiments associated with this. The figures clearly show different areas characterizing the properties of the compositions associated with flow and deformation, i.e., Newtonian or pseudoplastic nature. These parameters, called “rheological constants”, are characterized by certain values that do not depend on the conditions for their measurement or on the design of measuring instruments.

Using the data obtained from a rotational viscometer, according to the formula (${\mu }_E=k·\dot{\gamma }$ⁿ⁻¹) given in [1], the effective viscosity values for the studied SGCs were calculated.

The work [1] provides an analysis of experimental observations, which showed that the effective and Newtonian viscosities of SGCs prepared on fresh water decrease with a rise in alkali concentration, while the same properties of SGCs prepared on combined formation water increase.

At the same time, the results of the studies showed that the rheophysical properties of SGCs, for a number of reasons, depend on the mineralization of the solvent, the concentrations of caustic soda and polymer, the shear rate, and the temperature [1].

At a low polymer concentration in SGCs, the distance between macromolecules is large compared to their sizes. Therefore, when a polymer is added to a Newtonian fluid (solvent) to a certain concentration, the viscosity of the SGCs will increase, and the linear relationship between shear stress (t) and shear rate (y) will not be violated [1]. However, when a certain concentration is reached, this linear dependence will be violated, which will lead to an anomaly in viscosity. In this case, SGCs will exhibit pseudoplastic properties, and their effective viscosity will decrease with increasing shear rate (Table 4, at ionomer concentrations “L” of 0.5; 1%).

On the other hand, it is known that the conformation of macromolecules (the spatial arrangement of atoms and groups of atoms, which is specified by the set and sequence of configurational isomers and their relative mutual arrangement in the chain) determines the viscosity of polymer solutions in various solvents [1,14,17,18,19,20]. In a weakly mineralized medium, the interaction of intrinsic polar groups causes the straightening of macromolecular chains and an increase in their size.

In a mineralized medium, the intrinsic charges of the polar groups are partially neutralized, and the macromolecular chains fold and become more compact. Therefore, the viscosity of SGCs prepared in fresh water is higher than that of SGCs prepared in collected formation water (see Figure 6).

In addition, when a freshwater lye is added to SGCs, the salinity of the solvent increases and the viscosity of the SGCs decreases. When it is added to the collected formation water, the mineralization of the solvent decreases due to the precipitation of part of the salts in the sediment, and therefore the viscosity of SGCs increases.

The decrease in the effective viscosity of SGCs with increasing temperature is associated with both a decrease in the viscosity of the solvent and a decrease in the viscosity and viscoelastic properties of the polymer under the influence of temperature [15,16,17,18,19].

Thus, as the analysis of the performed experimental studies showed, the concentration of the components included in SGCs, type of solvent, temperature, and shear rate significantly affect the rheological properties of SGCs, and the obtained regularities are the basis for regulating the properties of gel-forming systems. For the broadest analysis and interpretation of the results of the experimental studies performed, the results are also presented in the form of two- and three-dimensional distributions of rheological constants depending on the concentrations of alkali, polymer, and medium. Real images are shown in Figure 6.

Thus, as a result of experimental studies using statistical methods of data processing and information analysis, an assessment of the physicochemical properties of gel-forming compositions was made, according to which the simulation of the rheological characteristics of sediment-gelling compositions was carried out, taking into account the composition and medium concentration of various components (polymer, alkali), temperature, and water salinity.

4. Conclusions

Studies have established that the rheological characteristics of sediment-gelling compositions are influenced by both the components included in them and the degree of salinity of formation water. In fresh water, due to the absence of calcium and magnesium ions, polymers have good solubility and the ability to increase the viscosity of solutions. As the concentration of the displacing agent increases, the viscosity of the solutions increases. The results obtained in this chapter lead to the following conclusions:

• The viscosity of SGCs prepared with fresh water is higher than the viscosity of SGCs prepared with brine water.
• It is shown that the physicochemical properties and the nature of the flow of sediment-gelling compositions depend on the concentrations of the polymer and alkali, the temperature, and the salinity of water, and at low polymer concentrations, the composition exhibits a Newtonian character.
• When alkali prepared in fresh water is added to SGCs, the salinity of the solvent increases and the viscosity of SGCs decreases. The addition of alkali to the collected formation water reduces the salinity of the solvent due to the precipitation of some of the salts, and therefore the viscosity of the SGCs increases.
• The physicochemical properties and the nature of the flow of sediment-gelling compositions depend on the concentrations of the polymer and alkali, the temperature, and the salinity of water, and at low concentrations of the polymer, the composition exhibits a Newtonian character.
• Simulation of the rheological characteristics of sediment-gelling compositions is carried out; taking into account the composition and medium concentration of various components (polymer, alkali), temperature and water salinity, expressions are obtained that characterize the dependence of rheological constants on temperature and on polymer and alkali concentrations.

The obtained results of assessing changes in the rheological characteristics of SGCs depending on variations in temperature and polymer and alkali concentrations as well as data on the physicochemical properties and flow patterns of SGCs can later be used in practice in the case of using gel-forming systems in creating barrier waterproofing in bottom-hole wells, which will increase the efficiency of oil production and reduce the risk of watering. In this case, the proposed compositions of SGCs will improve oil recovery from reservoirs as well as reduce water inflows due to variations in rheological characteristics, and they also allow for the possibility of creating selective filterability in areas with high water saturation.