Reza Rahimi, AmirHossein Saeedi Dehaghani

Department of Petroleum Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran

ABSTRACT Being one of the most commonly performed EOR methods, polymer injection is used to increase the mobility ratio and decrease water relative permeability to allow the injected fluid to sweep more oil towards the production well.Before the polymer solution is injected into the reservoir through the injection wells, the process of polymer injection must be simulated using commercial numerical reservoir simulators.In order to be able to simulate the process, the viscosity behavior of the solution must be known.Therefore, a model is required to estimate the viscosity of the injected fluids versus shear rate and polymer concentration.In this study, a new mathematical function based on the power-law fluid equation is presented,which can be applied to predict the viscosity of SPAM solutions.The two required parameters of the power-law equation are obtained by fitting a power-law function to the viscosity-shear rate data.Samples in different polymer concentrations (using two SPAM polymers with different molecular weights) were prepared and their viscosity was measured against different shear rates.The results were fitted to the power-law equation and their corresponding power-law parameters were recorded.A mathematical function was introduced and tested for each parameter.The new functions combined with the power-law equation were used to estimate the viscosity of different polymer solutions with different SPAM concentrations.The results showed that the model is capable of estimating the viscosity with acceptable precision.Furthermore, it is applicable in various temperatures and water salinities.

Keywords:Enhanced Oil Recovery EOR SPAM Polymer solution Apparent viscosity

1.Introduction

Due to limited oil reserves of the world and the fact that most of the world’s oil production is from mature oil fields, the need for methods to increase the oil recovery in reservoirs is felt [1,2].For this purpose,different methods of EOR(Enhanced Oil Recovery)are being tested and performed on reservoirs across the world.Water flooding is one of the most commonly performed methods to assist the natural energy of the reservoir.In water flooding, water is injected into the reservoir through an injection well to push the oil towards the production well and hence to increase the oil production.However,this method’s recovery is highly sensitive to the water-oil mobility ratio and reservoir heterogeneity.Mobility ratio is defined as follows:

Where M is the mobility ratio of the displacing fluid to the displaced fluid,kwis the water permeability,kois the oil permeability,μwis the water(displacing fluid)viscosity and μois the oil viscosity(displaced fluid) [3-5].In most oil reservoirs, especially heavy oil reservoirs, oil viscosity is noticeably greater than that of the water[6,7].As a result of this,water(displacing fluid)tends to flow easier than oil can and thus,it bypasses the trapped oil and leaves a large amount of oil unswept.This phenomenon is known as viscous fingering which is a major problem in water flooding [8-10].Furthermore, in heterogeneous reservoirs, a high degree of heterogeneity causes the injected water to find high permeability canals and pass through these formed canals as well, hence intensifying the problem [4].

Fig.1.Molecular structure of polyacrylamide.

A promising method to deal with the problem of high mobility ratio is introducing polymers, especially polyacrylamide, to the injected water[11,12].Polymers are macromolecules constructed of thousands and/or millions of smaller parts named monomers that are repeated throughout the polymer molecules’ structure.Generally,adding polymers to water greatly increases the viscosity of the water[13-16].Polymer molecular weight can be defined as the distribution of the polymer molecule size,which is responsible for the polymers’ characteristics.One of the ways to characterize the polymer molecular weight (Mw) is to use weigh average molecular weight[17].

Not only are these polymers used in the oil industry to enhance oil recovery, but also they are used with the purpose of carrying proppants in hydraulic fracturing processes [18].Hydrolyzed Polyacrylamide, a polymer, is widely used in the petroleum industry with the purpose of modifying the displacing fluids’ viscosity (water viscosity) to improve the recovery of water flooding[19,20].Along with the widely used HPAMs, Sulfonated Polyacrylamides(SPAM)are being accepted as new viscosifying agents in Enhanced Oil Recovery, too, which is a result of the fact that sulfonated polyacrylamides can be stable in high temperatures up to 120°C.Compared to the other widely used member of the polyacrylamide family, HPAM solutions, SPAM solutions are more thermally stable and can maintain their viscosifying effects up to several months [21-23].Figs.1-3 demonstrate the molecular structures for PAM,HPAM and SPAM,respectively.HPAM and SPAM are polyacrylamide polymers in which a portion of the amide groups (CO-NH2) have been replaced by an anionic group(Carboxylate and sulfonate group for HPAM and SPAM, respectively).This negative charge causes the polymers to be soluble in water[24].Being dissolved,HPAM and SPAM create polyelectrolyte solutions, implying that they have properties of both polymer solutions and electrolyte solutions [25].Although they behave similarly to other polymers while dissolved in pure water, in aqueous solutions,they are surrounded by the salt ions.The counter ions act as agents neutralizing some of the negative charges on polymer structure and as a result of this, the viscosifying effect of polyelectrolytes is limited in aqueous solutions.Being more flexible compared to SPAMs,HPAM solutions easily coil up in the presence of salt ions and experience more viscosity reduction [24].

In addition to their effect on viscosity of the displacing fluid,polymers are able to modify the relative permeability of water[26].A combination of reduced water relative permeability and modified water viscosity,can cause the recovery of water flooding to improve[27].

Since SPAM flooding is relatively new compared with HPAM flooding, a comprehensive study on their viscosity is needed.Although there have been multiple studies conducted on SPAM rheology, retention, injectivity, gelation and relative permeability reduction, to our knowledge, there is no comprehensive study conducted to evaluate the viscosity change of SPAMs in different conditions [23,24,28-31].Polymer solutions are shear thinning liquids meaning that their viscosity decreases with shear rate.In addition, polymer solutions’ viscosity changes with their concentration due to mixing with brine (dilution) and the effects of adsorption, salinity, pH, and temperature[27,32].

Fig.2.Molecular structure of HPAM.

The main focus of this research is to introduce a correlation to govern the viscosity behavior of SPAM solutions against shear rate and polymer concentration.For this purpose, two sulfonated polyacrylamide polymers(SPAM)with different molecular weights were used.A series of viscosity measurements were conducted on samples and the results were used to introduce the new model.The model was tested for validity in different salt concentrations and temperatures.According to the fit parameters and the results of the estimated viscosities using the model, it is applicable in a wide range of concentrations, shear rates and temperatures.

2.Materials and methods

2.1.Materials

In this research, two types of SPAM polymers with different molecular weights were used.The polymers were supplied under the commercial name AN 125 and AN 125 VLM with molecular weights of 8 and 2 million Daltons, respectively.Given that both polymers are sulfonated polyacrylamides with the same sulfonation degree, the only difference between the polymers is their molecular weights.Both polymers are supplied by SNF Corporation(France).Deionized water was used as the main solvent for preparing the polymer solutions.In order to prepare samples with different salinities, NaCl (Merck)was used.

2.2.Sample preparation

Fig.3.Molecular structure of sulfonated polyacrylamide.

Samples of both polymer solutions in polymer concentrations of 1000, 2000,3000,5000,7000 and 10,000 ppm were prepared.All polymer solutions with the above concentrations were prepared using a base sample with a polymer concentration of 20,000 ppm.To prepare the base samples, 2 g of each polymer was added to every 98 g of distilled water, separately.The base solutions were stirred on a stirrer using a magnet at 100 RPM for 48 h.After 48 h,the samples seemed clear and homogenous.Test samples with the required concentrations were prepared by diluting the base polymer solutions.

To test the validity of the model in different salt concentrations,samples with the aforementioned polymer concentrations were prepared in 0 wt%, 0.2 wt% and 0.5 wt% of salt using AN 125 polymer.

2.3.Viscosity measurement

The viscosity of the polymer solutions was measured at 4 different temperatures(15°C,25°C,35°C,45°C)to investigate the effect of temperature on the viscosity-temperature behavior of the solutions.Using a rheometer(Anton Paar QC viscometer,Germany)the viscosity of each sample was measured within the shear rate range of 10-200 1/s via the proper spindle (CC39).The rheometer was connected to a circulator to provide the tests with the required temperatures.

3.Results and discussions

3.1.Correlation development

The base equation used in this research is the Power-law equation (Equation (1)).It is used to govern the viscosity behavior of the shear thinning fluids, such as polymer solutions used in EOR [27].

Where τ is shear stress (pa), γ is shear rate (1/s), k is the flow consistency index (Pa.sn) and n is the flow behavior index(dimensionless).Combining equation (2) and equation (3), equation(4)can be derived for the viscosity of a shear thinning fluid as a function of shear rate.

Fig.4.Viscosity vs shear rate for different concentrations of AN 125 polymer at 15 °C.

Fig.5.Viscosity vs shear rate for different concentrations of AN125 VLM polymer at 15°C.

As illustrated in Equation (4), the model requires two parameters to be able to estimate the viscosity behavior of a shear thinning polymer solution.In fixed conditions(fixed salinity, fixed polymer concentration, fixed temperature and pH), the parameters k and n are constant.Nonetheless, in a polymer flooding process, the concentration of the polymer in the solution changes as it penetrates the reservoir.This occurs due to the polymer being mixed with reservoir brine as well as being mixed with the slug water (the water injected after the polymer solution is injected).Therefore, a correlation is required to provide an estimation of K and n in different polymer concentrations.

Fig.6.Experimental and estimated K values for AN125 and AN125 VLM.

Fig.7.Experimental and estimated n values for AN125 and AN125 VLM.

Fig.4 and Fig.5 show the viscosity of the solutions versus shear rate at 15°C for AN 125 and AN 125 VLM,respectively.The data in these two figures were used to develop the viscosity model for the polymer solutions.

As it is shown in Figs.4 and 5, the higher the concentration of the polymer solution,the higher the viscosity of the solution in all ranges of shear rate.The solutions’viscosity can be governed using the power-law fluid model.

As mentioned earlier,the model requires two parameters(K and n) to be able to predict the viscosity of the polymer solutions in different shear rates.Since these values change with polymer concentration, the first step in developing a model is to find two accurate functions of K and n versus polymer concentration in polymer solutions.In order to find the best fit,viscosity data of all samples at 15°C were fitted against the power-law model and their respective K and n values were recorded.Figs.6 and 7 show the K and n values,of both polymer types,respectively.As can be seen in the figures, the parameters exhibit a certain trend, which can be utilized to model their behavior in different concentrations.To find the proper function for the purpose of estimating K and n variations with polymer concentration, the viscosity data was fitted against many analytical functions, such as polynomials, exponentials and power functions.Equation(5)and Equation(6)show the functions with the best fitting parameters.

Fig.8.SPAM solution viscosity for two polymer types and the viscosity estimated using the correlation.

Fig.9.Viscosity vs shear rate for different concentrations of AN 125 polymer at 15 °C.

Fig.10.Viscosity vs shear rate for different concentrations of AN 125 polymer at 25 °C.

Fig.11.Viscosity vs shear rate for different concentrations of AN 125 polymer at 35 °C.

3.2.Flow behavior index (n)

At zero polymer concentration, the solution reduces to its solvent (water or brine).Since both these fluids are considered Newtonian fluids,n must be 1 to be able to satisfy the Newtonianfluid requirement.Therefore,parameterd2(Equation(6))is 1.Thus,Equation (6) changes to Equation (7).

Fig.12.Viscosity vs shear rate for different concentrations of AN 125 polymer at 45 °C.

Fig.13.Viscosity vs shear rate for different concentrations of AN 125 polymer(0.2 wt%NaCl) at 15 °C.

Fig.14.Viscosity vs shear rate for different concentrations of AN 125 polymer(0.5 wt%NaCl) at 15 °C.

3.3.Flow consistency index (K)

Equation (5) shows the function describing the variation of K versus the polymer concentration.Given that the function holds true for both polymer types,it can be used to estimate the value of K in different concentrations.At zero polymer concentration, the polymer solution reduces to its simple solvent (in the case of this study, distilled water).It is well-known that water is a Newtonian fluid; hence, it exhibits no viscosity change versus shear rate.The viscosity must be constant and equal to water viscosity.Therefore,Parameterd1must be fixed to the solvent viscosity at the temperatures at which the tests are performed.Equation(8)shows the modified version of equation (5).

In the experiments conducted in this research for pure polymer solutions at 15°C,μsis 0.00132 Pa s.

3.4.Model validation

To validate the model, the data for four concentrations of each polymer were used to estimate the viscosity of the other two remaining concentrations in the given shear rate range.The solutions with concentrations of 2000 and 7000 were selected to be the test concentrations.Given that,the concentrationsused for the purpose of developing the model are 1000,3000,5000 and 10,000 ppm.Table 1 and Table 2 list the fitting parameters for both polymers.

Table 1 The fit parameters of the proposed model for AN 125 and AN 125 VLM polymer solutions (Flow Consistency Index).

Table 2 The fit parameters of the proposed model for AN 125 and AN 125 VLM polymer solutions (Flow Behavior Index).

Table 3 The fit parameters of the proposed model for AN125 at different temperatures (Flow Consistency Index).

Table 4 The fit parameters of the proposed model for AN125 at different temperatures(Flow Behavior Index).

Table 5 The fit parameters of the proposed model for AN125 in different salinities (Flow Consistency Index).

Table 6 The fit parameters of the proposed model for AN125 in different salinities (Flow Behavior Index).

Fig.8 shows the applicability of the model in estimating the viscosity of polymer solutions in different concentrations.As evidenced,the model is highly acceptable(highR2and low errors)and can estimate the solutions’ viscosity with negligible error.

3.5.Model applicability at different temperatures

It is well-known that the viscosity of polymer solutions decreases with temperature.Figs.9-12 demonstrate the viscosity of AN 125 in different concentrations at 15°C,25°C,35°C and 45°C,respectively.Unsurprisingly, the viscosity of all the solutions decreases with increased temperature.

The proposed model was tested for validity in different temperatures using AN 125 polymer solutions in different concentrations.Tables 3 and 4 list the fitted model parameters for different temperatures.As suggested by the results showed in Tables 3 and 4,the proposed model is capable of estimating the polymer solutions’viscosity at different temperatures(highR2and low RMSE).

3.6.Model applicability in different salinities

Using NaCl,samples with different salinities were prepared and their viscosities were measured and recorded against shear rate.Fig.13 and Fig.14 demonstrate the results obtained for 0.2 wt%,and 0.5 wt%salinities,respectively.The data for each salinity was fitted to the proposed model in order to investigate the model’s applicability at different salinities.As reported in Tables 5 and 6,the sets of data are in great agreement with the data estimated using the model for all salinities ranging from 0 wt% to 0.5 wt%.

As supported by the data listed in Tables 3 and 4, the model is capable of predicting the power-law equation parameters with acceptable precision in different salt concentrations.

4.Conclusions

A comprehensive experimental study was conducted on the viscosity of SPAM solutions, and its dependency on shear rate,temperature and salinity was studied.The main aims of this study are:investigating the effects of shear rate,salinity and temperature on the viscosity of two SPAM solutions and developing a new model capable of estimating the viscosity of SPAM solutions with acceptable accuracy.

First,using the data in this study,a viscosity model based on the power-law viscosity model was developed and used to estimate the viscosity of the polymer solutions in the absence of any salts and at15°C.The data for four of the six concentrations was used to predict the viscosity of the other two polymer concentrations at different shear rates.Fortunately,the model was able to predict the viscosity of the aforementioned two concentrations with acceptable accuracy (high R2and a low error).Moreover, the same process was implemented for another SPAM with a different molecular weight(AN125 VLM),and the results confirmed that the model can be used for SPAMs with different molecular weights.

In the second part of this study, the effect of temperature and salinity on the ability of the model to predict the viscosity of AN 125 was studied.In this case,also,the model successfully estimated the viscosity of SPAM solutions in different temperatures and salinities,and hence,proving the validity of the model in different conditions.The authors of this study suggest that future researchers focus on the validity of the model in different pH, in the presence of other salts and the combined effect of the aforementioned factors on the viscosity of polymer solutions to achieve a more comprehensive model.

Declaration of competing interests

The authors declare that they have no conflict of interests.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.petlm.2020.03.007.