Introduction

Today, global oil demand has forced oil companies to produce and maintain mature reservoirs1,2,3,4. These reservoirs are usually associated with the problem of pressure drop and excess water production5,6,7,8,9. To solve the pressure drop problem, a significant amount of water is usually injected into the oil reservoirs or aquifers, increasing excess water production10,11,12,13. Various methods are used to reduce water cuts, including in-situ gel injection14,15,16,17,18,19. In this method, the mixture of polymer, crosslinker, or any other additive is prepared on the surface of the earth (which is called gelant), and before turning into a gel, it is injected into a water injection well or an oil production well that has the problem of producing excess water9,20,21,22,23,24.

This method significantly reduces excess water production if the gelant is designed correctly and a firm and durable gel is achieved5,25,26,27,28,29. However, designing and achieving a stable gel has different challenges. One of these challenges is the adsorption of polymer and crosslinker on formation rock particles, which reduces its concentration in the gelant and reaches areas far from the well19,30,31,32,33,34. In this case, some amount of crosslinker will be adsorbed to the surface of the rock, and when it reaches the target area, its composition will change and will not be following the optimal composition, and therefore, the formed gel will be weaker and will not be effective35,36,37,38. Therefore, it is essential to consider the adsorption values ​​of the materials in the gelant for the optimal design of the operation30,38,39,40,41,42,43.

In many research studies, the adsorption behavior of different polymers on sandstones and carbonate reservoirs has been investigated and tested in the laboratory33,35,42,44,45,46. Also, the effect of impurities and other additives such as salt, nanoparticles, and surfactants on this process has been investigated22,47,48,49,50. Most of the results show that the adsorption of polymers on the particles of sandstone or carbonate reservoirs is characterized by the Langmuir adsorption isotherm model51,52,53,54,55,56,57. This fact shows that the adsorption of polymers on the surface of stones is in the form of a single layer, and they occupy the adsorption sites on their surfaces34,43,58,59,60,61,62. Also, many researchers have reported that the increase in salinity or the presence of nanoparticles reduces the intensity of the adsorption of polymers, which also confirms the mechanism of the Langmuir model because, in this case, part of the adsorption sites related to rocks are occupied by other materials45,63,64.

Also, the effect of temperature on the adsorption intensity of polymers has been investigated, and the results show that polymer adsorption increases with increasing temperature30,35,38,43,65. Researchers consider this behavior related to reducing viscosity and increasing the mobility of polymer molecules66,67. It should be noted that the effect of temperature on polymers is precisely the opposite of the behavior of surfactants. Surfactants, widely used materials in enhanced oil recovery, have been modeled significantly for their adsorption in different reservoirs32,68,69,70,71. This adsorption modeling is not only instrumental in the field of experiment design, but it is also helpful in the surfactant selection process, and depending on the lithology of the reservoirs and the obtained adsorption models, the most suitable surfactant with less adsorption is selected45,60,72,73.

The adsorption behavior and dynamic and static modeling of adsorption of different surfactants on rocks with different lithology, such as sandstone, carbonate, and clay, have been extensively studied and investigated31,40,74,75,76. Today, large oil companies benefit from the data obtained by researchers when designing operations to enhance oil recovery77,78. Also, significant work has been done to discuss the adsorption of polymers on the surfaces of various rocks because polymer injection is not only about the injection of the gel but is also used in fracturing fluid or solving viscous fingering problems79,80,81. On the other hand, no special attention has been paid to modeling and investigating the adsorption behavior of crosslinkers in gelants, and this issue has not usually been studied and investigated. Urotropine is one of the crosslinkers used in the in-situ gel injection field, sometimes injected into sandstone reservoirs. Urotropine consists of 6 methyl groups and four amino groups, which have wide applications in various industries, including medicine, pharmaceuticals, and oil82,83,84,85.

Sandstone reservoirs often have clay particles, which have a high adsorption capacity due to their lamellar structure and high specific surface and can strongly affect the gelant composition in areas far from the wellbore86,87. There are different types of clay, one of the most common types of which is kaolinite. So far, no study has been done on the adsorption behavior and adsorption modeling of Urotropine on kaolinite. This process has been specially addressed in this research.

While significant research has focused on polymer and surfactant adsorption in enhanced oil recovery processes, the adsorption behavior of crosslinkers, particularly Urotropine, on reservoir rock components has received comparatively less attention. Urotropine is a widely utilized crosslinker in in-situ gel systems, crucial for modifying rheological properties and ensuring gel stability in heterogeneous porous media88,89,90. Its interaction with reservoir minerals directly impacts gelant integrity and placement efficiency, yet comprehensive studies elucidating its adsorption mechanisms, especially on common clay minerals like kaolinite, are scarce. Kaolinite, a prominent aluminosilicate clay, is ubiquitous in sandstone reservoirs and possesses a high specific surface area and lamellar structure, making it a critical adsorbent. This research uniquely addresses this knowledge gap by providing a detailed investigation into the adsorption isotherms and thermodynamics of Urotropine on purified kaolinite particles, thereby offering fundamental insights into crosslinker-mineral interactions that are vital for robust gelant design and accurate predictive modeling of water shut-off treatments in mature oilfields.

In this research work, Urotropine adsorption values ​​in solutions with different concentrations on very fine and pure kaolinite particles at 25 °C were done. The laboratory data obtained by widely used adsorption isotherm methods and models were fit, and the most suitable model was selected for this purpose. Then, by repeating the experiments at higher temperatures, the effect of temperature on this process was also investigated. Also, by thermodynamic modeling of adsorption behavior at different temperatures, process enthalpy changes, entropy changes, and Gibbs free energy were calculated, which show whether the process is spontaneous or forced. Since adsorption in porous media may not be the same as the results of batch experiments due to the complexities and presence of inaccessible areas, six kaolinite sandpacks were flooded with \({10}^{5}\) ppm Urotropine solution at different temperatures.

Materials and methods

Materials

Adsorbent (kaolinite)

In current research, kaolinite particles were used as adsorbents. Kaolinite is a type of clay that may be abundant in sandstone reservoirs. Usually, the phenomenon of fine migration is attributed to the presence of kaolinite particles. These particles are usually aluminosilicate; their overall composition is Al2Si2O5(OH)4. The structure of kaolinite crystals is usually layered, and the particle size of this mineral is tiny and smaller than 2 µm32,91,92,93,94,95. These two features have caused kaolinite to have a high adsorption capacity. The chemical structure of kaolinite can be seen in Fig. 1.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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Chemical structure and composition of kaolinite crystals.

The kaolinite used in this study, sourced from Pars Ore Company, boasts over 97% purity. Its XRD analysis results are presented in Table 1.

Table 1 XRD analysis results for kaolinite particles used in this study.
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To prevent the integration of particles, grind them first and then use screen mesh No. 400 passed.

Adsorbate (Urotropine)

The organic compound Urotropine has the chemical formula C6H12N4. Urotropine comprises six methylene units (–CH2–) and four amino groups (–NH2). The main application of Urotropine in the oil and gas industry is as a crosslinker in in-situ gel injection processes. After some time, this substance turns the polymer solution into a gel by dissolving it in the polymer solution and keeping it at the right temperature. This gel is usually used in water shut-off processes, and depending on the need, it may be injected into oil production wells and water injection wells22,29,59,96,97,98.

Urotropine used in this research was purchased from Merck with more than 99% purity. It should be noted that the solubility of this substance in water is very high, but it is usually used in concentrations of 0.5–4% by weight in the oil industry. With the aim of a more comprehensive study, solutions containing 0.01 wt% to 10% wt% (\({10}^{2}\) to \({10}^{5}\) ppm) were studied in this research.

Experimental procedure

Preparation of aqueous solution

In this research, dozens of Urotropine solution samples were made in distilled water, with a concentration between \({10}^{2}\) and \({10}^{5}\) ppm. In this regard, the specified and measured amounts of Urotropine were added to one hundred milliliters of distilled water and mixed with a magnetic stirrer at 400 rpm. Due to the high solubility of this material in water, the prepared solution was seen as homogeneous and uniform after less than a minute, but to ensure more certainty, the mixing process was continued for 10 min.

These solutions, which had specific concentrations of Urotropine, were used to calibrate the UV device and validate its results. UV device was used to detect the concentration of solutions containing Urotropine. Its chemical structure is indicated in Fig. 2.

Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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Chemical structure of Urotropine.

Since the accuracy and correctness of the information are very important in modeling the adsorption behavior of different substances, the device used is calibrated with high accuracy, and its measurement accuracy (error less than 0.1%) is ensured by measuring the concentration of specific solutions. Became.

Adsorption test as a batch experiment

The amount and intensity of Urotropine adsorption on kaolinite particles were measured and calculated according to the following procedure. This procedure has been recommended and suggested in various articles and books to measure the adsorption of surfactants on stone particles99,100,101.

  1. 1.

    100 mL of the initial solution with a specific concentration of Urotropine was made according to the principles mentioned in the previous section.

  2. 2.

    The amount of 20 g of powdered kaolinite was poured into each Urotropine solution and stirred for 24 h by a magnetic stirrer at 400 rpm until the adsorption process reached its maximum value.

  3. 3.

    The aqueous phase containing Urotropine adsorbent kaolinites for 30 min in a centrifuge machine with a dose of 6000 rpm was set. At this stage, all the kaolinite particles related to the device were collected at the end of the tube, and there were no kaolinite particles in the upper parts of the tube.

mL of the solution was removed from the top of the centrifuge tube, and its concentration was measured using a UV device. The UV device used in this step is MAPADA V-100 D.

5. Using the initial concentration, the concentration after the adsorption process and the mass of kaolinite were calculated based on Eq. 1.

$${q}_{e}=1000\frac{({C}_{i}-{C}_{e}){V}_{s}}{{m}_{k}}$$
(1)

where Ci refers to the concentration of adsorbate in the initial condition, Ce is the concentration of the same material in the equilibrium state when the adsorption is done. Vs stands for the volume of solution, and mk is the mass of kaolinite grains.

Adsorption measurement in porous media

The laboratory procedure explained in the previous part is related to the batch experiment mode so that the solution’s contact surface and adsorbent particles reach their maximum value. As a result, in such a test, the amount of adsorption will be higher than the actual state of the tank, which is a porous medium. The reason why researchers are interested in conducting batch experiments is the accuracy of the output models because the uncertainty parameters that exist in the porous medium do not occur in the batch experiment mode.

Nevertheless, evaluating the adsorption values of different solutions in porous environments is essential because the injected solutions are related to the porous environments of the rock in reservoirs and in the actual state. For this purpose, six sand-packs containing kaolinite particles were made and flooded with \({10}^{5}\) ppm Urotropine solutions at different temperatures. The procedure for this test is as follows.

  1. 1

    The sand-pack was made of kaolinite particles. For this purpose, a sleeve with an inner diameter of 1 inch and an outer diameter of 1.5 inches was chosen. Then, step by step, kaolinite particles were poured into it and pressed by the uniaxial device to complete the packing process. Then, on both sides of the sand-pack, two screen mesh No. 400 was glued to prevent kaolinite particles from coming out.

  2. 2

    The prepared sand-packs were placed in the Vinci core flooding setup’s core holder, and a confining pressure of 1000 psi was applied at the test temperature.

  3. 3

    For 4 h, the system was tested at the temperature until all the components reached the mentioned temperature.

  4. 4

    A solution of \({10}^{5}\) ppm Urotropine was made to the size of 10 pore volume and poured into the accumulator.

  5. 5

    10 times the volume of the holes were injected into the sandpack from the Urotropine solution. If possible, this test should be continued until the Urotropine concentration in the outlet fluid is the same as the injection fluid.

  6. 6

    Calculating the amount of adsorption is calculated through Eq. 2.

    $${q}_{e}= \frac{{V}_{o}.({10}^{5}-{C}_{e})}{{m}_{s}}$$
    (2)

    where Vo is the volume of Urotropine solution in the outlet and ms refers to the dry weight of the kaolinite sandpack. Note the raw experimental data are available in the supplementary material.

Modeling method and data analysis

Adsorption isotherm models

Different isotherm models, including Langmuir, Freundlich, Temkin, and linear adsorption models, were used to analyze Urotropine adsorption data on kaolinite particles. The analysis was such that the obtained laboratory data were drawn in a graph where the X-axis was ce, and the Y-axis was qe. Then, regression methods matched the mentioned models with the laboratory data in the best possible way. By drawing the studied models along with the laboratory data through statistical methods, the best model describing fluid behavior was selected, which was used for other steps. Brief explanations about the relationships and theories of these models are given in this section.

Langmuir isotherm model

The primary assumption of this model is the uniformity of adsorption in the process. This model assumes that all adsorption sites are similar and independent at the adsorbent level. Therefore, the effectiveness of this model in predicting the adsorption of a type of chemical substance that is adsorbed as a single layer on the adsorption site of the adsorbent is appropriate. The primary relationship of this model is given in Eq. 3.

$$q_{e} = q_{o} \frac{{K_{L} C_{e} }}{{1 + K_{L} C_{e} }} \to \frac{{q_{e} }}{{q_{o} }} = \frac{{K_{L} C_{e} }}{{1 + K_{L} C_{e} }} \to \frac{1}{{q_{e} }} = \left( {\frac{1}{{K_{L} q_{o} }}} \right)\frac{1}{{C_{e} }} + \frac{1}{{q_{o} }}$$
(3)

In this equation, KL is the Langmuir equilibrium constant (L/mg), and qo refers to the adsorption capacity determined by the Langmuir isotherm model.

Due to its simplicity and capacity for accurate predictions, this model is commonly utilized in adsorption research102.

Temkin model

In this model, it is assumed that the adsorption occurs in multilayers, and the adsorption energy decreases with the number of layers. This means that the adsorption energy for the third adsorbate layer on the adsorption site corresponding to the adsorbent is lower than that of the first layer. This model is non-linear, based on the interaction between adsorbate molecules with each other and with the adsorbent surface. It should be noted that most adsorption isotherms models are non-linear because the adsorption behavior is often non-linear. The general relationship of the Temkin model is written in Eq. 4.

$${q}_{e}b=RT(\text{ln}\left({K}_{T}\right)+\text{ln}\left({C}_{e}\right))\to {q}_{e}=\frac{RT}{b}\text{ln}\left({K}_{T}\right)+\frac{RT}{b}\text{ln}({C}_{e})$$
(4)

where KT refers to the Temkin equilibrium constant, b stands for the Temkin constant, T is the temperature at which adsorption occurs, and R denotes the global gas constant103.

Freundlich model

Like Temkin, this model assumes multi-layered adsorption behavior, with the difference that in the Freundlich model, it is assumed that the adsorbate surface is completely heterogeneous, and the adsorption process occurs heterogeneously. This model is also non-linear like the previous two models and is generally described by Eq. 5.

$$qe=\left({K}_{f}\right){\left({C}_{e}\right)}^\frac{1}{n}\to \text{ln}\left({q}_{e}\right)=\text{ln}\left({K}_{f}\right)+\frac{1}{n}\text{ln}\left({C}_{e}\right)$$
(5)

The Freundlich model includes Kf, a process constant related to adsorption capacity, and n, an exponent that shows the deviation from a linear isotherm. It’s especially efficient for describing multi-layered and non-linear adsorption, providing insight into changes in adsorption behavior104.

Linear model

This model is a straightforward and low-accuracy method to describe the adsorption behavior of adsorbate on adsorbent surfaces. The accuracy of this method is more acceptable at low concentration when most adsorption sites are still empty. As the solution concentration increases, the performance accurateness of this model also decreases in forecasting the adsorption behaviorperformance In general, Eq. 6, the equation of a straight line, describes the linear model.

$${q}_{e}=K{C}_{e}+I$$
(6)

where K is the linear isotherm model constant and equals the slope, and I denotes to the intercept of the linear model105.

Error analysis and model accuracy

The actual adsorption values were plotted with the values ​​predicted by the models in a graph, and then the points predicted by the model were compared with the experimental values. This comparison can also be made visually by comparing the trends of the graphs and the amount. The values ​​of the models can be close to the laboratory values, and different statistical analyses can be used in this regard. In this study, different models were evaluated using statistical studies. The models used are as follows.

ARE (Absolute Relative Error)

ARE is used as a measure to evaluate the accuracy of models and compare them with actual values. This method is straightforward, understandable, and simultaneously practical, and the results obtained are reliable. Equation 7 calculates ARE values106.

$$ARE=\frac{1}{n}\sum_{i=1}^{n}{\left|\frac{{q}_{e,cal-}{q}_{e,lab}}{{q}_{e,lab}}\right|}_{i}$$
(7)
ASE (Absolute Sum of Errors)

This statistical indicator shows the total amount of errors. In this method, larger values ​​are more effective, and in this research work, it can be claimed that the ASE method focuses more on the adsorption error of higher concentrations of Urotropine on kaolinite107. This quantity is calculated from Eq. 8.

$$ASE=\frac{1}{n}\sum_{i=1}^{n}{({q}_{e,cal-}{q}_{e,lab})}_{i}^{2}$$
(8)
Correlation coefficient (R2)

R2 statistically represents how much of the dependent variable’s variation is accounted for by the independent variables within a regression model. The value of this statistical quantity is a thread to evaluate the effectiveness of predictive models. It should be noted that values ​​close to 1 for this quantity indicate higher predictive model accuracy108.

Thermodynamic modeling of the adsorption process

The effect of temperature on the adsorption of Urotropine on kaolinite was investigated through thermodynamic modeling. This powerful method aids in understanding the adsorption mechanism and in quantifying the energy changes that occur. From experimental adsorption data collected across a range of temperatures, essential thermodynamic parameters such as ΔH°, ΔS°, and ΔG° can be precisely determined109.

Gibbs free energy deviations (ΔG°) calculation

Equation 9 can be used to calculate the Gibbs free energy change for an adsorption process.

$${\Delta G}^{0}=-RTln({K}_{D})$$
(9)

Equation 9 introduces KD​, the thermodynamic equilibrium constant, which is given in units of moles of water per mole of adsorbent. This constant is obtained by finding the intercept of a plot of qe​/Ce​ against qe​. R signifies the universal gas constant, and T is the experimental temperature measured in Kelvin. Subsequently, in accordance with the second law of thermodynamics, the value of ΔG° is calculated using Eq. 10.

$${\Delta G}^{^\circ }={\Delta H}^{^\circ }-T{\Delta S}^{^\circ }$$
(10)

Here, ΔH° denotes the system’s enthalpy change, and ΔS° represents the entropy change. A negative ΔG° value indicates a spontaneous process, whereas a positive value signifies a non-spontaneous one110. By integrating Eqs. 9 and 10, Eq. 11 is formed.

$$\text{ln}\left({K}_{D}\right)=-\frac{{\Delta H}^{^\circ }}{RT}+\frac{{\Delta S}^{^\circ }}{R}-1.204$$
(11)

In which 1.204 transfers the unit of KD from mole water/mole rock to grwater/grrock. Regarding Eq. 11, by plotting ln(KD) versus 1/T, \({\Delta H}^{^\circ }\) and \({\Delta S}^{^\circ }\) will be found:- slope × R and (intercept + 1.204) × R111.

Results and discussion

Adsorption behavior modeling

The adsorption test was made for solutions with different concentrations of Urotropine, which ranged from \({10}^{2}\) to \({10}^{5}\) ppm, and their adsorption values ​​were measured on kaolinite particles at a temperature of 25 °C. The mentioned data are shown in Fig. 3. In this figure, the separate points are related to the results obtained in the laboratory, and the connected lines are related to the trend and prediction obtained from the behavior of Urotropine adsorption on kaolinite particles, which were obtained based on the same laboratory data.

Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Experimental adsorption data obtained for Urotropine on kaolinite particles and modeling results.

As presented in Fig. 3, the Langmuir adsorption isotherm predicts the values ​​and trends of adsorption with higher accuracy than other models. Nevertheless, it is essential to perform a statistical investigation and review the accuracy of the prediction of various methods. In Table 2, the obtained constants and equations for different models are written, as well as the statistical values ​​of the prediction accuracy of each of them. All three statistical quantities express the high accuracy of the Langmuir model. This model estimates the adsorption capacity (qo) of Urotropine on kaolinite particles to be 112 mg- Urotropine/g-kaolinite. Each gram of kaolinite in the batch experiment can adsorb about 0.112 g of Urotropine. This adsorption rate is relatively high and can challenge the composition of the injection gel in areas far from the well.

Table 2 Results of experimental adsorption data and authentication of various models.
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Regarding the Table 2 and the results of statistical analysis, Langmuir model has the lowest error and the highest correlation with the results obtained from the laboratory.

The robust fit of the Langmuir model (R2 = 0.992, ARE = 0.12%) over other isotherm models signifies a monolayer adsorption of Urotropine onto the kaolinite surface. This suggests that Urotropine molecules primarily occupy a finite number of active sites on the kaolinite, with no significant interaction among adsorbed molecules. The determined maximum monolayer adsorption capacity (q0​) of 112.1 mg/g-kaolinite at 25 °C is notably high, implying a strong affinity between Urotropine and the kaolinite surface. This high adsorption capacity is critical from a practical standpoint, as it indicates a substantial loss of crosslinker concentration from the gelant solution before it reaches the target zone in the reservoir. Such a reduction in Urotropine concentration can compromise the integrity and strength of the formed gel, potentially leading to suboptimal water shut-off performance. The adsorption mechanism is likely driven by hydrogen bonding among the amine groups of Urotropine and the hydroxyl groups present on the kaolinite surface, as well as potential electrostatic interactions given the slightly negative charge of kaolinite surfaces in aqueous solutions. The uniform nature of adsorption sites, as implied by the Langmuir model, aligns with the well-defined crystal structure of kaolinite.

Temperature effect on adsorption behavior

The experiment measuring the adsorption values ​​of Urotropine solutions on kaolinite particles at higher temperatures, including 35, 50, 65, 80, and 95 °C, was also repeated. The laboratory data obtained from this step is revealed in Fig. 4. Based on this figure, increasing the temperature increases the adsorption values. This trend signifies that the process is endothermic. Therefore, the enthalpy of the Urotropine adsorption process on quartz is expected to be a negative number, which will be calculated with higher accuracy in the following sections.

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
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Experimental adsorption obtained at different temperatures.

Based on the data in the above figure, the Langmuir model was also utilized to the results obtained from the laboratory at higher temperatures, and the statistical analyses showed a perfect and acceptable adaptation of this model. The constants related to the Langmuir model and the results of their statistical study are given in Table 3.

Table 3 Langmuir model constants obtained from testing in various temperatures.
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Based on this table, both the adsorption capability and the equilibrium constant increase with increasing temperature, both of which show that this process is endothermic. The adsorption capacity, which was 112 mg/g-kaolinite at 25 °C, reaches 182 at 95 °C, and the equilibrium constant of the process increases from 0.73 to 0.98.

Thermodynamic modeling

This part modeled and investigated the thermodynamic behavior of the Urotropine adsorption process on kaolinite particles. In this regard, the first qe/ce was drawn in terms of qe for the adsorption behavior measured at different temperatures. Based on the thermodynamic modeling method explained in the previous section, the interception of these lines indicates Kd. This parameter is critical and valuable in thermodynamic study. Figure 5 shows the diagram related to this part, and the gravity equations are also evident.

Fig. 5
Fig. 5The alternative text for this image may have been generated using AI.
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Qe/ce plot versus qe in different temperatures used for thermodynamic study.

Based on the above figure, the Kd values ​​obtained for different temperatures were obtained and are presented in Table 4. Different values ​​of Kd at different temperatures indicate that this parameter has a direct relationship with temperature. Then, in the next step, by plotting Ln (Kd) VS. 1/T, the values ​​of entropy and enthalpy changes can be calculated using Eq. 11. Based on this, the process enthalpy value of 9354 J/mole was obtained. The positive value of this quantity for the Urotropine process on kaolinite shows that this is an utterly endothermic process, and higher temperatures help increase the balance of the process to the right. Based on the principles of regression and performing calculations, the amount of entropy changes was also obtained as 78.35 J/mole.K. According to Eq. 11, which calculates the amount of Gibbs free energy changes at a specific temperature, it can be found that this value is for the adsorption process of Urotropine on kaolinite particles at temperatures higher than -153 °C, which is a negative number. Therefore, it is an entirely spontaneous process.

Table 4 Thermodynamic results obtained from modeling of adsorption behavior in various temperatures.
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The positive enthalpy change (ΔH° = 9354 J/mole) definitively confirms the endothermic nature of Urotropine adsorption on kaolinite. This is a crucial finding, indicating that the adsorption procedure is favored by increasing temperature, as observed in the experimental data where adsorption capacity systematically increased from 112 mg/g @ 25 °C to 177 mg/g @ 95 °C. This endothermic behavior contrasts with many typical physical adsorption processes, which are often exothermic. The positive entropy change (ΔS° = 78.35 J/mole.K) further suggests an increase in the randomness or disorder at the solid–liquid interface during the adsorption. This can be ascribed to the displacement of water molecules from the kaolinite surface by Urotropine molecules or increased conformational freedom of the adsorbed Urotropine at higher temperatures. The consistently negative values of Gibbs free energy (ΔG°) across all studied temperatures, ranging from − 13,994.3 J/mole at 25 °C to − 19,478.8 J/mole at 95 °C, unequivocally demonstrate the spontaneous nature of Urotropine adsorption on kaolinite. The increasing negativity of ΔG° with temperature further reinforces that higher temperatures enhance the spontaneity and favorability of the adsorption process. In practical terms, this implies that in warmer reservoir environments, a greater amount of Urotropine will be adsorbed onto the kaolinite, necessitating adjustments in gelant formulation to ensure sufficient crosslinker reaches the target zone for effective gelation.

Table 4 calculates Kd values ​​and Gibbs free energy changes for different temperatures, confirming the explanations presented in this section.

The above table confirms the spontaneity and endothermicity of the Urotropine adsorption on kaolinite particles. This upsurge in adsorption capacity and process balance can be interrelated to the increased movement and speed of Urotropine molecules. Urotropine particles communicate with kaolinite surfaces based on hydrogen bonding and are adsorbed on it, increasing the process’s speed and viscosity reduction.

Adsorption performance in porous media

At this section, six kaolinite sand-packs were made using the previously mentioned method. A large quantity of \({10}^{5}\) ppm Urotropine solution was then made. This solution was continued at different temperatures, including 25, 35, 50, 65, 80, and 95 °C, into the sand-packs until the concentration of Urotropine in the output fluid reached the initial value. The results of this part and the general features of sand-packs are given in Table 5.

Table 5 Flooding sand-pack specifications and results obtained from porous media adsorption experiment.
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The above table, like the results from the previous sections, designates that this procedure is endothermic, and the adsorption capacity increases by temperature. The adsorption capacity was 66 mg/g-rock at 25 °C, while this quantity was associated with an increase of 112 at 95 °C.

Another essential thing evident in this table is the lower adsorption rate in the injection into the porous media compared to the batch tests. In the porous medium, there are complications in the direction of the solution flow, and part of the holes and part of the surface of the particles are accessible for the injection solution. In the batch experiment, the entire surface of the kaolinite particles was exposed to the Urotropine solution, and therefore, the adsorption process happened more intensively and quickly.

The complexity of the porous medium and the inaccessibility of some particles for injection solutions caused the adsorption capacity to decrease from 112 to 66 at 25 °C, and this decrease was from 182 to 114 at 95 °C.

Conclusion

In this research, the adsorption performance of Urotropine was tested at various temperatures and conditions, and this adsorption behavior was compared with different models. In the next step, thermodynamic modeling of the behavior of this adsorption process was also done. Finally, a solution containing \({10}^{5}\) ppm of Urotropine was injected into kaolinite sand-packs to check the adsorption values ​​of this substance on kaolinite in the porous medium. In general, the results obtained are as follows:

  1. 1

    The Langmuir isotherm model is the best model that describes the adsorption behavior of Urotropine solution at different temperatures on kaolinite particles. Adsorption capacity reached 112 mg/g-rock at a temperature of 25 °C, which is a relatively high figure, and it is necessary to consider this material as a polymer crosslinker in industrial designs when injecting it.

  2. 2

    With increasing temperature, the intensity and capacity of this process increased, which shows that this adsorption process is endothermic, and its enthalpy is estimated to be positive. In addition to constant adsorption capacity, the equilibrium of the process also increased with increasing temperature.

  3. 3

    Thermodynamic modeling of the laboratory data showed that the enthalpy of the progression is 9354 J/mole, and its entropy changes are 73.85 J/mole.K. In fact, at temperatures higher than − 153 °C, the Gibbs free energy changes were negative and spontaneous, indicating this endothermic process.

  4. 4

    In the last step, Urotropine solution with a concentration of \({10}^{5}\) ppm was injected into kaolinite sand-packs at various temperatures. These results, like the previous part, showed the endothermal nature of the procedure and the increase in the adsorption capacity of Urotropine on kaolinite particles with increasing temperature. It was also found that the adsorption capacity in the porous-media was lower than the batch tests, which is related to the complication of the porous-media and the inaccessibility of some of the particles.

In general, this thermodynamic modeling investigates the adsorption performance of Urotropine. This substance is a strong crosslinker in the in-situ gel injection operation. The results of this test show this substance’s high adsorption rate on clay particles. Therefore, it is essential to pay attention to this point in the operation design to prevent its failure and failure.