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      Reducing well heat loss is key to efficient development of geothermal resources. Creating a long-term stable, well-insulated wellbore through cementation is a reliable solution. This article uses cement, hollow glass beads, foaming agent and stabilizer as the main raw materials, and adds other traditional additives to prepare cement-based composite insulation materials. Polystyrene foam and hollow glass beads can introduce a gas with low thermal conductivity into the cement, thereby improving the thermal insulation properties of the composite. The foam is produced through a chemical molding process using foaming agents developed based on electrochemistry and thermodynamics. Foam stabilizers help the foam to be distributed stably and evenly in the cement mortar. 10–13% hollow glass beads can significantly reduce the thermal conductivity of hardened cement without significantly detrimental effects on the rheology and strength of the material. The thermal conductivity of composite insulation materials can be as low as 0.2998 W·(m·K)-1, which is 62% lower than that of ordinary cement. The compressive strength is 6.10 MPa, which meets engineering requirements. Accordingly, a thermal conductivity prediction method based on the Maxwell model is proposed, the prediction error of the newly created model is within 2%. These studies can provide technical support for the efficient development of geothermal resources.
       As global energy demand continues to rise and traditional energy supplies continue to dwindle, various alternative energy sources are gradually gaining everyone’s attention. Geothermal energy is widespread throughout the world and has large reserves. It is a green renewable resource. In recent years it has been developed in many countries. As a tool for geothermal resource development, geothermal wells must be of high quality in order to efficiently utilize geothermal energy. However, as high-temperature fluid flows from the bottom of the well to the surface, large heat losses occur, which is the main bottleneck limiting the effective use of geothermal wells3,4. This is a real solution for creating a long-term stable wellbore with a good thermal insulation effect, which places higher demands on the thermal insulation and mechanical properties of the cementing fluid3,4.
       Cementitious fluids are primarily cement-based materials. In recent years, cement-based insulation materials have been widely researched and applied in the construction industry, but their application in oil and gas wells, especially geothermal wells, is rare5. On the one hand, insufficient attention is paid to wellbore insulation during the development of geothermal wells; on the other hand, there is a lack of relevant research on insulating cement mortars suitable for geothermal wells6; Polystyrene foam is produced by introducing air bubbles into cement-based materials through chemical foaming and/or physical foaming. It has low density and good thermal insulation properties, and can also be used to insulate geothermal wells7. However, the use of mechanical methods for nitrogen production requires a number of equipment and associated systems5,8, and the associated workflow is complex and expensive. The use of chemical methods for nitrogen production has the advantages of ease of operation and low cost, but the efficiency of gas production from conventional chemical blowing agents is low9,10. Hollow glass microspheres have many hollow structures, low thermal conductivity, and simple fabrication process11,12,13. However, to achieve ideal thermal insulation properties, the use of hollow glass microspheres requires a larger quantity. This will have a more significant impact on the performance of the cement slurry and the cost of the glass beads will increase14.
       Thermal conductivity studies of composite materials provide good guidance for the fabrication of insulating cementitious systems15,16. The Maxwell model can be used to calculate the thermal conductivity of cement composites, provided that the dispersed phase particles are uniformly distributed in the continuous phase medium and do not interact with each other. In addition, the particle shape is assumed to be spherical and randomly distributed. In porous hollow materials, pores are most often cavities of various shapes18. The thermal conductivity of the structure will depend on the thermal conductivity of the solid particles and pores, as well as the size, shape and distribution of the pores. When Zhang Weiping [19] studied the thermal conductivity model of concrete, he divided the thermal conductivity prediction models of two-phase composite materials into three categories: series-parallel models, which do not consider the thermal resistance of the interface; series-parallel models that do not take into account; interface thermal resistance; series-parallel model that takes into account the thermal resistance of the interface; series-parallel model that does not take into account the thermal resistance of the interface; Maxwell’s model and its extension without taking into account the thermal resistance of the interface; Maxwell’s model and its extension, which takes into account the thermal resistance of the interface. However, there are still no targeted studies of the thermal conductivity model of multicomponent composite systems containing foam cement mortar.
       Chemical nitrogen foaming additives are selected according to the principle of chemical nitrogen production. The influence of nitrogen foam and hollow glass beads on the strength and thermal conductivity of hardened cement was analyzed. An analysis of the thermal conductivity of cement mortar was carried out and a model for predicting the thermal conductivity of cement-based composite materials was created. Based on this, a new type of thermal insulating cement mortar was developed, which for the first time was successfully used in ultra-deep wells with heavy oil. This study provides a reference for the design and engineering application of geothermal well cementation fluids.
       G grade oil well cement (Jiahua, Sichuan), HX-36L polymer retarder (AMPS/AA/DMAA/IA copolymer, self-produced), QS-20S dispersant (Chengdu Omax Petroleum Technology Co., Ltd.), nano- Stabilizer Agent NS-2 (nanosilicate particles, homemade). The chemical nitrogen foaming agent is manufactured in laboratory conditions.
       It is known that the degree of oxidation of nitrogen can be positive (+5, +4, +3, +2, +1), zero or negative (-1, -2, -3). The reaction that produces nitrogen is a redox reaction, so the oxidation state of nitrogen drops to zero. On this basis, reagents containing nitrogen in various valence states were tested, and based on the basic principles of chemical reactions, a combination of reagents with the lowest Gibbs free energy was selected as a foaming agent. In addition, taking into account the influence of reagents and products on the properties of the cement slurry, the reactivity and total amount of nitrogen formed were experimentally tested. In this regard, highly effective chemical gas-generating agents were developed – NGR systems: NGR-I and NGR-II. NGR-I is a white fine powder, NGR-II is a colorless liquid, both are soluble in water. Once the two materials meet, they react to release nitrogen gas.
       Foam cement mortar is a thermodynamically unstable system. Foam stabilizers are necessary to stabilize the foam system9,20. The free liquid of the cement mortar has high mineralization and high alkalinity, so the foam stabilizer must have high resistance to salt and alkalis10. Therefore, taking into account the temperature and alkali resistance of protein foam stabilizers and the film-forming properties of surfactants, a highly alkaline and salt-resistant highly effective foam stabilizer SK-1 was developed.
       Hollow glass beads are hollow spheres made from soda borosilicate glass. They have the characteristics of low density, small particle size and high pressure withstanding ability. In recent years, they have been widely used for density reduction and thermal insulation11,12,13. The main performance parameters of the hollow glass microspheres used in this study are: true density 0.35 g/cm3, compressive strength 69 MPa; The particle size is mainly distributed in the range of 15~85μm, the maximum particle size (diameter) is 122.73. microns, and the average particle size is 122.73 microns. The diameter is 52.55 microns. The particle size distribution is uniform, as shown in Figure 1.
       The water used in this article is tap water. Sodium hydroxide (NaOH), sodium dodecylbenzenesulfonate (SDBS) and other drugs were purchased from Sinopharm Group and are chemically pure.
       Regular Cement Mortar: Regular cement mortar is manufactured in accordance with API RP 10B-4-201321.
       According to the characteristics of chemically induced nitrogen foam cement mortar on site, chemically induced nitrogen foam cement mortar is prepared by injection, mixing and stirring in a closed system. First, open a homemade closed mixing device and add a certain amount of water and foam stabilizer, then mix well cement and NGR-I foaming agent evenly at a column rotation speed of 4000 rpm for 15 seconds; Mixing Apparatus While closed, inject the required amount of NGR-II Foaming Agent within 5 seconds, continue mixing at 12,000 rpm for 35 seconds, and finally completely fill the entire closed mixing container with foamed cement slurry.
       Considering that the solubility of nitrogen in water is very low, the gas productivity of the foaming agent was assessed using the water displacement method.
       Density test. The density of the cement slurry was tested using an API density meter in accordance with API 10B-4-2004, Recommended Practice for the Preparation and Testing of Foamed Cement Mortar at Atmospheric Pressure.
       Rheological properties. The rheological properties of the cement slurry were tested using an API six-speed viscometer in accordance with API 10B-4-2004. The rheological properties of the cement slurry are characterized by the fluidity index n and consistency coefficient K. The calculation method is as follows:
       In the formula: θ300 and θ100 are the viscometer readings at 300 and 100 rotor revolutions, respectively, when testing cement mortar, n is the fluidity index, and the greater the value of n, the better the fluidity of the cement mortar K; — consistency coefficient, K value. The higher the value, the thicker the cement mortar.
       Loss of water. According to API 10B-4-2004, the cement slurry should be cured at normal pressure or in a pressurized concentrator for 20 minutes, and then the water loss in the cement slurry should be checked using a high temperature and high pressure loss meter.
       Compressive strength and elastic modulus. A uniaxial compression test system was used to evaluate the compressive strength of hardened cement. The test specimens were prepared using a cubic mold measuring 50.8 mm x 50.8 mm x 50.8 mm. The sample was placed on the machine support block for uniaxial compression testing. Before testing, ensure that the spherical base and support block are free to tilt and that there is no buffer or solid buffer between the specimen and the support block. The stress-strain curve of hardened cement is recorded by gradually applying load. The compressive strength of a cement block is the ratio of the maximum stress to the cross-section of the cement block.
       Thermal conductivity. The thermal conductivity of the cement blocks was measured using a transient thermal conductivity meter (hot wire method, TC3000E, Xi’an Xiaxi Electronic Technology Co., Ltd.). The specific steps of the instrument are as follows: place the probe between two samples and place a support weight on the top of the sample; Determine the thermal balance of the sensor before testing (temperature detection fluctuation <0.05/10 min is considered temperature). scales); Select the appropriate test conditions or the name of the substance in the program, and then measure the thermal conductivity.
       Thermal expansion coefficient. For cement-based materials, the coefficient of thermal expansion (CTE) is the main parameter characterizing its thermal expansion characteristics. The CTE of cement depends on the moisture content, internal relative humidity, porosity and the formation of cement hydration products. In recent years, most research has focused on the thermal expansion properties of hardened cement pastes under water-saturated conditions. CTE is tested using the Yuhuan Bu22 method.
       Scanning electron microscope. Cement samples were glued onto a copper sample holder using conductive adhesive, coated with vacuum gold, and then examined using a Zeiss EVO 25 electron microscope (Zeiss, Germany).
       Free water in cement mortar is usually a saturated solution of Ca(OH)2, which provides a strong alkaline environment and can influence the redox reaction to produce nitrogen9. Therefore, nitrogen production (NGR system) at different pH values ​​was tested as a function of time. The experimental formula is 6.0 g NGR-I + 2.2 g NGR-II + 100 g NaOH solution (pH is controlled by adjusting the concentration of NaOH), and the generated nitrogen is collected by water displacement method, as shown in Figure 2a.
       The results show that the NGR system with foaming agent can still produce nitrogen under high alkalinity conditions, adapt to the alkaline environment of cement slurry, and achieve the goal of chemical nitrogen induction. The pH value has a large influence on the initial rate of nitrogen reaction; production. The lower the pH value, the higher the initial rate of nitrogen production in the NGR system. When the pH values ​​were 8, 10, 12, and 14, the final nitrogen volumes were 1102, 1100, 1095, and 1083 mL, respectively, indicating that as the pH increased, the final nitrogen volume decreased slightly.
       In Fig. Figure 2b shows the effect of temperature on the production of nitrogen by the foaming agent. It can be seen that the NGR foam system can react quickly to generate nitrogen at low temperature (0°C), so it can be used in low temperature conditions. Temperature has a significant effect on the initial rate of the nitrogen formation reaction. The amount of nitrogen produced at the beginning of the reaction is very small. However, the reaction speeds up as it progresses due to the release of heat. Within 5 minutes the reaction rate increased significantly and the volume of nitrogen increased significantly. When the temperatures are 20°C, 10°C, 12°C, and 4°C, the final volumes of nitrogen produced are 1082, 1065, 1060, and 1052 mL, respectively, indicating that the final volume also decreases slightly with decreasing temperature. temperature.
       Use the half-life of the foam solution to evaluate the effectiveness of the foam stabilizer. Since foam is a thermodynamically unstable system, as placement time increases, the foam will continue to explode and the liquid film will continue to break down. The half-life of a foamy liquid is defined as the time until 50% of the bubbles collapse23. The foam stabilization effect of SC-1 was tested at 25℃. The results show that the initial foam volume is 580 ml and the liquid half-life is 120 min. The foam volume is still 565 ml during the half-life of the liquid, demonstrating excellent foam stabilization ability.
       The density of the foam cement mortar stabilized with various stabilizers at 25°C was checked, and its foam stabilizing ability was further analyzed. The cement slurry system used is as follows: Grade G cement + 0.6% SC-1 foam stabilizer/sodium dodecyl benzene sulfonate (SDBS) + 50% tap water. The results are shown in Figure 3: the density of the cement slurry with the addition of foam stabilizer SK-1 increased rapidly within 10 minutes, then the increase in density slowed down, and the increasing trend was less after 30 minutes. After curing for 70 minutes, the density of the cement slurry increased from 1.48 to 1.553 g/cm3, with an increase rate of 4.9% and the system was relatively stable. In contrast, foamed cement mortar in which SDBS was used as a foam stabilizer. larger foam diameter and poor stability. After holding for 70 minutes, the density of the cement mortar increases from 1.54 g/cm3 to 1.759 g/cm3, while the degree of increase in density is 14.22%. The test results fully show that the SK-1 foam stabilizer has good foam stabilizing ability.
       Analyze the effect of nitrogen foaming additives on the strength and thermal conductivity of cement paste, as shown in Table 1.
       It can be seen that as the amount of NGR foaming agent increases, the amount of nitrogen generated in the cement mortar continues to increase, and the density of the mortar after foaming gradually decreases accordingly. At a dosage of 2%, the surface density can be reduced to 0.7 g/cm3. The compressive strength test shows that the compressive strength of hardened cement at 48 hours also decreases with increasing NGR content. This is due to the fact that foam affects the integrity of the cement structure, which leads to a decrease in the mechanical strength of the cement. The expansion coefficient of cement at 100°C is less than at 60°C, which may be due to the volumetric shrinkage of cement caused by dehydration of the CSH and Ca(OH)2 gel in the cement slurry at higher temperatures. temperature. At the same time, the coefficient of thermal expansion decreases slightly after adding a foaming agent within 100°C. Generally speaking, the addition of additives has little effect on the expansion coefficient of hardened cement over the test temperature range and does not have a significant effect on the characteristics of the hardened cement and the structure of the subsequent cement shell.
       Moreover, analysis of the mechanical properties and expansion coefficient of cement, as shown in Table 1, shows that the compressive strength of hardened cement is positively correlated with CTE. As a rule, the CTE of hardened cement with a dense structure will be greater. Therefore, foam cement has a much lower CTE of hardened cement than conventional cement.
       Thermal conductivity tests show that foam cement has good thermal insulation properties. At 2% NGR content, the thermal conductivity of hardened cement is reduced to 0.3998 W (m K)-1, which is almost 50% lower than the thermal conductivity of conventional cement paste (0.7877 W (m K)-1. )-1 ). 1). This shows that the thermal conductivity of hardened cement can be significantly reduced by introducing foam.
       During the preparation process, the cement mortar is subjected to dynamic high-speed shear. To evaluate the shear strength of hollow glass microspheres, a variable speed mixer was used to test the density change behavior of low-density cement mortars with different contents of hollow glass microspheres after continuous shearing. The suspension was stirred at 4000 rpm for 50 seconds and 150 seconds, first at 4000 rpm for 250 seconds and then at 12000 rpm for a certain period of time, respectively. The suspensions were then checked for density. As shown in Figure 4, the hollow beads have good resistance to shear damage. When used at 10% concentration they exhibit good shear resistance at low shear rates (4000 rpm) and high shear rates (12000 rpm). However, when the dosage is 20%, the shear strength of the glass beads decreases slightly during high-speed cutting. This may be due to the fact that at high dosage, the probability of collision between the balls and the blade increases significantly, thereby increasing the strength. probability of breakdown.
       The influence of the content of hollow glass beads on the properties, mechanical properties and thermal conductivity of cement mortar was tested. The results are shown in Table 2. The results show that hollow glass beads can effectively reduce the density of cement slurry. The net density of the cement mortar is 1.71 g/cm3. After adding 5% microbeads, the density of the cement slurry quickly decreased to 1.53 g/cm3. At a dosage of 20%, the density of the cement slurry can be reduced to 1.29 g/cm3. Rheological tests show that as the content of hollow glass beads gradually increases from 0% to 15%, the rheological properties of the cement slurry deteriorate. However, when the dosage exceeds 15%, the hollow glass beads will exhibit a “spherical effect” due to their spherical characteristics, thereby improving the rheological properties of the cement slurry.
       The compressive strength test shows that as the content of hollow glass beads increases, the compressive strength of cement mortar gradually decreases. But this reduction is less than that of conventional cement mortar. Thermal conductivity tests show that hollow glass beads can significantly reduce the thermal conductivity of cement paste. In addition, as the number of hollow glass beads increases, the thermal conductivity of the cement mortar gradually decreases, but the decrease in thermal conductivity is less than that of the foam cement mortar;
       The cost of nitrogen-infused chemical foam is lower, which results in lower thermal conductivity of the hardened cement, but therefore lower strength. Hollow glass beads can effectively reduce the thermal conductivity of cement mortar and have relatively little effect on the compressive strength, but their price is high. Therefore, the effect of the combination of foam and hollow glass beads on the properties of cement was further investigated. To ensure good fluidity of the cement mortar, an appropriate amount of dispersant is added to it. The dosage of foaming agent and foam stabilizer is 2%, and the water-cement ratio is set at 0.44. The test results for cement paste density, rheological properties, compressive strength and thermal conductivity are shown in Table 3. The appearance of the cement paste is shown in Figure 5.
       Appearance of grout with a combination of chemically induced nitrogen foam and glass bead additives.
       It can be seen that with the addition of glass beads, the thermal conductivity of the hardened cement decreases rapidly, but the compressive strength also decreases to a certain extent. With a glass bead content of 12.5, the thermal conductivity is only 0.2998 W·(m·K)-1, which is 62% lower than the thermal conductivity of ordinary cement (0.7877 W·(m·K)-1). , and a compressive strength of 6.10 MPa, still meets the technical requirements. This shows that the combination of chemically induced nitrogen foam and glass bead additives can achieve low-density, high-strength cement performance.
       Select different cement samples to observe the microstructure of the hardened cement. Figure 6 is a cross-sectional SEM of hardened cement without hollow glass beads and with 12.5% ​​hollow glass beads. It can be seen that in hardened foam cement without hollow glass beads, even with a density of only 1.035 g/cm3, the bubbles are uniform in size and exist in separate forms. This not only improves the stability of the foam cement mortar, but also gives the foam cement better properties such as low permeability, high compressive strength and good thermal insulation performance.
       Microstructure of foam cement: (a, b) – hardened cement without hollow glass beads (c, d) – hardened cement containing 12.5% ​​hollow glass beads;
       For hardened foam cement containing 12.5% ​​hollow glass beads, the glass beads are evenly distributed in the hardened cement and have less damage. This shows that the optimized hollow glass microspheres have good pressure resistance and the prepared solution is stable, which can guarantee the complete and uniform dispersion of the hollow glass microspheres in the hardened cement. This is because the main chemical component of microbeads is silicate, which can quickly react with calcium released by the cement hydration reaction to form calcium silicate hydrate. At the same time, it can be seen that the addition of hollow glass beads does not affect the stability and dispersion of bubbles in the hardened cement, the pores exist independently, and the size distribution is relatively uniform. The results show that glass beads have good compatibility with foam stabilizers. It can also be seen that some high-performance hollow glass beads are peeling off, indicating that there are still weak bonding points between the glass beads and the cement, which may be one of the main reasons for the decrease in compressive strength of cement after use. Add hollow glass beads.
       Polystyrene foam contains a large amount of nitrogen. Due to the compressibility of nitrogen, the volume of nitrogen in foam cement changes significantly with changes in pressure/temperature. During the cementing process, the pressure/temperature usually increases and the density of the foam cement paste usually increases. In addition, the thermal conductivity of cement should also take into account the volume fraction of the insulating material in the solution, so it should reflect the change in the volume fraction of nitrogen in the solution in the annulus. To reflect the relationship between the density and pressure of a foam cement mortar system, this study tested the density of a foam cement mortar system at a certain pressure and examined the effect of pressure changes on the microstructure of foam cement. Discussions were conducted with the aim of creating an experimental basis for rational calculation of the density and thermal conductivity of foam cement mortar.
       Since temperature and pressure increase simultaneously with increasing well depth, various combinations of temperature and pressure were determined as the cement slurry hardening conditions, and the density, thermal conductivity, and compressive strength of the cement slurry were calculated and tested. The results are shown in Table 4. The results show that the thermal conductivity of cement increases with increasing temperature and pressure. Generally speaking, the thermal conductivity of cement increases as the pore volume decreases. According to the gas equation of state, gas volume is directly proportional to temperature and inversely proportional to pressure, with pressure increasing with wellbore depth much faster than temperature. Therefore, the pore volume of foam cement decreases with increasing well depth. However, its performance is still better than that of non-foamed cement mortar, indicating that foamed cement still has good thermal insulation effect under high pressure.
       For the thermal conductivity of filled composite materials, the Maxwell model and the Russell model were chosen to simulate the process of thermal conductivity in hardened cement. The Maxwell model and Russell model can be expressed by equation (1): (2) and (3) are respectively written as follows:
       In the formula, λc is the thermal conductivity of the composite material, λf is the thermal conductivity of the uniformly distributed filler phase, λm is the thermal conductivity of the filler matrix, Vf is the volume fraction of the spherical filler phase.
       In the formula, λ is the thermal conductivity of the composite material, λp is the thermal conductivity of the uniformly distributed filler phase, λf is the thermal conductivity of pores (air), Vf is the volume fraction of the spherical filler phase.
       Using the example of hollow glass beads with a mass fraction of 5%, the density is 0.35 g/cm3, the dosage of cement powder is 600 g, the density is 3.5 g/cm3, the density is 1 g/cm3; cm3. The equivalent volume fraction is 13.75%. Plug these parameters into the calculation model and the results are shown in Table 5. It can be seen that the Maxwell model predicts thermal conductivity better than the Russell model. Considering that the model is simplified using the above formula, it can be considered that the real situation of composite materials is basically consistent with Maxwell’s model.
       The Maxwell model has shown good results in predicting the thermal conductivity of composites with spherical fillers. When the filler is hollow glass beads, the prediction error is about 10%. The foam prepared by chemical nitrogen filling method has uniform foam size distribution and good sphericity, which is suitable for the Maxwell model. According to Equation (2), the key to accurately predicting thermal conductivity is to determine the volume fraction of the spherical filling phase. For glass beads, the volume fraction can be calculated from dose and density. The gas filling the foam cement solution is nitrogen, and compressibility is affected by temperature and pressure. Therefore, different methods should be taken into account when calculating.
       For hardened foam cement, the filling phase is nitrogen and the filling matrix is ​​hardened cement. Instruments can be used to measure thermal conductivity. In this way the nitrogen filling volume Vf can be calculated. Actual NGR gas production can be measured experimentally to validate the model. Combining the above assumptions and experimental results, the theoretical mass reduction of the system after foaming can be calculated as ΔM = V total nitrogen·ρ nitrogen (1-Vf), by weighing the mass of the system before and after the experiment, this can be verified; whether the decrease in the mass of the system is within the limits of theoretical calculations. The corresponding summary is presented in Table 6.
       Based on the previous analysis, repeat the suspension experiment and weigh the reaction vessel. After complete reaction, the first weighing (0.36 grams) was carried out when the container returned to normal pressure, and the second weighing was carried out three minutes later, which was 0.91 grams. From this, the Vf of nitrogen can be calculated as 43% and the final predicted thermal conductivity of cement can also be calculated as 0.3845 W·(m·K)-1. The calculation shows that the mass of the escaping gas is within the theoretical design range. Considering the simplification and measurement error of the corresponding model, it can be considered that this model has good application potential in foam insulation cement mortar systems prepared by chemical nitrogen infill.
       So far this model works for the grout mentioned earlier. However, due to the presence of filled glass beads in the foam, when the amount of a certain material is increased to a certain value, the multicomponent composite material as a whole can be considered as an equivalent filled matrix. On this basis, the relationship between the amount of added material and thermal conductivity can be studied. Based on the above analysis combined with the relevant data and the actual situation of this test, the thermal conductivity of hardened cement with 10% and 12.5% ​​microsphere content can be converted to 7.5% content as shown below. Table: Table 7 It can be seen that to simplify the calculation of the thermal conductivity of multicomponent composite materials, an equivalent method can be used. Taking into account the changes in the water-cement ratio in two series of experiments and the errors of the model itself, we can assume that the real situation with multicomponent composite materials basically corresponds to the theoretical model.