Determination of Fuel Saturated Dissolved Water Content and Its Influencing Factors

. The presence of undissolved water in fuel can significantly impact the safety, stability, and durability of engine operation. Karl Fischer titration is a cost-effective and convenient approach to accurately measure the total water content in the fuel. The undissolved water content can be determined by subtracting the saturated dissolved water content from the total water content. This paper outlines a methodology for preparing dissolved water saturated fuel and investigates the effect of temperature and interfacial tension on the saturation solubility of water in 0# diesel fuel and 3# jet fuel. The results show that the saturated dissolved water content of the two fuels is linearly and positively correlated with the temperature; the use of surfactants was shown to decrease interfacial tension, thereby promoting the combination of fuel and water molecules and increasing saturated water solubility; molecular surfactants were more effective at combining fuel and water molecules than ionic surfactants when interfacial tension was held constant.


Introduction
In the fields of transportation and military engineering, fuel is commonly utilized. However, during the storage and transportation of fuel, water can easily mix with the fuel as an impurity. The water present in the fuel exists mainly in two forms: dissolved and undissolved [1] . As the dissolved water reaches saturation, newly added water is converted into undissolved water. Despite its low content, undissolved water has a significant impact on engine safety, stability, and service life. The hazards associated with undissolved water include: it reacts with sulfide in the fuel to create acid, leading to chemical corrosion of engine parts; it produces cavitation in lowpressure areas of the circulation system, forming bubbles that rupture in high-pressure areas; it speeds up fuel oxidation, causing the generation of sticky sludge, which reduces fuel fluidity, lubrication, and combustion; it condenses into fine ice crystals in low-temperature conditions, blocking the engine circulation system, particularly at the screen, resulting in an increase in fuel filter pressure difference; it adsorbs and dissolves particular additives in the fuel, resulting in fuel performance degradation and increasing the risk of fuel flammability and explosion; it also creates favorable conditions for microbial growth, with microbial metabolites in the tank forming biofilm and producing odor, thereby affecting the fuel quality [2][3][4][5] .
For effective fuel quality control, the measurement of undissolved water content (C U ) is essential, and it should be rapid, accurate, and cost-effective. However, current detection methods do not balance economy and convenience when measuring undissolved water content.
Techniques for detecting water in fuel can be categorized into off-line detection techniques, such as Karl Fischer titration, Aqua-Glo diaphragm, distillation, and chromatography [6][7][8][9][10] ; and on-line detection techniques, such as capacitance, microwave, and ultrasonic methods [11][12][13][14] . The Aqua-Glo diaphragm method is extensively utilized in the aviation industry for the detection of undissolved water content in jet fuel. However, its adoption is constrained by its high measurement cost. The feasibility of its direct use in measuring undissolved water content in other fuel types, such as diesel fuel, requires validation. The Karl Fischer titration method is widely used, simple, fast, and easy to operate. However, it measures the total water content (C T ) in the fuel, and accurate knowledge of the saturated dissolved water content (C S ) is required to calculate the undissolved water content. In this study, we present a method to prepare dissolved water saturated fuel by controlling parameters like stirring time and magnetic stirrer rotational speed. We also investigate the effect of temperature and interfacial tension on C S .

Assessment of the representativeness of Karl Fischer titration samples
In the Karl Fischer titration method, a small sample solution is required to measure trace water in fuel, typically in grams. However, since undissolved water exists in the fuel as discrete particles, it is necessary to evaluate the representativeness of the sample solution in the gram scale to ensure that the sample taken is representative. Electron microscopy observation of the particle size of water droplets in fuel containing trace amounts of undissolved water showed that they were distributed in the range of 5 μm to 200 μm [15] . Assuming a fuel sample with C S = 70 ppm and C T = 90 ppm, the C U would be 20 ppm per 1 g of sample, which translates to 2 10 -5 g of water being contained in the sample. The number of droplets present can be calculated and presented in Table 1. The number of water droplets present in a 1 g fuel sample, which has been estimated to be at least 4.78 10 , ensures that the Karl Fischer method is representative for measuring samples that contain trace amounts of undissolved water. The risk of measurement inaccuracies due to the potential loss of droplets during sampling is low, as the number of droplets is sufficiently high.
In this study, SCKF105 Karl Fischer titrator of Shengkang Electric Company and YT1004 analytical balance of Kunshan Youkeweite Company were used to measure the water content of fuel. The Karl Fischer titrator meets the GB 7600-2014 standard.

Dissolved water saturated fuel preparation
To create a fuel sample that is saturated with dissolved water, the ISO 16332 method [16] was followed. A beaker was used to hold 75 mL of the test fuel, and a syringe was used to slowly add 25 mL of water from the bottom of the beaker. The beaker was sealed and placed in a magnetic stirrer with water bath. The fuel-water mixture was stirred at less than 60 rpm for at least 5 hours, while ensuring that the interface between the fuel and water was not disrupted.
The measured water content of jet fuel saturated with dissolved water at room temperature of 25 °C is only 31.39 ppm, which is lower than the values reported by Carpenter (CS > 60 ppm), Charro (CS > 50 ppm), West (CS > 60 ppm), Lam (CS > 40 ppm), and other studies that utilized different measurement techniques [17][18][19][20] . Therefore, further improvements in the testing method are necessary.
Verification by test is necessary for determining the appropriate fuel-water ratio, stirring time and magnetic stirrer rotational speed for preparing dissolved watersaturated fuel. In this study, 0# diesel fuel and 3# jet fuel were chosen for testing, and the specific parameters of the fuel are presented in Table 2. To determine the appropriate fuel-water ratio for preparing dissolved water saturated fuel, it is important to ensure that the water is completely submerged in the stirrer without disrupting the fuel-water interface. Therefore, 25 ml of water was added to a 100 ml standard beaker. In this experiment, six 100 ml beakers were used, and 40 ml, 50 ml, 60 ml, 70 ml, 80 ml, and 90 ml of 0# diesel fuel and 3# jet fuel were added to achieve fuel-water ratios of 1.6:1, 2:1, 2.4:1, 2.8:1, 3.2:1, and 3.6:1, respectively. The stirrer was operated at two different rotational speeds, 50 rpm and 100 rpm, and samples were collected at 30-minute intervals. The obtained test data are presented in Figure 1 and 2.   The results presented in Figure 1 and 2 indicate that the fuel-water ratio does not significantly affect the preparation of dissolved water-saturated fuel samples. The critical factor in this regard is to ensure that the water phase is fully submerged in the stirrer and that the fuel-water interface remains undisturbed during the stirring process. Therefore, any fuel-water ratio that meets these conditions is suitable for preparing dissolved water-saturated fuel samples.
Subsequently, the time required to achieve dissolved water saturation and the optimal magnetic stirrer rotational speed were determined. In this regard, the rotational speed was varied between 50-220 rpm, and samples were collected at 30-minute intervals over a 5hour period. The obtained test data are presented in Figure 3 and 4.
The experimental results indicate that: (1) With increasing magnetic stirrer rotational speed from 0 to 140 rpm (in diesel fuel) or 170 rpm (in jet fuel), the water content in fuel increases rapidly within 0-30 minutes, followed by slight fluctuations. The maximum water content attained in the fuel increases with the rotational speed, while the fuel-water interface remains clear and stable within this range of rotational speeds. Figure 5(a) presents the water-saturated diesel fuel obtained using a rotational speed of 140 rpm.
(2) When the magnetic stirrer rotational speed is within the range of 150-160 rpm (in diesel fuel) or 180-200 rpm (in jet fuel), the fuel-water interface remains clear during the initial 0-60 minutes, and the water content in fuel shows significant fluctuations after initially increasing. After 90 minutes, emulsification occurs between the fuel and water phases, leading to the formation of an emulsion layer, as depicted in Figures  5(b) and 5(c).
(3) At the magnetic stirrer rotational speed of 170 rpm (in diesel fuel) or 210 rpm (in jet fuel), the water content in fuel increases rapidly, the fuel-water interface breaks up completely, and the fuel phase mixes with the water phase, as illustrated in Figure 5(d).  Upon initiation of stirring, the water in the fuel gains kinetic energy and enters the fuel phase to form dissolved water through the process of combination with fuel. Once the fuel phase becomes saturated with water, the water and fuel begin to form emulsified droplets at the interface. From the experimental tests conducted, the rotational speed at which the emulsion layer first appears is referred to as the critical rotational speed, and the moment at which the emulsion layer appears is known as the critical time.  The following method for preparing dissolved water saturated fuel is derived from the above experiments: (1) Prepare 8 beakers, each containing 75 ml of test fuel, and place a magnetic stirrer in each beaker. Slowly inject water into the beakers from the bottom using a syringe until the stirrer is submerged. Seal the beakers and place them in a water bath at T°C.
(2) Set the stirrer rotational speed to 50, 60, 70, 80, 90, 100, 110, 120 rpm, respectively, and stir for 10 minutes. Visually observe the lowest rotational speed X (rpm) at which the fuel-water interface breaks down. If there is no fuel-water interface damage, the 50 rpm stirrer rotational speed is adjusted to 130 rpm, and the 60 rpm stirrer rotational speed is adjusted to 140 rpm... Until the fuel-water interface damage was observed.
(3) Set the stirrer rotational speed to X-10, X-20, X-30, and X-40 rpm, respectively, and continue stirring for 2 hours. Observe the lowest rotational speed Y (rpm) at which the emulsion layer is produced. This rotational speed Y (rpm) is the critical rotational speed at which the fuel reaches a water-saturated state.
(4) Take 8 beakers and set the stirrer rotational speed to Y (rpm). Measure the water content (C S1 , C S2 , …, C S8 ) of each beaker when the emulsified layer is produced. Take the average value as the saturated dissolved water content (C S ) of the test fuel sample at this temperature.

Effect of temperature and interfacial tension on the saturated water content of fuel fuel
Prior to testing, the fuels underwent white clay and diatomaceous earth treatment, along with complete adsorption of additives. The respective parameters of the two fuels are presented in Table 3. The interfacial tension of the fuel was assessed using a SCZL202 tensiometer, produced by Sheng Kang Electric Co. Considering that a large number of additives in the refined fuel leads to a decrease in the interfacial tension of the fuel, the two fuels adjust the interfacial tension according to the following methods to simulate the actual situation: (1) The standard method (M1) involved using white clay and diatomaceous earth to completely absorb the fuel additives.
(2) The interfacial tension was adjusted by adding surfactant glycerol monooleate to the M1 method, resulting in the high interfacial tension method (M2), which adjusted the fuel interfacial tension to 20±2 mN/m, and the low interfacial tension method (M3), which adjusted the fuel interfacial tension to 11±2 mN/m.
(3) The interfacial tension was adjusted by adding surfactant petroleum sulfonate to the M1 method, resulting in the high interfacial tension method (M4), which adjusted the fuel interfacial tension to 20±2 mN/m, and the low interfacial tension method (M5), which adjusted the fuel interfacial tension to 11±2 mN/m. The test temperatures were 5, 20, 40 and 60 °C. The test data are shown in Figure 6 and Figure 7. The correlation between temperature and the water content of diesel fuel and jet fuel were investigated, and the results showed a positive linear relationship. The slope of the relationship between temperature and water content for both fuels was determined, with good linear regression and high goodness of fit (R 2 ) values (>0.980 for diesel fuel and >0.975 for jet fuel).
The introduction of surfactants into fuel systems is known to reduce interfacial tension by facilitating the association of fuel and water molecules. In this study, the effect of glycerol monooleate and petroleum sulfonate on the interfacial tension and C S of 0# diesel fuel and 3# jet fuel was investigated. The results indicate that the addition of glycerol monooleate led to a decrease in interfacial tension, resulting in a C S . increase of 32.3%  and 82.3% when the interfacial tension of 0# diesel fuel was reduced to 20 mN/m and 11 mN/m, respectively. Likewise, petroleum sulfonate was found to lower the interfacial tension of 0# diesel fuel, resulting in the C S increase of 10.1% and 40.1% when the interfacial tension was reduced to 20 mN/m and 11 mN/m, respectively. For 3# jet fuel, the addition of glycerol monooleate and petroleum sulfonate resulted in interfacial tension reduction and subsequent C S increase of 46.7%, 87.8% and 36.0%, 62.9%, respectively, for the same interfacial tension values.
Furthermore, at the same temperature and interfacial tension, the fuel prepared with molecular surfactant glycerol monooleate exhibited higher C S values than the fuel prepared with ionic surfactant petroleum sulfonate.

Conclusion
The Karl Fischer titration method, which requires a small sample size, is highly dependent on sample representativeness. In this study, the representativeness of the Karl Fischer titration method was validated, indicating that samples in the range of 20-200 ppm were representative.
The ISO 16332 method for preparing dissolved water saturated fuel samples is too strict in terms of fuel-water ratio and stirring time, and the low magnetic stirrer rotational speed results in unsaturated fuel samples. This study proposes an improved method, wherein watersaturated fuel samples are prepared by stirring the fuel with water at a critical rotational speed until emulsification occurs, and the water content of such samples can be measured using C S .
In the future studies, it would be beneficial to compare the results of this test method with those obtained from preparing fuel samples saturated with dissolved water through the application of principles such as Henry Law.
The C S in fuel is directly proportional to temperature and inversely proportional to interfacial tension. Molecular surfactants are more efficient than ionic surfactants in binding fuel-water molecules, especially under the same interfacial tension.
It is recommended for future studies to investigate the influence of key additives in diesel fuel and jet fuel, as well as low temperatures ranging from -40°C to 0°C, on C S . This study aimed to enhance and optimize the measurement approach for the saturated dissolved water content in fuel. The findings highlight that the dissolved water content in fuel cannot be overlooked under conditions of high temperature or low interfacial tension. Furthermore, it was revealed that the total water content determined by Karl Fischer titration cannot be employed as the undissolved water content directly.