1. Introduction
Natural gas is a high-quality, eco-friendly energy source and fuel, and its share of the world’s primary energy constituent is growing. Sour gas reservoirs are abundant and widely distributed all over the world, which is an important part of natural gas exploitation [
1]. When the sulfur concentration exceeds the sulfur solubility during the development of sour gas reservoirs, dissolved elemental sulfur will be precipitated from natural gas and deposited in the formation as pressure decreases. Solid sulfur deposition will significantly reduce the porosity and permeability in conventional sour reservoirs. The formation temperature of some HTHP sour gas reservoirs is higher than the melting point of elemental sulfur (119 °C), and the sulfur precipitated exists in the liquid phase. When the liquid sulfur saturation exceeds the residual saturation, two phase gas–liquid sulfur percolations form in the reservoir. The continuous precipitation and deposition of liquid sulfur reduces porosity and permeability, affecting the gas flow ability and reducing the gas well productivity [
2]. The measurement of the gas–liquid sulfur relative permeability is useful for studying the effect of liquid sulfur on gas well productivity and gas reservoir development, and it is critical for analyzing the gas well production status, predicting the gas reservoir production performance, and guiding the development of gas reservoir development plans.
The liquid sulfur precipitation process is similar to the gas condensate and asphaltene precipitation processes. Changes in pressure or temperature cause the fluid’s constituents to precipitate. Liquid sulfur precipitation has a lower flow capacity than condensate precipitation, and the precipitation is more similar to asphaltene precipitation, which is difficult to deal with. At the moment, research on gas-condensate relative permeability and asphaltene precipitation has made some headway. Jamolahmady [
3] carried out a gas-condensate relative permeability measurement experiment of a low permeability core. Kalla [
4] conducted relative permeability measurements and concluded that laboratory measurements must be performed under reservoir conditions using actual reservoir fluids. Rahimzadeh [
5] studied the effect of condensate blockage on the pressure drop near the well bore. Hassan [
6] analyzed and summarized the condensate removal treatments as well as the causes and instants of condensate banking in gas reservoirs. Khormali [
7,
8] investigated the effect of reservoir pressure and temperature on the amount of asphaltene precipitation, and developed a new asphaltene inhibitor to reduce the occurrence of the asphaltene precipitate. The above research findings are helpful to investigate the impact of liquid sulfur precipitation on sour gas reservoirs.
However, the relevant experimental study on the relative permeability of gas–liquid sulfur is insufficient. Existing studies have mainly focused on the theoretical study and the impact of solid sulfur deposition on sour gas reservoirs and gas wells. Kuo [
9] established the empirical relationship between sulfur deposition and permeability. Based on thermodynamics, Chrastil [
10] developed an equation model that can be used to calculate the sulfur solubility. Roberts [
11] fitted the Chrastil model and investigated the effect of sulfur deposition near the wellbore, believing that the rate of sulfur buildup in the formation is inversely proportional to the square of the radial distance from the well. Mei [
12] presented an evaluation method for assessing the effect of sulfur deposition on gas deliverability. Guo [
13] developed a gas–liquid–solid mathematical model to predict sulfur deposition based on the characteristics of the composition and phase behavior of a gas–liquid system. Mahmoud [
14] developed analytical and numerical models to predict the effect of sulfur adsorption and deposition on near-wellbore damage. Hu [
15] established a reservoir damage model in the presence of non-Darcy flow, which can be used to describe the pressure changes caused by deposited sulfur. Guo [
16] established a modified sulfur saturation prediction model and investigated the effect of sulfur deposition on the gas well deliverability. Li [
17] proposed a numerical simulation method for high sulfur gas reservoirs with released sulfur in liquid form. Hu [
18] proposed an analytical model for dual porosity media that took sulfur deposition into account in order to analyze the effects of sulfur deposition on the well performance in sour carbonate fractured gas reservoirs. Liu [
19] developed a model for predicting the gas–liquid sulfur relative permeability by combining a flow resistance model with the fractal theory of porous media. Xu [
20] proposed a mathematical model for sulfur deposition that took into account the sulfur particle release; the model could reflect the flow transport during the sulfur deposition process in porous media. Li [
21] presented a fractal model for predicting the elemental sulfur saturation in the presence of natural fracture. Based on the partition model and transient percolation theory, Zou [
22] developed a numerical model to predict production from fractured horizontal wells in high-sulfur-content gas reservoirs, taking into account the effect of sulfur deposition with pressure changes on the reservoir porosity and permeability.
In terms of experimental research, Coşkuner [
23] carried out microvisualization experiments on a gas–water–liquid sulfur three-phase system and discovered that liquid sulfur had little effect on the gas percolation ability. Abou-Kassem [
24] investigated the deposition of elemental sulfur in carbonate cores in two separate sets of experiments and discovered that the severity of sulfur plugging depended on the flow rate and initial sulfur concentration. Shedid [
25] experimentally studied the influence of elemental sulfur and asphaltene on reservoir damage under joint deposition. Guo [
26] investigated the effect of sulfur deposition on reservoir permeability in a sour gas reservoir from a laboratory perspective, and the experimental results showed that the higher the hydrogen sulfide concentration, the more sulfur deposition occurs, and the rock permeability decreases rapidly. Hu [
27] carried out core sulfur deposition experiments, and the results indicate that non-movable water can help improve core permeability. Yang [
28] developed a method of determining the elemental sulfur deposition at a formation temperature and pressure. Mahmoud [
29] performed a coreflood experiment to determine the effect of sulfur deposition on the permeability, porosity, and wettability of carbonate rocks. Maffeis [
30] used PVT laboratory equipment to simulate the conditions for the formation of elemental sulfur plugs in wells.
In summary, previous studies have primarily focused on the influence of solid sulfur deposition on the formation physical properties and gas well production due to the shallow burial depth and low formation temperature of previously developed sour gas reservoirs. The majority of liquid sulfur research is based on theoretical models that simulate or predict reservoir damage. There have been few experimental studies on liquid sulfur, particularly on the relative permeability of gas and liquid sulfur.
The experimental equipment and process of the HTHP oil–gas–water seepage test device were improved in this study, and an experimental method for measuring the gas–liquid sulfur relative permeability curve proposed to measure the gas–liquid sulfur relative permeability of different core types, temperatures, and confining pressures by the unsteady method, and the characteristics of the gas–liquid sulfur relative permeability curve were analyzed. The findings can be used to assess the productivity of HTHP sour gas wells and guide the rational development of sour gas reservoirs.
3. Results and Discussion
3.1. Characteristics of Gas-Liquid Sulfur Relative Permeability Curve
The relative permeability curves measured for each core had roughly the same shape and were all concave curves. As shown in
Figure 3, the gas–liquid sulfur relative permeability curve of Core 1 was used as an example (test temperature 150 °C, pressure 50 MPa) to analyze the curve characteristics.
It can be seen that as the liquid sulfur saturation increased, the gas relative permeability decreased rapidly while the liquid sulfur relative permeability increased slowly. The critical flow saturation of liquid sulfur is high, and it can only flow when the saturation of liquid sulfur exceeds 40%. The gas–liquid sulfur co-flow interval is narrow, with a liquid sulfur saturation range of 40–80% in the co-flow interval. As a result, as the amount of liquid sulfur precipitated far from the wellbore is usually small, the majority of the precipitated liquid sulfur in the reservoir will not flow during the production of sour gas reservoirs. Liquid sulfur is easily adsorbed in reservoir pores. For the near-wellbore zone, the amount of precipitated liquid sulfur is large due to the large pressure drop. Meanwhile, a small amount of liquid sulfur far from the wellbore will be carried by gas to the near-wellbore zone, resulting in a relatively high liquid sulfur saturation and mobility. However, high liquid sulfur saturation reduces the gas relative permeability, resulting in lower gas well productivity.
3.2. Effect of Core Type on Relative Permeability Curve
The relative permeability of the gas–liquid in Cores 1, 2, and 3 was measured at the same experimental temperature and confining pressure (150 °C, 30 MPa). The results are shown in
Figure 4 and
Figure 5 and
Table 5.
Comparing the relative permeability curves of Core 1 and Core 2, it can be seen from
Figure 4 that the overall curve of Core 2 moved to the lower right. Compared with Core 1, the gas relative permeability of Core 2 was slightly lower, while the liquid sulfur relative permeability was more obvious. The residual liquid sulfur saturation was greater, and the gas–liquid sulfur co-flow interval was narrower. The liquid sulfur saturation at the isopermeability point was higher, while the relative permeability at the isopermeability point was lower. Because Core 2 has good overall physical properties and high absolute permeability, the relative permeability of gas and liquid sulfur was low. Furthermore, the greater the porosity and permeability of the core, the easier it is to form gas breakthrough channeling, resulting in a smaller gas sweep area to the core and lower displacement efficiency to the liquid sulfur. This indicates that in reservoirs with poor physical properties, the adsorbed and deposited liquid sulfur is relatively easy to flow. However, it will be more difficult for liquid sulfur to flow in reservoirs with better physical properties, and the damage to the physical properties of the reservoir will be more severe.
From
Figure 5, compared with Core 2, the relative permeability curve of Core 3 moved to the lower right. The gas relative permeability of Core 3 was larger, but the gas–liquid sulfur co-flow interval was narrower, and the gas relative permeability decreased more as the liquid sulfur saturation increased. The saturation of residual liquid sulfur was higher. At the gas–liquid sulfur isopermeability point, the liquid sulfur saturation was higher and the relative permeability was lower. This suggests that the pore structure of reservoir rocks has a significant impact on the relative permeability of the gas–liquid sulfur. The presence of fractures in the reservoir increases the gas permeability, reduces the residual gas saturation, and allows for more gas production. However, it reduces the gas’s displacement efficiency to liquid sulfur. The relative permeability of the gas decreases more rapidly as the liquid sulfur saturation increases. As a result, for wells with natural and artificial fractures in the near-wellbore zone, liquid sulfur adsorption and deposition have little effect on gas well productivity in the early and middle production stages, but productivity declines rapidly in the late production period when the near-wellbore zone liquid sulfur saturation exceeds the critical flow saturation.
3.3. Effect of Temperature on Relative Permeability Curve
The relative permeability of Core 1 was measured at 130 °C, 140 °C, and 150 °C by changing the experimental temperature, and the results are shown in
Figure 6.
It can be seen that temperature had an effect on gas relative permeability, but less so on the liquid sulfur relative permeability. The gas relative permeability decreased as the temperature rose, while the liquid sulfur relative permeability decreased slightly but essentially remained unchanged. The isopermeability point shifted to the lower left, the corresponding liquid sulfur saturation and relative permeability dropped, and the area of the two-phase co-flow interval remained essentially unchanged. This phenomenon corresponds to previous theoretical research findings [
33]. This is because temperature changes cause changes in the density, viscosity, and other physical properties of the gas, reducing the gas flow capacity. Furthermore, as temperature rises, the core skeleton is slightly deformed and expanded, some throats close and dead pores form, reducing the effective porosity and permeability of the core [
34,
35]. Furthermore, temperature changes may affect the adsorption capacity of liquid sulfur on the rock surface, affecting the relative permeability of liquid sulfur and gas. However, the related phenomenon is still unknown, and more research is required. With increasing temperature, these combined effects result in a significant decrease in the gas relative permeability.
3.4. Effect of Confining Pressure on Relative Permeability Curve
The relative permeability of Core 1–3 was measured under simulated formation pressures of 10 MPa, 30 MPa, and 50 MPa by changing the experimental confining pressure, and the results are shown in
Figure 7,
Figure 8 and
Figure 9.
It can be seen that the gas–liquid sulfur relative permeability curves of different cores showed roughly the same trend. The relative permeability of gas and liquid sulfur decreased as the confining pressure increased, and the influence on the gas relative permeability increased. The liquid sulfur saturation and relative permeability corresponding to the isopermeability point decreased as the isopermeability point moved to the lower left, and the range of the gas–liquid sulfur co-flow interval decreased slightly. This is because increasing the confining pressure increases the effective stress on the core, reducing the pore volume and throat radius and even closing part of the pore throat, reducing the gas and liquid sulfur permeability. Furthermore, because the gas is more sensitive to effective stress due to its higher compressibility, the decrease in gas phase permeability is more significant.
Comparing the gas–liquid sulfur relative permeability curves of different cores, it was shown that the gas relative permeability of Core 3 decreased more with the increase in confining pressure, indicating that the stress sensitivity of the fractured core was more significant. This is because the presence of fractures increases the contact area between the liquid sulfur and core, resulting in more liquid sulfur absorption and deposition in the core pores, resulting in less pore space occupied by gas. At the same time, the fracture space is the primary gas flow channel, and gas easily forms cross-flow in the fracture. The fracture space is more compressible than the pore space of matrix cores. As a result, the gas permeability damage in fractured cores with effective stress is more severe.
Due to the experimental conditions and safety concerns, the gas used in this paper was standard nitrogen, which has physical properties that differ from the actual sour gas. However, these findings are still important for understanding the characteristics of the gas–liquid sulfur phase permeability curve and guiding the efficient and reasonable development of sour gas reservoirs. It is suggested that the experimental equipment and process can be improved further in order to conduct gas–liquid sulfur permeability measurements with various actual sour gases and study the effect of sour gas components and content on the gas–liquid sulfur relative permeability.