Figure 1 shows the schematic diagram of the volume element of the single well model.

Pore volume of volume elements within the formation: Δ V = 2 π r h φ d r (1) Where △V is the pore volume of volume element, cm³; r is the reservoir radius, cm; h is the thickness of reservoir, cm; ϕ is the porosity, %.

The amount of change in the volume of the water phase is as follows due to the decrease of water saturation in the system caused by the evaporation of the water phase: d V w = 2 π r h φ dS w d r (2) Where V _w is the amount of change in the volume of the water phase, cm³; S_w is the water content saturation, %.

The pressure in the near-well zone decreases, causing evaporation of the aqueous phase and an increase in water saturation as the gas flows through. The water phase change within the volume element can also be expressed as follows: d V w = qdtd ω (3) Where q is the gas production volume, cm³/s; t is the production time, s; ω is the saturated content of water vapor in natural gas, cm³/cm³.

And the content of water vapor in natural gas is as follows: ω = A p B (4) Where p is the pressure, MPa; A and B are the correlation factor.

In steady seepage, the radial pressure drop in a gas well based on Darcy’s law is as follows; d p d r = μ g B g 2 π r h K K rg q (5) Where μ _g is the viscosity of gas, mPa·s; B _g is the volume factor; K is the reservoir permeability, mD; K _rg is the gas phase relative permeability.

Combining Eqs 3–5, the following equations are obtained: d S w dt = A B μ g B g q 2 p B − 1 4 π 2 r 2 h 2 φ K K rg (6)

The expression of the volume factor is as follows: B g = T p sc Z T sc p (7)

Combining Eqs 6, 7, the following equation is obtained: d S w dt = A B μ g T p sc Zq 2 p B − 2 4 π 2 r 2 h 2 φ T sc K K rg (8)

The formation water has a certain salinity, the presence of salt inhibits the evaporation of the water phase, reducing the water vapor content in the gas phase, according to Morin’s theory, certain modifications to Eq 8: d S w dt = A B μ g T p sc Zq 2 p B − 2 4 π 2 r 2 h 2 φ T sc K K rg 1 − 0.02865 c 1.44 (9) Where c is the molar concentration of salt in formation water, mol/L.

The value of c is mainly based on whether the formation water is in a saturated state during salt deposition, and c is expressed as follows: c = S wi S w c i c c c i < c c c i ≥ c c (10) Where c _i is the molar concentration of salt in formation water under initial conditions, mol/L; c _c is the molar concentration of salt when the formation is saturated with water, mol/L; S _wi is the initial water content saturation, %.

Water vapor content in the gas phase is related to temperature, pressure and salinity. During the flow of gas to the wellbore, the pressure gradually decreases and the water vapor content in the gas phase increases. The salinity of the formation water around the wellbore increases, and even salt deposition occurs. Assume that no transport of formation water occurs in the reservoir, so the salt ion content remains constant at any point in the formation: S wi × C i = C o n s t (11)

As the pressure decreases, evaporation of formation water accelerates and the salinity of formation water will change S wi × C i = S wi + 1 × C i + 1 (12)

Therefore, the salinity of the formation water under a certain moment is as follows: C i + 1 = S wi × C i S wi + 1 (13)

Salt deposition occurs in the formation when C > C _critical.

Where S _wi is the water content saturation at moment i, %; S _wi+1 is the water content saturation at moment i+1, %; C _i is the salinity of formation water at moment i, mol/L; C _i+1 is the salinity of formation water at moment i+1, mol/L; Const is the constant.

The p, C _i, S _wi at time i is brought into the Eq 13 to obtain the salinity of the formation water at time i+1. The phase software is used to calculate the solubility of NaCl at different pressure and salinity, and when the salinity of the formation water exceeds the solubility of NaCl, which is used to determine the values C _i in Eq 13 at different times: C i + 1 = S wi × C i 1 − 0.53 ln 0.53 A B μ g T p sc Zq 2 p B − 2 4 π 2 r 2 h 2 φ T sc K 1 − 0.02865 C i 1.44 t i + 1 + 4.65 − 1.75 (14)

The formation salt deposition model is more complex, and the solution needs to rely on numerical simulation software before it can be calculated. The idea of solving the near-well water content saturation distribution model is shown in Figure 2.

To simplify the simulation, pure CH₄ is used for both the formation fluid and injection gas composition for the simulation. The model mainly considers the effect of salt deposition on the production capacity and storage capacity of UGS. Na⁺ and Cl⁻ in the formation water are supersaturated to precipitate NaCl crystals. NaCl crystals affect the reservoir properties by depositing in the pore space. The main chemical reaction equation is shown in Eq 15. Na + + Cl − ⇔ NaCl (15)

Salt deposition and evaporation of formation water can lead to changes in reservoir porosity and permeability. The pore-permeability relationship is given by the experimental data. K = 0.0016 e 55.281 ϕ (16)

The relative permeability curve is taken from laboratory long core experiments. The relative permeability is shown as in Figure 3.

In order to study the effect of formation salt formation caused by formation water evaporation on the production and storage capacity of gas storage, the radial mechanism model of multi-cycle injection and production single well of gas storage was established by using numerical simulation software CMG. The model grid was divided into 10×1×5, and the radial mesh size was 1m, 2m, 3m, 5m, 8m, 13m, 21m, 34m, 40 m and 47 m, respectively. The layer is 40 m thick and 200 m longitudinally. The grid plane distribution and three-dimensional distribution are shown in Figure 4. The reservoir parameters are set according to the field data of the gas reservoir. The average permeability is 10.66mD, the average porosity is 11.16%, the bound water saturation is 0.35, and the formation water salinity is 300000ppm. Table 1 shows the parameters used in modeling and their values.

A well of UGS is set up in the middle of the model, and all layers are shot open. The basic program is set up in 2 phases, including cushion gas stage and UGS multi-cycle production stage.

(1) Cushion gas stage: The gas injection volume of single well is about 400,000 m³/d.

The bottomhole pressures in injection wells and production wells are shown in Figures 5, 6. There is no significant change in bottom flow pressures in injection wells and production wells without considering salt deposition. In the condition of considering salt deposition, the bottom flow pressures of injection well rise to the maximum pressure as the production cycle increases. The reason for this phenomenon is that salt deposition is more severe in the near-well zone and a larger pressure is required to inject the same amount of gas. Similarly, the bottom flow pressure of injection well reaches the minimum pressure earlier without considering salt deposition.

The impact of salt deposition on production capacity of gas well can be divided into two parts. Firstly, the evaporation of formation water increases the flow space and the flow capacity of gas, thus increasing the production capacity. In addition, salt crystals can block the pores in the formation and reduce the production capacity of the gas well. These two mechanisms affect the production capacity of gas well.

Two scenarios with different conditions are calculated in this work. The first is a comparison of the effect of salt deposition on gas well production capacity under considering water evaporation conditions and without considering water evaporation conditions. Then this work investigates the effect of salt deposition on gas well production capacity with formation water supplement. The results are shown in Figure 7. The evaporation of formation water increases the gas phase flow capacity without formation water supply.

The comparison of cumulative gas production under different water production conditions with considering movable water is shown in Figure 8. The damage of salt deposition gradually increases and the production capacity of gas wells is severely reduced under the conditions of formation water supplement.

A pressure drop funnel is formed in the near-wellbore during production of a gas well. The natural gas in the reservoir evaporates the formation water causing ion oversaturation during the gas from the far-end to the bottom of the well, resulting in salt deposition., The dry gas flows from the bottom of the well to the far-end and evaporates formation water during the gas injection process. More space can be used to store natural gas, enhancing the storage capacity of the UGS.

The drying volume is the volume of evaporation of formation water under reservoir conditions. The proportion of increase in geological reserves is the percentage of increased reserves to the control reserves of a single well. The calculation methods of the drying volume and the proportion of increase in geological reserves are as follows. V m = π r 2 h S w (17) where V _m is the drying volume, “r” is the drying radius, “h” is the thickness of reservoir and S _w is the initial water saturation. V p = V m B g (18) where V _p is the volume of natural gas underground conditions and “B _g” is the volume factor of natural gas. K = V p G (19) where K is the proportion of increase in geological reserves and “G” is geological reserves of natural gas.

Table 2 shows the calculation results of the drying volume, working gas volume and geological reserves with the various production cycle. The drying radius of reservoir is expanding with the increase of production cycle under initial water saturation conditions. The working gas volume increased by 5.4×10⁶ m³ by the tenth cycle. The geological reserves increased by 1.4% compared to the control reserves of single well.

Four groups of schemes were set, and salt formation damage under different production rates was studied by comparing the daily production rates (20, 40, 60 and 80×10⁴ m³/d), the salinity was 300000ppm, the lower limit of bottom-hole flow pressure in production Wells was 20MPa, and the upper limit of gas injection Wells was 38.6 MPa.

The cumulative gas production curves under different production rates are shown in Figures 9–12. When the production rate is 40×10⁴ m³/d, there is no significant change in cumulative gas production. When the output is 60×10⁴ m³/d, there is a significant decrease in daily gas production in the 7th cycle. When the yield was 80×10⁴ m³/d, the salt formation damage was aggravated in the 5th cycle. As shown in Figure 12, the cumulative gas production capacity decline rate histogram shows that when the production is 60×10⁴ m³/d, the gas production capacity decline rate rises to 22.89% after ten cycles, and the salt formation damage is serious. The conclusions are as follows: the higher the production, the greater the salt formation risk and the more serious the formation salt formation. When the production is greater than 60×10⁴ m³/d, the daily gas capacity decreases significantly and the salt formation is serious. Low gas production is conducive to controlling the risk of salt formation, and it is recommended to produce less than 60×10⁴ m³/d.