In 2019, China's natural gas consumption reached 3100×10⁸ m³. According to the forecast by the “China Energy and Chemical Industry Development Report 2020”, China's natural gas demand will further increase to 3290×10⁸ m³ in 2020. Clearly, China has an urgent demand to develop underground gas storage (UGS). Of the four main gas storage types in the world, the working gas volume of gas reservoir type storage accounts for about three-quarters of the total, and is the most important peak staggering facility for gas supply^[1,2,3]. At present, gas storage construction in North America, Canada, and other countries is in a stable development stage. As of 2010, a total of 307 depleted gas storages had been built in North America, of which 279 were gas reservoir and 10 were condensate gas reservoir. UGS in gas reservoir had a total working gas volume of approximately 980×10⁸m^3[4]. The development of UGS in China began relatively late. In the 1970s, the Daqing Oilfield first tried to use depleted gas reservoir to build gas storage, but to little success due to lack of technology and experience. In 2009, the Dagang Oilfield built 6 UGSs from condensate reservoirs, including Dazhangtuo, ect.^[5]. Although the peak staggering demand of Beijing and Tianjin was relieved to a certain extent, problems such as low capacity rate and small working gas volume still exist.

UGS in a condensate gas reservoir is more complicated in phase behavior than a gas reservoir. Changes in phase behavior during operation will cause changes in storage capacity and condensate oil recovery^[6]; at the same time, gas storage is quite different from gas reservoir in terms of production mode and operation law. During the development of condensate gas reservoir, due to the loss of retrograde condensation, a considerable amount of condensate oil hasn’t been produced. In the process of building UGS from a condensate gas reservoir, multiple rounds of gas injection and production can not only achieve the purpose of building gas storage^[7], but also can extract part of the condensate oil by retrograde vaporization to improve condensate oil recovery^[8,9]. Guo Ping et al.^[10] and Yang et al.^[11] recently studied phase characteristic changes during the natural depletion process of condensate gas reservoir. Jiao Yuwei et al.^[12] and Zhu Zhongqian^[13] investigated fluid phase change characteristics during the gas injection cycle in condensate gas reservoir. Tang Yong et al.^[14], Pan Yi et al.^[15], and Wang et al.^[16] examined the influence of formation water on the phase characteristics of condensate gas reservoir.

Some researchers have analyzed the influence of different factors on multi-cycle injection-production process of UGS in condensate gas reservoir by numerical simulation, and predicted gas storage injection-production performance with mathematical models. For example, Moradi et al.^[17] studied the changes in condensate oil saturation and gas relative permeability in zones near and far from well during gas storage multi-cycle injection-production with a mechanism model. Mehdi et al.^[18] investigated the effect of injected gas composition and volume on the condensate oil production during gas storage operation, based on history matching of a condensate gas reservoir. Tuna et al.^[19] found that in the multi-cycle injection-production process of gas storage, mass transfer between oil and gas would be more effective, bringing about reduction of crude oil viscosity and oil recovery enhancement. Sukru^[20] predicted the effect of gas injection-production rate and gas injection volume on gas storage temperature and pressure by numerical simulation. Fu^[21] proposed that intermolecular diffusion and medium deformation would impact the dynamic performance of gas storage. Lü Jian et al.^[22] studied composition changes of acid gas produced during multi-cycle injection-production process of gas storage in an acid gas reservoir with a component model. Wang Jieming et al.^[23] established a gas injection-production dynamic prediction model for UGS in gas-cap oil reservoir to predict injection-production storage capacity indices. Sun Chunliu et al.^[24] analyzed gas-liquid seepage during the multi-cycle injection-production process of UGS in gas reservoir t by physical modeling.

In summary, physical modeling has focused on condensate gas retro-condensation, phase behavior in single gas injection and cyclic gas injection in condensate gas reservoir, and seepage characteristics of multi-cycle injection-production. Research on gas storage has focused on multi-cycle injection-production parameters and scheme design. For UGS rebuilt on condensate gas reservoir, it is lacks of phase changes physical simulation research form the depletion produce to muilt-cycle injection and production process. Although commercial PVT (pressure, volume, temperature) phase behavior software packages have phase behavior simulation for constant volume depletion experiments, they lack the ability to simulate gas storage multi-cycle injection-production process. The existent studies can’t reflect the composition of complex formation fluids in the later stage of condensate gas reservoir production^[25], or the influence of phase change on condensate oil production and storage capacity during the multi-cycle injection-production process after storage construction.

In this work, a multi-cycle injection-production phase balance experimental test method was proposed in line with gas storage operating characteristics and a theoretical model for simulation thermodynamics was built considering the difference between gas storage operation and gas reservoir development. Taking a gas storage of condensate gas reservoir type as an example, the composition of produced fluid and remaining fluid, the phase state of remaining fluid, retrograde condensate oil saturation, and condensate recovery degree during multi- cycle injection-production were studied. The research method and results provide a technical reference for the design, storage capacity dynamic analysis, and operation scheme optimization of condensate gas reservoir type gas storage.

Because the original formation fluid could not be obtained when the gas storage was built, the experimental fluid was prepared by combining samples taken from the ground. The Shuang 6 gas storage in the Liaohe Oilfield had an original formation pressure of 24.76 MPa, and formation pressure of 4 MPa when the gas storage was built. It is a depleted condensate gas reservoir. The well fluid in this experiment was compounded with ground condensate oil and ground natural gas according to the phase-state recovery method^[26,27], in which the condensate oil was sampled during the production of the gas storage and the ground natural gas was prepared according to composition. Sample matching was carried out based on the saturation pressure. The sample was prepared according to saturation pressure, at the formation temperature of 89 °C and saturation pressure of 24 MPa. Different from conventional sample preparation, an appropriate amount of black oil from the adjacent well oil ring was added in this experiment in order to ensure that the experimental fluid was consistent in gas-oil ratio with the original condensate gas. After check, the final sample gas-oil ratio was 2548 m³/m³ and the saturation pressure was 24 MPa. This was consistent with the original condensate gas reservoir fluid and met the experimental requirements. The original formation fluid composition is shown in Table 1, in which the C₁₁₊ had a relative density of 0.84 and relative molecular mass of 190.68. The injected gas in this experiment was made up of C₁, C₂, C₃, iC₄, nC₅ and N₂, at the mole fractions of 92.27%, 5.61%, 1.80%, 0.24%, 0.01% and 0.07%, respectively. The main component was methane.

The main experimental equipment is a DBR-PVT tester, and the multi-cycle injection-production device is shown in Fig. 1. In the figure, the displacement pump is connected to the sampler, and the sample end of the sampler thereof is connected to the DBR-PVT tester. The pump was used to drive the piston to transfer the gas sample into the DBR-PVT tester. The equipment had an accurate temperature and pressure sensing and testing system to measure the phase behavior in the PVT cell. The displacement pump had a maximum pressure of 100 MPa and a displacement of 0.001-200.000 mL/min. The highest bearing pressure of DBR-PVT tester is 70 MPa, and the highest temperature is 200 °C. The separator was connected to the DBR-PVT tester production line to separate the produced oil and gas. The compositions of oil and gas were calculated and analyzed by gasometer and chromatograph.

In line with the characteristics of condensate gas reservoir natural depletion development and gas storage operation, experiments simulating depletion development of condensate gas reservoir and gas storage multi- cycle injection-production operation were designed. First, the condensate gas reservoir was developed in constant volume depletion (CVD) under the original formation pressure, and the pressure dropped to 4 MPa before the gas storage was built. Then gas was injected step-by- step to simulate the gas storage process until the PVT cell pressure reached the upper limit pressure of the gas storage. After reaching balance, the gas production process was simulated. The gas was produced in CVD until the pressure dropped to the lower limit pressure of the gas storage. Then the second cycle of gas injection was carried out, and the above process was repeated. During the experiment, the amount and composition of oil and gas produced in each cycle were measured, and changes of condensate oil content in the PVT cell before and after injection and production were photographed and tested.The specific experimental steps were as follows: (1) In constant composition expansion tests, the condensate gas sample was transferred into the PVT cell through the pump at the experiment temperature of 89 °C, and the cell pressure was maintained at the original formation pressure of 24.76 MPa, after mixing and reaching stable single phase, flash experiment and constant mass expansion test were conducted to obtain the composition, GOR, and dew-point pressure of the experimental fluid. (2) The natural depletion process of condensate gas reservoir was simulated, and the condensate gas sample in PVT cell was produced from dew-point pressure (24 MPa) in step-by-step constant volume depletion to the current formation pressure (4 MPa). Condensate oil saturation, oil and gas volume and components of the produced fluids were tested under different depletion pressures (Fig. 2a, 2b). (3) The gas injection stage of the gas storage was simulated, gas was injected into the remained fluid sample from the top of the PVT cell through displacement pump. Changes in condensate oil saturation during the injection process were tested and the gas injection volume at each stage was recorded, until the pressure of the PVT cell reached the upper limit of the preset gas storage operating pressure (Fig. 2b, 2c). (4) To simulate the gas production stage of the gas storage, starting from 24 MPa, the gas was produced under pressure reducing step by step in constant volume depletion until reach the lower limit pressure of 10 MPa. The condensate oil saturation in the PVT cell, the amount of oil and gas produced, and the components of oil and gas under different pressures were tested (Fig. 2c, 2d). (5) The multi-cycle injection and production of the gas storage operation was simulated, and steps (3) and (4) were repeated (Fig. 2d-2f).

Based on the physical modeling process of the multi- cycle injection-production of condensate gas storage, the theoretical simulation model for phase-state change of the process was established. The constant volume depletion (CVD) experiment simulated the natural depletion process of the original gas reservoir. The injection process simulated the gas injection stage to calculate the gas injection volume when the gas storage reached the upper limit of operating pressure. The CVD variable-composition fluid experiment simulated the gas production stage.In the model, it was assumed that the produced fluid was made up of n different components, and the initial total amount of substance was 1 mol. The phase equilibrium between the injected gas and the remaining fluid in the PVT cell reached instantaneously. The impact of expansion and compression on the PVT cell volume was not considered. The equilibrium parameters after each depletion experiment were calculated by flash distillation simulation. The multi-cycle injection-production calculation model consisted of the phase equilibrium flash distillation model, the constant volume depletion model, and the composition calculation model for the mixed gas injection system. The flash and constant volume depletion simulations were used to determine phase behavior parameters including the condensate oil saturation, P-T phase diagram, composition of produced fluid and the remaining fluid in the PVT cell etc.

The phase equilibrium calculation model is used to calculate the mole fractions of gas and liquid phases when the k-th depletion reaches equilibrium, as well as the mole fraction of each composition in the gas and liquid phases. The equation for calculating material equilibrium by isothermal flash distillation is as follows:

The thermodynamic equilibrium equation is:

Fugacity is calculated by the Peng-Robinson equation of state^[28,29]:

The volume of 1 mol condensate gas under the original formation condition was calibrated as the constant volume:

After k times of flash distillation at reduced pressure, the mole of formation fluid and the mole fraction of component i in the produced fluid are calculated as follows:

The mole of cumulative produced fluid after k steps of depletion production is:

The mole fraction of the i component in the remaining oil and gas system after k steps of depletion production is:

The remaining condensate oil saturation at the pressure of the k step of depletion is:

The mole of the injected gas required for the m-th injection cycle is expressed as:

The amount of component i in the oil and gas system after the m-th gas injection cycle is:

Firstly, CVD simulation of the original formation fluid was conducted, and the flash calculation was done at each depletion pressure level point to obtain the produced fluid composition, gas-liquid mole fraction, remaining oil saturation, and other parameters at each pressure level. The multi-cycle injection-production model was used to calculate the gas injection amount under each specified pressure. The fluid after gas injection was normalized, and the CVD simulation was run again. The flash distillation calculation was conducted step by step to obtain the produced fluid composition and characteristic parameters at each cycle. Gas injection and CVD calculation were repeated to simulate multi-cycle injection-production.

P-T phase diagrams of the original fluid and retrograde condensate oil saturation are shown in Figs. 3 and 4. It can be seen from them that the dew point pressure was 24 MPa at the original formation pressure of 89 °C, and retrograde condensate oil saturation reached the maximum of about 10.23% when the pressure dropped to 15 MPa. The formation retrograde condensate oil saturation was 7.05% when the pressure dropped to 4 MPa.

The formation fluid composition when the gas storage was built is shown in Table 2. The fluid properties of the gas reservoir before and after the gas storage building are shown in Table 3. The phase diagrams of condensate gas and retrograde condensate oil are shown in Fig. 5. It can be seen from this figure that the formation fluid had two phases when gas storage was built, the gas phase had lighter composition, characteristic of wet gas, and GOR of 75 000 m³/m³. A large amount of intermediate hydrocarbon retrogradely condensates into condensate oil phase, and the condensate oil increased in density. The gas reservoir fluid had a higher GOR than the original formation fluid when the gas storage was built. Due to the influence of retrograde condensation, a large amount of condensate oil was retained in the formation.

3.2.1. Composition changes of the produced gas

The experiment tested the composition changes of produced fluid during CVD (Fig. 6) and C₂, C₃, and C₇₊ in the produced gas during the five injection-production cycles (Fig. 7). It can be seen from the figures that the heavy hydrocarbon content (C₁₁₊) in the formation fluid decreased during CVD, which also demonstrates the occurrence of retrograde condensation. By comparing compositions of the injected and produced gas, it is found that the contents of C₂, C₃, and C₇₊ of the produced gas in the first cycle were higher than those of the injected gas. Meanwhile, the absolute C₇₊ mole fraction of the produced gas in the first two cycles were higher than that of the gas phase when gas storage was built, indicating that some of the C₇₊ in the condensate oil was extracted into the gas phase, and evaporation was significant.

Changes of C₁, C₆, and C₁₁₊ mole fractions in the produced gas in the high-pressure gas production cycles (20-24 MPa) and low-pressure gas production cycles (10-14 MPa) were compared (Fig. 8). It is found that the amount of heavy hydrocarbon (C₁₁₊) extracted under high pressure is greater than that under low pressure condition. The methane content in the produced gas at the end of each cycle (10-14 MPa) was higher (Fig. 8), indicating that the low-pressure gas production stage wasn’t conducive to extraction of condensate oil. In the fourth injection-production cycle, the produced gas was almost the same in composition with the injected gas, indicating that the injected gas could not extract condensate oil anymore.

3.2.2. Condensate oil recovery

The recovery and cumulative recovery of condensate oil at each injection-production cycle are shown in Fig. 9. It can be seen that multi-cycle injection and production had a significant effect on improving condensate oil recovery, and the condensate oil recovery of the five cycles of cyclic injection-production is 42% higher than that of natural depletion. The recovery of natural depletion to the formation pressure of 4 MPa was about 23%. After five cycles of cyclic injection-production, the cumulative recovery of condensate oil was 65%. From the perspective of condensate oil recoveries of individual cycles, the first two cycles had more significant enhancement of condensate oil recovery, with a condensate oil recovery of 14.8% and 7.8%, respectively. The injected gas in the first two cycles had stronger extraction to condensate oil.

3.2.3. GOR of produced fluid

The GOR of condensate gas was 75 000 m³/m³ when the gas storage was built. With the ongoing of multi-cycle injection and production, the GOR of produced fluid was 10 000-60 000 m³/m³ within the operating pressure range (10-24 MPa) of the gas storage (Fig. 10). The GORs of the produced gas under various pressures in the first cycle decreased significantly then that when the storage was built, which indicates that gas injection has a significant effect on extracting condensate oil in this period. Starting from the second cycle, with the increase of injection-production cycle, the variation amplitude of GOR of the produced gas decreased under the same pressure. This suggests that the extraction of injected gas to condensate oil gradually weakened as the number of cycles increased until the system reached a relatively stable state.

3.3.1. Condensate oil saturation

The changes of condensate oil content in the PVT cell during the gas injection at 10-24 MPa in the first cycle injection-production are shown in Fig. 11, of which Fig. 11a is a diagram. The red line in the Fig. 11b represents the condensate oil volume height, which decreases with the increase of injection pressure, indicating that the condensate oil saturation in the PVT cell decreased. At the same time, the condensate oil saturation decreased more significantly in the high-pressure gas injection stage (20-24 MPa), indicating evaporation was stronger under high pressure.

The condensate oil contents in these cycles when formation pressure decreased to 10 MPa are shown in Fig. 12. After five injection-production cycles, the condensate oil saturation almost fell to 0, indicating that multi-cycle injection-production had significant extraction to retrograde condensate oil. This is also the primary mechanism of extracting condensate oil retained in the formation.

The condensate oil saturations at the end of the cycles calculated by the theoretical model in natural depletion development and tested by experiment at the end of the cycles are shown in Fig. 13. It can be seen from the figure the calculated saturation values are consistent with the experimental results, indicating that the model can reflect the evaporation of injected gas. The condensate oil saturation at the storage construction was around 7%, and as the injection-production cycle increased, the condensate oil saturation decreased continuously. After five cycles, the condensate oil saturation was almost zero.

3.3.2. Composition and phase state of remaining formation fluid

The composition of remaining formation fluid at the end of each gas production cycle during the multi-cycle injection-production process was calculated with the theoretical model (Table 4). After five cycles of injection and production, the C₁ mole fraction of the remaining formation fluid increased from 66.95% to 92.05%. Clearly, as injection-production cycles increased, the remaining formation fluid became lighter in composition, finally, the remaining fluid was similar in composition to the injected gas.

Fig. 14 shows the phase diagram of remaining formation fluid at the end of each gas injection and gas production cycle. The dew point pressures of the fluid system at 24 MPa of all the cycles were less than 24 MPa. Moreover, as injection-production cycles increased, the dew point pressure decreased (Fig. 14a), indicating that the injected gas had significant evaporation effect and the system had less heavy hydrocarbon at equilibrium.

As the injection-production cycles increased, the dew point pressure of the remaining fluid overall decreased when the formation pressure decreased to 10 MPa in all the cycles (Fig. 14b), suggesting that the heavy hydrocarbon content in the system decreased. However, when formation pressure decreased to 10 MPa in the first two cycles, the dew point pressure of the remaining fluid system was higher than at the end of gas injection. This is because the intermediate hydrocarbon contents in the remaining fluid after gas production in the first two cycles decreased, while the proportion of C₁ composition increased, the content of C₁₁₊ composition changed little; with greater property differences between the components in the system, mutual dissolution of the components required higher pressure; thus, the dew point pressure increased.

In general, all dew point pressure values were greater than 10 MPa when the pressure dropped to 10 MPa in the first four cycles. This means that the system was two-phase with condensate oil present at this point, which is also consistent with the experimental results. But when the pressure dropped to 10 MPa during the fifth cycle of gas production, the formation fluid had a dew point pressure of less than 10 MPa and only gas phase .This is also consistent with the retrograde condensate oil saturation of zero in the fifth cycle of the experiment.

The cumulative injected gas volume in each cycle is shown in Fig. 15. As injection cycles increased, the cumulative gas injection volume under the maximum operating pressure in the cycles increased. This suggests that with the ongoing of injection and production, the storage volume under the same operating pressure range increased. Moreover, the first two cycles had higher condensate oil recovery degree, and thus bigger increments of cumulative gas injection volume than the last several cycles. The cumulative gas injection volume in the fifth cycle increased by about 25% than the first cycle, demonstrating a clear volume-increase effect of gas storage in the later stage. This increase of gas storage capacity was due to the decrease of condensate oil saturation from about 7% before storage construction to zero in the fifth cycle. The extraction of condensate oil provided more space for gas storage, with the storage volume increasing by about 7.5%.

The phase change characteristics under the actual temperature and operating pressure of gas storage were modeled in the PVT cell. The main controlling factors of phase change are temperature, pressure, and composition. The PVT cell can be considered as a pore in porous media, and the phase state experiment in the PVT cell reflects the phase state change in the gas storage. But the porous media in the actual gas storage make oil-gas contacting ratio uneven, so the extraction and evaporation of the injected gas to oil aren’t uniform. Some area may contact more injected gas and has more significant counter-evaporation. In addition, the capillary pressure makes the injection pressure higher than the pressure in the PVT cell.

There are some differences in dynamic phase state changes between the simulation experiment in this work and actual multi-cycle injection-production. The phase equilibrium state in the experiment and theoretical simulation is equivalent to retrograde evaporation of injected gas to condensate oil and phase change of condensate oil in one pore of the porous media. Compared with the actual gas storage, this is a highly microscopic experiment and phase state simulation, but it can reflect the essence of phase changes of condensate oil. But in gas storage, the mixed proportions between injected gas and condensate oil vary at different areas. After gas injection, the injected gas would take dominance around the injection well, and the mass ratio of injected gas to condensate oil would be very high. Therefore, in the initial stage of gas production of gas storage, the injected gas is mainly produced, and the gas-oil ratio would be greater than the experimental and theoretical simulation results.

The experimental method for condensate gas storage multi-cycle injection-production and phase equilibrium simulation model established in this study can simulate dynamic phase state changes during gas storage multi- cycle injection-production process, providing technical support for predicting phase state during condensate gas storage operation.

The experiments show that the injected gas has strong evaporation and extraction to the formation condensate oil, which are most significant in the first two cycles. Moreover, higher gas injection pressure is more favorable for evaporating and extracting condensate oil. At the high-pressure stage of each injection cycle (at the end of gas injection), the formation condensate oil was almost completely evaporated into gas phase. Multi-cycle injection-production can effectively improve condensate oil recovery and after five cycles of injection-production, compared with natural depletion, the condensate oil recovery increased by about 42%. The extraction of condensate oil after five injection-production cycles increased the volume of the gas storage. Compared with the first cycle, the gas injection volume in the fifth cycle increased by about 25% and storage volume increased by about 7.5%.

a—coefficient of intermolecular attraction, MPa·cm⁶/mol²;

b—volume correction coefficient, cm³/mol;

f_g,i—fugacity of i-component in the gas phase, MPa;

f_l,i—fugacity of i-component in the liquid phase, MPa;

i—the serial number of component;

j, k—No. of depletion depressurization times;

K_i—equilibrium constant of i-component in the gas and liquid phases;

K_i,k—equilibrium constant of i-component in the gas and liquid phases at the k-th constant volume depletion;

m—number of injection cycle;

n—total number of components of the produced fluid;

n_i—mole fraction of i-component substance in the oil-gas system, mol;

n_i(m)—mole fraction of i-component in the oil-gas system after the m-th cycle of gas injection, mol;

n_i(m-1)—mole fraction of i-component in the oil-gas system after the (m-1)th cycle of gas injection, mol;

n_inj(m)—mole fraction of the injected gas substance at the m-th cycle, mol;

n_l,k—mole fraction of liquid phase under equilibrium at the k-th constant volume depletion, %;

n_g,k—mole fraction of gas phase under the equilibrium at the k-th constant volume depletion, %;

N_p,j—amount of the produced fluid substance in the j-th constant volume depletion, mol;

N_p,k—amount of the cumulatively produced fluid after the k-th depressurization, mol;

N_p,k-1—amount of the cumulatively produced fluid after the k-1th depressurization, when k=1, N_p,0=0, mol;

p—pressure of hydrocarbon system, MPa;

p_a—pressure before gas injection in the m-th cycle, MPa;

p_f—original formation pressure, MPa;

p_h—pressure after gas injection in the m-th cycle, MPa;

p_k—formation pressure at the k-th constant volume depletion, MPa;

R—molar gas constant, MPa·cm³/(mol·K);

S_l,k—saturation of formation retrograde condensate oil after the k-th depressurization, %;

T—temperature of hydrocarbon system, K;

T_f—original formation temperature, K;

T_r—reduced temperature, dimensionless;

v—mole fraction of gas phase in the system under equilibrium, %;

V—specific volume, cm³/mol;

V_f—volume of 1 mol condensate gas under the original formation pressure, cm³;

x_i—mole fraction of i-component in the liquid phase, %;

y_i—mole fraction of i-component in the gas phase, %;

y_i,k—mole fraction of i-component in the produced fluid in k-th constant volume depletion, %;

z_i—mole fraction of i-component in the original produced fluid, %;

z_i,inj—mole fraction of i-component in the injected gas, %;

z_i,k—mole fraction of i-component in the remaining fluid at the k-th constant volume depletion, %;

Z_a(m)—compressibility factor of the equilibrium gas phase before gas injection at the m-th injection-production cycle;

Z_h(m)—compressibility factor of the equilibrium gas phase after gas injection at the m-th injection-production cycle;

Z_f—compressibility factor of gas phase under original formation pressure;

Z_l,k—compressibility factor of liquid phase in the k-th constant volume depletion depressurization;

Z_g,k—compressibility factor of gas phase at the k-th constant volume depletion;

α(T_r,ω)—temperature function, dimensionless;

ΔN_p,k—amount of the produced fluid in the k-th constant volume depletion, mol;

ω—acentric factor.