1. Introduction
During the development of gas condensate reservoirs using the pressure depletion approach [
1], a significant pressure drop occurs around the wellbore, leading to retrograde condensation of reservoir fluids. Retrograde condensation is a phenomenon that occurs in natural gas reservoirs when the pressure within the reservoir decreases to a point where the gas reaches its dewpoint. At dewpoint, the gas starts to condense into a liquid phase as pressure continuously decreases. This retrograde condensation near the wellbore causes condensate blockage and a rapid decline in gas well productivity [
2]. To effectively develop condensate gas reservoirs, it is crucial to accurately describe the phase behavior of the reservoir fluid over a wide P-T-x (i.e., pressure, temperature, and composition) range using equation of state (EOS) models. EOS models can be used to estimate the extent of retrograde condensation and its evolution over the production period, both around the wellbore and in the reservoir. Furthermore, the same EOS model can also be used for wellbore fluid flow and surface facility design calculations [
3].
When a pressure drop occurs in a gas condensate reservoir, starting from the production well and gradually reaching the far-end boundary of the single well control range, the reservoir pressure will gradually decrease until it reaches the dewpoint pressure of the reservoir fluid [
4]. Consequently, condensate oil will start to appear and accumulate in the pore space throughout the entire reservoir. As the condensate saturation in the pore space reaches or exceeds the residual oil saturation (or critical oil flowing saturation), the condensate oil will begin to flow towards the production well. This leads to a rapid increase in liquid saturation around the production well and the formation of blockages in the gas seepage channels near the wellbore [
5,
6]. These blockages have a significant impact on the productivity of gas wells and the overall development efficiency of the gas condensate reservoir [
7,
8].
At present, the QS gas condensate reservoir is in its early development stage. Therefore, it is vital to accurately determine the properties of the reservoir fluid and assess the extent of retrograde condensation. Understanding the condensate saturation distribution with respect to time and space within the reservoir is essential for planning and implementing effective strategies for the future development of the QS gas condensate reservoir.
Understanding the complexity of a gas condensate reservoir undergoing either pressure depletion or gas recycling development processes requires the use of compositional reservoir simulation techniques. These techniques help model different production scenarios and optimize the production plan [
9,
10,
11]. Compositional reservoir simulation models are able to predict well performance, pressure, and condensate/gas saturation distribution during the development process of gas condensate reservoirs [
12]. For severe condensate blockage, gas lift and wax deposition in the wellbore also needs to be considered [
13]. This information is extremely valuable for evaluating the performance of single wells or the entire field in a gas condensate reservoir.
However, it is important to note that the modeling process using compositional reservoir simulators can be quite time-consuming [
14,
15]. This is because it involves numerically solving systems of nonlinear differential flow equations and coupled phase equilibrium calculations simultaneously [
16,
17]. Additionally, an equation of state (EOS) model [
18,
19] is used to solve phase equilibrium and fluid PVT (pressure-volume-temperature) properties during the simulation [
20,
21]. To ensure accurate representation of reservoir fluid properties, the EOS model needs to be tuned based on experimental PVT data [
22,
23,
24,
25,
26].
Recently, machine learning models have been applied to interpret the behavior of gas condensate reservoirs. Ghaffarian et al. [
4] developed an optimal multi-layer perceptron configuration of an artificial neural network (ANN) model using build-up well testing data for gas condensate reservoir model identification. Alakeely and Horne [
27] used customized deep-learning algorithms to forecast well liquid and multiphase restricted flow rates using wellhead surface measurements and demonstrated application of their algorithms to real field data. These models offer new solutions for modeling the underlying physical relationships of multiphase flow using incomplete knowledge [
4,
27,
28].
In this study, a series of detailed PVT experiments were conducted on a sample of QS gas condensate reservoir fluid. Through the process of tuning the EOS model using the gas condensate PVT data, a general procedure and workflow specifically for gas condensate reservoirs was developed. This allowed us to accurately predict the phase envelope and quality lines of the QS gas condensate reservoir fluid, providing a rough estimation of the extent of retrograde condensation during the pressure-depletion development process. Furthermore, the tuned EOS model was used in a commercial compositional reservoir simulator to calculate the distribution of condensate oil saturation around both vertical and horizontal wells, as well as within the reservoir itself. This application of the EOS model and compositional simulator helped us obtain accurate information about the condensate oil saturation in different areas of the reservoir.
3. EOS Tuning and the Extent of Retrograde Condensation Evaluation
Based on the provided experimental data (
Table 1,
Table 2,
Table 3 and
Table 4), a proposed workflow is depicted in
Figure 2 to fit the PVT data and obtain accurate EOS parameters representing QS gas condensate fluid. Reservoir fluid characterization involves a comprehensive process of identifying optimized EOS parameters that can effectively represent the PVT and phase behavior of the target reservoir fluid. This is achieved by minimizing the number of pseudo-components, which describe the properties of the C7+ group, based on the experimental composition data through a series of component splitting and lumping operations (
Figure 2).
In
Figure 2, the reservoir fluid characterization process is divided into four main steps: (1) Obtaining a detailed composition distribution, either from experimental data or distribution models; (2) calculating parameters for single carbon number (SCN) components; (3) lumping SCN components into several pseudo-components; (4) EOS tuning to determine the optimized parameters for the pseudo-components. This workflow aims to refine the representation of the QS gas condensate fluid by accurately characterizing pseudo-components and corresponding EOS parameters.
For example, when C7+ or C11+ components are grouped as a single component in a PVT report, in order to obtain accurate EOS simulation results, it is often necessary to split a single C7+ group using an appropriate probability model. This allows us to obtain a detailed distribution of the single carbon number (SCN) group. Then, one can select an appropriate method to determine the EOS parameters of the SCN component after splitting. In the present study, once the SCN group distribution and its EOS parameters were clearly defined, the mixing rules were used to lump the SCN components into several pseudo-components. This helped reduce the total number of components in the EOS model.
After lumping, the reservoir fluid model with a few pseudo-components representing the C7+ fraction was tuned against PVT experimental data. This tuning process improved the EOS prediction performance. During the tuning process, the EOS parameters of the pseudo-components, volume shift parameters, and binary interaction parameters were adjusted based on the experimental PVT data.
In this study, the Whitson’s method [
22,
23,
24] was selected for the splitting of the C7+ component to obtain the detailed distribution of SCN components. The Kesler-Lee method [
24] was used for calculating single-carbon group EOS parameters. The Newley-Merrill’s method [
25] combined with Hong’s mixing rule was adopted for SCN component lumping [
29]. The obtained EOS model parameters are shown in
Table 5 (columns indicated by ‘After EOS tuning’).
The EOS parameters (
Table 5, columns indicated by ‘Before EOS tuning’) without PVT fitting were used to calculate the phase diagram of QS gas condensate (
Figure 3), and it was found that the calculated phase envelope showed a large gap with the experimental saturation pressure.
Figure 3 indicates that the EOS parameters, before tuning against experimental data, are unable to represent the correct phase behavior of the QS gas condensate reservoir.
Regarding PVT fitting, there may not be a universal standard procedure that can be applied to all kinds of reservoir fluids [
26]. In this study, the EOS parameters of the PC1-PC4 pseudo-components were selected as adjustable parameters. These parameters were used to fit the EOS-calculated phase envelopes to the experimental saturation data.
During the initial stage of saturation pressure fitting process, it was observed that the calculated saturation pressure curve was noticeably lower than the experimental saturation pressure (as shown in
Figure 3). To address this issue, the critical temperature of PC1-PC4 components was adjusted appropriately. Increasing the critical temperature of the pseudo-component expanded the gas-liquid two-phase region, thereby reducing the discrepancy between the EOS modeling results and the experimental data.
However, it is important to note that for a specific reservoir fluid, the critical temperature (Tc) of each component has a specific correlation with its critical pressure (Pc), acentric factor (ω) and molecular weight (Mw). Therefore, when the critical temperature changes, other variables such as critical pressure, acentric factor, and molecular weight may also need to be adjusted accordingly. In this study, the empirical correlations between critical temperature and critical pressure and acentric factor and molecular weight were determined firstly based on the data provided in
Table 5 (specifically the columns labeled ‘Before EOS tuning’). Additionally, the other parameters associated with the change in critical temperature were obtained by fitting a power function.
By observing the data trend in
Table 5 (specifically the columns labeled ‘Before EOS tuning’) and excluding some components with poor regularity (such as CO
2, C
1, N
2, etc., the lightweight components, and PC
3 and PC
4, the heaviest components), the data for C
3 through to PC
2 components were selected in
Table 5 as the original data for fitting the relationship between Tc and other EOS parameters (Pc, Mw, ω). The power function
was used for fitting, where
Y represents individual EOS parameters among Pc, Mw, and ω for pseudo-components (PC1 to PC4),
X represents Tc, and a and b are undetermined parameters (as shown in
Table 6). As a result, the relationship between EOS parameters and critical temperature for QS gas condensate reservoir fluid samples was obtained, and is shown in
Figure 4.
The correlation between Tc and other EOS parameters (Pc, Mw, ω) presented in
Figure 4 and
Table 6 was demonstrated during the saturation pressure fitting process. The experimental saturation pressure was adjusted through repeated calculations by increasing Tc to a certain proportion (not exceeding 15%). The fitting process is illustrated in
Figure 5a, and the final results are presented in
Figure 5b.
Figure 5a displays the calculated results of the QS gas condensate phase envelope when Tc is increased by different percentages. The corresponding parameters, such as Pc, Mw, and ω, are obtained from the Equation (1). As the value of Tc gradually increases, the saturation pressure curve shifts upwards on the P-T phase diagram. Eventually, when Tc reaches 1.12 times the values listed in
Table 5 for the pseudo-components, the best fitting effect for the saturation pressure is achieved, as shown in
Figure 5b. It is evident that the calculated results of the phase envelope then align closely with the experimental saturation pressure data after the tuning of EOS parameters for the pseudo-components. The obtained EOS parameters are shown in
Table 5, labeled as ‘After EOS tuning’.
The EOS parameters in
Table 5 (labeled as ‘After EOS tuning’) were employed to simulate the CCE and CVD experiments using an in-house PVT package [
21,
26,
30]. The average error between the theoretical calculations and experimental CCE data was approximately 1.14% at three different temperatures, as depicted in
Figure 6.
Figure 7 shows that the EOS model-calculated liquid volumes at different pressure levels in the CVD experiment agree well with experimental CVD data. Volume shift parameters were tuned during the CCE and CVD fitting processes. Through comparison between EOS modeling and the PVT data (both CCE and CVD data), it is evident that the EOS parameters presented in
Table 5 can provide an accurate representation of the saturation pressure (
Figure 5) and PVT properties (
Figure 5 and
Figure 6) for the QS gas condensate fluid system.
As a result, the accurate phase envelope and the quality lines distribution within the two-phase region of QS gas condensate were calculated using the EOS model (
Figure 8a), in which PR-EOS [
18] and Michelsen’s phase envelope tracing algorithm [
31] were used for calculating the phase envelope and quality lines. In
Figure 8b, the pressure and temperature path of the reservoir fluid in the development of the QS gas condensate reservoir is depicted. Within this specific pressure and temperature region, it was observed that the maximum amount of liquid saturation does not exceed 3%. This information suggests that the reservoir fluid remains predominantly in the gaseous phase, with only a small fraction of liquid present, even under conditions where condensation may occur (
Figure 8). Comparing the initial phase envelope obtained in
Figure 3 with the results in
Figure 8, it is obvious that the fluid characterization procedure depicted in
Figure 2 is suitable for QS gas condensate reservoirs, in which natural gas contains a small fraction of condensate oil.
4. Single-Well Compositional Reservoir Simulation
Using the production data and reservoir geological information from the QS well area, single-well compositional reservoir simulation models were developed using CMG GEM 2020.10 software. These models considered both vertical and horizontal well cases to predict the distribution of condensate oil saturation within the reservoir and around the wellbore during the pressure depletion development process. The parameters that were used within these single-well compositional reservoir simulation models are shown in
Table 7.
Furthermore, the oil-water and gas-oil relative permeability curves (
Figure 9) were experimentally determined using cores extracted from the QS well area. The connate water saturation was approximately 34.3%, indicating that the initial water saturation of reservoir was high. Additionally, the residual oil saturation was estimated to be around 27.2%, indicating high residual oil saturation. Indeed, these high connate water and residual oil saturations suggested that the gas reservoir is susceptible to liquid blockage. The presence of significant amounts of connate water and residual oil can hinder the flow of gas through the reservoir, potentially leading to reduced production rates and decreased overall reservoir performance.
During the reservoir simulation process, the production data from the target vertical and horizontal wells were used to perform a historical match with the corresponding simulation models. This matching process ensured that the simulation models accurately represented the actual reservoir performance. The results of this historical match are depicted in
Figure 10 (for the vertical well) and
Figure 11 (for the horizontal well). Once the production history match was achieved, the simulation models were considered reliable for predicting the condensate oil saturation distribution around the wellbore and within the reservoir, as well as the extent of retrograde condensation, over a specific period of production time. These compositional simulation models provided valuable insights into the behavior and dynamics of the condensate reservoir during production.
Figure 12 shows the evolution of condensate saturation distribution around the vertical well over a specific period of production time under the current production rate.
Figure 12 displays four images, arranged from left to right, showcasing the condensate saturation data of the third layer in the vertical well simulation model. These images represent the condensate saturation distribution around the same wellbore at four different production dates: 1 April 2022, 1 July 2022, 1 January 2023, and 1 May 2023.
Figure 12 reveals that within the entire control range of the vertical well, as production continued, the retrograde condensation phenomenon occurred in the reservoir; the extent of retrograde condensation steadily increased over time. Notably, the condensate saturation in the near-well zone, which encompasses a radius of 18 m, exceeded the upper limit (0.5%) indicated by the color bar. In fact, the maximum value of condensate saturation in this zone was seen to reach as high as 30%. Even during the early stages of gas well operation, the condensate saturation content in the near-well zone was significant, surpassing 10%.
Figure 13 illustrates the progression of high condensate saturation in the near-well area over the course of gas production. From April 2022 to January 2023, over a span of nine months, the contour line representing a condensate saturation of 10% expanded by approximately 5 m in its radius from the well’s center. Additionally, the radius of the contour line, indicating a condensate saturation of 10% in the near-well area, increased from around 12 m to 17 m (
Figure 13a–c). Production continued until May 2023 (
Figure 13d), resulting in further expansion of the high condensate saturation region. By this time, the radius of the contour line representing a condensate saturation of 10% in the near-well area had extended to around 18 m (
Figure 13d).
Furthermore, the contour line indicating 30% condensate oil saturation around the wellbore is located approximately 5~6 m from the well’s center (
Figure 13). This indicates that despite the relatively mild extent of retrograde condensation within the entire control range of a single well, the condensate contamination in the near-well area remained significant. It is worth noting that the numerical simulation results obtained for this vertical well aligned closely with the calculation results reported by Le et al. [
32] and Zou et al. [
33]. Le et al. [
32] proposed that the maximum extent of retrograde condensation occurs within a range of between 1.6 to 3.2 m around the wellbore. On the other hand, Zou et al. [
33] put forward the notion that within a 20 m range around the wellbore, a notable retrograde condensation phenomenon can be anticipated. Additionally, they identified the critical condensate flowing saturation point to be located at a distance of 7.3 m away from the center of the well. These findings from Le et al. [
32] and Zou et al. [
33] provide valuable insights into the behavior of retrograde condensation and its spatial distribution around the wellbore. These observations highlight the dynamic nature of condensate saturation and the increasing influence of production on its distribution in the near-well area. Additionally, the gas condensate fluid characterization procedure depicted in
Figure 2 provides a solid foundation for reservoir fluid properties and phase behavior calculation during compositional reservoir simulation.
Figure 14 displays the rising trend of condensate saturation at different production times in the reservoir after averaging the condensate saturation of all of the grids in the reservoir simulation model. It reveals that, for vertical wells, the condensate saturation in the QS well area exhibits an approximate linear increase with production time. The average monthly rise rate of condensate saturation is approximately 0.018% (equivalent to 0.22% per year). Overall, the extent and trend of retrograde condensation are relatively mild. on average. However, it is crucial to pay close attention to the extent of condensate accumulation near the wellbore, as depicted in
Figure 12 and
Figure 13. These figures highlight significant condensate build-up in the near-well region, emphasizing the need for appropriate measures to manage and mitigate the effects of retrograde condensation in this region for vertical gas wells.
In the horizontal well model, the simulation time was significantly increased compared to the vertical well model due to the larger grid size and increased model complexity caused by the addition of fractures. However, the simulation results displayed a pronounced retrograde condensation phenomenon near the well in the horizontal well model. To evaluate the extent of retrograde condensation around the horizontal well, two dates in the well production history were selected (1 February 2023 and 1 May 2023) for comparison purposes. These specific dates captured the change in spatial distribution of condensate oil over a span of approximately three months.
Figure 14 and
Figure 15 depict the spatial distribution of condensate oil saturation around the horizontal well within the reservoir during these selected time intervals.
Figure 15 displays the condensate saturation cloud map within the horizontal well’s control area on 1 February and 1 May 2023, respectively. After approximately 3 months of production, the average condensate saturation changed from 0.135% (
Figure 15a) to 0.271% (
Figure 15b). The average monthly rise rate of condensate saturation for the horizontal well was approximately 0.045% per month (equivalent to 0.54% per year), which is faster than that of the vertical well.
Figure 16 indicates a significant change in the condensate saturation contour around the horizontal well after a 3-month production period. In February 2023, when the contour line of condensate saturation reached approximately 0.3%, it covered an area near the well that spanned approximately 912 m in length and 100 m in width (
Figure 16a).
By May 2023, the contour line indicating a condensate saturation of 0.3% had extended to an area near the well that spanned approximately 970 m in length and 310 m in width. This represents a spread area that is 3.3 times larger compared to the previous measurements (as shown in
Figure 16a). Furthermore, unlike the vertical well, the horizontal well model demonstrated a maximum condensate saturation of no more than 1.5%, which is significantly lower than the maximum condensate saturation (i.e., which exceeds 30%) observed in the vertical well model. The main reasons for this are that firstly, the production history of the horizontal well is relatively short compared to the vertical well, and secondly, due to the presence of fractures around horizontal wells, there is good flow conductivity and multiple fluid discharge channels. As a result, it is difficult for condensate oil to accumulate to high saturation levels around the horizontal well.
5. Conclusions
Through the research conducted in this paper, the following understandings have been formed:
(1) This paper establishes a comprehensive workflow and methodology for determining the extent of retrograde condensation near the well in gas condensate reservoirs with a depletion development mode. This is achieved through a series of experiments and theoretical calculations, utilizing PVT experimental data, EOS tuning, field production data, and compositional reservoir simulation. This methodology enables the quantitative description of the distribution pattern of condensate oil saturation with respect to both time and space in the near-wellbore area of gas condensate production wells. Additionally, it provides a valuable reference and basis for making adjustments to the production system of condensate gas wells.
(2) The PVT experiments conducted in this study have revealed that the difference between the reservoir pressure and the saturation pressure of the QS gas condensate reservoir is relatively small, at approximately 2.9 MPa. As a result, during the production process, pressure reduction will inevitably lead to the occurrence of the retrograde condensation phenomenon within the reservoir. Based on the analysis of the PVT experiment results and P-T phase diagram, it has been determined that the maximum condensate saturation remains below 3% within the actual pressure and temperature range. This estimation considers the P-T conditions of the reservoir, wellbore, and surface separator, without taking into account the fluid flow. Consequently, the presence of condensate contamination within the QS gas condensate reservoir is minimal.
(3) In the case of vertical wells, the condensate saturation around the wellbore tends to be higher, but the average condensate saturation is relatively low. The average increase rate in condensate saturation is approximately 0.22% per year. On the other hand, horizontal wells exhibit the opposite pattern, with higher average condensate saturation and a higher rate of increase (around 0.54% per year). Furthermore, the maximum value of condensate saturation near the wellbore of the horizontal wells is 1.5%, which is significantly lower than that of 30% for vertical wells. This indicates that horizontal wells have better flow conductivity, making it difficult to form a high saturation region near the wellbore. Therefore, for the QS well area, it is anticipated that the condensate contamination of vertical wells may become more severe in the middle and later stages of reservoir development. It is advisable to consider decontamination and treatment methods for addressing retrograde condensation blockage in vertical wells in advance.
(4) Currently, the overall extent of retrograde condensation in the QS condensate gas reservoir is relatively low. In the near-wellbore region, considering the residual oil saturation based on the oil-gas relative permeability curve (as shown in
Figure 9b), the critical flow radius of condensate oil in the vertical well is estimated to be within 6 m around the wellbore. This region corresponds to the coverage area where the condensate saturation exceeds 27% (as shown in
Figure 13). The numerical simulation results obtained in this study agree with the research conclusions of Zou et al. [
33]. Given that the maximum condensate saturation near the well is significantly lower than the residual oil saturation determined from the oil-gas relative permeability curve, it can be inferred that there is no significant condensate oil flow occurring in the current production process of the horizontal well.