Study on Nonlinear Parameter Inversion and Numerical Simulation in Condensate Reservoirs

Abstract

The B6 metamorphic buried hill condensate gas reservoir exhibits a highly compact matrix, leading to a rapid decline in bottom-hole pressure during initial production. The minimal difference between formation and saturation pressures results in severe retrograde condensation, with multiphase flow further increasing resistance. Conventional numerical simulations often overestimate reservoir energy supply due to their failure to account for this additional resistance, leading to inaccuracies in bottom-hole pressure predictions and gas–oil ratio during history matching. To address these challenges, this study conducted research on nonlinear numerical simulation for buried hill condensate gas reservoirs and established a method for calculating a multiphase pressure sweep range based on the well testing theory. By correcting and fitting the pressure propagation boundaries with numerical simulation, the nonlinear flow parameters applicable to the B6 gas field were inversed. This study revealed that conventional Darcy flow is inadequate for predicting pressure propagation boundaries and that it is possible to reasonably characterize the pressure sweep range through nonlinear flow. This approach resulted in an improvement in the accuracy of historical matching for bottom-hole pressure and gas–oil ratio, which improve the historical fitting accuracy to 85%, providing valuable insights for the development of similar reservoirs.

1. Introduction

The B6 buried hill condensate reservoir is deeply buried with a compact pore-throat structure [1,2]. Due to the poor physical properties of the reservoir, additional resistance arises during the porous flow process, resulting in a fluid–solid interaction boundary-layer effect [3,4]. The application of conventional Darcy flow in numerical simulations fails to accurately predict the pressure propagation range, leading to an unrealistic distribution of condensate oil. Consequently, the simulation results often diverge substantially from actual production data, severely compromising the efficacy of history matching.

Numerous studies have demonstrated that nonlinear flow can effectively characterize the additional resistance encountered during the flow process caused by reservoir and fluid properties [5]. Blom [6] pointed out that, during the pressure depletion development of condensate gas reservoirs, the precipitation of condensate oil induces multiphase flow, which increases flow resistance. This necessitates the use of non-Darcy flow to characterize the permeability loss in the near-well region caused by reservoir contamination. Ding et al. [7] posited that the threshold pressure gradient (TPG) in tight gas reservoirs is dynamic, and they demonstrated through experiments that a decrease in formation pressure leads to a reduction in TPG. In recent years, research on nonlinear flow has primarily focused on deriving characterization equations for the nonlinear segment using mathematical methods and determining the threshold pressure gradient or nonlinear flow parameters through physical experiments [8,9,10]. However, Fan et al. [11] argued that experimental test parameters do not accurately reflect actual reservoir characteristics and proposed a nonlinear parameter inversion method based on genetic algorithms utilizing wellbore pressure test data. Nevmerzhitskiy [12] developed a theoretical one-dimensional single-phase flow model under different reservoir geometries; based on this, methods for characterizing nonlinear flow parameters were investigated.

Several scholars have conducted comprehensive studies on non-Darcy flow, including well testing and numerical simulations [13,14,15]. Wang et al. [16] developed a mathematical model for the threshold pressure gradient in tight reservoirs utilizing fractal theory, in which relationships between boundary-layer thickness, permeability, fluid viscosity, and the threshold pressure gradient were explored. In recent years, non-Darcy flow has garnered significant attention in the study of dual-media flow in fractured reservoir matrices [17,18,19]. Zhang et al. [20] employed component equations and the discrete fracture model (DFM) to investigate the impact of the threshold pressure gradient on deep condensate gas reservoirs containing natural fractures. Their study revealed that the threshold pressure gradient significantly slows the propagation speed of pressure towards the far end of the reservoir, reducing the pressure propagation speed by 55% compared to Darcy flow. However, for deep condensate gas reservoirs, nonlinear flow better characterizes the changes in flow resistance under different pressure gradients. Notably, this research did not consider the impact of nonlinear flow.

Recently, the phase behavior of fluids influenced by the high temperature and high pressure of the reservoirs has become increasingly complex with the increasing development of deep oil and gas reservoirs such as buried hills and shale. Consequently, more scholars have engaged in the study of compositional models [21,22,23]. Ma et al. [24] argued that the use of homogeneous models tends to overestimate the cumulative production of fluids in nanopores. Additionally, traditional equations of state often lead to inaccurate calculations of fluid density. Zhang et al. [25] explored the phase behavior within condensate gas reservoirs during cyclic gas injection and analyzed the phase transition mechanisms involved in the displacement of condensate oil by various pure gases. This included examining the impact of injected gases, such as CO₂ and N₂, on the phase behavior of the condensate oil. In the development of condensate gas reservoirs, the phenomenon of retrograde condensation occurs as the pressure drops, resulting in the presence of multiphase flow consisting of oil, gas, and water, which significantly impacts the fluid migration patterns, alters the flow resistance, and affects the extent of pressure propagation within the reservoir [26,27,28]. A performance prediction model for multiphase flow systems in condensate reservoirs, which incorporates the effects of condensate blockage, was proposed based on the similarity method [29]. Additionally, Guo et al. and Yang et al. [30,31] conducted studies on fractured gas reservoirs that focus on numerical simulation and gas injection limits, respectively. Results indicate that favorable development outcomes can be achieved when the permeability gradation in dual-porosity media is less than 15.

In summary, due to the tight nature of the reservoir in the B6 buried hill condensate gas field, it is essential to conduct nonlinear flow numerical simulations to achieve higher predictive accuracy. However, current research on nonlinear flow in condensate gas reservoirs is limited, with unclear extents of nonlinear effects and a lack of theoretical basis for selecting nonlinear parameters. In response to these challenges, this study undertakes nonlinear numerical simulation research for condensate gas reservoirs, proposing an analytical process for nonlinear parameter inversion in which the limitations of traditional models were addressed and the accuracy of historical matching for the gas–oil ratio and bottom-hole pressure were enhanced in typical wells of the B6 gas field.

2. Materials and Methods

This study employs a compositional model to conduct numerical simulations of condensate gas reservoirs. The model incorporates three phases (oil, gas, and water) and seven components. The assumptions of the model include isothermal flow and the neglect of gravitational effects. The reservoir’s porosity and permeability are considered homogeneous, and both fluid and rock are treated as slightly compressible. The detailed fluid phase behavior, flow control equations, and parameters are as follows.

2.1. Fluid Phase Characteristics

Based on the experimentally measured fluid property data, PVT matching was conducted for Well W4. The reservoir fluid was divided into six components for numerical model calculations. These components include N2-C1, C2+, C4+, C7+, C11+, and C21+. The corresponding components and their molar compositions are detailed in

Table 1. Model calculation of fluid components.

Component	Molar Mass	Molar Percentage (%)
N2-C1	17.49	65.99
CO2-C2-C3	34.67	19.01
C4-C6	75.39	4.55
C7-C10	111.93	5.33
C11-C20	195.64	3.93
C21-C80	378.64	1.18

.

Through PVT analysis, the saturation pressure, condensate gas density, condensate oil density, and gas–oil ratio for W4 were fitted to both calculated and experimental data to ensure the accuracy of fluid phase behavior in the numerical simulation study, as shown in

Table 2. Main fluid property parameter fitting.

Fitting Parameter	Experimental Measurement	Model Calculation
Dew point pressure, MPa	40.20	39.53
Gas-oil ratio, m3/m3 (0.1 MPa, 20 °C)	890.00	902.10
Formation gas density, g/cm3 (51.4 Mpa, 186 °C)	0.42	0.36
Condensate oil density, g/cm3 (0.1 Mpa, 20 °C)	0.80	0.80

. The P-T phase diagram for the B6 condensate gas reservoir (Figure 1) illustrates the fitted data, with dashed lines representing ISO liquid lines. During the pressure depletion development, the reservoir undergoes retrograde condensation, resulting in the continuous precipitation of condensate oil. When the reservoir pressure falls to the maximum retrograde condensation pressure, the condensate oil re-evaporates into the gas phase. Consequently, the liquid phase percentage initially increases and then decreases.

2.2. Numerical Simulation Methodology

For the flow in condensate gas reservoirs, individual fluid components coexist in both the gas and oil phases. For the fitted six components, multiphase multicomponent continuity equations are established for each component i. The equation for component i is as follows:

$$\nabla ({\displaystyle \frac{x_i{v}_g}{B_g}}+{\displaystyle \frac{y_i{v}_o}{B_o}})+q_i={\displaystyle \frac{\partial }{\partial t}}(\varphi z_i({\displaystyle \frac{s_{\mathrm{g}}}{B_g}}+{\displaystyle \frac{s_o}{B_o}}))$$

(1)

Due to the insolubility of formation fluid components in the aqueous phase, the continuity equation for the water phase is presented as Equation (2):

$$\nabla ({\displaystyle \frac{v_w}{B_w}})+q_w={\displaystyle \frac{\partial }{\partial t}}({\displaystyle \frac{\varphi s_{\mathrm{w}}}{B_w}})$$

(2)

The additional equation is as follows:

$$s_{\mathrm{g}}+s_{\mathrm{o}}+s_{\mathrm{w}}=1$$

(3)

$${\displaystyle \sum _{i=1}^6{x}_i}=1\hspace{1em}\hspace{1em}{\displaystyle \sum _{i=1}^6{y}_i}=1\hspace{1em}\hspace{1em}{\displaystyle \sum _{i=1}^6{z}_i}=1$$

(4)

$$z_i=L{x}_i+(1-L)y_i$$

(5)

where $x_i$, $y_i$, and $z_i$ represent the mole fractions of component i in the gas phase, liquid phase, and the overall system, respectively; $v_g$, $v_o$, and $v_w$ represent the percolation velocities of the gas phase, oil phase, and water phase, respectively; $s_g$, $s_o$, and $s_w$ represent the saturation of the gas phase, oil phase, and water phase, respectively; $B_g$, $B_o$, and $B_w$ represent the volume factors for the gas phase, oil phase, and water phase, respectively; $q_i$ and $q_w$ represent the source and sink terms for component i and the water phase, respectively; $\varphi$ represents the porosity; t represents time; and L represents the ratio of the molar quantity of the gas phase to the total molar quantity in the mixture system.

The state equations are described using the Peng–Robinson (P-R) equation [32], which predicts gas–liquid phase equilibrium and enhances the accuracy of liquid phase density calculations, as shown in Equation (6):

$$P={\displaystyle \frac{RT}{V-b_c}}-{\displaystyle \frac{a_c\alpha }{V(V+b_c)+b_c(V-b_c)}}$$

(6)

$$a_c=0.457235{\displaystyle \frac{R^2{T}_c^2}{P_c}}$$

(7)

$$b_c=0.077796{\displaystyle \frac{R{T}_c}{P_c}}$$

(8)

$$\alpha ={[1+(0.37464+1.54226\omega -0.26992{\omega }^2)(1-T_r^{0.5})]}^2$$

(9)

where P represents pressure; T represents absolute temperature; V represents the volume of the gas phase; R represents the gas constant; $P_c$ represents the critical pressure; $T_c$ represents the critical temperature; $T_r$ represents contrast temperature; and $\omega$ represents eccentricity factor.

Next, a numerical simulation study on nonlinear flow for low-permeability condensate gas reservoirs is conducted and compared with conventional Darcy flow to analyze the suitability of different flow laws. For Darcy flow, Equation (1) can be reformulated as follows:

$$\nabla (x_i{\displaystyle \frac{K{k}_{rg}}{{\mu }_g{B}_g}}\nabla P_g+y_i{\displaystyle \frac{K{k}_{ro}}{{\mu }_o{B}_o}}\nabla P_o)+q_i={\displaystyle \frac{\partial }{\partial t}}(\varphi z_i({\displaystyle \frac{s_{\mathrm{g}}}{B_g}}+{\displaystyle \frac{s_o}{B_o}}))$$

(10)

Yang et al. [33] developed a nonlinear flow continuity model based on the flow characteristics of low-permeability oil and gas reservoirs which simultaneously considers the minimum threshold pressure gradient and the effects of the nonlinear flow regime. It has been widely applied in the production practices of low-permeability oil and gas reservoirs. The curve intersects the x-axis at the point (1 − a)/b, where the intersection intercept represents the magnitude of the apparent starting pressure gradient. Furthermore, the selection of different a and b parameters can alter the shape of the nonlinear curve’s bend. The specific form of the equation is given by Equation (11):

$$v={\displaystyle \frac{K}{\mu }}\nabla P(1-{\displaystyle \frac{1}{a+b\nabla P}})$$

(11)

where K represents the absolute permeability; $k_{rg}$, $k_{ro}$, and $k_{rw}$ represent the relative permeabilities of the gas phase, oil phase, and water phase, respectively; ${\mu }_g$, ${\mu }_o$, and ${\mu }_w$ represent the viscosities of the gas phase, oil phase, and water phase, respectively; a is the influence factor of the nonlinear seepage curve, with a > 0; and b is the influence factor of the starting pressure gradient.

In this paper, Petrel Re 2024 software, which is a numerical reservoir simulator, was used to solve Equations (10) and (11). An equation of state equilibrium property package (PVTi) was used to calculate fluid phase behaviors and thermodynamics properties based on Peng–Robinson EOS.

2.3. Solution of DOI for Three-Phase Flow

For tight gas reservoirs, the presence of the TPG causes the pressure derivative response curve to exhibit an upward trend in the final flow stage. As the TPG increases, the slope of the curve gradually becomes steeper [34,35]. From the pressure response curve of Well W4 (Figure 2), it can be observed that due to the presence of natural fractures, the pressure derivative displays a concave curve characteristic. Additionally, in the final flow stage, the curve deviates from the 0.5 horizontal line and shows an upward trend, reflecting the characteristics of nonlinear flow.

Behmanesh et al. [36] developed a method for calculating the drawdown pressure boundary (DOI) in single-phase reservoirs based on control Equation (12). Their research indicated that the pressure prediction propagation boundary has a good linear relationship with the square root of the diffusivity coefficient and time. For a constant bottom-hole flowing pressure model, the DOI calculation is given in Equation (14):

$${\displaystyle \frac{{\partial }^{2}p}{\partial y^2}}+c{({\displaystyle \frac{\partial p}{\partial y}})}^2={\displaystyle \frac{1}{\eta }}{\displaystyle \frac{\partial p}{\partial t}}$$

(12)

$$\eta ={\displaystyle \frac{\gamma k}{\phi \mu c_t}}$$

(13)

$$y=\sqrt{6\eta t}$$

(14)

where $\gamma$ represents the unit coefficient; $\eta$ represents the single-phase pressure gradient coefficient; and $c_t$ represents the overall compressibility coefficient.

However, in the development of condensate gas reservoirs, the retrograde condensation effect leads to the presence of oil, gas, and water three-phase flow. The single-phase diffusivity coefficient used in Equation (14) does not account for the interactions among the multiphase fluids. Therefore, a multiphase diffusivity coefficient is introduced to more accurately predict the pressure propagation boundary [37].

$${\eta }_t={\displaystyle \frac{\beta k_m[{\rho }_{ostd}(\frac{k_{ro}}{{\mu }_o{B}_o}+\frac{R_v{k}_{ro}}{{\mu }_o{B}_o})+\frac{{\rho }_{gstd}{k}_{rg}}{{\mu }_g{B}_g}+\frac{{\rho }_{wstd}{k}_{rw}}{{\mu }_w{B}_w}]}{{\phi }_m[\frac{{\rho }_{gstd}(c_r+c_g)S_g}{B_g}+{\rho }_{ostd}(\frac{(c_r+c_g)R_v{S}_g}{B_g}+\frac{(c_r+c_o)S_o}{B_o})+\frac{(c_r+c_w){\rho }_{wstd}{S}_w}{B_w}]}}$$

(15)

3. Results

In this section, we first employed the model established in Section 2.2 to perform a quantitative analysis of the nonlinear flow characteristics and conduct a detailed comparison with conventional Darcy flow. This included examining pressure variations and condensate oil distribution patterns over different production periods. Subsequently, a sensitivity analysis of various nonlinear parameters was conducted. Finally, using the well testing DOI analysis theory from Section 2.3, the pressure propagation patterns in the B6 gas reservoir were predicted. By matching these predictions with numerical simulation results, the method was then utilized to carry out the nonlinear parameter inversion study.

A depletion development mechanism model for Well W4 was established using the actual reservoir and fluid parameters of the B6 gas reservoir. The condensate gas phase parameters were derived from the fitted results in Section 2.1. Other key parameters for the numerical simulation are presented in

Table 3. Main parameters for the model calculation.

Parameter	Value
Initial formation pressure (MPa)	51.4
Initial formation temperature (°C)	186
Porosity (%)	4.1
Permeability (mD)	0.1
Gas volume factor (m3/m3)	0.0047
Formation water volume factor (m3/m3)	0.35
Bottom-hole pressure (MPa)	30
Nonlinear impact factor (dimensionless)	0.5
Threshold pressure gradient factor (MPa−1)	10

.

In this section, a comparative analysis was conducted between Darcy flow and nonlinear flow regarding the pressure propagation range and their impact on the retrograde condensation behavior in the condensate gas reservoir. Additionally, a sensitivity analysis was performed for different nonlinear parameters and permeabilities. The specific results are as follows.

3.1. Comparison of Darcy and Nonlinear Flow

Figure 3 and Figure 4 illustrate the variations in the pressure distribution under the Darcy flow and nonlinear flow modes, respectively. In the case of Darcy flow (Figure 3), the pressure field shows that, due to the absence of additional flow resistance typically present in low-permeability reservoirs, there is no significant pressure drop region around the production well. As production continues, the pressure across the entire reservoir tends to level out and maintain a uniform distribution. In contrast, the pressure propagation range under nonlinear flow exhibits a distinct boundary (Figure 4). This phenomenon occurs because the presence of nonlinear flow introduces increasing flow resistance to fluid migration under smaller displacement pressure gradients. Consequently, the pressure propagation rate significantly diminishes at the boundary while the near-wellbore region remains unaffected. This results in a substantial pressure drop around the production well, whereas the pressure in the far-field region remains close to the original reservoir conditions and is not utilized.

Figure 5 illustrates the bottom-hole pressure profiles for Darcy and nonlinear flow at various production times. At the initial development stage, the bottom-hole pressure remains at 40 MPa for Darcy flow while non-Darcy flow drops to 35 MPa. The near-wellbore pressure for Darcy flow is higher compared to nonlinear flow while the pressure in the far-field region is lower (the far-field pressure for nonlinear flow remains at the original reservoir pressure). Additionally, the pressure decline for Darcy flow exhibits a linear trend.

From the condensate oil precipitation perspective, it can be observed that Darcy flow—due to not considering the additional resistance generated by the fluid flow that predicts an optimistic pressure maintenance level near the wellbore, which results in a sufficient energy supply in the near-well region—prevents condensate oil from precipitating during the first five years of production (Figure 6a). Secondly, Darcy flow prematurely utilizes the reservoir energy from the far-field region and the overall pressure falls below the saturation pressure after 20 years of production, leading to the precipitation of condensate oil throughout the entire reservoir area (Figure 6b,c). For nonlinear flow, the pressure propagation range can be more accurately predicted. In the early development stage, a significant amount of condensate oil precipitates in the near-well region (Figure 7a), causing an increase in the gas–oil ratio. As production time progresses, although the precipitation range of condensate oil gradually expands, the rate of increase slows down, and no condensate oil precipitates in the far-field region (Figure 7b,c). Therefore, nonlinear flow allows for a more precise quantitative characterization of the utilized range in low-permeability buried hill reservoirs.

3.2. Impact of Nonlinear Parameter

The nonlinear influence factor a is one of the key parameters determining the shape of the nonlinear segment in the motion equation. Figure 8 and Figure 9 compare the effects of different nonlinear factors on the pressure propagation and the precipitation range of condensate oil. The results indicate that a smaller a value corresponds to a stronger degree of nonlinearity, resulting in greater flow resistance and a pressure propagation range more confined to the vicinity of the production well. Conversely, as the a value increases, the characteristics of nonlinear flow increasingly resemble those of Darcy flow, with the pressure propagation range expanding and the pressure boundary becoming less distinct (Figure 8). From the perspective of condensate oil distribution, although a larger a value results in a wider pressure propagation range, the pressure in the far-field region does not drop below the saturation pressure. Therefore, the precipitation range of condensate oil is the largest when a = 0.5.

Figure 10 compares the gas–oil ratio variation trends for Darcy flow and three different nonlinear flow scenarios. From the production dynamics perspective, the GOR for Darcy flow remains stable and does not increase over the first 15 years, which significantly deviates from the actual production behavior of the condensate gas reservoir shown in Figure 1. The insufficient energy supply of nonlinear flow, which results in a significant pressure drop near the wellbore, leads to a rapid increase in the gas–oil ratio within a short period. As production continues, the rate of increase in the GOR gradually slows down. Additionally, because smaller nonlinear parameters result in greater flow resistance, the retrograde condensation phenomenon near the wellbore becomes more pronounced, shortening the stabilization period of the GOR and accelerating its increase.

3.3. Inversion of Nonlinear Flow Parameters

The pressure propagation distance at different production times was calculated using the actual parameters of the B6 gas reservoir. As shown in Figure 11, the pressure propagation speed is relatively fast during the initial development phase and then gradually slows down. After one year of production, the pressure boundary reaches 1085 m and extends to 1535 m after two years. In Section 2, a numerical simulation study of nonlinear flow and pressure propagation range prediction was conducted. By setting different nonlinear parameters for the condensate gas reservoir, the numerical simulation results were fitted to the DOI predicted values until a successful alignment was achieved. Through this method, the nonlinear flow parameter for the low-permeability condensate gas reservoir in the B6 buried hill was determined to be a = 0.75.

4. Field Application

The B6 condensate gas reservoir exhibits complex fluid phase behavior, characterized by a small pressure difference between formation pressure and saturation pressure. When the bottom-hole pressure drops below the saturation pressure, the phenomenon of retrograde condensation causes a significant amount of condensate oil to precipitate in the near-well region, leading to a rapid increase in the gas–oil ratio. W4 is a production well that exemplifies the typical characteristics of retrograde condensation. Figure 12 illustrates the well location of the B6 gas reservoir testing area and the production dynamic curves of W4 over the first three years of production. The data indicate that the reservoir pressure remains stable only during the initial phase of development. However, due to poor reservoir permeability and insufficient energy supply, the bottom-hole flowing pressure starts to decline six months after production begins. Consequently, the GOR increases from 1000 m³/m³ to 1500 m³/m³ within one year.

In applying the nonlinear flow numerical simulation method to the B6 condensate gas reservoir, a history matching study for Well W4 was conducted using the nonlinear parameters obtained through inversion in Section 3. The production scheme was set to constant oil production. Figure 13 compares the history matching results between traditional numerical simulation software and the nonlinear flow numerical simulation method. It can be observed that the traditional numerical simulation method predicts a higher bottom-hole flowing pressure and a slower increase in the gas–oil ratio, with retrograde condensation only occurring after 1.5 years of production. This contradicts actual production dynamics. In contrast, the nonlinear numerical simulation method achieves a fitting accuracy of over 85%, confirming the existence of nonlinear flow and the reasonableness of the parameter fitting. Therefore, in the subsequent development of the B6 condensate gas reservoir, the design of a reasonable well pattern and spacing should fully consider the impact of nonlinear flow.

5. Discussion

In the early development stage of production wells in the B6 buried hill condensate gas field, a rapid decline in bottom-hole pressure and a sharp increase in the gas–oil ratio were observed, reflecting the characteristics of low-permeability reservoir development. Due to the dense nature of the reservoir’s porosity and permeability, the emergence of multiphase flow after condensate dropout further exacerbates flow resistance. Although nonlinear flow was often employed in the study of unconventional reservoirs, there has been limited research specifically targeting buried hill condensate gas reservoirs. Therefore, this paper undertakes research on nonlinear flow in condensate gas reservoirs and conducts an in-depth comparative analysis with traditional models.

Darcy flow tends to overestimate the energy supply of the reservoir, leading to a uniform pressure decline across the entire field as production progresses. This results in an initially high pressure near the wellbore during the early stages of development (Figure 5a), which results in no significant retrograde condensation phenomena (Figure 6a), contradicting the actual production dynamics, as shown by the blue line in Figure 13. In contrast, the nonlinear model reveals that pressure depletion is confined to the near-well region, offering a more realistic depiction of reservoir pressure maintenance (Figure 5b). This study successfully enhances the accuracy of historical matching, as demonstrated by the red line in Figure 13. Moreover, most current studies derive the parameters of nonlinear equations through physical simulation experiments, which not only lack a solid theoretical foundation but also involve high experimental costs. Consequently, this paper introduces a method for nonlinear parameter inversion by utilizing nonlinear numerical simulation results and the well testing theory, thereby addressing the scientific challenges in nonlinear parameter selection.

The research primarily focuses on the actual data from Well W4 in the B6 gas field. However, as more development wells are put into production in the B6 gas field, with each well encountering different reservoir physical properties, future work should consider the establishment of a nonlinear zonation model, which would allow for a more accurate representation of the actual reservoir heterogeneity by characterizing nonlinear parameters in different zones.

6. Conclusions

This paper conducted a study on nonlinear flow numerical simulation methods and pressure propagation boundary prediction. It provided a detailed comparison between Darcy flow and nonlinear flow in terms of pressure and condensate oil distribution patterns, inverted the nonlinear flow parameters for the B6 condensate gas reservoir, and achieved history matching for the production dynamics of Well W4. The specific conclusions are as follows:

(1)

For the buried hill condensate gas reservoir, Darcy flow overestimates the near-well pressure maintenance level, resulting in low accuracy in production dynamics fitting. Compared to Darcy flow, nonlinear flow can more reasonably depict the pressure propagation boundary and accurately predict the pressure spread patterns.

(2)

The larger the nonlinear parameter, the smaller the flow resistance, making the fluid flow closer to Darcy flow. This results in a weaker retrograde condensation phenomenon, a longer single-phase flow period, and a slower increase in the gas–oil ratio.

(3)

A method for predicting the pressure propagation range in three-phase flow was established. By fitting the DOI predicted values with the numerical simulation results, the nonlinear flow parameter a = 0.75 suitable for the B6 gas reservoir was inverted, achieving a history matching accuracy of 85% for Well W4.