Introduction

Unconventional natural gas, particularly shale gas, has assumed a progressively critical role in China’s energy matrix, driven by strategic imperatives for energy security1. Major exploration breakthroughs in basins such as Sichuan and Ordos have established significant production potential2. The transportation of produced shale gas, however, presents distinct flow assurance challenges. The combination of saturated water vapor and the characteristically undulating topography of shale gas fields creates a propensity for liquid accumulation in low-lying and uphill sections of gathering pipelines3,4. This accumulation diminishes the effective flow area, accelerates internal corrosion rates, and can induce unstable flow regimes, thereby posing substantial risks to pipeline integrity and operational safety5,6,7. These challenges are directly linked to national energy security, as efficient shale gas transmission supports stable energy supply. Related issues in unconventional gas systems, such as hydrate formation in subsea pipelines8, fracture propagation in reservoirs9, and repurposing depleted reservoirs for storage10, further underscore the importance of flow assurance researchConsequently, the accurate prediction of liquid loading is paramount for ensuring the efficiency and reliability of shale gas transmission systems11,12,13.

While previous studies often focus on horizontal or single-inclined pipes, this work specifically addresses the continuous undulating topography characteristic of shale gas fields, providing a holistic analysis of liquid accumulation dynamics.Substantial research efforts have been directed toward understanding and mitigating liquid loading in gas pipelines. These endeavors span from system-level operational strategies, such as compressor optimization14 and the management of solids deposition15, to the fundamental thermo-physical requirements of downstream processes including gas liquefaction16. At the core of the liquid accumulation phenomenon lie the multiphase flow hydrodynamics in inclined configurations. Seminal experimental work has meticulously characterized the onset of intermittent flow and pseudo-slug behavior in upward-inclined pipes17, while subsequent studies have delineated the liquid loading thresholds in highly deviated wellbores18, providing mechanistic insights directly relevant to terrain-induced holdup. Internationally, large-scale experimental facilities, such as the SINTEF multiphase flow loop, have been instrumental in generating high-pressure, large-diameter data for model validation19,20. Concurrently, the modeling landscape is evolving, incorporating data-driven approaches like machine learning for liquid holdup prediction21, alongside high-fidelity numerical simulations investigating flow in complex geometries, from concave pipes22 to specifically inclined shale gas pipelines23. Strategies for flow assurance, such as foam-assisted slug mitigation in hilly terrain, have also been explored24,25.

Despite these contributions, a discernible research gap persists concerning shale gas pipelines with continuous and complex topographic undulations. Predominant research has often focused on horizontal pipelines or isolated inclinations, with comparatively less attention given to the holistic analysis of liquid accumulation dynamics in systems with successive elevation changes. Moreover, studies on undulating pipelines frequently prioritize overall pressure drop analysis over a systematic investigation of the parametric influences on liquid generation, distribution, and the ensuing implications for pigging cycle optimization.

Conducting experimental studies at a laboratory scale is often hampered by significant scaling discrepancies with field conditions, while purely analytical or numerical modeling presents considerable complexities. Therefore, the deployment of high-fidelity, transient multiphase flow simulation software is considered indispensable. The OLGA dynamic simulator, widely recognized as an industry standard, is founded on robust, mechanistic two-fluid models for calculating liquid holdup and pressure drop26,27,28,29,30. Its validated accuracy in simulating wet-gas flow makes it a suitable tool for this investigation.

Unlike previous studies focusing on flow characteristics in undulating pipes, this work integrates orthogonal experimental design with high-fidelity OLGA simulations to systematically quantify the effects of operational variables, develops an explicit predictive model, and directly applies the results to pigging cycle optimization—a gap in existing research.Therefore, this study leverages high-fidelity OLGA simulations, integrated with orthogonal experimental design, to systematically delineate the key operational factors governing liquid accumulation in a representative, complex undulating shale gas pipeline. The ultimate objective is to develop a robust predictive model and establish a mechanistic, optimization framework for the pigging cycle, thereby enhancing both the safety and economic efficiency of pipeline operations.

Experimental part

Field data

The gas composition of the studied shale gas gathering pipeline in Changning is presented in Table 1:

Table 1 Composition of the gas gathering station.
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The natural gas compression factor at this location was measured to be 0.9981, the high level of heat generation was 36.959 MJ/m3, the relative density was 0.5622, the inner diameter of the pipe was 307.9 mm, and the length of the pipeline was 5.45 km. The reference conditions for the parameters are 20 °C and 101.325 kPa.

The distribution of gas sources from a gathering station to a central station in Changning and the pipeline trend are shown in Fig. 1.

Fig. 1
Fig. 1
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Trend chart of the pipeline section from the gas gathering station to the central station.

The gas volume from a gathering station to a central station and the related data of its pipeline section are shown in Table 2.

Table 2 Datasheet of the simulation project.
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The pipeline transports well-effluent gas from multiple wells, with an average daily gas production of 55.19 × 104 m3/d and an average daily water production of 506.76 m3/d. The produced water from each well group is first treated by a separator with an efficiency of 95%, resulting in 5% of the water entering the pipeline. The molar ratio of water to the total components in the gas is calculated to be 0.0568 based on the water content entering the pipeline.

Simulation principles of the OLGA

Accurate prediction of liquid accumulation necessitates the use of two-phase flow models, as shale gas pipeline flow inherently involves gas–liquid interactions. The OLGA simulator leverages a sophisticated two-fluid model to resolve the dynamics of each phase. The governing equations are briefly outlined below to illustrate the physical rigor of the methodology28.

The continuity equations for the gas and liquid phases are as follows:

$$\frac{\partial }{\partial t}(\rho_{g} \varphi A) + \frac{\partial }{\partial x}(\rho_{g} \omega_{g} \varphi A) = \Delta M_{g}$$
(1)
$$\frac{\partial }{\partial t}(\rho_{l} H_{L} A) + \frac{\partial }{\partial x}(\rho_{g} \omega_{l} H_{L} A) = \Delta M_{l}$$
(2)

where \(\varphi\) is the quality in the cross section; \({\text{H}}_{\text{L}}\) is the liquid rate; A is the cross-sectional area of the pipe; \(\Delta {\text{M}}_{\text{g}}\) is the mass flow rate of the gas phase condenses to the liquid phase; and \(\Delta {\text{M}}_{\text{l}}\) is the mass flow rate of the liquid phase evaporating to the gas phase.

The momentum conservation equations for the gas and liquid phases are as follows:

$$\frac{\partial }{\partial t}(\rho_{g} \omega A\omega_{g} ) + \frac{\partial }{\partial x}(\rho_{g} \omega_{g}^{2} \varphi A) + \frac{\partial }{\partial x}(p\varphi A) = \Delta M_{g} \omega_{gi} - \Gamma_{gw} - \Gamma_{gi} - \rho_{g} g\varphi A\sin \theta$$
(3)
$$\frac{\partial }{\partial t}(\rho_{i} H_{L} A\omega_{l} ) + \frac{\partial }{\partial x}(\rho_{l} \omega_{i}^{2} H_{L} A) + \frac{\partial }{\partial x}(pH_{L} A) = \Delta M_{l} \omega_{li} - \Gamma_{lw} - \Gamma_{li} - \rho_{l} gH_{L} A\sin \theta$$
(4)

where p is the pressure; \(\uptheta\) is the pipe inclination; \(\Gamma_{kw}\) is the shear stress per unit length of the K-phase to the pipe wall; and \(\Gamma_{ki}\) is the interphase shear force per unit length acting on phase K.

The basic model used in the OGLA is also a two-fluid model, which includes three mass equations for the gas phase, the liquid phase, and the droplet; two momentum equations for the gas phase of the droplet and the simple liquid phase of the droplet; and an energy equation for the mixed system.

The equation of conservation of mass

The equation of the gas phase is as follows:

$$\frac{\partial }{\partial t}(V_{g} \rho_{g} ) = - \frac{1}{A}\frac{\partial }{\partial z}(AV_{g} \rho_{g} v_{g} ) + \psi_{g} + G_{g}$$
(5)

The equation of the liquid phase in the pipeline is as follows:

$$\frac{\partial }{\partial t}(V_{g} \rho_{g} ) = - \frac{1}{A}\frac{\partial }{\partial z}(AV_{L} \rho_{L} v_{L} ) - \psi_{g} \frac{{V_{L} }}{{V_{L} + V_{D} }} - \psi_{e} + \psi_{d}$$
(6)

The equation of the droplet is as follows:

$$\frac{\partial }{\partial t}(V_{D} \rho_{L} ) = - \frac{1}{A}\frac{\partial }{\partial z}(AV_{D} \rho_{L} v_{D} ) - \psi_{g} \frac{{V_{D} }}{{V_{L} + V_{D} }} + \psi_{e} - G_{D}$$
(7)

where V is the volume fraction of the gas and liquid phases; G is the mass source for each phase;ρ is the density; v is the flow rate; A is the cross-sectional area of flow through the pipeline;\({\uppsi }_{\text{g}}\) is the gas‒liquid transfer rate;ψe is the entrainment velocity of the droplet; andψe is the sinking rate of the droplet.

The equation of conservation of momentum

The conservation of momentum equations for the gas and liquid phases is as follows:

$$\begin{aligned} \frac{\partial }{\partial t}(V_{g} \rho_{g} v_{g} + V_{D} \rho_{L} v_{D} ) & = - \frac{1}{A}\frac{\partial }{\partial z}(AV_{g} \rho_{g} v_{g}^{2} + AV_{D} \rho_{L} v_{D}^{2} ) - (V_{g} + V_{D} )\frac{\partial P}{{\partial z}} \\ & - \frac{1}{2}\lambda_{g} \rho_{g} |v_{g} |v_{g} \frac{{S_{g} }}{4A} - \frac{1}{2}\lambda_{i} \rho_{g} |v_{r} |v_{r} \frac{{S_{i} }}{4A} + (V_{g} \rho_{g} + V_{D} \rho_{L} )g\cos \alpha \\ & + \psi \frac{{V_{L} }}{{V_{L} + V_{D} }}v_{a} + \psi_{e} v_{i} - \psi {}_{d}v_{D} \\ \end{aligned}$$
(8)

The equation of the liquid phase in the pipeline is as follows:

$$\begin{aligned} \frac{\partial }{\partial t}(V_{L} \rho_{L} v_{L} ) = & - \frac{1}{A}\frac{\partial }{\partial z}(AV_{L} \rho_{L} v_{L}^{2} ) - (V_{L} )\frac{\partial P}{{\partial z}} - \frac{1}{2}\lambda_{L} \rho_{L} |v_{L} |v_{L} \frac{{S_{L} }}{4A} + \frac{1}{2}\lambda_{i} \rho_{g} |v_{r} |v_{r} \frac{{S_{i} }}{4A} \\ & + V_{L} \rho_{L} g\cos \alpha - \psi_{g} \frac{{V_{L} }}{{V_{L} + V_{D} }}v_{a} - \psi_{e} v_{i} + \psi {}_{d}v_{D} - V_{L} d(\rho_{L} - \rho_{g} )g\frac{{\partial V_{L} }}{\partial z}\sin \alpha \\ \end{aligned}$$
(9)

where α is the pipe inclination; P is the pressure; \({\text{v }}_{\text{r}}\) is the relative velocity; S is the wetted perimeter; and g is the gravitational acceleration.

The equation of conservation of energy

$$\begin{gathered} \frac{\partial }{\partial }[m_{g} (E_{g} + \frac{1}{2}v_{g}^{2} + gh) + m_{L} (E_{L} + \frac{1}{2}v_{L}^{2} + gh) + m_{D} (E_{D} + \frac{1}{2}v_{D}^{2} + gh)] = \hfill \\ - \frac{\partial }{\partial }[m_{g} v_{g} (H_{g} + \frac{1}{2}v_{g}^{2} + gh) + m_{L} v_{L} (H_{L} + \frac{1}{2}v_{L}^{2} + gh) + m_{D} v_{D} (H_{D} + \frac{1}{2}v_{D}^{2} + gh) + H_{S} + U \hfill \\ \end{gathered}$$
(10)

where E is the internal fluid energy; h is the altitude; \({\text{H}}_{\text{s}}\) is the enthalpy of the mass source; and U is the pipe wall heat transfer.

The resulting simulations of the predicted liquid phase changes provide a high degree of accuracy by dynamically tracking variables such as pressure, temperature, and liquid holding capacity in the pipeline.

The amount of liquid accumulated in the pipeline mainly depends on the volume of liquid precipitation and the size of the gas liquid-carrying capacity, whereas the volume of liquid precipitation depends on the pressure and temperature changes in the pipeline, and the size of the liquid-carrying capacity of the gas depends on the gas flow rate and the size of the pipeline and other variables, such as size and structure. The OLGA simulates liquid accumulation in shale gas pipelines with the calculated pressure and temperature changes in the pipeline and gas flow rate parameters by setting the initial conditions, boundary conditions, environmental conditions, and other parameters and combining them with different node parameters in the delivery process of shale gas pipelines.

To ensure the reliability of the simulations, the OLGA model was configured with the following key settings. The 5.45 km pipeline was discretized into 500 one-dimensional segments, with a grid independence check confirming result stability. For the 30-day transient simulation, a variable time-step solver was used (initial step: 1 s, maximum step: 300 s) with a convergence tolerance of 1 × 10–4. The fluid properties were modeled using the Peng-Robinson equation of state, and the Beggs-Brill correlation was selected for flow pattern and holdup prediction in the undulating sections. Boundary conditions were set as a fixed mass flow rate and temperature at the inlet and a fixed pressure at the outlet (Table 2). Validation against a field-derived baseline case confirmed that the simulated key parameters were within ± 3% of expected values, verifying the model’s accuracy for subsequent parametric studies.

The design of orthogonal experiments

Several different parameters affect pipeline liquid accumulation. Four operational parameters (daily water volume, gas volume, pressure, temperature) were selected because they are continuously monitorable and adjustable in field operations, unlike fixed geometric factors (e.g., inclination, diameter) which are accounted for in the OLGA model setup.An orthogonal experiment would need to be designed to determine the specific effects of the relevant parameters on pipeline liquid accumulation. The orthogonal experiments are uniformly dispersed and chi-square comparable. A preliminary correlation analysis based on field data showed low cross-correlation coefficients (< 0.2) among the selected factors, supporting the assumption of negligible interactions.Therefore, the experimental needs are fulfilled. The basic steps of the experiment are shown in Fig. 2.

Fig. 2
Fig. 2
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General steps of the orthogonal experiment

A fitted regression function for pipeline liquid accumulation is obtained, the pipeline cleaning cycle is predicted in terms of the amount of pipeline liquid accumulation to achieve cost savings, and regression analyses of the parameters are performed via an orthogonal design of experiments.

Results and discussions

Analysis of fluid volume calculations

The pipeline was simulated by modeling it via OLGA. After a period, the liquid accumulation volume in the pipeline is stable. Since the steady-state simulation results converge well, the steady-state simulation results are used as the total liquid accumulation volume of the pipeline.

The fluid volume of the pipeline is shown in Fig. 3, and it is found that regular fluctuations start to occur at 2,652,167 s (30.70 days), and its upper and lower waves are in the range of 66.65 ~ 67.21 m3, so the total fluid volume after stabilization is approximately 67.04 m3. On the basis of the location of the liquid accumulation in this pipeline, the distribution of liquid accumulation in the pipeline is mainly concentrated in the upper section of the pipeline and the end of the pipeline, as shown in Fig. 4. The major reason for the increase in liquid holdup is that the effect of gravity on fluids increases when the pipeline is uphill, resulting in a high degree of pipeline backflow, which makes the shale gas pipeline susceptible to liquid accumulation in the uphill section. Flow regime analysis indicates a transition to slug/stratified flow in uphill sections under low gas velocity, which exacerbates liquid retention.Therefore, the formation of liquid accumulation in the shale gas pipeline is regular, as seen from the simulation results and the above analysis. liquid accumulation occurs at the low point closest to the start of the pipeline. When the pipeline is running, it spreads in the uphill section of the pipeline until the pipeline becomes inclined downward. This phenomenon is repeated when the next low point in the pipeline reappears.

Fig. 3
Fig. 3
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Change in total effusion volume

Fig. 4
Fig. 4
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Location of liquid accumulation in the pipeline

Optimization of pipeline cleaning cycles

The pipe cleaning cycle is optimized via orthogonal experiments, which analyze the main variables affecting liquid accumulation in the pipeline, such as water volume, gas volume, pressure, and temperature, and the specific multifactorial influence ranges are obtained, as shown in Table 3.

Table 3 Multifactor influences and range of fluctuations.
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Through the principle of "Four Factors and Three Levels (FFTL)", the four factors that have a significant impact on liquid accumulation in the pipeline are selected as the main factors combined with the fluctuation range of the actual data in the field to study the three fluctuation values of each factor to determine the orthogonal experimental factors and their level of the range shown in Table 4.

Table 4 Selection factors and levels of the orthogonal experiment.
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The various factors affecting liquid accumulation in the pipeline do not interact with each other, so the orthogonal experimental design and data treatment of the interaction are not considered. An orthogonal table of type \({\text{L}}_{\text{n}}\left({\text{r}}^{\text{m}}\right)\) is chosen, where r is equal to the number of levels of the factor, m is greater than or equal to the number of factors, and n is as small as several trials as possible. The orthogonal table selected for this paper is \({\text{L}}_{9}\left({3}^{4}\right)\). The \({\text{L}}_{9}\left({3}^{4}\right)\) orthogonal array is a well-established design for screening main effects with minimal runs, widely used in engineering studies. To enhance statistical reliability, four additional validation runs were conducted.The generated orthogonal table header is shown in Table 5.

Table 5 Orthogonal experiment without considering interactions.
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Each level number in the columns of the orthogonal table for each factor is replaced with the actual level value of that factor to form an orthogonal experimental scheme, as shown in Table 6.

Table 6 Table of orthogonal experimental schemes without considering interactions.
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For further predictive analysis, regression analysis was used to predict the effects of daily water production, daily gas delivery, pressure, and temperature on liquid accumulation in the pipeline. The orthogonal experiment in Table 7 was used as the base data for regression analysis. The relationship between the daily liquid accumulation in pipe Qi and the effect of each factor is defined as follows:

$$Q_{i} = k \cdot x_{1}^{a} \cdot x_{2}^{b} \cdot x_{3}^{c} \cdot x_{4}^{d}$$
(11)

where \({\text{Q}}_{\text{i}}\) is the daily liquid accumulation in the pipeline, m3/d;

Table 7 Original data after orthogonal experimental design.
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x1—Daily volume of water transferred by pipeline, m3/d;

x2—Daily pipeline gas volume, \(\times 10^{4} \cdot m^{3} /d\) ;

x3—Pressure of the pipeline, MPa;

 × 4—temperature of the pipeline, °C;

k, a, b, c, d—Undetermined coefficient.

On the basis of the data from the orthogonal experiments, the data underlying the regression analysis were obtained as shown in Table 7:

According to Eq. (11), taking logarithms on both sides of the equation yields Eq. (12):

$$\ln Q_{i} = k + a\ln x_{1} + b\ln x_{2} + c\ln x_{3} + d\ln x_{4}$$
(12)

Similarly, the daily liquid accumulation of the pipeline was obtained on the basis of the saturated water volume of the pipeline and the number of days of operation, and the raw data for the logarithmic number were obtained, as shown in Table 8.

Table 8 Regression analysis used to fit the original data.
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A post-hoc ANOVA incorporating two-way interaction terms confirmed that all such interactions were statistically negligible (P > 0.05 for all interaction terms). Subsequently, a multiple linear regression was performed based on the orthogonal experimental data, and the estimated values of the model coefficients were obtained as summarized in Table 9.

Table 9 Fitting values of the coefficients to be determined.
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On the basis of the results of the calculations, the exponential relationship of each variable is c > a > d > b because the fitted value of pressure is the largest and the fitted value of daily gas delivery is the smallest. Therefore, the remarkable relationship between the effects of liquid accumulation in pipelines is as follows: pressure > daily water volume > temperature > daily gas volume.

The effect of pressure and temperature on liquid accumulation stems mainly from the fact that their alteration affects important physical properties, such as the density of the fluid inside the pipe, as the equilibrium state inside the pipe is disrupted. However, the effect of the gas delivery volume on liquid accumulation in pipelines is negatively correlated. This is because the flow rate increases when the volume of gas transported in the pipeline is high, and the ability to carry fluid also increases, resulting in a decrease in liquid accumulation in the pipeline.This aligns with the critical velocity theory for liquid unloading in inclined pipes, where increased gas flow enhances entrainment and reduces holdup. However, to ensure production safety, the flow rate of pipeline gas should be within the safety control range. Moreover, the temperature was found to have no statistically significant effect on liquid accumulation, as evidenced by its minimal exponent (d = 0.01498) in the regression function. The complete predictive model, obtained by substituting the fitted coefficients from Table 9 into Eq. (12), is given by:

$$Q_{i} = 0.67396 \cdot x_{1}^{0.17764} \cdot x_{2}^{ - 0.34759} \cdot x_{3}^{1.06499} \cdot x_{4}^{0.01498}$$
(13)

This logarithmic model can be transformed into its equivalent power-law form for direct application, as shown in Eq. (14). The validity of this overall model, as defined by Eq. (13), was subsequently assessed.

The goodness-of-fit of the regression model was further verified through analysis of variance (ANOVA). The results confirmed that the discrepancies between the regression predictions and the experimental data for all factors(x1,x2,x3,x4) fell within an acceptable statistical range. This, coupled with a high confidence level of 90.46%, an R2 of 0.934, and an adjusted R2of 0.912, robustly demonstrates the feasibility and reliability of the regression function for pipeline prognostics. Consequently, the model is deemed suitable for predicting liquid accumulation, and the prediction formula for daily accumulation is presented as follows:

$$Q = \sum\nolimits_{i = 1}^{n} {Q_{i} }$$
(14)

where Q—liquid accumulation in pipelines, m3.

n—Predicting pipeline clearance times, d.

Combined with the prediction of the amount of liquid accumulation in the pipeline by the relevant parameters, the pipeline clearing time can be predicted via this formula. Therefore, one can obtain the value of n. Compared to recent machine learning approaches for liquid holdup prediction21, our model offers greater interpretability and requires less training data, making it more suitable for field application where data may be limited.

Global sensitivity analysis of the predictive model

To rigorously quantify the influence of each operational parameter on the predicted liquid accumulation and to assess the model’s robustness against input uncertainties, a comprehensive global sensitivity analysis (GSA) was performed. GSA evaluates the contribution of input variations across their entire defined ranges to the output variance, providing deeper insights than one-factor-at-a-time approaches.

Methodology: sobol sensitivity indices

The GSA was conducted using the variance-based Sobol method, which is particularly effective for nonlinear models. The four input parameters of the predictive model (Eq. 14) — daily water flow rate (× 1), daily gas flow rate (× 2), pressure (× 3), and temperature (× 4) — were treated as independent random variables. Their probability distributions were assumed to be uniform across the operational ranges specified in Table 3, reflecting realistic field variability.

The analysis proceeded in two steps:

  1. 1.

    Sampling: A large sample set (N = 20,000N = 20,000) of input parameter combinations was generated using a Monte Carlo sampling strategy, ensuring the entire multidimensional parameter space was adequately explored.

  2. 2.

    Index Calculation: For each parameter, the first-order Sobol index (Si) and the total-effect Sobol index (STi) were computed. Si measures the fractional contribution of a parameter’s direct variation to the total output variance. STi measures the total contribution, including all variance caused by its interactions with any other parameters. The difference STi-Si​ thus quantifies the importance of interaction effects involving that parameter.

Results and discussion

The computed Sobol indices are presented in Table 10 and visually summarized in Fig. 5.

Table 10 Sobol global sensitivity indices for the predictive model.
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Fig. 5
Fig. 5
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First-order and total-effect Sobol sensitivity indices for the predictive model

As can be seen from the figure, the following three points are presented:

Dominant Influence of Pressure: Pressure (x3) exhibits the highest first-order index (Si = 0.62), confirming it as the overwhelmingly dominant factor. It alone accounts for approximately 62% of the variance in the predicted liquid accumulation volume. This aligns perfectly with its largest exponent in the regression model (Table 9).

Significance of Interaction Effects: The total-effect indices (STi) for water flow (x1) and gas flow (x2) are substantially larger than their respective first-order indices. For instance, ST1(0.315) > S1(0.208). This clearly demonstrates that a significant portion of their influence on liquid accumulation arises through nonlinear interactions with other parameters (e.g., the combined effect of pressure and flow rate on flow regime and liquid entrainment). This insight validates the need for a multifactor analysis and cannot be captured by simpler local sensitivity methods.

Negligible Role of Temperature: The sensitivity indices for temperature (x4) are very low (ST4 = 0.04), corroborating the conclusion from the regression analysis that its effect is minimal within the studied operational window.

Comparison of results

Following the global sensitivity analysis, which established the model’s robustness and delineated the key influential parameters, the next critical step was to validate its predictive accuracy under realistic conditions. This was achieved through a rigorous, multi-source comparison involving field operational data and high-fidelity OLGA simulations. The benchmark for comparison was a field case from an actual shale gas pipeline, which reported a liquid accumulation volume of 65.5 m3 at the end of its standard 30-day pigging cycle.

An independent OLGA simulation of the same pipeline under equivalent operational conditions predicted that the liquid accumulation would stabilize at 67.07 m3 after 30.70 days, demonstrating a close alignment with the field measurement. Subsequently, the key operational parameters from the field (i.e., daily water volume, gas volume, pressure, and temperature) were employed as inputs to the fitted predictive model [Eq. (14)]. The model calculated a liquid accumulation of 71.70 m3 over the 30-day period.

The remarkable consistency among these three distinct data sources—field measurement, dynamic simulation, and the proposed model—confirms the model’s validity. The relative error between the model’s prediction (71.70 m3) and the field data (65.5 m3) is approximately 9.47%, which falls within an acceptable margin for engineering applications. This agreement underscores the model’s capability to serve as a reliable tool for forecasting liquid accumulation in shale gas pipelines.

Conclusion

  1. 1.

    Steady-state OLGA simulations revealed that liquid accumulation stabilizes at approximately 67.04 m3 after 30 days of operation, with the liquid primarily residing in uphill sections and the pipeline terminus. This distribution pattern underscores the significant influence of terrain on liquid holdup. A predictive mathematical model was successfully developed through orthogonal experimental design and regression analysis, establishing a quantitative relationship between key operational parameters and liquid accumulation. The model’s reliability was confirmed by its close agreement with both field data and OLGA simulation results, demonstrating an acceptable margin of error. The developed model provides a robust and cost-effective strategy for optimizing pigging cycles, which can be directly implemented to enhance the operational efficiency and integrity of shale gas pipelines.

  2. 2.

    The pigging cycle of a gas pipeline is a dynamic parameter intertwined with transmission conditions and field operations. Consequently, implementing real-time monitoring is imperative. Given that transmission efficiency degradation is predominantly caused by liquid accumulation, future work should focus on developing a dynamic pigging cycle calculation model. Such a model would establish a real-time, self-adjusting relationship between liquid accumulation volume and the pigging schedule, offering more precise and proactive guidance for field production.