This study develops an analytical and computational framework for investigating coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. Unlike conventional transient-flow approaches that treat inflow and outflow processes independently, the proposed formulation establishes a unified coupled source-sink model capable of describing their dynamic interaction within a single transmission system. Using the Charny regularization approach, the governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation. The pipeline is decomposed into three interacting spatial regions connected through continuity-based pressure and mass-flux interface conditions, and closed-form analytical solutions for the dimensionless pressure field are derived in the Laplace domain. A practical Laplace-domain approximation is introduced for computational evaluation of transient pressure redistribution. The results reveal the existence of a characteristic balancing point separating injection-dominated and withdrawal-dominated behavior and demonstrate rapid convergence toward a quasi-steady redistribution regime. Optimization analysis shows that redistribution-induced hydraulic disturbance is minimized near a balanced source-sink operating condition. The proposed framework provides new mathematical and physical insight into coupled transient redistribution phenomena and extends the analytical theory of non-stationary gas dynamics through coupled redistribution analysis, asymptotic stabilization behavior, and redistribution-oriented optimization within a unified Laplace-domain formulation.

This study develops an analytical and computational framework for coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. The aim is to describe source–sink interactions within a single transmission system, unlike conventional approaches that treat inflow and outflow processes independently. The governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation using Charny regularization. The pipeline is divided into three interacting regions connected through pressure-continuity and mass-flux coupling conditions. Closed-form Laplace-domain solutions are derived for the dimensionless pressure field, and a practical Laplace-domain approximation is used for computational evaluation of transient pressure profiles. The results reveal a characteristic balancing point separating injection-dominated and withdrawal-dominated regions and show rapid convergence toward a quasi-steady redistribution regime. A pressure-deviation-based objective function is introduced to evaluate hydraulic disturbance, and the optimization analysis shows that the minimum disturbance occurs under a near-balanced source–sink operating condition. The obtained pressure profiles, asymptotic behavior, and regional redistribution patterns confirm the physical consistency of the proposed model. The framework provides a mathematically interpretable basis for analyzing coupled redistribution dynamics, hydraulic stabilization, and asymptotic equilibrium in gas transmission systems.

This study examines commercial real estate market dynamics and valuation performance using an applied panel-data econometric framework within the context of an emerging market economy. While traditional valuation approaches primarily emphasize static income–capitalization relationships, they often overlook the combined influence of liquidity conditions, market risk, and macroeconomic environment on commercial real estate performance. The empirical analysis is based on a balanced panel dataset of commercial properties in Azerbaijan covering the period 2021–2025. The dataset includes net operating income, capitalization rates, liquidity conditions, market risk indicators, and macroeconomic variables. A two-equation modelling framework is employed to separate valuation determinants from capitalization rate dynamics, thereby reducing potential endogeneity between property values and return expectations. The empirical findings indicate that net operating income is consistently and positively associated with commercial property values across the estimated panel-data models. In addition, the results suggest that market liquidity and market risk provide complementary information for understanding commercial real estate performance within the analyzed emerging market setting. Higher values of the risk index are positively associated with capitalization rates, while the estimated relationship between market risk and property value remains sensitive to model specification. Macroeconomic variables exhibit limited statistical significance and are interpreted primarily as indicators of common market-wide conditions. The study contributes to the literature by applying an integrated panel-data framework to an illustrative emerging market case (Azerbaijan) while providing a transparent empirical framework that may be adapted to comparable commercial real estate markets.

Real estate valuation increasingly requires methodologies that combine predictive accuracy, economic interpretability, and model transparency. This study proposes a Generalized Explainable Hybrid Econometric–Machine Learning Framework integrating econometric modelling, machine learning, and Explainable Artificial Intelligence (XAI) within a unified analytical architecture. The framework is organized around a generalized conceptual valuation equation and implemented through a workflow comprising data quality assessment, econometric benchmarking, hyperparameter optimization, nonlinear machine-learning modelling, five-fold cross-validation, and SHAP-based explainability. The methodology is demonstrated using an internally constructed Azerbaijan commercial real estate dataset and independently assessed using the publicly available UCI residential benchmark dataset through an identical Python-based computational pipeline. Under the complete income-capitalization benchmark, the Artificial Neural Network achieved the highest predictive performance for the Azerbaijan dataset, whereas Random Forest performed best for the external benchmark. A leakage-reduced robustness analysis further showed that the framework retained meaningful predictive capability after excluding Net Operating Income and the Capitalization Rate, with XGBoost providing the strongest performance under the reduced specification. SHAP analysis identified economically meaningful valuation drivers, highlighting income generation in the commercial market and transport accessibility in the residential benchmark. The proposed framework provides a transparent, explainable, and transferable decision-support methodology for modern real estate valuation.

Leakage-induced transients in natural gas transmission pipelines can significantly affect operational safety and emergency response. This study develops a physics-based analytical framework for predicting transient pressure evolution, leakage dynamics, and emergency valve response in high-pressure gas pipelines while deriving a closed-form criterion for optimal valve spacing. The governing equations of compressible gas flow are reduced to a diffusion-type model incorporating acoustic wave propagation and frictional attenuation. A dynamic Robin-type boundary condition is introduced to describe valve–pipeline interactions, and closed-form analytical solutions are obtained using the Laplace transform method. An analytical leakage function and an explicit valve spacing criterion are derived directly from the governing equations and boundary conditions. Parametric investigations under representative transmission pipeline operating conditions demonstrate that the optimal valve spacing depends systematically on attenuation characteristics, activation thresholds, and allowable response times. The analytical solution further predicts a narrow quasi-invariant valve activation interval of approximately 112–116 s, which is theoretically explained through the dominant acoustic–diffusive balance of the proposed model. Verification against an independent finite difference solution shows excellent agreement, with the maximum relative deviation remaining below 1%, thereby confirming the accuracy and numerical consistency of the analytical formulation. The proposed framework provides a physically interpretable and computationally efficient tool for leakage assessment, emergency valve design, and safety-oriented analysis of conventional natural gas transmission pipelines.

Transient pressure redistribution in ring gas pipelines is governed by both withdrawal intensity and spatial configuration, which determine circumferential flow redistribution and the location of the hydraulic junction. This study develops an analytical framework for transient pressure dynamics and hydraulic-junction localization in ring pipelines with multiple discrete withdrawals. A closed-form Fourier-series solution is derived and numerically verified against an independently implemented finite-difference model, demonstrating close analytical–numerical agreement. The hydraulic-junction coordinate is identified from the transient pressure-extremum condition, while a dimensionless localization factor is introduced to characterize its position relative to the geometric midpoint. Two contrasting ring configurations reveal distinct behaviors: For the investigated 30 km configuration, the hydraulic junction remains localized near the geometric midpoint under the considered proportional-withdrawal scenarios. In the second, increasing withdrawal loading causes progressive upstream migration toward a withdrawal-controlled limiting location. A steady balanced flow-reversal criterion provides a physical interpretation of the limiting junction position without being extended to globally unbalanced transient states. The results further show that efficient distributed withdrawal requires consideration of both pressure retention and hydraulic-junction behavior. The proposed framework provides a mathematically interpretable basis for assessing transient hydraulic states and withdrawal strategies in ring gas pipelines.