Analysis Of Gas Flow Research Articles

Experimental and numerical analysis of gas flow in nodeless antiresonant hollow-core fibers for optimization of laser gas spectroscopy sensors

In this paper, we present the pressure-driven gas flow studies in nodeless antiresonant hollow-core fibers (ARHCFs) for laser absorption spectroscopy (LAS) applications. The OpenFOAM® software was used for gas flow modeling for comparison with experimental data. The experimental LAS-based setup utilizing a 14.73 m long fiber, was used to gas exchange time measurements for various pressure differences (1.5–5 bar). The obtained results have shown that the application of a precise fiber geometrical representation and a compressible flow model improves the correlation between simulations and experiments for nodeless ARHCFs, in comparison to cylindrical channel approximation and an incompressible model. We believe that our work will help optimize the selection of the proper ARHCF during sensor design, where the fiber type and length can significantly determine the obtainable response time of the detector and its overall compactness.

A multi-scale quadruple-continuum model for production evaluation of shale gas reservoirs considering complex gas transfer mechanisms and geomechanics

Shale gas reservoirs are uniquely characterized by extremely low values of permeability, porosity, and complex fracture network which adequately hinders gas transfer and production evaluation. At the reservoir scale, the analysis of complex gas flow and transfer mechanisms from one domain to another is still a challenge. In this regard, a fully coupled multi-scale quadruple-continuum model is proposed, where the gas transfer mechanisms across the four domains (Kerogen, inorganic matrix, natural fractures, and hydraulic fractures) are adopted and the flow terms are corrected to suit real gas and account for shale deformation considering dynamic effective stress. The complexity of modeling gas transfers from the kerogen to the inorganic matrix to fracture system (natural and hydraulic fractures) and the production well is overcome by using the Warren-Root and Vermeulen transfer terms, respectively. The current model matches field data from typical shale reservoirs and accurately predicts gas production. Numerical simulation results show that increasing the kerogen pore volume and stress sensitivity coefficient decreases cumulative gas production. Increasing domain permeability, porosity, number of natural fractures, and the width and length of natural fractures improve the flow of gas, leading to higher cumulative gas production. Moreover, crisscrossing natural fractures and larger stimulated reservoir domain (SRD) could extend the area of contact with the unstimulated reservoir domain (USRD), thus allowing more gas to flow to the production well. Overall, more gas is produced when the four domains are considered than when either of them is ignored. This study introduces a comprehensive understanding of the four domains' primary flow and transfer mechanisms. It provides a practical baseline for evaluating gas production in fractured shale reservoirs.

Development of an Easily Reproducible Cough Simulator With Droplets and Aerosols for Rapidly Testing Novel Personal Protective Equipment.

The current COVID-19 pandemic has produced numerous innovations in personal protective equipment, barrier devices, and infection mitigation strategies, which have not been validated. During high-risk procedures such as airway manipulation, coughs are common and discrete events that may expose healthcare workers to large amounts of viral particles. A simulated cough under controlled circumstances can rapidly test novel devices and protocols and thus aid in their evaluation and the development of implementation guidelines. Physiologic cough simulators exist but require significant expertise and specialized equipment not available to most clinicians. Using components commonly found in healthcare settings, a cough simulator was designed for clinicians to easily assemble and use. Both droplet and aerosol particle generators were incorporated into a bimodal experimental system. High-speed flash photography was used for data collection. Using a gas flow analyzer, video recordings, and high-speed digital photography, the cough and particle simulators were quantitatively and qualitatively compared with known physiologic cough parameters and in vivo Schlieren imaging of human coughs. Based on our validation studies, this cough and particle simulator model approximates a physiologic, human cough in the context of testing personal protective equipment, barrier devices, and infection prevention measures.

Artificial dissipation model applied to Euler equations for analysis of supersonic flow around a geometric configurations ramp and diffusor type

Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D_EULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow of helium gas along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the linear artificial dissipation model of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors.

Selected Mathematical Models Describing Flow in Gas Pipelines

The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of load and supply will help us find out the value of pressure or flow rate at selected points or along selected sections of the network. Transient gas flow may be described by a set of simple or partial differential equations classified as hyperbolic or parabolic. Derivation of the mathematical model of transient gas flow involves certain simplifications, of which one-dimensional flow is most important. It is very important to determine the conditions of pipeline/transmission network operation in which the hyperbolic model and the parabolic model, respectively, should be used. Parabolic models can be solved numerically in a much simpler way and can be used to design simulation programs which allow us to calculate the network of any structure and any number of non-pipe elements. In some conditions, however, they describe the changes occurring in the network less accurately than hyperbolic models do. The need for analysis, control, and optimization of gas flows in high-pressure gas pipelines with complex structure increases significantly. Very often, the time allowed for analysis and making operational decisions is limited. Therefore, efficient models of unsteady gas flows and high-speed algorithms are essential.

Внутренняя гидродинамика инспекционного снаряда для газопроводов низкого давления

Speed control of an inspection projectile in low-pressure gas pipelines can be performed by changing the cross-section of the central channel when turning the flap, and it is more effective the lower the resistance to gas flow through the central channel. Peripheral bypass channels are used to reduce the resistance. We conducted analysis of gas flow in these channels with cut-outs intended to accommodate the flap turning device and brakes. A design of the channels that provides a 15% decrease in drag force is proposed (the maximum decrease in force in the design with bypasses without cut-outs is 20%). The dependence of the damper drag force on the angle of its rotation, used in controlling the movement of the inspection projectile, was also calculated. In a wide range of angles, the drag force was found to be proportional to the fraction of the overlapped area.

Thermal and hydrodynamic behavior of forced convection gaseous slip flow in a Kelvin cell metal foam

Porous metallic foams are a key material in numerous thermal and hydraulic applications. Gas flows in such micro/nanoporous systems deviate from classical continuum descriptions due to nonequilibrium in gas dynamics, and the resulted heat and mass transport show variation by rarefaction. This study performed a wide range of pore-level analysis of convective gas flows in a Kelvin cell model at different porosities and working conditions. Rarefaction effects onto permeability and heat transfer coefficients were calculated through Darcy to Forchheimer flow regimes. Permeability increased up to 60% by increasing rarefaction while this enhancement decreased by increasing porosity. At the same time, rarefaction lessened inertial effects such that Forchheimer coefficients decreased substantially. At high flow velocities, the increase in rarefaction considerably decreased the effect of drag forces. Hence, hydrodynamic enhancement due to rarefaction was found to increase by increasing Reynolds number. On the other hand, positive influence of boundary slip and negative influence of temperature jump developing between gas and solid almost canceled each other for the studied low heat flux region of highly conductive metal foam structures. Hence, Nusselt numbers were found mostly related to Reynolds number independent from rarefaction. We described Nusselt value based on power law model as a function of Reynolds and porosity. Results and the proposed model are important to accurately predict the thermal and hydrodynamic performance of metal foams in the 80 PPI range.

Permeability analysis of hydrate-bearing sediments considering the effect of phase transition during the hydrate dissociation process

Permeability is the most important factor affecting water and gas production in hydrate-bearing sediments (HBS). In this study, we combined in-situ microfocus X-ray computed tomography (CT) and pore network model simulation to obtain insights into the dynamic permeability of the hydrate dissociation process. Microfocus X-ray CT is used to visualize the three-dimensional pore structures of the specimen. Then an equivalent pore network can be extracted, which is used as input to pore network flow simulator to simulate the water and gas flow process. Results show that secondary hydrate formation causes effective permeability keff decreases and effective connate water saturation increases as hydrate saturation Sh increases from 0.40 to 0.48. The water relative permeability krw decreases and gas relative permeability krg increases due to larger patchy hydrates (Sh = 0.33). The krw and krg are largely affected by the pore and throat sizes and pore space connectivity. Hydrate dissociation in HBS also influences its permeability anisotropy. Secondary hydrate formation causes keff decreases in the x, y, and z directions when Sh increase from 0.40 to 0.48. Large patchy hydrates influence preferential flow direction for water flow. Predicting the dynamic permeability of the hydrate dissociation process would improve pore-scale water and gas flow analyses in HBS.

Permeability Analysis of Hydrate-Bearing Sediments during the Hydrate Formation Process

Permeability is a critical factor for controlling water and gas flow and influencing hydrate growth and distribution in hydrate-bearing sediments (HBS). In this study, we used in situ microfocus X-ray computed tomography to obtain three-dimensional information on microstructures of xenon hydrates in sedimentary matrices (Fujian sand) under excess-gas conditions. It was found that the hydrates in the specimen develop cementing and grain-coating pore habits, and the predominant hydrate pore habit is grain coating. We combined a pore network model simulation to analyze the effect of hydrate formation on the permeability in HBS. The results indicate that the water relative permeability decreases during the hydrate formation process. Gas relative permeability decreases at high water saturation (>0.20). The reason is that hydrate formation causes a decline in the pore space size and connectivity, and then, the gas and water flow are inhibited. Moreover, hydrate formation in HBS has an impact on its permeability anisotropy. Effective permeability decreases in x, y, and z directions with hydrate formation. The predominant hydrate pore habit in the pore space has a small influence on the evolution of the preferential flow direction of the water and gas. Predicting the dynamic permeability of the hydrate formation process would improve pore-scale water and gas flow analysis in HBS.

Pressure and Volume Control in a new Emergency Mechanical Ventilator based on PLC and Industrial Pneumatic Parts in Peru.

This work details a methodology of design and test of a new prototype emergency mechanical ventilator called Fenix for the COVID-19 crisis in Peru. This equipment was manufactured with industrial equipment for the embedded and pneumatic systems, such as a Programmable Logic Controller (PLC), proportional flow valves, sensors, uninterruptible power supply (UPS), industrial panel HMI 15" and other electrical and pneumatic parts from Festo and Schneider Electric. This selection was in accordance with safety requirements based on ISO 80601-2-12: 2020-02. This study included two ventilatory modes, pressure- controlled in continuous mandatory ventilation (PC-CMV) and volume-controlled in continuous mandatory ventilation (VC-CMV), these control algorithms were evaluated analytically and experimentally in a FLUKE VT-650 Gas Flow Analyzer and an Acculung Fluke connected with a computer for comparing 9 ventilatory parameters in 4 different states as μ, simulation of the variation of the pressure control in a patient, and ϴ, simulation of alveolar recruitment in an intensive care patient, both states to PC-CMV, and also β, simulation of the variation of the flow control in a patient, and α, simulation of alveolar recruitment in an intensive care patient, both last states to VC-CMV. Additionally, we study the pressure, volume, and flow graphs in the Fenix user interface for comparison with data recovered from Fluke Medical VT650 Gas Flow Analyzer. The results demonstrate an error in the flow measurement for the 4 states due to the peaks that are not detected by the low-pass filter of the sensor, however, a similar trend is seen in the control ventilatory graphs of the calibrator. Finally, the ventilator prototype provides ventilatory support, with a maximum tidal volume error of 12.93 % and inspiratory pressure of -20.15 % with respect to the set value; and it allows to monitor the main ventilation parameters with a calculation error between -6 to 25 %.Clinical Relevance - Established the design of emergency mechanical ventilator using PLC and industrial components.

A steady-state energy flow analysis method for integrated natural gas and power systems based on topology decoupling

The existing analyses of integrated natural gas and power systems generally ignore gas temperature variations, which may misjudge gas pressure and jeopardize natural gas transmission. Furthermore, the conventional Newton-Raphson based natural gas flow analysis methods may cause non-convergence or unnecessary computational burden. Based on topology decoupling, an efficient energy flow analysis method is proposed in the paper for integrated natural gas and power systems with the consideration of temperature distribution in natural gas systems. A lumped parameter model of natural gas flow in pipelines considering temperature is developed based on the Weymouth and Shukhov formulas. A natural gas flow model considering temperature is then established. According to the topological characteristics of natural gas systems, a topology decoupling based natural gas flow analysis method is proposed to improve computational efficiency and to lower the requirement of initialization. An energy flow analysis method for integrated natural gas and power systems is presented based on a Newton-Raphson method. The correctness and adaptability of the proposed method are verified using three widely-used test systems. The obtained simulation results show that the temperature distribution and natural gas pressures of a natural gas network can be accurately described and estimated to ensure the secure operation of integrated natural gas and power systems, and the computational efficiency and convergence performance are largely improved.

1D–3D Coupling Algorithm of Gas Flow for the Valve System in a Compression Ignition Engine

Emission control devices such as selective catalytic reduction (SCR), exhaust gas recirculation (EGR), and scrubbers were installed in the compression ignition (CI) engine, and flow analysis of intake air and exhaust gas was required to predict the performance of the CI engine and emission control devices. In order to analyze such gas flow, it was inefficient to comprehensively analyze the engine’s cylinder and intake/exhaust systems because it takes a lot of computation time. Therefore, there is a need for a method that can quickly calculate the gas flow of the CI engine in order to shorten the development process of emission control devices. It can be efficient and quickly calculated if only the parts that require detailed observation among the intake/exhaust gas flow of the CI engine are analyzed in a 3D approach and the rest are analyzed in a 1D approach. In this study, an algorithm for gas flow analysis was developed by coupling 1D and 3D in the valve systems and comparing with experimental results for validation. Analyzing the intake/exhaust gas flow of the CI engine in a 3D approach took about 7 days for computation, but using the developed 1D–3D coupling algorithm, it could be computed within 30 min. Compared with the experimental results, the exhaust pipe pressure occurred an error within 1.80%, confirming the accuracy and it was possible to observe the detailed flow by showing the contour results for the part analyzed in the 3D zone. As a result, it was possible to accurately and quickly calculate the gas flow of the CI engine using the 1D–3D coupling algorithm applied to the valve system, and it was expected that it can be used to shorten the process for analyzing emission control devices, including predicting the performance of the CI engine.

가스유동 해석을 이용한 선박용 전기집진기의 전극판 및 집진판 형상에 따른 집진효율 예측

In order to reduce air pollution caused by fine dust, the emission standards for environmental pollutants generated from ships are being strengthened. The fine dust reduction device for ships needs a function that can be used in combination with SCR(Selective Catalytic Reduction) due to the limited space of the engine room. In this study, gas flow analysis was performed to predict the dust collection efficiency of the electrostatic precipitator to develop the electrostatic precipitator with low back pressure for 300 kW class of marine diesel engine. In order to analyze the dust collection efficiency according to the shape of the electrode and collecting plate, the gas flow was analyzed by modeling the three shapes, and the theoretical dust collecting efficiency was calculated for the three models. Based on the results of gas flow analysis, the dust collecting efficiency of the semicircular designed the electrode and collecting plate was found to be the highest. In the future, the gas flow analysis results of this study will be used to develop the semicircular electrode and collecting plate as well as to improve the dust collection efficiency of the electrostatic precipitator.

Development of Digital Ventilator with Internet of Things for Preparation of the Next Outbreak in Indonesia

The emergency of the healthcare device unit, such as a ventilator, has been experienced during the COVID-19 pandemic in 2020. Therefore, ventilator usage is not hard suggested anymore for COVID-19 patients compared to the outbreak beginning. Despite that, it is still essential to have the ventilator ready, if possible, in each house, for the upcoming respiratory syndrome outbreak. Therefore, in this paper, a digital ventilator development is presented. The digital ventilator is comprised of three main parts, such as respiration mechanism (I), controller Internet of Things (IoT) module (II), and website application (III). The developed digital ventilator has been tested by comparing the measurement of respiratory data between the developed digital ventilator and gas flow analyzer. Results show that the respiratory data, such as Pressure Peak (PPeak), Positive End Respiratory Pressure (PEEP), Inspiratory Expiratory Ratio (IE Ratio), Breath per Minute (BPM), and Tidal Volume can be monitored and controlled both directly and online via website application consistently (standard deviation around 10%) with PPeak absolute error of 1.35 mbar, the PEEP absolute error of 0.16 mbar. Furthermore, the average time response of the digital ventilator to the input command from the website application is 0.23 s. Therefore, it is safe to assume that the doctor can use the website application to control the digital ventilator remotely.

Numerical and Experimental Analysis of Gas Flow in a Coaxial Nozzle Applied to Directed Energy Deposition (DED)

create a melt pool on the substrate. A nozzle is used to carry metal powder within a gas flow until the melt pool, concentrating the flow at the same point. Coaxial nozzles usually have also a shield gas flow to prevent oxidation and an internal flow to protect the optical system. A right flow configuration must be selected to avoid high turbulence at the nozzle exit, leading to an efficient, inexpensive, and high-quality process. Due to the complexity of the process, CFD – Computer Fluid Dynamics are becoming necessary to understand the behaviour of those gas flows in DED processes. CFD can offer results close to reality and may allow an optimization of the whole nozzle designs, besides selecting the best gas flows for each application. The present work develops a CFD simulation of the gas flow behaviour in a coaxial nozzle with three internal annular channels (internal, carrier and shield). An initial set of gas flow was selected, based on previous experience of the manufacturer, and then improved. It searches for the low gas consumption, to form a focal point coinciding with the laser focus and a low velocity, which favours the deposition quality. To check the accuracy of the proposed CFD model, experimental measurements of gas velocity were performed and compared with simulated results.

Comparison of two gas volume measurement systems by evaluating biochemical methane potential

AbstractThe objective of this study is to compare and analyze the efficiency of an automated measurement system for biogas flow with a control performed by a programmable logic controller (PLC) called the SAMB compared to commercial equipment widely disseminated for this purpose, the automatic methane potential test system (AMPTS II). The objective is to identify the accuracy in gas flow analysis of the two systems. The experiments were conducted in triplicate at a constant temperature of 37°C in anaerobic reactors. Two synthetic substrates and two natural substrates combined with a microbial inoculum were used. Considering the different ways the two systems capture data, the results show that all samples differed statistically between them (p < 0.01) in each system. However, in relation to paired substrates between systems, the samples did not present statistically significant differences (p > 0.05). Thus, with the advancement and globalization of knowledge, it is necessary to develop systems capable of generating standardized, precise, and accurate data. In this context, the systems evaluated here present different forms of methane measurement but the results have no significant statistical differences.

1D–3D Coupling for Gas Flow Analysis of the Air-Intake System in a Compression Ignition Engine

Devices for reducing environmental pollutant emissions are being installed in ship compression ignition (CI) engines; alternatively, the designs of intake and exhaust pipes and ports are being modified to tune the performance according to the user’s needs. In both cases, substantial computation time and cost are required to simulate the gas flow of the CI engine with an air-intake system. In order to simulate the air-intake system of the CI engine, which changes according to the user’s needs, at a low cost and in a short time, we aimed to analyze the gas flow using a 1D–3D coupled method. The 1D zone was analyzed using the method of characteristics, and the 3D zone was analyzed using the commercial computational fluid dynamics (CFD) code Ansys Fluent R15.0, whereas their coupling was achieved by applying the developed 1D–3D coupling algorithm to Ansys Fluent R15.0 using user-defined functions (UDFs). In the comparison of the pressure of the intake pipe with the experimental result, the average error was 0.58%, thereby validating the approach. In addition, when analyzing the intake pipe and port in a 3D zone, the results of the velocity and pressure were expressed as contours, allowing them to be visualized. It is expected that the 1D–3D coupling algorithm of the air-intake system can be used to reflect the user’s needs and can be used as a method to quickly and accurately calculate the gas flow within tens of minutes.

Temporal Scale Analysis of Gas Flow in Tight Gas Reservoirs considering the Nonequilibrium Effect

The fractal geometry, anisotropy, discontinuity, and non-Darcy flow of tight reservoirs exert a significant effect on well production performance. In this study, the reservoir fractal geometry is represented by exponential functions on the basis of microseismic data, while the discontinuity of the fractures is presented as a nonequilibrium effect. The impact of the nonequilibrium effect and the low velocity non-Darcy flow on the temporal scale of the wellbore pressure is predicted herein. Results showed that the time scale analysis accurately simulates gas flow in a tight reservoir. The wellbore pressure gradually increases, whereas the pressure in the matrix lags when the nonequilibrium effect is considered. The wellbore pressure is affected in the early period by the nonequilibrium effect. However, at the later stage, the pressure in the matrix is mainly affected by the non-Darcy flow. When the non-Darcy flow is dominant, the pores without gas flowing through are better presented.

Fractal permeability model for dual-porosity media embedded with natural tortuous fractures

Coal is a dual-porosity medium with an internal pore-fracture structure that serves as a channel for the migration of coalbed methane. Understanding the relationship between permeability and pore-fracture structure characteristics is therefore of great significance to accurately predict coalbed methane productivity. In this work, we analyze the pore-fracture structure characteristics of real coal samples and establish a new fractal permeability model of dual-porosity media embedded with natural tortuous fractures. Compared with the traditional dual-porosity medium model with embedded parallel plane fractures, this model not only considers the characteristics of pore tortuosity but also those of fracture tortuosity. The results show that the predicted permeability values obtained from the proposed model are 1–2 orders of magnitude lower than those of the traditional model, which implies that the latter overestimates coal seam permeability. The coal matrix permeability is approximately 13 orders of magnitude lower than the fracture permeability, and the latter mainly controls the overall coal seam permeability. Gas flow analysis of the coal seam is conducted in COMSOL Multiphysics, in which a fracture structure image is transformed to the computational domain. We use the results to discuss the relationships between coal permeability and fracture geometric characteristic parameters. The results show that the porosity ϕf and fractal dimension Dl of the fracture substantially affect coal seam permeability and follow a strong power-law relationship. The numerical simulation results are in good agreement with the theoretical predicted values (the average error is about 11.97%), which verifies the accuracy of the proposed model.

The Partial Transformational Decomposition Method for a Hybrid Analytical/Numerical Solution of the 3D Gas-Flow Problem in a Hydraulically Fractured Ultralow-Permeability Reservoir

SummaryThe analysis of gas production from fractured ultralow-permeability (ULP) reservoirs is most often accomplished using numerical simulation, which requires large 3D grids, many inputs, and typically long execution times. We propose a new hybrid analytical/numerical method that reduces the 3D equation of gas flow into either a simple ordinary-differential equation (ODE) in time or a 1D partial-differential equation (PDE) in space and time without compromising the strong nonlinearity of the gas-flow relation, thus vastly decreasing the size of the simulation problem and the execution time.We first expand the concept of pseudopressure of Al-Hussainy et al. (1966) to account for the pressure dependence of permeability and Klinkenberg effects, and we also expand the corresponding gas-flow equation to account for Langmuir sorption. In the proposed hybrid partial transformational decomposition method (TDM) (PTDM), successive finite cosine transforms (FCTs) are applied to the expanded, pseudopressure-based 3D diffusivity equation of gas flow, leading to the elimination of the corresponding physical dimensions. For production under a constant- or time-variable rate (q) regime, three levels of FCTs yield a first-order ODE in time. For production under a constant- or time-variable pressure (pwf) regime, two levels of FCTs lead to a 1D second-order PDE in space and time. The fully implicit numerical solutions for the FCT-based equations in the multitransformed spaces are inverted, providing solutions that are analytical in 2D or 3D and account for the nonlinearity of gas flow.The PTDM solution was coded in a FORTRAN95 program that used the Laplace-transform (LT) analytical solution for the q-problem and a finite-difference method for the pwf problem in their respective multitransformed spaces. Using a 3D stencil (the minimum repeatable element in the horizontal well and hydraulically fractured system), solutions over an extended production time and a substantial pressure drop were obtained for a range of isotropic and anisotropic matrix and fracture properties, constant and time-variable Q and pwf production schemes, combinations of stimulated-reservoir-volume (SRV) and non-SRV subdomains, sorbing and nonsorbing gases of different compositions and at different temperatures, Klinkenberg effects, and the dependence of matrix permeability on porosity. The limits of applicability of PTDM were also explored. The results were compared with the numerical solutions from a widely used, fully implicit 3D simulator that involved a finely discretized (high-definition) 3D domain involving 220,000 elements and show that the PTDM solutions can provide accurate results for long times for large well drawdowns even under challenging conditions.Of the two versions of PTDM, the PTD-1D was by far the better option and its solutions were shown to be in very good agreement with the full numerical solutions, while requiring a fraction of the memory and orders-of-magnitude lower execution times because these solutions require discretization of only the time domain and a single axis (instead of three). The PTD-0D method was slower than PTD-1D (but still much faster than the numerical solution), and although its solutions were accurate for t < 6 months, these solutions deteriorated beyond that point.The PTDM is an entirely new approach to the analysis of gas flow in hydraulically fractured ULP reservoirs. The PTDM solutions preserve the strong nonlinearity of the gas-flow equation and are analytical in 2D or 3D. This being a semianalytical approach, it needs very limited input data and requires computer storage and computational times that are orders-of-magnitude smaller than those in conventional (numerical) simulators because its discretization is limited to time and (possibly) a single spatial dimension.