High-temperature High-pressure Gas Research Articles

Upper limit estimate to wellhead flowing pressure and applicable gas production for a downhole throttling technique in high-pressure–high-temperature gas wells

In recent years, China has explored and exploited several high-pressure deep gas fields. Normally, high-pressure gas wells are gathered and processed through multichoke manifolds on well sites, creating hazards such as high wellhead flowing pressure (Pt) and high risk for on-site operation personnel. Moreover, downhole chokes have been used in place of surface chokes. In doing this, the Joule–Thomson (JT) effect is geothermally regulated, alleviating the formation of hydrates in surface facilities. However, its applicability to high-pressure gas wells is less explored. In an effort to guide its use, the objective of this study is to set selection criteria in terms of the allowable wellhead Pt and gas flow rate. First, isenthalpic lines are separately estimated for dry gas and high liquid hydrocarbon (LHC) content gas condensate at various inlet temperatures with the use of commercial software. Next, by analysis of the resulting isenthalpic curves, several results are obtained on the JT inversion curves and throttling process through a choke. Third, building on these insights, a method for projecting the maximum Pt is presented, leading to a value of 52.5 MPa. Finally, multiparameter models are separately run for two deep gas wells (8100 m and 5000 m), reinforcing the result of the pressure upper limit while maintaining a maximum daily gas production of 14 E4 m3. Both upper limits with a maximum Pt of 52.5 MPa and daily gas production of 14 E4 m3 are corroborated with field data records. These findings are vital to the selection of a viable high-pressure gas well for applying the downhole throttling technique.

Application of Six Equation Compressible Multifluid Model For the Numerical Simulation of Under-water Explosion

A two phase, six-equation compressible multifluid formulation, three-dimensional code is developed. In this paper, numerical simulation of underwater explosion near a free surface is presented as an application of the code developed. The flow structures and the processes are unsteady. Finite volume method is used for spatial discretization with HLLC scheme with second order accuracy for flux computation. Explicit, classical four stage Runge-Kutta method is used for temporal discretization. The main focus is to study the wave travel and capture the physics when a high-pressure high temperature gas explosion happens in water near to the free surface.

Results of conjugate modeling and analysis of the thermal state of a high-pressure turbine blade

Numerical modeling for the purpose of receiving the temperature field of cooled rotor blades and its improvement is an integral process of modern design of gas turbine engines since the issue of cooling at gas temperature at the combustion chamber outlet over 1800-2000 K is becoming one of the key ones. To ensure the specified parameters of turbine operation during its design, it is necessary to obtain reliable calculation data. The article presents an algorithm for forming a calculation model to determine the thermal state of the working blade of a high-temperature high-pressure gas turbine in the Ansys program. The process of preparation of geometric and grid models is described, the boundary conditions used to set up the project in Ansys CFX Pre are given. A method for determining the cooling efficiency factor using Ansys CFX Post is also presented. The distributions of the temperature field and the coefficient of cooling efficiency over the surfaces of the blade to be cooled are obtained. Integral values of the coefficient of cooling efficiency for the designed blade at various cooling air flow rates were compared with statistical data. On the basis of the comparison a conclusion was made that the working blade considered in the work corresponds to the modern level of cooling efficiency.

Sensitivity analysis of the temperature profile changing law in the production string of a high-pressure high-temperature gas well considering the coupling relation among the gas flow friction, gas properties, temperature, and pressure

The temperature profile plays an important role in well integrity, flow assurance, and well test. Meanwhile, the impact of engineering conditions should not be ignored while calculating the well temperature profile. Therefore, in this study, we established a model to analyze the changing law of the temperature profile inside the production string of a high-pressure/high-temperature gas well (HPHT gas well). The proposed model considers the flow friction caused by a high production rate. Meanwhile, the variations in gas properties are taken into account to increase the model accuracy, including gas density, flow velocity, and viscosity. The analysis indicates that the temperature in the production string decreases more and more quickly from the reservoir to the wellhead. The wellhead temperature changes more and more slowly with time. When the reservoir temperature is too low to maintain production, it is useful to regulate the production rate or inject the thermal insulating fluid into the annulus to avoid the block caused by wax deposition or hydrate deposition. Considering the sensitivity, feasibility, and cost, it is recommended to change the well temperature profile by adjusting the production rate. If not applicable, the thermal conductivity can also be optimized to change the temperature profile.

Response analysis and safety control of tubing vibration in HPHT and ultra-deep gas wells

Under the condition of high pressure, high temperature(HPHT) and high yield in ultra-deep wells, the buckling deformed tubing will produce violent vibration when opening and closing the well or production fluctuation, which will make the tubing bear large periodic fluctuating load, cause the failure of tubing thread seal, form fluid leakage channel, and induce the problem of sustained casing pressure(SCP). Serious annulus pressure will lead to increased tubing leakage, casing failure or more serious consequences. In order to explore the failure process of well barrier caused by tubing vibration in HPHT and ultra-deep wells, a fluid solid coupling vibration model of tubing is established, and the coupling vibration equation is numerically solved by the characteristic line method. Finally, an example of a gas well in the west is analyzed. The calculation results show that there is an obvious Poisson coupling effect between the tubing and the gas in the pipe in well X. The axial stress of the tubing is always in an unstable pulsating alternating stress state, reciprocating vibration along the axis and gradually attenuated to stability; the closer to the wellhead, the more violent the gas fluctuation in the pipe, and the greater the axial vibration amplitude of the upper part of the tubing away from the wellhead; large vibration of tubing may induce seal failure, resulting in oil jacket connection and pressure on a annulus; finally, the allowable annulus pressure of the example well is calculated, and the annulus pressure control measures are put forward. The research results have good guiding significance for well barrier failure analysis and annulus pressure control caused by tubing vibration in HPHT ultra-deep wells.

Thermal-Hydraulic analysis of axial gas turbine blade

A gas turbine engine service life is mainly determined by the lifespan of high-pressure turbine blades. Computational simulations are becoming increasingly important for safe design and optimized blade profile for achieving maximum efficiency. The impact of high-pressure high temperature gas on a rotor blade in motion can result various failure mechanism along the blade profile. A detailed computational analysis has been presented in this paper to investigate the effects of turbine speed and inlet conditions on the 1st stage of an axial flow high pressure gas turbine. A Finite element simulation software was used to assess the thermal hydraulics of high energy fluid flow under a variety of mass flow and temperature conditions. The developed wall shear stress under such a compressible flow domain was found to be dependent on blade speed considered in this analysis.

Predicting Sand Production Rate in High-Pressure, High-Temperature Wells in the Tarim Basin

Summary Sand production has been a very serious concern for the high-pressure, high-temperature (HPHT) gas wells in the Tarim Basin. However, the possible reasons and mechanisms remain unclear because there is no sufficient model to predict both onset of sanding and sand-production rate. The objective of this study is to develop a three-dimensional (3D) numerical sand production-prediction model and apply it to these HPHT gas wells to determine the main mechanisms for sand production and to propose completion designs to minimize sand production. This paper presents the development of a fully coupled 3D, poro-elasto-plastic sand-production model and the simulation results for two key wells that are prone to sanding. The sand-production model was used to model the different completion designs and flowback strategies that were used in the field. The model couples multiphase fluid flow and elasto-plasticity to simulate pressure transient behavior and rock deformation during production. The sanding criterion is a combination of both mechanical failure (shear/tensile/compressive failure) and fluid erosion. A novel cell-removal algorithm has been implemented to predict the dynamic (time dependent) sand-production process. In addition, the complex geometry of the wells and perforations are explicitly modeled to show cavity propagation around hole/perforations during sand production. For this case study, triaxial tests on core samples were conducted, and the stress-strain curves under different confining stresses are analyzed to obtain rock properties for both the preyield and post-yield period. The wells were categorized into ones that had massive sand production and ones that showed much less sand production. Operational and mechanical factors that were empirically found to result in sand production were identified. The sand-production model was run to verify the role played by different factors. It is shown that completion design, rock strength, and post-failure behavior of the rock are key factors responsible for the observed sanding in these wells. In addition, the drawdown strategy and the associated bottomhole pressure (BHP) change and the extent of depletion play an important role in the sanding rate. Several strategies for minimizing sand production are suggested for these wells. These include drawdown management, completion, and perforation design. In this study, we show for the first time that data from HPHT gas wells that have severe sand-production problems can be analyzed quantitatively with the developed model to determine the mechanisms of sand production. This allows us to make operational recommendations to minimize sanding risk in these wells.

The Erskine Field, Block 23/26b, UK North Sea

AbstractThe Erskine high-pressure–high-temperature gas condensate field was the first such field developed in the UK Continental Shelf. Since production started in 1997, the field has produced over 350 bcf of gas and 70 MMbbl of condensate. The reservoir pressure has depleted from an initial pressure of 960 bar (13 920 psi) down to 140–400 bar (2030–5800 psi), resulting in some compaction and sand production in some of the wells. Free water production has led to the formation of wellbore scale, which has required interventions to remove.The reservoirs are sandstones of the Jurassic Puffin, Pentland and Heather formations. Estimates of hydrocarbons in place made using production and pressure data compare favourably with the initial estimates made during field development planning, although the Pentland Formation volume is some 20% below the sanction estimate.Several major field outages have occurred, such as a condensate fire in 2010 and a blockage of the multiphase export pipeline in 2007. In addition, the field has experienced flow assurance problems related to scale and wax deposition. A new pipeline section was installed in 2018 to bypass a full pipeline blockage which occurred due to wax deposition.

Prevention of Barite Sag in Oil-Based Drilling Fluids Using a Mixture of Barite and Ilmenite as Weighting Material

Drilling high-pressure high-temperature (HPHT) wells requires a special fluid formulation that is capable of controlling the high pressure and is stable under the high downhole temperature. Barite-weighted fluids are common for such purpose because of the good properties of barite, its low cost, and its availability. However, solids settlement is a major problem encountered with this type of fluids, especially at elevated downhole temperatures. This phenomenon is known as barite sag, and it is encountered in vertical and directional wells under static or dynamic conditions leading to serious well control issues. This study aims to evaluate the use of barite-ilmenite mixture as a weighting agent to prevent solids sag in oil-based muds at elevated temperatures. Sag test was conducted under static conditions (vertical and inclined) at 350 °F and under dynamic conditions at 120 °F to determine the optimum ilmenite concentration. Afterward, a complete evaluation of the drilling fluid was performed by monitoring density, electrical stability, rheological and viscoelastic properties, and filtration performance to study the impact of adding ilmenite on drilling fluid performance. The results of this study showed that adding ilmenite reduces sag tendency, and only 40 wt.% ilmenite (from the total weighting material) was adequate to eliminate barite sag under both static and dynamic conditions with a sag factor of around 0.51. Adding ilmenite enhanced the rheological and viscoelastic properties and the suspension of solid particles in the drilling fluid, which confirmed sag test results. Adding ilmenite slightly increased the density of the drilling fluid, with a slight decrease in the electrical stability within the acceptable range of field applications. Moreover, a minor improvement in the filtration performance of the drilling fluid and filter cake sealing properties was observed with the combined weighting agent. The findings of this study provide a practical solution to the barite sag issue in oil-based fluids using a combination of barite and ilmenite powder as a weighting agent to drill HPHT oil and gas wells safely and efficiently with such type of fluids.

Defect Engineering of Titania and Hematite Thin Films By Advanced Plasma Deposition Triggers High Photoelectrochemical Water Splitting Activity

The development of highly efficient energy conversion/storage devices has attracted attention from scientific and technological researchers due to the increasing concerns about the environment and the depletion of fossil fuels. In this context, the development of cost-competitive materials capable of producing fuels or electricity directly from the energy harvested from sunlight offers a desirable approach towards fulfilling the need of clean energy. Semiconductor metal oxides (e.g., TiO2, α-Fe2O3, WO3 or ZnO) are the most widely adopted materials for the conversion of solar energy into storable and transportable chemical energy such as hydrogen (H2) via the photo-electrochemical water splitting (PEC-WS), where they serve as so-called photoanodes. Especially hematite (α-Fe2O3) and titania (TiO2) based photoanodes have attracted great amount of interest in the field of PEC-WS, however their overall efficiency for solar-driven applications still remain rather low for practical application. The defect engineering (DE) has become an important research direction for improving the optical and electronic properties of these materials towards highly efficient PEC processes. For example the discovery of black TiO2 by Chen and Mao in 2011 [1] with its substantially enhanced solar absorption has recently triggered a worldwide research interest. In spite of their remarkable enhancement in visible light absorption black TiO2 has demonstrated expected photocatalytic and PEC performance. The introduction of oxygen vacancies has been shown as an effective approach to improve the activity of α-Fe2O3 photoelectrodes [2].The main limitation related to the current DE approaches is that they are predominantly realized via a high-pressure high-temperature gas reduction. However, this methodology severely reduces the possibility to influence the DE process itself and the final properties of the material in a very fine manner, which is undoubtedly the key to precisely understand all the induced electronic changes and related phenomena. In the presented work, we address this significant drawback by utilizing a novel deposition method based on high-impulse magnetron sputtering (HiPIMS) for the deposition of titania and hematite films under the DE conditions. This method offers the desired capability of high process controllability due to the unique deposition plasma properties. By adjusting the deposition conditions, we can regulate the extent of induced defects and under significantly reduced temperature. [3, 4] Hematite, α-Fe2O3, is considered as one of the most promising materials for PEC-WS with a theoretical solar-to-hydrogen efficiency of 17%. However, the poor electrical conductivity and short diffusion length of photogenerated holes are substantial limitations reducing hematite’s efficiency in real experimental conditions. Here, we report on addressing these two drawbacks by deposition of very thin nanocrystalline hematite films (~ 30 nm) HiPIMS. Despite of computing models suggesting that the electrical conductivity is extremely anisotropic, revealing up to four orders of magnitude higher electron transport with conduction along the (110) hematite crystal plane, synthetic approaches allowing the sole growth in that direction have not been reported yet. We present a new strategy based on HiPIMS for tuning the crystal orientation of 2D thin hematite films by carefully controlling the energy of particles bombarding the substrate during the plasma assisted deposition procedure. [3] The PEC activity can be even boosted when commonly used fluorine doped tin oxide (FTO) conductive substrate is substituted by platinized substrate. Oriented platinum substrate can induce crystalline defects in hematite film during its growth under very high-energy bombardment, which are thermodynamically difficult to obtain. Such anomalies further considerably increase final PEC activity of hematite photoanodes. The enhanced photoactivity of α-Fe2O3@Pt is attributed to several synergistically contributing features ;namely: (i) a higher electrical conductivity due to self-doping oxygen vacancies; (ii) the formation of an intrinsic heterojunction between the distorted and typical hematite phases that ensures highly efficient separation of photogenerated charge carriers, and (iii) increased optical absorption due to enhance intensity in metal-to-ligand charge-transfer (MLCT). According to our best knowledge, the achieved photocurrent density of 1.1 mA/cm2 at 1.5 V vs. RHE represents the champion values among ultrathin undoped hematite based photoanodes. Acknowledgments The authors gratefully acknowledge the support by the Operational Programme Research, Development and Education - European Regional Development Fund, project no. CZ.02.1.01/0.0/0.0/15_003/0000416 of the Ministry of Education, Youth and Sports of the Czech Republic. References Chen, L. Liu, P. Y. Yu, S. S. Mao, Science, 2011, 331, 746-750.Forster, R. J. Potter, Y. Ling, Y. Yan et al., Chem. Sci., 2015, 6, 4009-4016.Kment, P. Schmuki, Z. Hubicka, et al., ACS Nano, 2015, 9, 7113-7123.Kment, Z. Hubicka, et al., Appl. Catal. B-Environ., 2015, 165, 344-350.

Experiments on Jet Noise Reduction with a Liquid Column

A liquid column is designed and placed into the tail tube to effectively reduce the gas jet noise of a single rocket. The diffusion and mixing process of high-temperature high-pressure gas flow in the liquid water column in the air is studied by means of a high speed photographic system. The gas–liquid mixture jet noise has also been measured. The experimental results indicate that, when the liquid water column is put into the tail tube, the jet flow structure is changed and the jet flow parameters (velocity, temperature, etc.) are decreased due to the interaction of the gas jet with the liquid column. In addition, the jet noise is significantly reduced in the presence of the liquid column, compared with the condition without the liquid column. When the mass of the liquid column increases to 1.485 kg, the jet noise is reduced to a minimum in the shooter location. The peak sound pressure level also decreases with increasing polar angle. Most importantly, the thrust performance of the rocket engine is maintained when the liquid column is introduced.

Prediction of Temperature and Pressure Distribution in HTHP Injection Gas Wells with Thermal Effect of Wellbore

In this article, a coupled system model of differential equations was derived in radial form to predict the pressure, temperature of formation, and temperature of wellbore in high-temperature–high-pressure gas wells. In the model, the thermal effect of formation was simplified as heat conduction, both the steady heat transmission model in the gas wellbore and the unsteady heat conduction model in the formation were considered, and the pressure effect due to variations in temperature was considered according to the gas equation of state, which links the temperature with the pressure. The finite difference method was used to simulate the solutions of the coupled models. The basic data for X Well (high-temperature–high-pressure gas well, 7,100 m deep) in China were used for case history calculations and a sensitivity analysis was performed for the models. Graphs of the curves for gas pressure and temperature along the depth of the well were plotted with different gradients, injection volumes, and the characteristic of heat transfer in the formation. The results provide technical reliability in well test design in high-temperature–high-pressure gas wells and the dynamic analysis of production.

Numerical Modelling Study of Oil–Gas–Water Three-phase Transient Bubbly Flow in HTHP Wells

A coupled system model of partial differential equations concerning pressure, temperature, and velocity of gas–liquid–liquid three-phase transient flow in high-temperature, high-pressure (HTHP) wells is presented, according to mass, momentum, and energy balances as well as the stated equation of gas. A solution framework shared by the basic models is built, which makes it convenient to perform the solution process. The finite difference method was adopted to simulate the model. Based on the unified solution framework, the singular value decomposition (SVD) algorithm is employed to solve the large linear equations for the proposed model. The average value is adopted to solve the redundancy of model. The basic data for X Well (a 7,110-m-deep HTHP well in Sichuan, China) were used for case history calculations. Pressure, temperature, and velocity curve graphs along the depth of the well were plotted at different times, intuitively reflecting the flow law and the characteristics of heat transfer along a formation. The results can provide technical reliability in the process of designing well tests for HTHP gas wells and a dynamic analysis of production.

Analysis on Casing Size and Steel Grade and Application in High-Temperature High-Pressure Gas Wells

Analysis on casing size and steel grade and application in high-temperature high-pressure gas wells are important in natural gas production engineering. This paper presents the standard casing size series, casing steel grade standard and code, types of casing steel grade, main problems in high-temperature high-pressure gas wells, using casing material suitable as solving means for high-temperature high-pressure gas well and application. For application, the study above is good and easy for on-the-spot application.

Low cycle cement fatigue experimental study and the effect on HPHT well integrity

Cement sheath is very important to maintain wellbore integrity in high pressure high temperature (HPHT) wells and steam injection wells. Due to the HPHT cycles experienced in the process of hydraulic fracturing, production and steam injection, the failure probability of low cycle cement fatigue is high in these wells and is likely to cause the failure of the zonal isolation and increase the casing failure probability. The experiment was set up to simulate conditions under which cement low cycle fatigue failure can occur. In the test, the casing was applied with zero based cyclic pressure to study the cement failure characteristics. The cement mechanical properties were measured at 14 days curing time under three different conditions: (1) room condition; (2) 167 °F, 14.7 psi; (3) 212 °F, 2610 psi; and used as the input data for finite element method analysis. The cement elastic strain and plastic strain developed in the experimental test was calculated by finite element method and thereby the cement cycles to failure can be predicted based on the strain–cycle relationship. As the confining pressure increase, the cement shows more plasticity and can hold more pressure cycles. At the temperature below 300 °F, the stress developed by thermal expansion has minor effect on the cement low cycle fatigue. The cement with higher Poisson's ratio and lower Young's modulus shows better low cycle fatigue behavior. The results of strain–cycle relationship were applied in HPHT gas wells in south Texas to predict the cement fatigue failure under different operations. This paper proposes the low cycle fatigue failure envelope that can help reduce the cement failure and improve the cement design in HPHT wells and steam injection wells.

HPHT viscosities measurements of mixtures of methane/nitrogen and methane/carbon dioxide

Gas production worldwide has been steadily increasing over the past 15 years. This growing demand for natural gas is driving the E&P industry to look for new resources in previously unexplored and deeper areas, where High Pressure High Temperature (HPHT) reservoirs may be encountered. These are reservoirs that exhibit pressures greater than 10,000 psia and temperatures over 300 °F. Thus, more attention must be paid to gas properties at HPHT conditions.Among all gas properties, viscosity is seldom measured in the laboratory and typically estimated through correlations. At HPHT conditions, the reservoir fluids will typically be very lean gases (e.g. methane with some degree of impurity) and therefore the gas properties may differ from those at lower pressures and temperatures. Consequently, the accuracy of gas viscosity correlations that are not experimentally validated at HPHT conditions may be doubtful.A review of a large database of published viscosity data for pure methane and mixed hydrocarbons revealed that they are limited in terms of both experimental conditions and quantity, and in some cases their accuracy is unknown.New HPHT gas viscosity correlations were derived using a set of viscosities of pure methane (CH4), mixtures of methane/nitrogen (CH4/N2) and mixtures of methane/carbon dioxide (CH4/CO2) measured using an oscillating piston viscometer at HPHT conditions.

Predicting on Distribution of Temperature, Pressure, Velocity, and Density of Gas Liquid Two-phase Transient Flow in High Temperature-High Pressure Wells

The authors present a predicting model concerning pressure, temperature, density, and velocity of gas liquid two-phase transient flow in high-temperature–high-pressure wells, according to mass, momentum, and energy balances. The finite difference method is used to solve the model. A high-temperature–high-pressure gas well (6,115 m deep) in Sichuan Province of China is used to check the efficiency of the proposed model and the algorithms.

HPHT 101-What Petroleum Engineers and Geoscientists Should Know About High Pressure High Temperature Wells Environment

On April 20, 2010, BP’s Deepwater Horizon oil rig exploded in the Gulf of Mexico. This turned out to be one of the worst environmental disasters in recent history. This high-profile blowout at the Macondo well in the Gulf of Mexico, brought the challenges and the risks of drilling into high-pressure, high-temperature (HPHT) fields increasingly into focus. New Technology, HSE regulations, new standards, such as newly recommended procedures by the American Petroleum Institute (API), and extensive training programs for the drilling crew seem to be vital in developing HPHT resources. High-pressure high-temperature fields exist in Gulf of Mexico, North Sea, Southeast Asia, Africa and the Middle East. Almost a quarter of HPHT operations worldwide are expected to happen in the American continent particularly in North America. Major oil companies have tried to identify key challenges in HPHT development and production, and several service companies have offered many insights regarding current or planned technologies to meet these challenges. However, there are so many factors that need to be addressed and learned in order to safely overcome the challenges of drilling into and producing from HPHT oil and gas wells.Drilling into HPHT wells is a new frontier for the oil and gas industry. The growing demand for oil and gas throughout the world is driving the exploration and production industry to look for new resources. Some of these resources are located in deeper formations. According to US Minerals Management Service (MMS), over 50% of proven oil and gas reserves in the US lie below 14,000 ft. subsea. As we drill into deeper formations we will experience higher pressures and temperatures.Drilling operations in such high pressure and high temperature environments can be very challenging. Therefore, companies are compelled to meet or exceed a vast array of technical limitations as well as environmental, health and safety standards. This paper explains the technological challenges in developing HPHT fields, deepwater drilling, completions and production considering the reports from the Bureau of Ocean Energy Management, Regulation and Enforcement (BOEMRE), formerly known as the Minerals Management Service (MMS). It reviews the HPHT related priorities of National Energy Technology Laboratory (NETL), operated by the US Department of Energy (DOE), and DeepStar Committees for Technology Development for Deepwater Research.

Analyzing Packer's Deformation of Tubular for Unsetting Process in HTHP Wells under Variable (T, P) Fields

In this paper, the axial stress and deformation of high temperature high pressure super-deep deviated gas wells are studied. A new model presents multiple nonlinear equation systems, which comprehensively consider the axial load of the tubular string, internal and external fluid pressure, normal pressure between the tube and well wall, friction and the viscous friction of fluid flowing under variable temperature and pressure fields, instead of the traditional methods. The initial axial load, the pressure effect, the friction, temperature effect and sucker-rod pumping effect are derived using a dimensionless iterative interpolation algorithm. Basic data from the X Well (high temperature-high pressure gas well), 6115 meters deep, are used for case history calculations. The results and some useful conclusions could provide technical reliability in oil and gas well testing design.

Predicting the Dryness Fraction of Gas, Pressure, and Temperature for Steam Injection Based on Unsteady Heat Transmission

Presently, a coupled system model of differential equations is proposed to predict the dryness fraction of gas, the pressure, the temperature in the wellbore, and the temperature in the stratum. In this model, the authors consider the energy loss caused by the friction of the stem flow and the unsteady heat transmission, which caused the change of the temperature in the stratum, from the second interface to the stratum. Then the fourth-order Runge-Kutta method and the finite difference method are interactively applied to solve the model. Finally, a high-temperature–high-pressure gas well (7,100 m depth) in the Sichuan province of China is used to check the efficiency of the proposed model and the algorithms.