B. Qi

Pressure and Temperature Prediction of Transient Flow in HTHP Injection Wells by Lax-Friedrichs Method

The authors present a system model of partial differential equations concerning the variation of the pressure and temperature at different time and depth in high temperature-high pressure (HTHP) gas wells. Finite difference methods with Lax-Friedrichs scheme are improved to solve this set of conservation equations. The basic data of X Well (HTHP well), 7,100 m deep, located in Sichuan basin, Southwest China, is used for case history calculations. Gas pressures, temperature curve graphs along the depth of the well are plotted at different time. Comparing with the results without considering the influence of heat-transmission, the calculating results are more fitting to the values of real measurement. The comparison indicates that the new method is of high accuracy.

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.

Analyzing axial stress and deformation of tubular for steam injection process in deviated wells based on the varied (T, P) fields.

The axial stress and deformation of high temperature high pressure deviated gas wells are studied. A new model is multiple nonlinear equation systems by comprehensive consideration of axial load of tubular string, internal and external fluid pressure, normal pressure between the tubular and well wall, and friction and viscous friction of fluid flowing. The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. The axial load, the normal pressure, the friction, and four deformation lengths of tubular string are got ten by means of the dimensionless iterative interpolation algorithm. The basic data of the X Well, 1300 meters deep, are used for case history calculations. The results and some useful conclusions can provide technical reliability in the process of designing well testing in oil or gas wells.

The Prediction of Distribution of Temperature, Pressure, Density, and Velocity in High-Temperature–High-Pressure Gas Wells

Abstract In this article, we present a coupled system model of differential equations concerning pressure, temperature, density, and velocity in high-temperature–high-pressure wells, according to mass, momentum, and energy balances. We present an algorithm solution model, along with the fourth-order Runge-Kutta method. The basic data of well X (high-temperature–high-pressure gas well), 7,100 m deep, in China, is used for case history calculations and a sensitivity analysis is made for the model. Gas pressure, temperature, velocity, and density curve graphs along the depth of the well are plotted with different outputs, intuitively reflecting the gas flow law and the characteristics of heat transfer along a formation. The results can provide technical reliability in the process of designing well tests in high-temperature–high-pressure gas wells and a dynamic analysis of production.

A Feasibility Analysis of Three Numerical Schemes for the Prediction of Two Phase Transient Flow

This paper presents a coupled system model of partial differential equations concerning the variation of pressure and temperature, velocity and density at different time and depth of two-phase flow wells in HTHP statement. LxF, CE/SE and GRP method are modified to solve this set of conservation equations. The basic data of ‘X Well’ (HTHP well), 7100 m deep, located in Sichuan basin, South-west of China, is used for the case history calculations. The comparison of pressures and temperatures calculated by those methods shows that the model is efficient and GRP method is of highest accuracy, which will be an important technical reliance for the process of designing well tests in HTHP wells.

Optimisation of Inclination for the Productivity in HTHP Slanted Well

A new mathematical model is set up to optimise the productivity in High temperature-High Pressure slanted well considering the effect of inclination in this paper. We constructed an optimisation method of the production calculated model based on the deviation value inclination and obtained the optimisation results. The simulation results are based on the historic calculation, using basic data of ‘X Well’ (HTHP well), 7100 m deep, located in Sichuan basin, South-West of China. The optimisation of the value in the model on wellbore inclination can efficiently enhance the production of slanted well, which can provide a theoretical guidance in well trajectory design.

Predicting the Distribution of Pressure, Temperature, Velocity, and Density of Three-phase Bubbly Flow in HTHP Wells

A one-dimensional, thermal, steady state mathematical model is presented, which can be used for determining the pressure, temperature, velocity and density distributions of three-phase flow. The numerical solution, which consists of mass, momentum, and energy conservation equations, is based on the four order Runge-Kutta method. Due to the sensitivity of gas holdup, an improved model is performed and makes the result more stable. The average value is adopted to meet the redundancy of model. The data of X Well, 7110 m deep, in Sichuan, China, is used for case calculations and a sensitivity analysis is made for the model.

The Prediction of Pressure, Temperature, Velocity, and Density of Two-phase Flow in Shut-in Procedures for the HTHP Gas Wells

A coupled system model of differential equations of pressure, temperature, velocity, and density of two-phase flow in shut-in procedures in HTHP gas wells is examined. The basic data of X Well in Sichuan, China, is used for case calculations. Fluid pressure, temperature, velocity, and density curve graphs along the depth of the well are plotted at different times.

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.

Prediction Pressure and Temperature in Shut-in Procedures for HTHP Deviated Wells

A coupled system model of differential equations of pressure, temperature in shut-in procedures for high-temperature and high-pressure (HTHP) deviated gas wells was developed. Based on the Cullender-Smith method, we focus on the heat transmission in the stratum, and then calculate the temperature through differential equation. The basic data of X Well (HTHP well), 7,100 m deep, in Sichuan, China, is used for case history calculations. Gas pressure and temperature curve graphs along with the well are plotted at different times, intuitively reflecting flow law and the characteristics of the shut-in procedures.