Flow Of Gas Wells Research Articles

Dynamic Simulation of the Stability of Annular Flows in Gas Wells

This paper provides a holistic view of the development and progression of multiphase gas-liquid annular flow in gas wells. With the help of a momentum balance, the stability of a fully developed annular flow is defined. The Euler-Euler model was used to model the multiphase flow system, while the Reynolds-Averaged Navier–Stokes (RANS) model was used to depict a time-dependent solution for a vertical fluid flow system, considering acceleration due to gravity and fluid compressibility. The resultant flow regime was tested for stability by gradually reducing the field velocity of flow and observing the effects using a computational fluid dynamics (CFD) software. The principal parameters considered are the superficial gas velocity and liquid film flow rate. The properties of the region where the flow becomes unstable are documented and related to the incidence of liquid loading in a typical gas well. The effect are critically observed and compared to flow regimes at lower superficial gas velocity. The resultant flow regime configurations are analyzed and compared to the annular flow system. This study will help researchers understand the behaviour of gas wells that have potential in developing liquid loading problems and the movement of liquid film on the wall of the tubing when in annular flow regime.

Study on water hammer effect and tubing string vibration in high-pressure high-production gas wells

The transient internal flow in high-pressure high-production gas wells generates severe water hammer and tubing string vibration, which accelerates fatigue damage, joint wear, thread loosening, and other wellbore integrity problems. Based on the analysis of transient flow in gas wells, a mathematical model for fluid pressure surge and the induced tubing string vibration is developed and validated by similarity experiments. This method considers fluid-structure interaction, initial loads of tubing string, and compressibility of natural gas, and can fill the gap in quantification of water hammer pressure and tubing sting dynamic load in high-pressure high-production gas wells. On this basis, the effects of valve closure time, production rate, liquid content, and tubing string structure on transient flow and tubing string characteristics are analyzed systematically. The calculations show that wellhead pressure increases rapidly, and pressure wave propagates along tubing string to induce vibrations in the string after an instantaneous shut-in at the wellhead. During this transient process, fluid pressure and axial stress at wellhead reach their maximum valves. Owing to the fixed constraint effect of wellhead and downhole packer, the lack of restrictions on tubing distant from wellhead and packer enhances the severity of axial vibration. As valve closure time increases, the maximum wellhead pressure, tubing vibration displacement, and velocity gradually decrease. Therefore, the most direct way to control water hammer effect and tubing string vibration is to extend the shut-in time or prevent a rapid shut-in of gas well. The methods used in this study and the results obtained therein can serve as both a theoretical framework and practical foundation for the prediction and control of water hammer effect and tubing string vibration in high-pressure high-production gas wells.

出砂对气井临界携液流量的影响

出砂对气井临界携液流量的影响

A new model for calculating the critical fluid carrying rate in inclined Wells

In the preparation of gas production plan and the study of gas well proration we often judge the fluid carrying capacity of gas well by the critical fluid carrying rate of the gas well, and then adjust the production plan. At present, spherical droplet model and ellipsoidal droplet model are often used to calculate the fluid flow in gas Wells, but the spherical cap droplet model has not been concerned by relevant scholars. Therefore, we studied the application range of spherical cap droplet model, established relevant mechanical expressions, and finally obtained the formula for calculating the minimum critical liquid carrying rate of spherical cap droplet model. The results show that the spherical cap droplet model cannot be ignored in the conventional droplet model and has a wide range of applications. At the same time, the model is validated by combining with gas Wells of H gas reservoir, and the model has good applicability.

The application of modified isochronal well test in a low-permeability condensate gas field

ABSTRACTThe modified isochronal well test is a deliverability test method suitable for gas wells in low-permeability gas reservoirs. Generally, the absolute open flow of gas wells is determined by modified isochronal well test, thereby establishing a reasonable working system for gas wells. It is also possible to obtain gas layer physical parameters, gas reservoir engineering parameters, heterogeneity, boundary characteristics, etc. In this paper, the actual test data of a condensate gas field are applied. By modified isochronal well test analysis, not only the deliverability equation of the gas well is obtained, but also the absolute open flow is determined. At the same time, the formation parameters such as reservoir permeability and skin factor are obtained and the acidification effect is evaluated.

Determination of Gas Well Productivity by Logging Parameters

The prediction and evaluation of reservoir productivity is a comprehensive index of the dynamic characteristics of gas reservoirs, which can provide a reasonable basis for the design and rational distribution of gasfield development plan. Proration of gas well is an important procedure in the development process, Absolute open flow as a key indicator of rational production of gas well. It is very important to determine the absolute open flow of the gas well. The Permian in Ordos Basin is a typical tight sandstone gas reservoir. The paper analyses correlation relations between different logging parameters and absolute open flow, and get the four parameters, porosity, permeability, storage coefficient（the product of porosity and effective thickness）with better correlation relations and effective thickness with best correlation relation by combining a large amount of gas logging data and static logging data and means of linear regression analysis, Then on the basis of this, a new empirical formula for calculating the absolute open flow of gas wells is obtained by using the method of multiple linear regression. The example shows that the result of this method is reasonable and reliable and the method can provide scientific basis for the prediction of natural gas absolute open flow of tight sandstone gas reservoirs.

A new method for calculating single-point productivity equation coefficient α in heterogeneous gas reservoir

Single-point test is mainly based on quantitative statistics of productivity well testing data to obtain average α value of gas fields or blocks, then corresponding single-point productivity equation can be obtained. However, for heterogeneous gas reservoir in Ordos Basin, because of the influences of reservoir physical property and test data, there are relatively big error between calculated average α value of gas field and actual α value of single gas well, which results in application of single-point empirical formula is limited. Through derivation of binomial productivity equation in this paper, it is found that there are good linear relationship between α and reciprocal of the square of pressure 1/pR2. Combined with actual test data of Jingbian gas field, the empirical formula between α and 1/pR2 for 20 gas wells is got through regression analysis. The results indicate that new method greatly improves computational accuracy for absolute open flow of gas wells, which has good application prospect in similar gas field.

A New Model for the Accurate Prediction of Liquid Loading in Low-Pressure Gas Wells

Summary The critical gas velocity and flow rate for unloading liquids from a gas well has been the subject of much interest, especially in old gas-producing fields with declining reservoir pressures. For low-pressure gas wells, Turner's model (also called Coleman's model) is judged as more suitable for predicting liquid loading in gas wells. However, field practice proves that there are still a number of low-pressure gas wells producing without loadup when the production rate is lower than Turner's minimum production rate. On the basis of experimental results, a new approach for calculating the critical gas-flow rate is introduced in this paper, which adopts Li's basic concepts, while taking into account the impact of the changes of gas-lifting efficiency caused by the rollover of droplets in the process of rising. A dimensionless parameter, loss factor S, is introduced in the new model to characterize the extent of the loss of gas energy. Well data from Coleman's paper (Coleman et al. 1991) were used in this paper for validation of the new model. The predicted results from the new model are better than those from Li's model, and even better than Turner's model. The new model is simple and can be evaluated at the wellhead when the pressure is less than 500 psia and the liquid/gas ratios range from 1 to 130 bbl/MMscf, which is suggested by Turner et al. (1969) to ensure a mist flow in gas wells.

A Rigorous Composite-Inflow-Performance Relationship Model for Multilateral Wells

Summary Use of multilateral wells for oil and gas production has gained strong momentum in the past 5 years. However, most of the multilateral wells do not deliver hydrocarbon fluids at expected production rates. One of the reasons for this is that the well planners overestimate the productivity of wells by using inaccurate methods for predicting composite-inflow-performance relationship (IPR) of well laterals. A more-accurate method for predicting composite IPR of multilateral wells is highly desirable. This paper fills the gap. Starting from terms familiar to petroleum engineers, a general well model was developed with consideration of reservoir-wellbore crossflow for lateral IPR and coupling of fluid flow from individual laterals to the main wellbore. The model allows different IPRs of laterals and permits crossflow between laterals. Pressure losses in the vertical-, curvic- and horizontal-hole sections are rigorously considered. Oil and gas wells are treated differently. The modified Hagedorn-Brown correlation is used for modeling the flow in the vertical sections, and the Beggs and Brill correlation is used for the curvic and horizontal sections for oil wells. The Cullender and Smith method was used for modeling the flow in gas wells. A computer simulator was developed based on the model for predicting multilateral-well production rate. Case studies have indicated excellent accuracy of the computer model. This work provides petroleum engineers a reliable and user-friendly tool for designing and evaluating multilateral wells.

On the determination of the skin factor and the turbulence term coefficient through a single constant gas pressure test

The best correlation for evaluating the turbulence term coefficient, D( μ), for transient flow in gas wells under constant flow rate conditions is currently that of Lee et al. [Lee, R.L., Logan, R.W., Tek, M.R., 1987. Effect of turbulence on transient flow of real gas through porous media. SPE Form. Eval. (March), 108–120]. Several authors have used this correlation to calculate the production decline for wells that produce under constant bottomhole pressure conditions, but it is not clear if this is correct. When exploiting any gas reservoir, the flow rate and the average reservoir pressure decrease with time. This process makes D( μ) increase, whereas D( μ) q sc decreases with time; in contrast, when a well is produced under constant flow rate conditions, D( μ) q sc increases with time. Due to this fact, it can be of considerable practical interest to analyze the behavior of the high velocity pseudoskin factor, D( μ) q sc, for gas wells that produce under constant bottomhole pressure conditions. This paper presents the results of a study aimed at obtaining a correlation of both the mechanical skin factor, s, and the turbulence term coefficient, D( μ), for constant bottomhole pressure conditions through the analysis of a single test. Results obtained through a radial real gas flow simulator, carefully validated for pseudosteady state conditions were used as a database for the development of the new correlations. The skin effect considered varies from 0 to 10. Two different gases are considered. Other variables studied are the constant pressure, the reservoir size r e/ r w and formation permeability. The correlation is presented by means of straight-line fits of s t/[ s(1− r w/ r d)] in the vertical axis and D( μ i) q sc in the horizontal axis. The correlation coefficient was 0.9976. The error obtained when one evaluates the skin factor, s, using the correlation presented in this work is less than 10%. The error is substantially less when production rates are low. These rates strictly correspond to the case of low permeability reservoirs, where the constant pressure boundary condition considered is this study closely apply.

Calculation of Friction Factors For Use In Flowing Gas Wells

Abstract A study of test data for a number of Alberta gas wells has revealed that flow during such tests is seldom in the "fully developed" turbulence region. Because computer programs used to calculate pressure profiles usually assume "fully developed" turbulent flow, they tend to underestimate the friction factor, and as a. result the pressure drop due to friction, in such wells. In order to avoid such bias, a subroutine, which generates the Moody friction factor chart, is present and recommended for use in computer calculation. THE CALCULATION of bottom-hole pressures or pressure profiles in flowing gas wells may be effected by various methods.(1–3) Despite the differences between these methods, they have one thing in common they all require the estimation or calculation of a friction factor. (Equation in full paper.) Although these approximate methods are handy and appropriate to desk calculation, the modern practice of calculating pressure profiles by means of high-speed computers has made such approximations unnecessary and in some instances inappropriate. For example, one may set up a simple subroutine for calculating friction factors, using the expressions employed by Moody, as is indicated in Figure 1. Such a program will permit the use of absolute roughness values other than 0＿0006 in., and will do away with approximation error. Because the Colebrook equation approaches the von Karman expression asymptotically, the point at which one changes from the former to the latter depends on the percentage error one is willing to accept at that point. Thus, if one is willing to accept a 1% error at the change-over point one should select the point Re=1600 d/E. On the other hand, one may use Re=3200 d/E for a 0.5% maximum error, as suggested by Moody, or Re = 16,000 d/E when the maximum permissible difference is 0.1 %＿ If, however, one is willing to incur the added cost of iteration in the region where f is essentially insensitive to further changes in Re, he may use the Colebrook equation for all values of Re greater than 4000. This is, in fact, the method that was employed by Aziz, Govier and Fogarasi(8). The subroutine shown in Figure 1 was tested against the Cullender – Binckley and Cullender-Smith methods at 12 points, as shown in Tables 1 and 2. This comparison showed that:friction factor remains reasonably constant over the length of the well, thereby verifying the common assumption that such is the case;flow in gas wells, of the type found in Alberta, is not usually in the fully developed turbulent region;the Cullender-Binckley method provides a reasonable estimate of friction factor in the transition region, whereas the Cullender-Smith method consistently underestimates the friction factor when turbulence is not fully developed. In addition, the comparison showed that the cost of application of the subroutine exceeds that of the Cullender-Smith method by less than 2 cents per hundred factors calculated. This subroutine was also compared to that proposed by Aziz-Govier-Fogarasi.

Parameters for Computing Pressure Gradients and the Equilibrium Saturation of Gas-Condensate Fluids Flowing in Sandstones

Abstract Data obtained by flowing two-phase fluids through sandstone cores were used to develop empirical equations for computing the pressure gradients and liquid saturations that will occur during the recovery of gas-condensate fluids like those in the Gulf Coast area. Equilibrium saturation may be computed for a given pressure, velocity, and liquid/gas ratio of flow. For this purpose, the minimum liquid flow saturation at high pressures, S, was developed for characterizing a core and a fluid. The effects of saturation on the mobility for Darcy flow and on the coefficient for non-Darcy flow are considered in an equation with parameters in addition to the Klinkenberg and Forchheimer coefficients. All parameters for these equations may be determined parameters for these equations may be determined either by routine measurements or by correlations. Introduction Fluid properties required for computing the transient flow of gas-condensate fluids and data obtained to meet this need were discussed at the 1966 SPE-AIME Fall Meeting. In the following year Dranchuk and Kolada described a means of analyzing laboratory data for nonlinear parameters pertaining to flow of gases. Gewers and Nichol pertaining to flow of gases. Gewers and Nichol investigated the effect of liquid saturation on the non-Darcy-flow term of the pressure-gradient equation. Modine and Fields used this kind of information to simulate turbulent flow in gas wells. An equation is needed for computing a more realistic value of the pressure gradient for flowing two-phase fluids than is possible with the Darcy equation. An equation is needed to compute as a boundary condition the liquid saturation possible in the porous medium near flowing wells. This paper describes two such equations that give effect paper describes two such equations that give effect to pressure, fluid velocity, liquid/gas ratio, and saturation. Seven parameters each required for the pressure-gradient and saturation equations may be pressure-gradient and saturation equations may be calculated by means of correlation equations that utilize routinely measured core properties. Concepts and Equations The Darcy equation was modified to include the Klindenberg effect "slip flow" and the Forchheimer coefficient to represent "inertial" or "turbulent" flow of gases in dry porous media,(1) By controlling the velocity (u) and pressure (p), measuring the gradient (dp/dx) and the viscosity [mu(p)], and calculating the density [p(p)], the properties k, b, and beta were determined for properties k, b, and beta were determined for representative cores by least-squares methods. As a step in the modification of Eq. 1 to obtain an equation applicable to the flow of two-phase fluids, mobility, A, for a two-phase fluid must replace the ratio of a known permeability to a viscosity, for the gas phase(2) The quantities k and mu(p) are to have the same* significance as in Eq. 1, except that mu(p) is the viscosity of a single-phase saturated gas. Relationships of liquid- and gas-phase mobilities, lambda and lambda, to fluid mobility, lambda, have been described in Appendix C of a previous publication. Briefly, lambda = lambda + lambda = f(S, p, F, u) k/mu(p). Now mu(p) is the viscosity of the flowing fluid mu under steady-state conditions only when F = 0.

Solutions of Unsteady-State Radial Gas Flow

Abstract Numerical solutions are presented to some problems of unsteady-state radial flow of gas in which Darcy's law holds. These solutions are intended to aid in explaining the observed behavior of gas wells during drawdown tests. The variation of viscosity and Z-factor with pressure is accounted for in the solutions. Results are presented for three types of problems:unfractured wells producing at a constant rate,fractured wells producing at a constant rate andunfractured wells producing through a critical flow prover. In the critical-flow-prover solutions, a correction of the calculated wellbore pressure to account for non-Darcy flow is made. A good correlation is shown between the solutions to the problem of Type 1 and the corresponding diffusivity-equation solution. Using this correlation, the diffusivity solution may be used to obtain gas-well solutions. The solutions to the problems of Type 2 illustrate the difference in drawdown-curve behavior to be expected between fractured and unfractured gas wells. Methods for estimating fracture radius and flow capacity are presented and verified from solutions of Type 2. The solutions to the problems of Type 3 illustrate the differences to be expected between critical-flow-prover drawdown tests and constant-rate tests. A equation is presented for correcting critical-flow-prover data to constant-rate conditions. A description of the methods used in obtaining the solutions appears in the Appendix. Introduction It is necessary for many engineering purposes, such as predicting future deliverability performance, to be able to relate bottom-hole flowing pressure, formation pressure and flow rate for conditions of stabilized flow in gas wells. This information is customarily given as a plot of (p -p ) vs q on logarithmic coordinates. It is desirable to be able to predict stabilized performance curves for gas wells based on data obtained from drawdown tests of short duration. Tests of long duration may be wasteful of gas, and low-permeability wells do not stabilize in a short-duration test. Although it is now commonly recognized that non-Darcy flow plays a significant part in gas-well behavior, it is believed that an understanding of transient behavior of systems obeying Darcy's law is still important in the interpretation of short-term test data, and the prediction of stabilized performance curves there from. In this connection, an equation for correcting Darcy flow solutions for non-Darcy flow effects has existed in the literature for some time. This equation is ......................................(1) It seems likely that solutions of the type presented herein, combined with the non-Darcy flow correction of the type of Eq. 1 and the usual laminar-flow skin factor, could provide a model which would adequately explain transient gas-well behavior for times after the non-Darcy flow region (which should be confined to a small area surrounding the well) has been established. The solutions presented in this paper are for three types of problems:unfractured wells producing at a constant rate,fractured wells producing at a constant rate andunfractured wells producing through a critical flow prover. In the problems of Types 1 and 2, no corrections for non-Darcy flow were made in the results presented, since it was reasoned that the constant-rate boundary condition would facilitate such a correction if it was desired later. For the problems of Type 3, however, a condition of varying flow rate required that a non-Darcy flow correction of the type of Eq. 1 be included. This was done. Based on the numerical results presented, a number of approximations and a correlation are presented which may be useful in analyzing gas-well test data. TYPE 1 PROBLEMS-UNFRACTURED WELL, CONSTANT FLOW RATE It is assumed that the system can be described as a finite cylindrical gas reservoir produced by a single cylindrical well located at the center of the reservoir. Flow is strictly radial. When the flow obeys Darcy's law, the governing differential equation is ..........(2) where M(p) = (2,703 x 10(–6) x 520), and f(R) =. Boundary and initial conditions are: ...................(3) JPT P. 549^

Determining Friction Factors for Measuring Productivity of Gas Wells

Abstract The theoretical background for calculating friction factors for flow in gaswells by two methods is presented. The first method, requiring pressures, temperatures and specific volumes of the flowing fluids at various depths inthe well bore, shows how the mechanical-energy-balance equation for verticalflow may be graphically integrated over the actual path of the expansion of thefluid in the well. Thus, assumptions regarding the effective temperature andeffective compressibility of the fluid in the well are avoided. The secondmethod presents an equation derived on a basis of the assumptions that both thetemperature and the compressibility are fixed at constant effective valuesthroughout the flowing column of gas. The second method provides a convenientand practical means of calculating friction factors for gas wells and lendsitself readily to the problem of calculating subsurface pressures in a flowinggas well. The application of both methods to actual test data taken on aflowing gas well is illustrated in the paper. Introduction As friction factors for the producing strings of flowing gas wells cannot bemeasured directly and must be calculated from flow-test data, study of themethods of arriving at friction factors is a necessary adjunct to understandingthe characteristics of flow in gas wells. There are two methods of calculatingfriction factors for gas wells; they differ from one another mainly in thetreatment of the path of expansion of the fluid in the well. In the flowingwell, the energy consumed in lifting the fluid from the bottom to the top ofthe well, overcoming the friction between the moving fluid and the pipe walls, and increasing the velocity of the fluid as it flows up the producing string issupplied by expansion of the flowing fluid. The available energy is determined, by the expansion of the fluid that follows a path determined by conditions oftemperature, compressibility and phase changes of the fluid during theexpansion. A means of evaluating the available energy in a flowing gas well anddetermining the proportion of the available energy used in lifting the gas, overcoming friction, and increasing the velocity of flow is developed in thisreport. Knowing how much energy is consumed in overcoming friction makes itpossible to calculate friction factors for given flow rates in given sizes ofpipes in wells. T.P. 2777

A Radial Turbulent Flow Formula

Abstract A radial turbulent flow formula has been developed which permits thecomputation of the pressure drop for radial flow in gas wells whether the flowis laminar, turbulent, or partially laminar and partially turbulent. Using theformula a complete back-pressure curve has been calculated and analyzed by acomparison with existing back-pressure curves. A procedure is presented forcomputing the permeability of the porous media when the porosity, sphericityand average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided newmethods for computing flow under turbulent conditions. The present study wasinitiated as an investigation of pressure-drop computations for flow throughporous sands in gas wells and as an analysis of present-day back-pressuretests. Although laminar flow exists in the producing formation of gas wells undernormal flow rates, turbulent flow does take place adjacent to the well bore. Asthe flow rate is increased, turbulent flow exists further and further into theproducing formation and under open-flow conditions in relatively deep wells aconsiderable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wellswithout resorting to extrapolation of curves drawn from data obtained inback-pressure tests or calculations made in the completely laminar region, itwas necessary to have some means of calculating pressure drop for flow throughporous sands under turbulent conditions. As a result, a radial turbulent flowformula was derived from the equations recently presented by Brownell andKatz. A rigorous solution of this equation involves a trial and error graphicalintegration. By making the assumptions of average viscosity, temperature andcompressibility factor of the flowing gas, it was possible to graphicallyintegrate the relation for the general case of radial flow of gases through theporous sand of gas wells. A chart has been prepared relating the value of theintegral to the radius of the well bore and to the Reynolds number of theflowing gas. The chart actually performs the graphical integration and thesolution of the formula is then reduced to a simple trial and errorcalculation. A typical back-pressure curve is calculated to show the transitionfrom laminar to turbulent flow. This paper will briefly describe the procedures for computing flow throughporous media, including a method for predicting sand permeability from porosityand grain size and shape. Flow Through Porous Media Brownell and Katz recently reported a correlation for computing flow of fluidsthrough porous media by the use of an enlarged Reynolds number and frictionfactor in which the porosity of the bed is included as an additional primevariable. T.P. 2304