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

1974 ◽  
Vol 14 (03) ◽  
pp. 203-215 ◽  
Author(s):  
Jerry D. Ham ◽  
James P. Brill ◽  
C. Kenneth Eilerts
Keyword(s):  
Turbulent Flow ◽  
Pressure Gradient ◽  
Gas Phase ◽  
Gas Condensate ◽  
Darcy Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Darcy Equation ◽  
Liquid Saturation ◽  
Gas Ratio

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.

A Robust Asymptotically Based Modeling Approach for Two-Phase Flow in Porous Media

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
M. M. Awad ◽  
S. D. Butt
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Single Phase ◽  
Present Model ◽  
Flow In Porous Media ◽  
Pressure Gradients ◽  
Two Phase ◽  
New Model ◽  
Proposed Model ◽  
Phase Liquid

A simple semitheoretical method for calculating the two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x≅0 is nearly identical to the single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x≅1 is nearly identical to the single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (ϕl2) or a two-phase frictional multiplier for gas flowing alone (ϕg2) as a function of the Lockhart–Martinelli parameter X. The advantage of the new model is that it has only one fitting parameter (p), while the other existing correlations, such as the correlation of Larkins et al., Sato et al., and Goto and Gaspillo, have three constants. Therefore, calibration of the new model to the experimental data is greatly simplified. The new model is able to model the existing multiparameter correlations by fitting the single parameter p. Specifically, p=1/3.25 for the correlation of Midoux et al., p=1/3.25 for the correlation of Rao et al., p=1/3.5 for the Tosun correlation, p=1/3.25 for the correlation of Larkins et al., p=1/3.75 for the correlation of Sato et al., and p=1/3.5 for the Goto and Gaspillo correlation.

A Robust Asymptotically Based Modeling Approach for Two-Phase Flow in Porous Media

2008 ◽  
Author(s):  
M. M. Awad ◽  
S. D. Butt
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Single Phase ◽  
Theoretical Method ◽  
Flow In Porous Media ◽  
Pressure Gradients ◽  
Two Phase ◽  
New Model ◽  
Proposed Model ◽  
Phase Liquid

A simple semi-theoretical method for calculating two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x ≅ 0 is nearly identical to single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x ≅ 1 is nearly identical to single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (φl2) or two-phase frictional multiplier for gas flowing alone (φg2) as a function of the Lockhart-Martinelli parameter, X. The advantage of the new model is that it has only one fitting parameter (p) while the other existing correlations such as Larkins et al. correlation, Sato et al. correlation, and Goto and Gaspillo correlation have three constants. Therefore, calibration of the new model to experimental data is greatly simplified. The new model is able to model the existing multi parameters correlations by fitting the single parameter p. Specifically, p = 1/3.25 for Midoux et al. correlation, p = 1/3.25 for Rao et al. correlation, p = 1/3.5 for Tosun correlation, p = 1/3.25 for Larkins et al. correlation, p = 1/3.75 for Sato et al. correlation, and p = 1/3.5 for Goto and Gaspillo correlation.

Prediction of Pressure Gradients in Pipeline Systems during Two-Phase Flow

1969 ◽  
Vol 184 (3) ◽  
pp. 24-32 ◽  
Author(s):  
D. Chisholm ◽  
L. A. Sutherland
Keyword(s):  
Turbulent Flow ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Friction Pressure ◽  
Pipeline Systems ◽  
Pressure Changes

Simple procedures using charts for predicting friction/pressure gradients during turbulent-turbulent flow in pipes and the pressure changes over bends, changes of section, and valves are presented. For friction/pressure gradients comparison is made with the procedures of Baroczy, Lockhart and Martinelli, Martinelli and Nelson, Collier, Becker et al., and Thom.

Review and Modeling of Two-Phase Frictional Pressure Gradient at Microgravity Conditions

2010 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Gradient ◽  
Single Phase ◽  
Present Model ◽  
Theoretical Method ◽  
Asymptotic Model ◽  
Pressure Gradients ◽  
Two Phase ◽  
Proposed Model ◽  
Microgravity Conditions ◽  
Phase Liquid

First, a detailed review of two-phase frictional pressure gradient at microgravity conditions is presented. Then, a simple semi-theoretical method for calculating two-phase frictional pressure gradient at microgravity conditions using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x ≅ 0 is nearly identical to single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x ≅ 1 is nearly identical to single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (φl2) or two-phase frictional multiplier for gas flowing alone (φg2) as a function of the Lockhart-Martinelli parameter, X. Comparison of the asymptotic model with experimental data at microgravity conditions is presented.

Two-Phase Flow Modeling in Microchannels and Minichannels

2008 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Gradient ◽  
Two Phase Flow ◽  
Effective Property ◽  
Theoretical Method ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Flow Modeling ◽  
Two Phase ◽  
Asymptotic Modeling ◽  
Modeling Approach

In the present paper, three different methods for two-phase flow modeling in microchannels and minichannels are presented. They are effective property models for homogeneous two-phase flows, an asymptotic modeling approach for separated two-phase flow, and bounds on two-phase frictional pressure gradient. In the first method, new definitions for two-phase viscosity are proposed using a one dimensional transport analogy between thermal conductivity of porous media and viscosity in two-phase flow. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. In the second method, a simple semi-theoretical method for calculating two-phase frictional pressure gradient using asymptotic analysis is presented. Two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the final method, simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient in minichannels and microchannels. In all cases, the proposed modeling approaches are validated using the published experimental data.

Modeling of Interfacial Component for Two-Phase Frictional Pressure Gradient in Microchannels and Minichannels

2011 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Single Phase ◽  
Simple Approach ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Interfacial Pressure ◽  
Proposed Model ◽  
Phase Liquid

A simple approach for calculating the interfacial component of frictional pressure gradient in two-phase flow in microchannels and minichannels is presented. This approach is developed using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. The proposed model can be transformed in two different ways. First, two-phase interfacial multiplier for liquid flowing alone (φl,i2) as a function of two-phase frictional multiplier for liquid flowing alone (φl2) and the Lockhart-Martinelli parameter, X. Second, two-phase interfacial multiplier for gas flowing alone (φg,i2) as a function of two-phase frictional multiplier for gas flowing alone (φg2) and the Lockhart-Martinelli parameter, X. This proposed model allows for the interfacial pressure gradient to be easily modeled. Comparisons of the proposed model with experimental data for microchannels and minichannels and existing correlations for both φl and φg versus X are presented.

Bounds on Two-Phase Flow: Part I — Frictional Pressure Gradient in Circular Pipes

2005 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Turbulent Flow ◽  
Pressure Gradient ◽  
Published Data ◽  
Two Phase ◽  
Working Fluids ◽  
Circular Pipes ◽  
Mass Fluxes ◽  
Wide Range ◽  
Flow Part ◽  
Fanning Friction Factor

Simple rules are developed for obtaining rational bounds for two-phase frictional pressure gradient. Both the lower and upper bounds are based on the separate cylinders formulation. The lower bound is based on turbulent-turbulent flow that uses the Blasius equation to represent the Fanning friction factor. The upper bound is based on an equation that represents well the Lockhart-Martinelli correlation for turbulent-turbulent flow. The model is verified using published experimental data of two-phase frictional pressure gradient versus mass flux at constant mass quality. The published data include different working fluids such as R-12 and R-22 at different mass qualities, different pipe diameters, and different saturation temperatures. It is shown that the published data can be well bounded for a wide range of mass fluxes, mass qualities, pipe diameters and saturation temperatures. The bounds models are also presented in a dimensionless form as two-phase frictional multiplier (φl and φg) versus Lockhart-Martinelli parameter (X) for different working fluids such as R-12, R-22, air-oil and air-water mixtures.

Compositional Modeling of Retrograde Gas-Condensate Reservoirs in Multimechanistic Flow Domains

SPE Journal ◽  
2006 ◽  
Vol 11 (04) ◽  
pp. 480-487 ◽  
Author(s):  
Luis F. Ayala ◽  
Turgay Ertekin ◽  
Michael A. Adewumi
Keyword(s):  
Natural Gas ◽  
Gas Phase ◽  
Gas Condensate ◽  
Pressure Gradients ◽  
Gas Reservoirs ◽  
Gas Condensate Reservoirs ◽  
Fluid Behavior ◽  
Diffusive Flow ◽  
Complex Fluid ◽  
Natural Gas Reservoirs

Summary A multimechanistic flow environment is the result of the combined action of a Darcian flow component (the macroscopic flow of the phase caused by pressure gradients) and a Fickian-like or diffusive flow component (diffusive flow caused by molecular concentration gradients) taking place in a hydrocarbon reservoir. The present work presents the framework needed for the assessment of the impact of multimechanistic flow on systems where complex fluid behavior—such as that of retrograde gas-condensate fluids—requires the implementation of compositional reservoir simulators. Because of the complex fluid behavior nature of gas-condensate fluids, a fully-implicit (IMPISC-type) compositional model is implemented and the model is used for the study of the isothermal depletion of naturally fractured retrograde gas reservoirs. In these systems, especially those tight systems with very low permeability (k < 0.1 md), bulk fluid flow as predicted by Darcy's law might not take place despite the presence of large pressure gradients. The use of an effective diffusion coefficient in the gas phase—which accounts for the combined effect of the different diffusion mechanisms that could take place in a porous medium—and its relative contribution to fluid recovery is discussed. The compositional tracking capabilities of the model are tested, and the conditions where Fickian flow can be the major player in recovery predictions and considerably overcome the flow impairment to gas flow posed by the eventual appearance of a condensate barrier—typical of gas-condensate systems—are investigated. Finally, a mapping that defines different domains where multimechanistic flow can be expected in compositional simulators of retrograde gas-condensate reservoirs is presented. Introduction In typical natural-gas reservoirs, all hydrocarbons exist as a single free gas phase at conditions of discovery. Depending on the composition of the initial hydrocarbon mixture in place and their depletion behavior, we recognize up to three kinds of natural gas reservoirs: dry gas reservoirs, wet gas reservoirs, and retrograde gas or gas-condensate reservoirs. The latter is the richest in terms of heavy hydrocarbons, and thus it is very likely to develop a second heavier hydrocarbon phase (liquid condensate) upon isothermal depletion. This situation is illustrated by Fig. 1. In contrast, dry gases and wet gases do not undergo phase changes upon reservoir depletion, as their phase envelope's cricondentherms are found to the left of the reservoir temperature isotherm.

Flow Performance Investigation of Rich Gas Pipelines

2008 ◽  
Author(s):  
Daoming Deng ◽  
Jing Gong
Keyword(s):  
Pressure Gradient ◽  
Gas Flow ◽  
Single Phase ◽  
Temperature Drop ◽  
Gas Condensate ◽  
Gas Pipelines ◽  
Liquid Holdup ◽  
Two Phase ◽  
Operating Data ◽  
The Rich

For the rich gas transfer schemes, extraction of NGL from the natural gas is not required in the oil field or gas condensate field, so the gas treatment processes in the field is simplified and the expense from the storage and transportation of NGL is saved, and the gas processing plant could be located far from the field. Rich gas can be pipelined in single phase and/or in two-phase mode. Compared with the gas-condensate ones, the rich gas pipelines behave with lower liquid loading, and are easily controlled operationally. Therefore, the rich gas pipelining modes are increasingly preferred especially in offshore and desert petroleum developments. Prediction of the performances of rich gas flow in pipelines covers a series of calculations for fluid phase behavior, fluid properties, pressure gradient, liquid holdup and temperature drop. In the paper, a hydraulic and thermodynamic model for the analysis of rich gas flow in pipelines with single-phase or two-phase modes is outlined. On account of the low liquid holdup of rich gas two-phase flow in pipelines, the constitutive relation resulting from Ottens et al (2001) correlation is selected. The iterative method to compute the pressure gradient, liquid holdup, and temperature drop of a pipe increment is developed, which shows fast convergence and good stability through case computations. In the end, the performances of non-isothermal rich gas flow in the undulating offshore long-distance pipeline in China is investigated by analyzing the profiles of pressure, temperature, velocity and liquid holdup. The predicted results in this study agree well with the operating data. The theoretical analysis, and comparison of calculated results with operating data and OLGA indicate that the presented model for analyzing rich gas flow behavior in small diameter pipelines looks reasonable.

scholarly journals Hydrodynamic Modeling of Oil–Water Stratified Smooth Two-Phase Turbulent Flow in Horizontal Circular Pipes

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5201
Author(s):  
Qi Kang ◽  
Jiapeng Gu ◽  
Xueyu Qi ◽  
Ting Wu ◽  
Shengjie Wang ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Pressure Gradient ◽  
Cross Section ◽  
Volume Flow Rate ◽  
Horizontal Tube ◽  
Water Interface ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Smooth Flow ◽  
Oil Water

In the petrochemical industry, multiphase flow, including oil–water two-phase stratified laminar flow, is more common and can be easily obtained through mathematical analysis. However, there is no mathematical, analytical model for the simulation of oil–water flow under turbulent flow. This paper introduces a two-dimensional (2D) numerical simulation method to investigate the pressure gradient, flow field, and oil–water interface height of a pipeline cross-section of horizontal tube in an oil–water stratified smooth flow, which has field information of a pipeline cross-section compared with a one-dimensional (1D) simulation and avoids the significant calculation required to conduct a three-dimensional (3D) simulation. Three Reynolds average N–S equation models (k−ε, k−ω, SST k−ω) are used to simulate oil–water stratified smooth flow according to the finite volume method. The pressure gradient and oil–water interface height can be computed according to the given volume flow rate using the iteration method. The predicted data of oil–water interface height and velocity profile by the model fit well with some available experiment data, except that there is a large error in pressure gradient. The SST k−ω turbulence model has higher accuracy and is more suitable for simulating oil–water two-phase stratified flow in a horizontal pipe.

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