Gas Two-phase Flow Research Articles

Development of a Multidimensional Method for the Interaction of Liquid–Gas Two-Phase Flows with Formation of an Interphase Boundary

A method of evaluating the liquid–gas interaction with the formation of an interphase boundary is presented. The method is verified on modeling of the propagation of a shock wave in a liquid medium with gas bubbles. Good agreement with experiment is obtained. The results of numerical modeling of the downward flow of a liquid over a stationary gas bubble are presented. Verification of the method will be continued on experiments with a model coolant.

Decay of the 3D inviscid liquid–gas two-phase flow model

We establish the optimal \({L^{p}-L^{2}(1 \leq p < 6/5)}\) time decay rates of the solution to the Cauchy problem for the 3D inviscid liquid–gas two-phase flow model and analyze the influences of the damping on the qualitative behaviors of solution. Compared with the viscous liquid–gas two-phase flow model (Zhang and Zhu in J Differ Equ 258:2315–2338, 2015), our results imply that the friction effect of the damping is stronger than the dissipation effect of the viscosities and enhances the decay rate of the velocity. Our proof is based on Hodge decomposition technique, the \({L^{p}-L^{2}}\) estimates for the linearized equations and an elaborate energy method.

Study of liquid–gas two-phase flow in horizontal pipes using high speed filming and computational fluid dynamics

A study of liquid–gas two-phase flow in short horizontal pipes was carried out experimentally using a High Speed Filming (HSF) Analysis and numerical simulations. In the experiments, the flow pattern was determined and HSF were recorded for six experimental cases. Those films were analyzed using an image analysis tool that was developed, and, consequently, the void fraction as a function of time was obtained. Numerical simulations of the two-phase mixture inside the pipe were carried out with a commercial CFD software, using the Volume of Fluid (VOF) method. The void fraction and the flow pattern were thus determined. The results of the numerical simulations were compared in terms of flow pattern with the experimental data and in terms of void fraction with the HSF analysis. A good agreement was found in both cases, especially for annular and slug flow patterns.

A semi-analytical method for forecasting wells completed in low permeability, undersaturated CBM reservoirs

Exploration and development of coalbed methane (CBM) reservoirs is ongoing in the Asia Pacific region, with low permeability, undersaturated coals being the target in some areas. Horizontal wells are typically required to produce low permeability CBM reservoirs at commercial rates, and may experience a period of single-phase (water) transient flow, followed by a transition to two-phase (water + gas) transient flow. Wells exhibiting this behavior are particularly difficult to model analytically, yet simple analytical and semi-analytical tools are desirable for making quick, but reasonably accurate forecasts. The purpose of this work is to therefore provide a new forecasting methodology for low permeability, undersaturated CBM wells.The new method for forecasting CBM wells introduced in this work is based on the concept of a dynamic drainage area (DDA), recently adapted to forecast tight black oil and gas condensate wells exhibiting two-phase flow. A critical advancement provided in the current work is modeling the transition from single-phase flow of water to two-phase flow of gas and water during the transient linear flow period, which was not attempted for the black oil/gas condensate cases. Above desorption pressure, material balance, performed on the dynamic drainage area to determine average pressure in the distance of investigation, is combined with the linear flow productivity index equation to forecast water production at each time step. For two-phase flow below desorption pressure, the two-phase version of the linear productivity equation and material balance equations for water and gas are solved iteratively for pressure, saturation and fluid production rate within the DDA. The gas material balance equation accounts for desorption effects. In order to calculate the DDA at each time step, the linear flow distance of investigation equation is used. Importantly, using the DDA method, variable operating conditions (flowing pressures) may be accounted for, which is critical for CBM wells during early stages of production.The new semi-analytical DDA model is used to history-match production data from an actual horizontal well completed in a low permeability, undersaturated, western Canadian CBM reservoir. Further, the match is compared to that obtained from rigorous numerical simulation. The history-match of the field data is reasonable with the new model and comparable to numerical simulation. The new model is however easier to setup and less data-intensive than numerical simulation, providing a practical alternative to CBM reservoir engineers who are responsible for generating a large number of forecasts.

E-10 マイクロチャンネル内非ニュートン流体気液二相流の圧力損失

E-10 マイクロチャンネル内非ニュートン流体気液二相流の圧力損失

Transient flow analysis and partial water relative permeability curve derivation for low permeability undersaturated coalbed methane wells

Rate transient analysis (RTA) is an important reservoir engineering tool used to extract reservoir and stimulation information from flow rates and pressures obtained from producing wells. Adaptation of analytical RTA methods for this purpose has been slow for coalbed methane (CBM) reservoirs because of the complexities of multi-phase flow, non-static absolute permeability, desorption, among others. Some progress has been made historically for high permeability CBM reservoirs, where depletion (boundary-dominated flow) occurs quickly, however low permeability CBM reservoirs are currently being evaluated internationally (e.g. China), which brings forward additional challenges. For example, in some instances, low permeability, undersaturated CBM wells exhibit long periods of transient flow, during which the transition from single-phase flow of water to two-phase flow of gas and water occurs. This behavior has not been dealt with rigorously in the development of analytical RTA methods. It is the purpose of the current work to extend RTA to apply to low-permeability, undersaturated CBM wells exhibiting this behavior.The horizontal CBM well studied in this work exhibits two periods of apparent transient linear flow separated by a transition, as determined from diagnostic analysis of water production data using a log–log plot of rate-normalized pressure (RNP) versus time. It is hypothesized that the well actually exhibits transient linear flow throughout the entire studied production period (supported by reservoir simulation) and that productivity changes leading to the apparent transition in flow regime are caused by the combined effects of relative permeability changes after desorption pressure is reached, and (possibly) fines migration and stress-dependent permeability. In order to extend the early single-phase linear flow analysis of this well (occurring above desorption pressure) to the multi-phase period (below desorption pressure), the RNP half-slope trend (linear flow) established during the single-phase flow period is extrapolated through the rest of the production period. An RNP ratio (RNPR) is then created by calculating the ratio of the extrapolated (corrected) RNP and the RNP of the uncorrected field data. The RNPR can then serve to correct the production data affected by multi-phase flow (and possibly fines migration and stress dependent permeability) and hence extend the amount of data that can be used for production analysis. Further, the RNPR squared, combined with water saturation calculations, may be used to derive water relative permeability curves from the transient data. These concepts are tested using both numerical simulation and field data. The resulting field-derived water relative permeability curve can be used as a solid starting point for simulation history-matching, although it covers a limited range of water saturations.This work should be of interest to professional engineers and geoscientists involved in CBM reservoir characterization efforts. Future work will determine if these concepts are applicable to other low-permeability reservoirs exhibiting the transition from single- to multi-phase flow during the transient linear flow period, such as tight oil and gas condensate reservoirs.

Pore scale simulation of liquid and gas two-phase flow based on digital core technology

Two-phase flow in two digital cores is simulated by the color-gradient lattice Boltzmann method. This model can be applied to two-phase flow with high-density ratio (on order of 1000). The first digital core is an artificial sandstone core, and its three-dimensional gray model is obtained by Micro-CT scanning. The gray scale images are segmented into discrete phases (solid particles and pore space) by the Otsu algorithm. The second one is a digital core of shale, which is reconstructed using Markov Chain Monte Carlo method with segmented SEM scanning image as input. The wettability of solid wall and relative permeability of a cylindrical tube are simulated to verify the model. In the simulations of liquid and gas two phase flow in digital cores, density ratios of 100, 200, 500 and 1000 between liquid and gas are chosen. Based on the gas distribution in the digital core at different times, it is found that the fingering phenomenon is more salient at high density ratio. With the density ratio increasing, the displacement efficiency decreases. Besides, due to numerous small pores in the shale, the displacement efficiency is over 20% less than that in the artificial sandstone and the difference is even about 30% when density ratio is greater than 500. As the density ratio increases, the gas saturation decreases in big pores, and even reaches zero in some small pores or big pores with small throats. Residual liquid mainly distributes in the small pores and the edge of big pores due to the wettability of liquid. Liquid recovery can be enhanced effectively by decreasing its viscosity.

Prediction of slug liquid holdup in high viscosity liquid and gas two-phase flow in horizontal pipes

Abstract Liquid holdup in slugs is a critical slug flow characteristic for predicting average liquid holdup and pressure gradient in two-phase pipeline systems and for designing downstream separation and process facilities. Liquid holdup in slugs for high viscosity two-phase pipe flow is poorly understood and inadequately predicted. The objective of this study is to experimentally investigate the effect of high liquid viscosity on slug liquid holdup in horizontal pipes and develop a physical explanation of the experimentally observed phenomenon. Viscous and inertia forces are found to govern the processes of the bubble entrainment, fragmentation and loss in the slug front. These processes, in turn, determine the slug liquid holdup. A new empirical closure relationship is proposed as a function of viscosity (viscous) and Froude (inertia) dimensionless numbers to predict the gas fraction in slugs for high viscosity liquid (180–587 mPa s) and gas flow in horizontal pipes. A validation and comparison study of the proposed empirical correlation with an independent data set showed improvement in accuracy with absolute average error and standard deviation of 11.35% and 9.59%, respectively, over the existing correlations.

Galvanic corrosion of aluminum–steel under two-phase flow dispersion conditions of CO2 gas in CaCO3 solution

Abstract Galvanic corrosion of aluminum (Al) and carbon steel (CS) coupled under two-phase flow gas–liquid dispersion conditions was investigated. A disc turbine mixer (Rushton turbine) was used to simulate two-phase flow dispersion conditions. The liquid was a CaCO 3 solution and the dispersed gas was CO 2 . The effects of agitation velocity (0–1000 rpm corresponding to Reynolds number of 0–299,000), CO 2 gas flow rate (0.34–1.6 m 3 /h), temperature (30–50 °C), and time on galvanic corrosion current and loss in weight of both metals in both free corrosion and galvanic corrosion were investigated. The trends of open circuit potential (OCP) of each metal and galvanic potential ( E g ) of the couple were, also, determined. The results revealed that Al was cathodic relative to CS in galvanic couple and its OCP was much more positive than that of CS for all investigated ranges of operating conditions. Increasing the agitation velocity led to a decrease in galvanic corrosion rate and also in free corrosion rate of each metal as well depending on CO 2 pumping rate through the solution. The increase in CO 2 gas flow rate, led to a decrease in galvanic corrosion rate especially at high agitation velocity due to a high dispersion of gas bubbles in the solution. Unstable trend of OCP and E g with agitation velocity and CO 2 gas flow rate was noticed. Clear increase in galvanic currents was observed with increasing temperature of the two-phase system. The galvanic current and the galvanic potential exhibited considerable decrease with time for the majority of the operating conditions.

Blow up criterion of strong solution for 3D viscous liquid–gas two-phase flow model with vacuum

In this paper, we establish a blow-up criterion to the local strong solution to the three dimensional (3D) viscous liquid–gas two-phase flow model only in terms of the divergence of the velocity field. Moreover, the initial vacuum is allowed, and there is no extra restriction on viscous coefficients. Both the Cauchy problem and initial-boundary value problem are considered in this paper.

Behaviors of Foamy Oil Flow in Solution Gas Drive at Different Temperatures

The role of foamy oil flow in the cold production of heavy oil in a solution gas drive has been extensively studied in recent years. In this study, solution gas drive tests were performed in micromodels and sandpacks to investigate not only the behaviors of foamy oil flow at different temperatures but also the effect of temperature on displacement efficiency. The micromodel tests indicated that three flow states existed with the solution gas drives at 54.0 and \(100.0\,^{\circ }\hbox {C}\), which were an oil phase flow, a foamy oil flow and an oil–gas two-phase flow. The micromodel test at \(150.0\,^{\circ }\hbox {C}\) showed a continuous gas phase, while the two-phase oil–gas flow was formed after the oil phase flow. The sandpack test results showed that foamy oil can improve the performance of a solution gas drive at temperatures below \(120.0\,^{\circ }\hbox {C}\). Unfortunately, the behavior of the foamy oil flow was not readily observed in the sandpack test at \(150.0\,^{\circ }\hbox {C}\). The results of this study also showed that there is an optimum temperature at which the highest oil recovery can be obtained in the solution gas drive and that the relative permeabilities of the gas and oil can be estimated from the sandpack test results. When the gas saturation is less than the cutoff gas saturation, the relative permeability ratio of the gas and oil at a higher temperature is higher than that at a lower temperature; the mobility ratio at \(100.0\,^{\circ }\hbox {C}\) was also shown to be lower than that at 54.0 and \(150.0\,^{\circ }\hbox {C}\).

On the well-posedness for a multi-dimensional compressible viscous liquid–gas two-phase flow model in critical spaces

This paper is dedicated to study of the Cauchy problem for a multi-dimensional (\({N \geq 2}\)) compressible viscous liquid–gas two-phase flow model. We prove the local well-posedness of the system for large data in critical Besov spaces based on the L p framework under the sole assumption that the initial liquid mass is bounded away from zero.

Non-invasive process tomography in chemical mixtures – A review

Decades of research, visualizing and monitoring chemical mixtures in the process plant non-invasively plays an important role in making sure that the system produces a high quality product without disturbing the nature of the plant. In this case, process tomography can be applied for the chemical mixtures. Thus, the objective of this paper is to review the current research on non-invasive process tomography for detecting chemical mixtures based on hard-field and soft-field tomography. The discussion on liquid–liquid, liquid–solid and liquid–gas two-phase flow for every type of non-invasive process tomography is explained in detail. Consequently, non-invasive process tomography has expanded strongly in chemical applications. Finally, potential future research on the chemical mixture based on ERT is addressed.

Global existence and optimal convergence rates for the strong solutions in [formula omitted] to the 3D viscous liquid–gas two-phase flow model

This paper is concerned with the Cauchy problem of the three-dimensional viscous liquid–gas two-phase flow model. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small and its L1-norm is bounded. Moreover, the optimal convergence rates are also obtained for such a solution.

A lumped element method for modeling the two-phase choking flow through hydraulic orifices

A novel lumped element methodology for modeling the oil–gas two-phase flow through the hydraulic orifice has been presented, focus on the choking condition. The proposed approach consists of a gas cavitation model developed based on “Full Cavitation Model” and a formulation considering the homogenous fluid assumption for evaluating the mass flow rate. The two-phase choking flow occurring at extreme condition is characterized in detail by using the present method, in terms of the critical pressure, sound speed, filling ratio and the critical speed of pump operation in the hydraulic circuit. Mach number is found to be 1 and the critical speed is estimated by the inlet volumetric flow rate at choking condition of the two-phase flow. The effects of different parameters including the orifice diameter, the upstream pressure and the cavitation model coefficient are investigated to find possible ways of improving the operation of the pump circuit. Reducing the cavitation model coefficient is identified to be both advantageous for reducing the critical pressure and increasing the critical speed.

Encapsulation of submicron particles with polymer

This article presents the results of experimental studies of polymer shell formation on the surface of submicron (including nano-) particles due to mixing of a pair of two-phase gas flows of submicron particles and fine-dispersed liquid monomer droplets. The possibility of changing the polymer shell thickness on the surface of submicron particles by controlling the ratio of charges and particle sizes due to variations of electrical field strength in discharge cameras for charging and the dispersion of submicron particles and fine-dispersed liquid monomer droplets is shown.

Developing a microwave tomographic system for multiphase flow imaging: advances and challenges

Since the 1980s, electrical tomographic imaging techniques based on low-frequency capacitance and resistance measurements have been developed for the monitoring of industrial processes and in some cases multiphase flows. Research on microwave tomography for oil and gas multiphase flow imaging began in the mid-1990s, even though the basic principle of microwave tomography was reported a decade earlier for biomedical imaging. In this paper, the development of a microwave tomographic imaging system for such an application since then is overviewed. It is shown by several examples that microwave tomography can effectively reconstruct the images of dielectric objects, moisture distribution inside processed food and oil–gas two-phase flows. It is also shown that the use of higher microwave frequencies would effectively lead to images of higher spatial resolution. Since real-time microwave tomography systems are currently available and ready for industrial applications, the challenges in developing a practical system with higher temporal resolutions suitable for the imaging of high speed multiphase flows in oil industry are highlighted and discussed in both hardware and image reconstruction aspects.

Numerical simulation of horizontal tube bundle falling film flow pattern transformation

It is important to study the falling-film pattern of a horizontal tube bundle in order to set up a heat and mass transfer model accurately. The falling-film pattern of a horizontal tube bundle is simulated in this paper. The technique is based on computational flow dynamics (CFD) for the two-phase flow of gas and water. The experimental results were used to validate the mathematical model. It indicates that the simulation results accord with experimental data well. The simulated results show that the flow pattern varies with different flow rates. Under the different flow rates, it observes the droplet, droplet-columnar, columnar, columnar-sheet and sheet flow patterns. The critical value is 0.0125 kg/s between droplet and columnar, and the critical value is 0.02 kg/s between columnar and sheet.

Simultaneous two-phase flow measurement of spray mixing process by means of high-speed two-color PIV

In this article, a novel high-speed two-color PIV optical diagnostic technique has been developed and applied to simultaneously measure the velocity flow-fields of a multi-hole spark-ignition direct injection (SIDI) fuel injector spray and its ambient gas in a high-pressure constant volume chamber. To allow for the phase discrimination between the fuel droplets and ambient gas, a special tracer-filter system was designed. Fluorescent seeding particles with Sauter mean diameter (SMD) of 4.8 µm were used to trace the gas inside the chamber. With a single high-speed Nd:YLF laser sheet (527 nm) as the incident light source, the Mie-scattering signal marked the phase of the fuel spray, while the fluorescent signal generated from the seeding particles tracked the phase of ambient gas. A high-speed camera, with an image-doubler (mounted in front of the camera lens) that divided the camera pixels into two parts focusing on the same field of view, was used to collect the Mie-scattering signal and LIF (laser induced fluorescence) signal simultaneously with two carefully selected optical filters. To accommodate the large dynamic range of velocities in the two phases (1–2 orders of magnitude difference), two separation times (dt) were introduced. This technique was successfully applied to the liquid spray and ambient gas two-phase flow measurement. The measurement accuracy was compared with those from LDV (laser Doppler velocimetry) measurement and good agreement was obtained. Ambient gas motion surrounding the fuel spray was investigated and characterized into three zones. The momentum transfer process between the fuel spray and ambient gas in each zone was analyzed. The two-phase flow interaction under various superheated conditions was investigated. A strengthened momentum transfer from the liquid spray to the ambient was observed with increased superheat degree.

A Generalized Framework Model for the Simulation of Gas Production in Unconventional Gas Reservoirs

Summary Unconventional gas resources from tight-sand and shale gas reservoirs have received great attention in the past decade around the world because of their large reserves and technical advances in developing these resources. As a result of improved horizontal-drilling and hydraulic-fracturing technologies, progress is being made toward commercial gas production from such reservoirs, as demonstrated in the US. However, understandings and technologies needed for the effective development of unconventional reservoirs are far behind the industry needs (e.g., gas-recovery rates from those unconventional resources remain very low). There are some efforts in the literature on how to model gas flow in shale gas reservoirs by use of various approaches—from modified commercial simulators to simplified analytical solutions—leading to limited success. Compared with conventional reservoirs, gas flow in ultralow-permeability unconventional reservoirs is subject to more nonlinear, coupled processes, including nonlinear adsorption/desorption, non-Darcy flow (at both high flow rate and low flow rate), strong rock/fluid interaction, and rock deformation within nanopores or microfractures, coexisting with complex flow geometry and multiscaled heterogeneity. Therefore, quantifying flow in unconventional gas reservoirs has been a significant challenge, and the traditional representative-elementary-volume- (REV) based Darcy's law, for example, may not be generally applicable. In this paper, we discuss a generalized mathematical framework model and numerical approach for unconventional-gas-reservoir simulation. We present a unified framework model able to incorporate known mechanisms and processes for two-phase gas flow and transport in shale gas or tight gas formations. The model and numerical scheme are based on generalized flow models with unstructured grids. We discuss the numerical implementation of the mathematical model and show results of our model-verification effort. Specifically, we discuss a multidomain, multicontinuum concept for handling multiscaled heterogeneity and fractures [i.e., the use of hybrid modeling approaches to describe different types and scales of fractures or heterogeneous pores—from the explicit modeling of hydraulic fractures and the fracture network in stimulated reservoir volume (SRV) to distributed natural fractures, microfractures, and tight matrix]. We demonstrate model application to quantify hydraulic fractures and transient flow behavior in shale gas reservoirs.