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**ABSTRACT **

Two-phase flow in vertical wells is a common occurrence in oil and gas production. High-liquid viscosity two-phase upward vertical flow in wells and risers presents a new challenge for predicting pressure gradient and liquid holdup due to the poor understanding and prediction of flow behavior, specifically flow pattern. Current two-phase flow mechanistic models were developed, validated, and tuned based on low-liquid viscosity two-phase flow data for which they show accurate flow pattern predictions. The objective of this study is to investigate the effect of liquid viscosity on two-phase flow pattern in vertical pipe flow. Further objective is to develop new/improve existing mechanistic flow-pattern-transition models for high-liquid viscosity two-phase flow in upward vertical pipe flow. High-liquid viscosity flow pattern two-phase flow data was collected from open literature, against which existing flow-pattern transition models were evaluated to identify discrepancies and potential improvements. The evaluation revealed that existing flow transitions do not capture the effect of liquid viscosity. Therefore, two bubble/dispersed bubble flow pattern transitions are proposed in this study for two different ranges of liquid viscosity. The first proposed model modifies Brodkey (1967) critical bubble agglomeration diameter by including liquid viscosity, which is applicable for liquid viscosity up to 100 mPa.s. The second model, which is applicable for liquid viscosities above 100 mPa.s proposes a new critical bubble diameter based on Galileo dimensionless number. Furthermore, the existing bubbly/intermittent flow transition model based on Taitel et al. (1980) critical gas void fraction of 0.25, is modified to account for liquid viscosity. For the intermittent/annular flow transition, Wallis (1969) was found to be accurate for high liquid viscosity two-phase flow and able to capture the high liquid viscosity data better than existing models. A validation study of the proposed transition models against high liquid viscosity data and a comparison with Barnea (1987) model revealed sensitivity to liquid viscosity and better results in predicting high viscosity liquid flow pattern data.

Artificial Intelligence, Barnea, bubble diameter, collision frequency, critical bubble diameter, diameter, experimental data, flow pattern, flow pattern transition, Fluid Dynamics, gas void fraction, liquid viscosity, MPa, multiphase flow, prediction, production control, production logging, production monitoring, Reservoir Surveillance, sensitivity, terminal velocity, transition, transition model, Upstream Oil & Gas

SPE Disciplines:

SUMMARY. This work proposes a hydrodynamic model for estimating gas void fraction, fg, in the bubbly and slug flow regimes. The model is developed from experimental work, involving an air/water system, and from theoretical arguments. The proposed model suggests that prediction of fg, and hence the bottomhole pressure (BHP), is dependent on such variables as tubing-to-casing-diameter ratio, densities of gas and liquid, and surface tension. Available correlations do not include these variables as flexible inputs for a given system. Computation on a field example indicates that slug flow is the most dominant flow mechanism near the top of liquid column at the earliest times of a buildup test. As buildup progresses, transition from slug to bubbly flow occurs in the entire liquid column. Beyond the after flow-dominated period, the effect of bubbly flow diminishes as gas flow becomes negligibly period, the effect of bubbly flow diminishes as gas flow becomes negligibly small. Comparisons of BHP's are made with the proposed and available correlations. Because the proposed model predicts fg between those of the Godbey-Dimon and Podio et al. correlations, BHP is predicted accordingly.

Introduction

Acoustic well sounding has become a well-established method for estimating BHP in a pumping oil well. The method involves determining the gas/liquid interface in the tubing/casing annulus. From the knowledge of the lengths of gas and liquid columns, BHP can be estimated by adding the pressures exerted by these columns to the casinghead pressure. Although simple in concept, this indirect BHP calculation presents potential problems in two areas: resolution of the acoustic device measuring the gas/liquid interface and estimation of the gas-entrained-liquid-column density. Significant progress has been made in the acoustic device's ability to monitor the movement of the liquid column as a function of time during a buildup test. Estimation of the changing liquid-column density, however, is still fraught with uncertainties. The dead-liquid gradient needs to be adjusted by the so-called gradient correction factor, Fg, (= 1 -fg) to reflect the true column density. Three Fgc correlations proposed by Gilbert, Godbey and Dimon, and Podio et al. have found wide use in the petroleum industry. Relative merits of these correlations were addressed recently. Research in two areas-mass transfer in gas/liquid systems and two-phase flow-has produced a wealth of information for predicting gas void fractions in stagnant liquid columns. None of predicting gas void fractions in stagnant liquid columns. None of these correlations, however, account for the effect of casing and tubing diameters on Fgc. Reliable Fgc prediction is critically important because afterflow, during which the gas continues to bubble through the liquid column, dominates a buildup test in a typical pumping well. In most cases, semilog period beyond afterflow is pumping well. In most cases, semilog period beyond afterflow is seldom reached to allow conventional analysis for estimating permeability-thickness product, skin, and static pressure. Thus, permeability-thickness product, skin, and static pressure. Thus, analysis of after flow-dominated transients provides a viable alternative to the conventional semilog analysis. The purpose of this paper is to explore the relevant literature and to develop a hydrodynamic model for a practical range of flow conditions encountered in a pumping-well annulus through theoretical considerations and experimental work.

Theoretical and Experimental Models

Concerning Bubbly Flow. Researchers of multiphase flow have usually correlated the void fraction with drift flux, u. Drift flux is a way of expressing the difference between the in-situ velocities of the two phases, vg and vt - i.e., "slip" - and is defined by the following expression:

(1)

Eq. 1 may be written in terms of the measurable superficial velocities of the phases, vgs and vls, by noting that vgs = fgvg and vls = (1 - fg)vl:

(2)

For ideal bubbly flow, Wallis suggests the following semitheoretical relationship between drift flux, gas void fraction, and terminal rise velocity of a gas bubble, v :

(3)

For a stagnant liquid column when vls = 0, substituting u from Eq. 2 into Eq. 3 gives

(4)

There are a number of correlations available for the terminal rise velocity, v , in an infinite medium. The equation proposed by Harmathy, which has been supported by data from independent sources, gives

(5)

Wallis suggested that the value of n = 2 be used along with Eq. 5 for v ; therefore, Eq. 4 becomes

(6)

There are disagreements over the exact value of n to be used in Eq. 4. The value of n is affected by impurities in the liquid, the way bubbles are introduced into the column, and the distance these bubbles travel from the point of injections Many workers have used a negative value for the exponent n and expressed fg/(1 -fg)m as a function of superficial gas velocity. For example, Mersmann proposes the following relationship: proposes the following relationship: (7)

Akita and Yoshida propose a similar equation with slightly different groupings of properties and values of constants.

SPEPE

P. 113

doi: 10.2118/13638-PA

SPE-13638-PA

bubble concentration, bubbly flow, Chern, correlation, diameter, Drillstem Testing, drillstem/well testing, Engineering, equation, equivalent diameter, flow pattern, flow regime, fraction, gas void fraction, Griffith, liquid column, slug flow, superficial gas velocity, transition, Upstream Oil & Gas, void fraction

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

Several studies reported the nonexistence of Taylor bubbles under conditions where slug flow is expected to occur [8], [9], [11], [12], [13] and [15]. Instead, they reported a gradual transition from bubble flow to various types of churn flow. However, as given in Table 1, the experimental facilities were short and the measurements were made at a dimensionless length, L/D, from inlet ranging from 30 to 65. Inevitably, these studies cannot disprove previous claims arguing that churn flow is an entrance phenomenon that can eventually develop into slug flow {Barnea (1989) [20], Taitel and Barnea (1987) [21]}. Hibiki and Ishii (2000) [22] and Ohnuki and Akimoto (2000) [23] reported "slug like behaviour" at low mixture velocities. These observations support the entrance length requirement as proposed by Barnea (1989) [20].

bhr group 2018, bubble energy density, bubble flow, diameter, energy density, Existence, flow pattern, holdup, international journal, mixture velocity, pipe diameter, pressure drop, probability density function, production control, production logging, production monitoring, Reservoir Surveillance, slug flow, taylor bubble, transition, translational velocity, two-phase flow, Upstream Oil & Gas

SPE Disciplines: Production and Well Operations > Well & Reservoir Surveillance and Monitoring > Production logging (1.00)

Abstract This paper presents a multiphase hydrodynamic model for design of the aerated mud hydraulics in vertical and moderately deviated directional wells with an angle of less than 20° from vertical. The model is capable of predicting flow pattern and pressure drop in two phase flow through the drillstring and the annulus. Bubbly, dispersed bubble, slug and churn flow patterns are accounted for down flow in the drillstring. In addition to these flow patterns; the annular flow is included for up flow in the annulus. Effect of cuttings loading on the bottomhole pressure is implemented to the model using the effective density concept. Carrying capacity of aerated mud is evaluated by incorporating two-phase flow properties into a cuttings transport model proposed for conventional drilling mud. Pressure drop across the bit is calculated using an adiabatic and frictionless flow model for homogeneous mixture of air and mud. In this study, the circulating system is divided into a number of small computational intervals to take into account temperature and pressure dependent properties of aerated mud. Based on the proposed model and computational algorithm, a computer program, UNDRILL~S, was developed to predict flow patterns, circulating pressures, optimum mud and air flow rates, bit hydraulics, and hole cleaning. The program provides a useful tool to help planning a low pressure drilling operation with aerated mud. Introduction Low pressure drilling with several distinct advantages over conventional mud drilling minimizes many serious problems associated with highly fractured low pressure formations and depleted reservoirs. These problems include partial or total loss of circulation, differential sticking, and formation damage. Moreover, increased penetration rate and extended bit life are other benefits of low pressure drilling. In recent years, accounting these advantages, aerated mud has been increasingly used for drilling depleted reservoirs, horizontal wells and highly fractured formations in both onshore and offshore areas.[1–5] Aerated mud is built by injecting air, either through the drillstring or into the annulus using a parasite string. Aeration of mud through the drillstring results in compressible two phase flow in the drillstring and at the bit. On the other hand, due to mixing of aerated mud with drilled cuttings, three phase flow occurs in the annulus. There have been limited attempts for predicting aerated mud hydraulics. Poetman and Bergman[6] developed a method for determining amount of air to be injected into the mud to obtain desired effective density. Their model accounts for only flow of homogeneous mixture of air and mud in the annulus. Guo et al[7] proposed a two phase dispersed bubble flow model for calculating pressure losses in the entire circulating system and carrying capacity of aerated mud. The model of Guo et al[7] does not involve in flow pattern prediction. Lage and Time[8,9] made a mechanistic approach for simulating the upward two phase flow in vertical concentric annuli developed during underbalanced drilling. This model does not consider the other parts of the circulating system and hole cleaning as well. Recently, Pérez-Téllez et al[10] developed an improved mechanistic model for predicting two phase flow patterns and calculating pressure drops in the whole circulating system for underbalanced drilling. However, the model is incomplete from the hole cleaning standpoint and does not consider effect of cuttings on the annular pressure. The main objective of this study is to develop a multi phase hydrodynamic model accounting for all aspects of low pressure drilling hydraulics in both vertical and directional wells. Based on the proposed model, it is also aimed to develop a computational algorithm integrated with a computer program to facilitate design and analysis of aerated mud for low pressure drilling. Flow Pattern Prediction In this study, it is first attempted to formulate a model for predicting flow patterns that occur during the flow of aerated mud through the drillstring and the annulus. The model development is based on the evaluation of the existing models associated with the flow situations expected in aerated mud drilling. For the downward flow in the drillstring, bubbly, dispersed bubble, and slug flow patterns are considered. In addition to these patterns, the model accounts for churn and annular flow for the upward flow in the annulus.

aerated mud, annular pressure drilling, bottomhole pressure, bubble rise velocity, diameter, drilling fluid chemistry, drilling fluid formulation, drilling fluid property, drilling fluid selection and formulation, drilling fluids and materials, expression, flow pattern, flow rate, fluid loss control, pressure drop, pressure gradient, taylor bubble, taylor bubble rise velocity, transition, Upstream Oil & Gas, upward flow, viscosity, void fraction

Country:

- Asia (0.68)
- North America > United States (0.67)
- Africa > Mozambique > Indian Ocean > Mozambique Channel (0.34)

SPE Disciplines:

ABSTRACT

Micro-bubble resistance reduction technology is a method of energy-saving that can be used on ships. In recent years, the concept of it is also emerging as an attractive method for viscous friction reduction for low speed ship. A low speed ship model with scale of 1:96 is investigated in this paper, high frequency piezoelectric ceramic energy transducers are pasted on the bottom surface of the ship to generate micro-bubbles in our research, bubble volume fraction and diameter are important parameters when study the effects of the micro-bubbles, and they are easy to control when using the high frequency piezoelectric ceramic energy transducers. Model tests are conducted with different incoming flow velocity, different micro-bubble diameters and different bubble volume fractions, results showed that resistance reduction rate increased with the increasing of the bubble volume fraction, the reduction rate also increased with the increasing of the Reynolds number when with high bubble volume fraction, but when the Reynolds number is big enough, the reduction rate varied little even decreased. In the range of our experiments, when the viscous drag reduction rate is 15%, the corresponding bubble volume fraction is 10% and the incoming flow Reynolds number is1.1×10^{6}.

Boundary Layer, bubble diameter, diameter, drag reduction, drillstring design, Efficiency, energy transducer, Engineering, experiment, flow velocity, fraction, micro-bubble resistance reduction, reduction, resistance reduction, resistance reduction rate, reynolds number, ship, University, Upstream Oil & Gas, water management

Industry:

- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Treatment (0.34)

SPE Disciplines:

Thank you!