Beggs and Brill Method

 

Beggs and Brill Method. The Beggs and Brill method was the first one to predict flow behavior at all inclination angels, including directional wells. Their test facility was 1-and 1.5-in. section of acrylic pipe, 90 ft long. The pipe could be inclined at any angel from the horizontal. The fluids were air and water. For each  pipe size, liquid and gas rates rates were varied sso o that, when the pipe was hor horizontal, izontal, all flow patterns were particular of flow rates so was established, the inclination of theobserved. pipe wasAfter varieda through theset range of angles that the effect of angle on holdup and pressure gradient were measured at angles from the horizontal of 0 , 5 , 10 , 15 , 20 , 35 , 55 , 75 , an and  90 . The correlations were developed from 584 measured tests. o

o

o

o

o

o

o

o

o

Beggs and Brill proposed the following pressure-gradient-equation for inclined  pipe.  f   n vm dp dL



2d 

2



  s g sin  

1  E k 

 

Where Ek  is  is given by Eq 4.53 and   s

 L ( )   g [1  H L ( ) ]  



Flow-Pattern Prediction. Fig. 4.16 illustrates the horizontal-flow pattern considered  by Beggs and Brill. On the basis of observed flow pattern for horizontal flow only, the prepared an empirical map to predict flow pattern. Their original flow-pattern map has been modified slightly to include a transition zone between the segregated- and intermittent-flow patterns. patterns. Fig 4.17 shows both the original and the modified (dashed lines) flow-pattern maps. Beggs and Brill chose to correlate flow-pattern transition boundaries with no-slip liquid holdup and mixture Froude number, given by  N Fr 

 



vm

2

 gd 

 

The equations for the modified flow-pattern transitio transition n boundaries are

 

 L1



316  L

0.302

 L2



0.000925  L

 L3



0.10  L

2.368



1.452



 

and   L4



0.5  L

6.738



The following inequalities are used to determine the flow pattern that would exist if the pipe were horizontal. This flow pattern is a correlating parameter and, unless the pipe is horizontal, gives no informatio information n about the actual flow pattern. Segregated.   L  0.01 and N Fr   L1 or    L  0.01 and N Fr   L2 Transition.    0.01 and L  N  L

2

Fr 

L

3

 Intermittent  0.01    L  0.4 and L3  N Fr   L1

 

or    L  0.4 and L3  N Fr   L4  Distributed    L  0.4 and N Fr   L1 or    L  0.4 and N Fr   L4

The Beggs and Brill model has been identified to be applicable in this research as it exhibits several characteristics that set it apart from the other multiphase flow

 

models: a) Slippage between phases is taken into account   Due to the two different densities and viscosities involved in the flow, the lighter  phase tends to travel faster than the heavier one –  one  –  termed  termed as slippage. This leads to larger liquid hold-up in practice than would be predicted by treating the mixture as a homogeneous one. b) Flow pattern consideration  consideration  Depending on the velocity and composition of the mixture, the flow behaviour changes considerably, so that different flow patterns pattern s emerge. These are categorized as follows:-segregated, intermittent and distributed. Depending upon the flow  pattern established, the hold-up and friction factor correlations are determined. c) Flow angle consideration  consideration  This model deals with flows at angles other than those in the vertical upwards direction. Some assumptions had been used in the development of this correlation: 1. The two species involved do not react with one another, thus the composition of the mixture remains constant. 2. The gaseous phase does not dissolve into the liquid one, and evaporation of the liquid into gas does not occur. The Beggs and Brill model [2] has the following pressure-gradient equation for an inclined pipe:

Where dP/dL dP/dL is the pressure gradient, f is the friction factor, ρn is the overall gas and liquid density relative to their mass fraction, vm is the mean velocity, g is the gravitational acceleration and Ek is a dimensionless term.

 

 

A reliable estimation of the pressure drop in well tubing is essential for the solution of a number of important production engineering and reservoir analysis problems. Many empirical correlation and mechanistic models have been proposed to estimate the pressure drop in vertical wells that produce a mixture of oil, water and gas. Although many correlations and models are available to calculate the pressure loss, these models developed based on certain assumption and for particular range of data where it may not be applicable to be used in different sets of data

INTRODUCTION Multiphase flow in pipes is the process of simultaneous flow of two phases or more. In oil or gas production wells the multiphase flow usually consist of oil, gas and water. The estimation of the pressure drop in vertical wells is quite important for cost effective design of well completions, production optimization and surface facilities. However, due to the complexity of multiphase flow several approaches have been used to understand and analysis the multiphase flow.

Oil & Gas industry is needed to have a general method for forecasting and evaluating the multiphase flow in vertical pipes (Poettmann, & Carpenter, 1952). Multiphase flow correlations are used to determine the pressure drop in the pipes. Although, many correlation and models have been proposed to calculate pressure drop in vertical well, yet it’s still arguing about the effectiveness of these proposed models.  Numerous correlations and equations have been proposed for multiphase flow in vertical, inclined and horizontal wells in the literature. Early methods treated the

 

multiphase flow problem as the flow of a homogeneous mixture of liquid and gas. This approach completely disregarded the well-known observation that the gas  phase, due to its lower density, overtakes the liquid phase resulting in “slippage”  between the phases. Slippage increases the flowing density of the mixture as compared to the homogeneous flow of the two phases at equal velocities. Because of the poor physical model adopted, calculation accuracy was low for those early correlations. Another reason behind that is the complexity in multiphase flow in the vertical pipes. Where water and oil may have nearly equal velocity, gas have much greater one. As a results, the difference in the velocity will definitely affect the pressure drop. Many methods have been proposed to estimate the pressure drop in vertical wells that produce a mixture of oil and gas. The study conducted by Pucknell et al. (1993) concludes that none of the traditional multiphase flow correlations works well across the full range of conditions encountered in oil and gas fields. Besides, most of the vertical pressure drop calculation models were developed for average oilfield fluids and this is why special conditions such as; emulsions, non Newtonian flow behavior, excessive scale or wax deposition on the tubing wall, etc. can pose severe problems. Accordingly, predictions in such cases could be doubtful. (Takacs, 2001) The early approaches used the empirical correlation methods such as Hagedron & Brown (1965) Duns & Ros, (1963), and Orkiszewski (1967). Then the trend shift into mechanistic modelling methods such as Ansari (1994) and Aziz et al (1972) and lately the researchers have introduced the use of artificial intelligence into the oil and gas industry by using artificial neural networks such as Ayoub (2004) and Mohammadpoor (2010) and many others. The main purpose of this study is to evaluate and assess the current empirical correlations, mechanistic model and artificial neural networks for pressure drop estimation in multiphase flow in vertical wells by comparing the most common methods in this area. The parameters affecting the pressure drop are very important i mportant for the pressure calculation Therefore, it will also be taken into account in the evaluation.

 

EMPIRICAL CORRELATIONS

The empirical correlation was created by using mathematical equations based on experimental data. Most of the early pressure drop calculation was based on this correlations because of its direct applicability and fair accuracy to the data range used in the model generation. In this study, the empirical correlations for pressure drop estimation in multiphase flow in vertical wells are reviewed and evaluated with consideration of its required dimensions, performance, limitation and range of applicability. Beggs & Brill Correlation (1973): The Beggs and Brill method was developed to  predict the pressure drop for horizontal, inclined and vertical flow. It also takes into account the several flow regimes in the multiphase flow. Therefore, Beggs & Bril (1973) correlation is the most widely used and reliable one by the industry. In their experiment, they used 90 ft. long acrylic pipes data. Fluids used were air and water and 584 tests were conducted. Gas rate, liquid rate and average system  pressure was varied. Pipes of 1 and 1.5 inch diameter were used. The parameters used are gas flow rate, Liquid flow rate, pipe diameter, inclination angel, liquid holdup, pressure gradient and horizontal flow regime. This correlation has been developed so it can be used to predict the liquid holdup and pressure drop.

 

 

 

 

 

  BEGGS AND BRILL METHOD FOR TWO PHASE FLOW CALCULATIONS  The Beggs and Brill correlation was developed from experimental data obtained in a small-scale test facility. The facility consisted of 1-inch and 1.5-inch sections of acrylic pipe 90 feet long. The pipe could be inclined at any angle. The parameters studied and their range of variation were:

1. Gas flow rates of 0 to 300 Mscf/D 2. Liquid flow rates of 0 to 30 gpm 3. Average system pressure of 35 to 95 psia 4. Pipe diameter of 1 and 1.5 inches 5. Liquid hold-up of 0 to 0.87 6. Pressure gradients of 0 to 0.8 psi/ft. 7. Inclination angles of –  of – 90 90 degrees to +90 degrees Fluids were air andwere water. For eachAfter pipe asize, liquid and gasflow ratesrates were varied so that used all flow patterns observed. particular set of was set,

 

the angle of the pipe was varied through the range of angles so that the effect of angle on holdup and pressure gradient could be observed. Liquid holdup and  pressure gradient were measured measured at angles from the horizontal at 0, plus and minus 5,10,15, 20, 35, 55, 75, and 90 degrees. The correlations were developed from 584 measured tests HORIZONTAL FLOW

Different correlations for liquid holdup are presented for each of the three horizontal flow regimes. The liquid holdup, which would exist if the pipe were horizontal, is first calculated and then corrected for the actual pipe inclination. Three of the horizontal flow patterns are illustrated on Figure 7-1. A fourth, the transition region, was added by Beggs and Brill to produce the map shown on Figure 7-2. The variation of liquid holdup with pipe inclination is shown on Figure 7-3 for three of the tests. The holdup was found to have a maximum at approximately degreesfriction from the horizontal and a minimum at approximately approximately –   –  50 degrees. A +50 two-phase factor is calculated using equations, which are independent of flow regime, but dependent on holdup. A graph of a normalized friction factor as a function of liquid holdupand input liquid content is given on Figure 7-4.

 

  Figure 7-1: Horizontal Flow Patterns

 

Figure 7-2: Horizontal Flow Pattern Map

Figure 7-3: Liquid Holdup vs. Angle

 

  Figure 7-4: Two-phase Friction Factor FLOW REGIME DETERMINATION

The following variables are used to determine which flow regime would exist if the  pipe was in a horizontal position. This flow regime is a correlating parameter and gives no information about the actual flow regime unless the pipe is completely horizontal.

 

  The horizontal flow regime limits are:

When the flow falls in the transition region, the liquid holdup must be calculated using both the segregated and intermittent equations, and interpolated using the following weighting factors:

 

HL(transition) = A x HL(segregated) + B x HL(intermittent)

 

 

 

  VERTICAL FLOW

For vertical flow, θ = 1, and dL = dZ, so;  so;  

The pressure drop caused by elevation change depends on the density of the two phase mixture and is usually calculated using a liquid holdup value. Except for high velocity situations, most of the pressure drop in vertical flow is caused by elevation change. The frictional pressure loss requires evaluation of the two-phase friction factor. The acceleration loss is usually ignored except for high velocity cases. VERTICAL FLOW REGIMES Bubble flow

In bubble flow the pipe is almost completely filled with liquid and the free gas  phase is present in small bubbles. The bubbles move at different velocities and except for their density, have little effect on the pressure gradient. The wall of the  pipe is always contacted by the li liquid quid phase. Slug flow

In slug flow the gas phase is more pronounced. Although the liquid phase is still continuous, the gas bubbles coalesce and form plugs or slugs, which almost fill the  pipe cross-secti cross-section. on. The gas bubble velocity is greater than that of the liquid. The liquid in the film around the bubble may move downward at low velocities. Both the gas and liquid have significant effects on the pressure gradient.

 

Transition flow

The change from a continuous liquid phase to a continuous gas phase is called transition flow. The gas bubbles may join and liquid may be entrained in the  bubbles. Although the liquid effects are significant, the gas phase effects are  predominant. Mist flow In mist flow, the gas phase is continuous and the bulk of the liquid is entrained as droplets in the gas phase. The pipe wall is coated with a liquid film, but the gas  phase predominantly controls the pressure gradient. Illustratio Illustrations ns of bubble, slug, transition, and mist flow are shown below.

Figure 7-5: Vertical Flow Patterns A typical two-phase flow regime map is shown on Figure 7-6.

 

  Figure 7-6: Flow Regime Map Where the following are the procedure equations for calculating vertical flow with Beggs and Bill method

 

  6) Calculate Superficial Velocities Vsg, Vsl,Vm

DETERMINE FLOW REGIME 5. Calculate Froude No. 7)

6. Calculate No-slip liquid holdup

7. Calculate dimension less “L” parameters  parameters 

8. Apply flow regime rules a. Is λL 〈 0.01 and Fr 〈 L1 ? ↓   No Yes → Segregated Segregated flow  flow   b. Is λL ≥ 0.01 0.01 and Fr 〈 L 2 ? ↓  → 

 

 No Yes Segregated flow c. Is λL ≥ 0.01 and L 2 ≤ Fr ≤ L3 ?  ?  ↓   No Yes → Transition Transition flow flow   d. Is 0 . 01 ≤ λL 〈 0 . 4 and L 3 〈 F r ≤ L 1 ?  ?  ↓   No Yes → Intermittent Intermittent flow flow   e. Is λL ≥ 0.4 and L3 〈 Fr ≤ L 4 ?  ?  ↓   No Yes → Intermittent Intermittent flow flow   f. Is λL 〈 0.4 and Fr ≥ L1 ?  ?  ↓   No Yes → Distributed Distributed flow flow   g. Is λL ≥ 0.4 and Fr 〉 L 4 ? Outside the range of the Beggs - Brill method DETERMINE LIQUID HOLDUP & TWO-PHASE DENSITY  9.Calculate H L (o) (the holdup which would exist at the same conditions in a horizontal pipe.)

For transition flow calculate HL (segregated) and HL (Intermittent).  10. Calculate N LV (the liquid velocity number)

11. Calculate c

 

  For transition uphill flow, calculate c (segregated) and c (intermittent). (C must be ≥ 0)  0)  12. Calculate Ψ  Ψ 

where φ is the actual angle of the pipe from horizontal. For vertical flow ø = 90. 13. Calculate the liquid holdup, HL (ø) For segregated, intermittent, and distributed flow:

For transition flow: HL (transition) = A • HL (segregated) + B • HL (intermittent) 

14. Calculate Hg = 1 –  1 –  H  HL (ø)  15. Calculate two phase density ρs = ρL ⋅ HL (ø) + ρg ⋅ Hg DETERMINE ELEVATION TERM

DETERMINE FRICTION TERM

 

  17. Calculate no-slip two-phase density ρn = ρL • λL + ρg • λg = ρL • λ + ρg • (1 − λL )  18. Calculate no-slip viscosity, μn  μn = μL • λL + m g • λg = μL • λL + m g • (1 − λL )  19. Calculate no-slip Reynolds No.

20. Calculate no-slip friction factor

21. Calculate

22. Calculate

23. Calculate the two phase friction factor

24. Calculate the friction loss term,

CALCULATE THE ACCELERATION TERM

 

25.

CALCULATE THE TOTAL PRESSURE GRADIENT

In this work attention was paid only to five methods. These are flow regime maps, the Duns-Ros method, the Orkiszewski method, the Hagedorn-Brown method and the Beggs-Brill method. They are the most often used. However, it is necessary to point out that in literature [19,20,25,26,27] it is possible to find a lot of other methods. Large numbers of correlations indicate that this problem has not been properly solved so far. Pressure loss in pipe is a function of a few parameters. The most important are sort of fluid mixture, working temperature and pressure, pipe diameters and inclination. In practice the best way to evaluate methods is to make measurement of pressure drop distribution in wells or pipes, and, next, adjust a proper correlation. It means that for various oil-gas fields different methods could satisfy the above requirements. For production purposes pressure gradient is often evaluated based on Gilbert’s type curves. This method is not accurate, but still is used.

BEGGS AND BRILL METHOD NOMENCLATURE A Flow area D Diameter Ek Beggs and Brill acceleration term Fr Froude number f Friction factor g Acceleration due to gravity gc Gravitational constant