The mechanical energy balance equation used for the mh-b correlation 1 (2-6) sg u

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1 Modified Haedron and Brown Method (mh-b) This is an empirica two-phase fow correation, the core of which is correation for iquid hod-up. Griffith correation is used for fow in the bubbe fow reion. The mechanica enery baance equation used for the mh-b correation 44 in oified units.- dp dh 5 ( 7.4E0 ) ( u / ) fw Δ m c ρ + + ρ (-5) ρ Δh Bubbe fow reime exists if λ < B where if B <. set B to.. B um.07.8 (-6) The input fraction of as λ is λ u s u m To find the iquid hod-up that is needed to cacuate the pressure radient from correations require the foowin dimensioness numbers iquid veocity.98 4 v u s (-7) σ ρ Gas veocity.98 4 v u s (-8) σ ρ Pipe diameter ρ (-9) σ

2 iquid viscosity.576μ 4 (-0) ρ σ Where superficia veocities u s in ft/sec, density ρ in b m /ft, surface tension σ in dynes/cm, diameter in feet. Usin mh-b method First find the fow reime. Cacuate mass fow rate w and density ρ as before. Cacuate the dimensioness numbers. Cacuate the veocities u & u u q 5.64 A t u q GRβ u u + u m At Usin find C from fi. - Then find the roup p 0. v v ( C ) p 0. a find y /ψ from fi -4 p here is the absoute pressure at the ocation of interest. v Compute from fi -5 we et ψ Get the iquid hod-up y y (y / ψ)/ψ ote: For ow viscosity fuid ψ wi eneray be. For f a phase Reynods number is be used

3 Re f from Moody diaram..e w μ μ y ( y ) Get pressure radient from, assumin no kinetic enery 44 dp dh ρ + fw 5 ( 7.4E0 ) ρ The Griffith correation For bubbe fow Griffith uses a different hod-up correation, bases the frictiona pressure radient on the in-situ averae iquid veocity. 44 The iquid hod-up is dp dh fw ρ + (-) 5 ( 7.4E0) ρ y u + m u u + m y 4 us us u s where sip veocity u s is.8 ft/sec. s (-) Reynods number is based on in-situ iquid veocity u ρ Re or μ.e w Re (-) μ

4 fiure - fiure -4

5 fiure -5 Equations to repace fiure - C 0 ( ) Y X X X o[ ( ) + ] Y X X to repace fiure -4 / ψ o X o X ( y ) [ ( ) ] [ ( ) + 6] [ o( X ) ] [ ( ) ] o X p ( C ) X v vg p a 4

6 for fiure -5 ψ X + X X if X >.0 for X <.0 then ψ +.5X 5.6 X vg.4 4 and for f f f.098 ε ε o o Re.857 Re 0.898

7 Find the pressure radient at 500 psi Tubin q o. 400 bpd o API oi q w. 600 bpd γ w.07 GR 500 cf/bb γ.65 σ o 0 dynes/cm σ w 70 dynes/cm μ o cp μ.05 cp γ o 4.5/ M.4*.9*50 +.6*.07* *.65* b/bb w M*q 78.6* b/day Find the fow reime u q 5.64 A t u q GRβ u u + u m At u.98 ft / sec u 7.84 ft / sec um u + u ft / sec B u m us B <. so B. λ 7.84 / um λ is arer than B so the fow reime is not bubbe. ρ M /5.64[oi cut x β o + water cut] 5.8/5.64[.4* ] 6 b/cf ρ M / β {GR Oi cut x R s } 4.8/.098{ *59}.75 b/cf

8 ρ 4 v u s σ σ 6 54 ρ 4 v u s ρ σ μ ρ σ From chart - C.00 p 0. v v ( C ) p 0. a E From chart -4 y /ψ.47 v From chart -5 Ψ so y.47.e w y ( y ) μ μ.e 7860 ( ) Re From the raph f dp fw ρ /44.08psi / dh 7.4E ρ 5 ( 7.4E0 ) ft

9 Homework Use the data from the previous homework and sove the pressure radient at 000 psi. Additiona data μ o 4 cp μ.0 cp σ o 0 dynes/cm σ w 70 dynes/cm

10 Ros Method Uses a pressure baance rather than a enery baance equation. So that in a sine phase fow the pressure radient is the sum of the static, friction and acceeration radients, dp dh ρv ρ + 4 f (-4) here with the acceeration radient neected. For phase fow the static term shoud be modified to aow for as sippae thouh the iquid. Ros introduced the a static radient ε ρ + ε ρ (-5) Where ε is the iquid and as hodup. Hodup is defined as the voume of that phase actuay present in a certain enth of pipe. By substitutin equation -6 into -5 ρ dp dh ρ ε + ( + ε ) + ρ friction term (-6) The density of as is sma compared to the oi so -7 can be rewritten; ρ dp dh ε + friction term (-7) Ros then conducted experiments to determine the infuence of varies factors, resutin in an empirica correation s for iquid hodup and wa friction which are very compex. A computer proram based on these correation s cacuate pressure radients that compare favoraby with Baxende & Thomas fied data. Gibert Method

11 Empirica based method, based on measured vaues of tubin fow pressure osses, a famiies of curves were derived that can be used for extrapoation and interpoation purposes. The foowin measurements were taken on a are number of wes; Tubin depth, ft Fowin BHP, tubin in-take pressure, psi THP, psi Fow rate, ross iquid, bb/day GR, mcf/bb Tubin size Assumin that the BHP depends ony on the other five isted variabes, roup the wes with the same tubin size, production rate, and GR to et a correation. Pot the BHP as a function of depth for these roups and a pot ike fiure -4 is obtained showin the pressure curves for severa THP. fiure -6

12 Take a point on the curve of a THP A at a seected depth and pace a vave there that can be opened in such a way that the pressure and production rate wi be unchaned when the vave at the tubin head is cosed. It can be seen that pressure curve beow this point wi aso be unchaned and that this point can now be viewed as the tubin head. So actuay a the curves are just extensions of one curve. This curve is iven in fiure -6. fiure -7 To use this curve to find the BHP at a iven depth, the equivaent depth of the THP is found on the curve and added to the tota enth of the tubin. For exampe if the THP is 00 psi, and the BHP at 0,000 is wanted, the depth on the curve of 00 psi is noted, say is 00, this is added to the 0,000, makin a depth of,00 which is used on the curve to find the BHP. It shoud be noted that at ow pressures it found that the correct shape of the curve is actuay concave downward or the reverse of the hiher pressure portion of the curve. This is seen if Poettmann and Carpenter method is used to cacuate the curves. Baxende and Carpenter ran very carefuy controed we tests and confirmed this shape at the ower pressures.

13 The Gibert Curves use GR as a parameter and there is one famiy of curves for each tubin size and fow rate. Two approaches to sovin fowin we probems. ) Find the IPR curve of the we, then find the pwf for different fow rates for a iven THP. The intersection of the pot of these two ines wi be the expected fow rate for the iven THP. 500 IPR & 00 THP IPR thp P wf psi q o bpd

14 ) After cacuatin the IPR curve, cacuate the pressure oss in the tubin at various fow rates. This wi ive a pot ike fiure -, it can be seen that for any fow rate a THP and BHP (pwf) can be found. Aso the fow rate for and THP can be found.