Page 57 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Petroleum Production Engineering, A Computer-Assisted Approach 0750682701_chap04 Final Proof page 48 22.12.2006 6:07pm

4/48 PETROLEUM PRODUCTION ENGINEERING FUNDAMENTALS
( " #)
1 « 5:0452 « 1:1098 7:149 0:8981 Liquid holdup depends on flow regime, fluid proper-
p ffiffiffiffiffi ¼ 4 log log þ ties, and pipe size and configuration. Its value can be
f F 3:7065 N Re 2:8257 N Re
quantitatively determined only through experimental
¼ 12:3255 measurements.
f F ¼ 0:006583
4.3.3 TPR Models
If Fig. 4.2 is used, the chart gives a Moody friction factor Numerous TPR models have been developed for analyzing
of 0.0265. Thus, the Fanning friction factor is estimated as multiphase flow in vertical pipes. Brown (1977) presents a
0:0265 thorough review of these models. TPR models for multi-
f F ¼ phase flow wells fall into two categories: (1) homogeneous-
4
flow models and (2) separated-flow models. Homogeneous
¼ 0:006625
models treat multiphase as a homogeneous mixture and do
Finally, the pressure drop is calculated: not consider the effects of liquid holdup (no-slip assump-
tion). Therefore, these models are less accurate and are
g r 2f F ru L
2
2
DP ¼ rDz þ Du þ usually calibrated with local operating conditions in field
g c 2g c g c D applications. The major advantage of these models comes
2
32:17 51:57 2(0:006625)(51:57)(2:34) (1000)
2
¼ (51:57)(966) þ (0) þ from their mechanistic nature. They can handle gas-oil-
32:17 2(32:17) (32:17)(0:188)
¼ 50,435 lb f =ft 2 water three-phase and gas-oil-water-sand four-phase sys-
tems. It is easy to code these mechanistic models in com-
¼ 350 psi
puter programs.
Separated-flow models are more realistic than the
4.3 Multiphase Flow in Oil Wells
homogeneous-flow models. They are usually given in the
In addition to oil, almost all oil wells produce a certain form of empirical correlations. The effects of liquid holdup
amount of water, gas, and sometimes sand. These wells are (slip) and flow regime are considered. The major disad-
called multiphase-oil wells. The TPR equation for single- vantage of the separated flow models is that it is difficult to
phase flow is not valid for multiphase oil wells. To analyze code them in computer programs because most cor-
TPR of multiphase oil wells rigorously, a multiphase flow relations are presented in graphic form.
model is required.
Multiphase flow is much more complicated than single-
phase flow because of the variation of flow regime (or flow 4.3.3.1 Homogeneous-Flow Models
pattern). Fluid distribution changes greatly in different Numerous homogeneous-flow models have been devel-
flow regimes, which significantly affects pressure gradient oped for analyzing the TPR of multiphase wells since the
in the tubing. pioneering works of Poettmann and Carpenter (1952).
Poettmann–Carpenter’s model uses empirical two-phase
friction factor for friction pressure loss calculations with-
4.3.1 Flow Regimes out considering the effect of liquid viscosity. The effect
As shown in Fig. 4.3, at least four flow regimes have been of liquid viscosity was considered by later researchers
identified in gas-liquid two-phase flow. They are bubble, including Cicchitti (1960) and Dukler et al. (1964). A
slug, churn, and annular flow. These flow regimes occur as comprehensive review of these models was given by
a progression with increasing gas flow rate for a given Hasan and Kabir (2002). Guo and Ghalambor (2005)
liquid flow rate. In bubble flow, gas phase is dispersed in presented work addressing gas-oil-water-sand four-phase
the form of small bubbles in a continuous liquid phase. In flow.
slug flow, gas bubbles coalesce into larger bubbles that Assuming no slip of liquid phase, Poettmann and Car-
eventually fill the entire pipe cross-section. Between the penter (1952) presented a simplified gas-oil-water three-
large bubbles are slugs of liquid that contain smaller bub- phase flow model to compute pressure losses in wellbores
bles of entrained gas. In churn flow, the larger gas bubbles by estimating mixture density and friction factor. Accord-
become unstable and collapse, resulting in a highly turbu- ing to Poettmann and Carpenter, the following equation
lent flow pattern with both phases dispersed. In annular can be used to calculate pressure traverse in a vertical
flow, gas becomes the continuous phase, with liquid flow- tubing when the acceleration term is neglected:
ing in an annulus, coating the surface of the pipe and with
droplets entrained in the gas phase. Dp ¼ r r þ k k Dh (4:8)
r r 144
4.3.2 Liquid Holdup where
In multiphase flow, the amount of the pipe occupied by a Dp ¼ pressure increment, psi
phase is often different from its proportion of the total r r ¼ average mixture density (specific weight), lb=ft 3
volumetric flow rate. This is due to density difference Dh ¼ depth increment, ft
between phases. The density difference causes dense
phase to slip down in an upward flow (i.e., the lighter and
phase moves faster than the denser phase). Because of
this, the in situ volume fraction of the denser phase will f 2F q M 2
2
o
be greater than the input volume fraction of the denser k k ¼ 7:4137 10 D 5 (4:9)
10
phase (i.e., the denser phase is ‘‘held up’’ in the pipe
relative to the lighter phase). Thus, liquid ‘‘holdup’’ is where
defined as f 2F ¼ Fanning friction factor for two-phase flow
q o ¼ oil production rate, stb/day
V L
y L ¼ , (4:7) M ¼ total mass associated with 1 stb of oil
V
D ¼ tubing inner diameter, ft
where
r
The average mixture density can be calculated by
r
y L ¼ liquid holdup, fraction
V L ¼ volume of liquid phase in the pipe segment, ft 3 r r ¼ r 1 þ r 2 (4:10)
V ¼ volume of the pipe segment, ft 3 2