DOElET/27141-4
(DE82009120) Distribution Category UC66c
GEOTHERMAL WELL DESIGN HANDBOOK
February, 1982
Prepared f o r Department o f Energy D i v i s i o n of Geothermal Energy Contract DE-AC03-78ET27141
Prepared by Laboratories for Applied Mechanics Denver Research I n s t i t u t e Denver, Colorado and Coury and Associates, Inc. Denver, Colorado
.. I I TABLE OF CONTENTS
Page Chapter 1
.
Chapter 1 1
.
Chapter 1 1 1 C h a p t e r 1V
.............. 1 D I S C U S S I O N OF HANDBOOK PROCESS . . . . . 3 SAMPLE CALCULATIONS . . . . . . . . . . 13 1NTRODUCTlON
.
.
P H Y S I C A L PROPERTIES GRAPHS AND TWO-PHASE 29 FLOW WELLHEAD PRESSURE GRAPHS
.....
I NTRODUCT I ON
I.
This handbook provides a simplified process for the user, at a desk and using a handheld calculator, to estimate the performance of geothermal
wells which are produced by natural, flashing flows. To accomplish this,
i
the user must indicate the well diameter and depth, and the reservoir conditions. The process presented here then enables the user to determine the total pressure drop in a flowing well, and therefore to find the
fluid pressure, temperature and steam quality at the wellhead. By applying the handbook process to several input data sets,the user can compile
sufficient information to determine the interdependence of input and output parameters.
For example, a graph of flowrate as a function of well-
/
head pressure may be constructed, or the effect of diameter changes on
j
1 4
pressure at the wellhead might be examined. To make the process of the handbook possible, several simplifying assumptions were made:
I
0
adiabatic wellbore flow (no heat transfer through we1 1 casing)
the
0
no dissolved solids in the geothermal fluid
0
no dissolved gases in the geothermal fluid
0
single phase flow in the wellbore at producing zone.
These assumptions allow the elimination of several additional variables
i
!
from the problem
formulation. This simplified formulation lends itself
well to the treatment given in the handbook. There are 5 (five) input parameters to be specified by the user: 0
We1 1 bore d iemeter
0
Depth of well to the top of the producing zone
2 0
Temperature of the fluid at the top of the producing zone
0
Total mass flowrate of fluid in the we 1
0
Pressure in the wellbore at the top of the producing zone.
The input pressure in the wellbore i s a function of the total mass flowrate, as explained in Chapter 1 1 , The process used to find wellhead fluid conditions for a given set of input parameters is divided into three major segments: 0
Calculation of single-phase pressure drop in the wellbore, performed on a hand-held ,calculator,
0
Determination o f two-phase pressure drop from graphs supplied in Chapter IV,
0
Evaluation of fluid conditions at the wellhead, using physical properties found in Chapter I V graphs.
A detailed explanation of the handbook process outlined above is presented
in Chapter I I .
A sample calculation that uses the step by step approach
of the Well Design Data Sheet comprises Chapter 1 1 1 . Outputs from the process noted above are the conditions of the geothermal fluid at the wellhead and consist of the following: 0
Fluid pressure
0
Fluid temperature
0
Steam Quality, or percent by weight of steam in the flowing fluid.
It is expected that the output described above will be used most
often in making economic analyses to determine the feasibility of geothermal energy projects.
Such analyses may include the number, size and
relative costs of several combinations of wellbore diameter and flowrate, or determination of necessary input values to supply sufficiently high wellhead temperatures and pressures to a specific conversion process. Chapter
I1 explores these possible uses o f the handbook results further.
3 II.
DISCUSSION OF THE HANDBOOK PROCESS The process used in this handbook to find the pressure drop in a <
geothermal well in two-phase flow is shown in schematic form in Fig. 1 and explained in this chapter. Assumptions have been made to permit the process to be presented in handbook form; these are also explained. Comments on use of the results of the process are given, ASSUMPTIONS Several assumptions were made to simplify the fluid mechanics of the well flow pressure drop calculation. These are as follows: 0
Adiabatic wellbore flow (no heat transfer through the well casing)
0
No dissolved solids In the geothermal fluid
0
No dissolved gases
0
Single phase flow in the wellbore at the producing zone.
-
in the geothermal fluid
The thermodynamics of the phase change from liquid water to steam In the flowing fluid are simplified by the first assumption.
The pure water
assumptions eliminate chemical interaction considerations from the pressur.e drop computation; dissolved constituents can also serve to change the point where two-phase flows begin. Additional information on the steam quality of the reser oir fluid i s needed to perform the handbook process
if there is flashing in the reservoir. This information Is difficult to estimate, and virtua ly impossible to measure, The occurrence of phase change in the reservoir is not common. Without these assumptions, the dimension of the pressure drop calculation becomes unmanageable in
B
hand-
book format, INPUT PARAMETERS There are 5 (five) input parameters that must be specified by the
~~
4
~
INPUT:
We1 1 Diameter Depth t o Producing Zone Production Temperature Production Pressure T o t a l Mass Flowrate
t
1
Calculate Length of Two-Phase Zone
Determine i f wellbore i s i n Single-phase Flow a t Top o f Produc i.ng Zone I
Find Wellhead Pressure from Parameterized Computer Output Graphs
S t a r t . S i ngle-Phase Pressure Drop Calculation: Find E l e v a t i o n Pressure Drop Per Foot o f Well Length Use Physical Properties Graphs t o Determine We1 lhead Temperature
I Evaluate Constants f o r SinglePhase F r i c t i o n Pressure Drop Per Foot of Well Length
I
t Calculate Steam Q u a l i t y a t the Wellhead from Enthalpy Cons idera t ions
I
Calculate T o t a l SinglePhase Pressure Drop per Foot o f Well Length
f Calculate Length of Zone of Single-phase Flow. I f Less Than We1 1 Depth, Proceed w i t h Two-Phase Pressure Drop Cal c u l a t ion
1
FJGURE 1.
Design Handbook U t i l i z a t i o n Sequence.
5 user.
They are: Wellbore diameter given i n inches;
-
i n s i d e diameter of the w e l l cas
Depth o f w e l l t o the top o f the producing zone, given i n feet; T o t a l mass f l o w r a t e of f l u i d i n t h e w e l l i n pounds per hour; Temperature of the f l u i d a t the top of the producing zone, under flow conditions given i n degrees Fahrenheit. Since a temperature gradient may e x i s t w i t h i n t h e producing zone, t h e value o f the b u l k f l u i d temperature a t t h e top of the producing zone may change when s h i f t i n g from s h u t - i n t o f l o w c o n d i t i o n s . A simple approath t o t h e determination of a reasonable value i s t o assume a uniform c o n t r i b u t i o n throughout the producing zone and t h e r e f o r e t o a v e r a g e t h e expected s h u t - i n temperatures a t the top and bottom of t h e producing zone. I f a d e t a i l e d temperature survey o f the producing zone Is a v a i l a b l e , a more accurate temperature can be determined. This input temperature w i l l be r e f e r r e d t o as "production temperature'' i n t h e t e x t ; 0
Pressure i n the wellbore a t the top o f t h e producing zone, under flow conditions, measured i n pounds per square inch, .absolute. It i s important t o note that the s p e c i f i e d pressure w i l l vary as a f u n c t i o n of f l o w r a t e because o f pressure drop i n the formation. This input pressure w i l l be r e f e r r e d t o as "production pressure" i n t h e t e x t .
Several o f the user inputs defined above are parameterized i n a d i s c r e t e range t o l i m i t the number o f two-phase f l o w wellhead pressure curves t h a t a r e presented.
If i t i s a t a l l p o s s i b l e f o r t h e user t o choose h i s input
wellbore diameter, mass f l o w r a t e and production temperature from the values l i s t e d i n Table 1, page 6
,
t
process o f f i n d i n g t h e
head c o n d i t i o n s i s s i m p l i f i e d considerably.
rrespond ing we 1 1
-
The need f o r i n t e r p o l a t i o n ,
and t h e r e f o r e . t h e e v a l u a t i o n o f m u l t i p l e Input data sets f o r a s i n g l e solution,
Is then eliminated.
An example o f a problem r e q u i r i n g i n t e r p o l a t i o n
i s presented i n Chapter 1 1 1 . I t i s p o s s i b l e t o use t h i s handbook t o evaluate wellhead pressure,
6 TABLE 1 Values o f Input Parameters Used in Construction of Two-Phase Wellhead Pressure Graphs Product ion Temperature: 3OO0F, 35OoF, 400°F , 45OoF 5OO0F, 55O0F, 6OO0F, 65OoF I
.
Mass Flowrate:
. s a \ I
I
,
200,000 lbs/hr 3OO,OOO l b d h r . 400,000 1 bs/hr 500,000 lbs/hr
.
600,000 800,000 1,000,000 1,200,000
1b d h r 1b d h r lbdhr lbs/hr
Wellbore Diameter: 6 inches Outside Diameter 7 5/8 inches OD 8 5/8 inches OD 9 5/8 inches OD 10 3/4 inches OD 1 1 3/4 inches OD 13 318 inches OD 16 inches OD
= 5.524 inches Inside Diameter
ID ID 9.063 inches ID 10.192 inches ID 11.15 inches ID 12.715 inches ID 15.375 inches ID
= 7.125 inches = 8.097 inches
= =
= = =
7 temperature and steam q u a l i t y f o r we 1s w i t h changes i n diameter.
This i s
done by t h i n k i n g o f such a . w e l 1 as a series o f constant (though d i f f e r e n t ) diameter w e l l s stacked upon.each other.
The f l u i d c o n d i t i o n s c a l c u l a t e d
f o r the top o f one constant diameter segment then become t h e input cond i t i o n s f o r the next higher segment i n the stack.
This technique i s ex-
p l a i n e d i n Chapter 1 1 1 , PROCESS TO FIND THE TOTAL-PRESSURE DROP
The sequence o f c a l c u l a t i o n s used i n t h i s handbook i s a common one: given the f l u i d c o n d i t i o n s a t the top o f the producing zone, the pressure d r o p ' i n t h e f l u i d as i t r i s e s up the wellbore i s computed. d r o p * c a l c u l a t i o n i s d i v i d e d i n t o two p a r t s :
s i n g l e phase and two-phase.
The s i n g l e phase pressure drop i s the sum o f two components: pressure drop and p i p e f r i c t i o n pressure drop. drop has three components:
The w e l l pressure
elevation
The two-phase pressure
an e l e v a t i o n pressure drop, pipe f r i c t i o n
pressure drop, and an a c c e l e r a t i o n pressure drop due t o t h e d e n s i t y change8 t h a t i s p a r t o f the phase change process.
The pressure o f the wellhead
i s then the d i f f e r e n c e o f the production pressure minus t h e sum o f the s i n g l e phase and two-phase pressure drops.
The sequence used here per-
m i t s c a l c u l a t i o n s t o be made by the user w i t h o u t any i t e r a t i o n steps on h i s part. I n summary, the handbook sequence i s used as f o l l o w s : 0
choose values f o r i n p u t parameters, ed on user's knowledge o f the r e s e r v o i r and conversion process o r end use o f resource;
0
evaluate f l u i d p r o p e r t i e s from Chapter I V graphs;
0
compute s i n g l e phase pressure drop and l o c a t i o n o f f l a s h horizon ( p o i n t o f trans! t i o n o f two-phase f l o w ) ;
0
f i n d wellhead pressure from two-phase pressure graphs o f Chapter I V ;
0
find we lhead temperature from saturation conditions graph; compute wellhead Quality.
Sinqle Phase Pressure Drop
To begin the single phase pressure drop sequence, a check should be made t o assure that the well is indeed in single phase flow at the top o f the producing zone.
T h e saturation pressure for the production tempera-
ture i s found o n the graph of saturation temperature-pressure relationships, ,
located in Chapter IV.
I
This pressure is then compared t o the production
pressure; if the production pressure is larger, the well is in single phase flow at the top o f the producing zone, and the handbook sequence can then be followed.
T h e first component o f the single phase pressure drop is the elevation pressure drop term.
It is a function o f the production temperature and is
read off the Properties Graph in Chapter I V . Several constants are required t o compute the friction pressure drop, the second component of the single phase pressure drop.
T h e friction
factor is the only constant found in the pressure drop formula, but it is a function of the Reynolds number o f the wellbore flow.
Reynolds
number is a dimensionless parameter computed from velocity and physical properties of the flowing flu d.
To compute the Reynolds number, it is
necessary to find the density and viscosity of the fluid, both o f which a r e functions o f temperature.
These values are obtained from Chapter I V
Properties Graphs. The friction factor, f, is a function o f Reynolds number, and t o a lesser extent, a function o f pipe diameter.
T h e Properties Graph that
shows the Reynolds Number, vs. friction factor curves indicates minimum, maximum and average values o f f with respect to pipe diameter,
T h e average
9 value can be used with reasonable accuracy since the friction pressure drop term contributes only 1 % to 5% of the single phase pressure drop. However, f values may be estimated from the graph for those who desire
to be as precise as possible. ~.
\
The single phase pressure drop is determined on a per foot o f we1 bore length basis.
The total available single phase pressure drop i s
then found by subtracting the saturation pressure (found in the initia 1
1
step to determine if single phase flow exists in the wellbore) from.the production pressure.
This saturation pressure is a function of the pro-
duction temperature, and if the pressure in the wellbore drops below this value, boiling must start. Since the available total pressure drop for single phase flow is known and the pressure drop per foot of wellbore in single phase flow
has been calculated, a simple division of the first by the second will equal the length of wellbore in single phase flow.
Thus we now know
how far from the top of the producing zone boiling begins.
The depth
to the producing zone is an input parameter, so a subtraction will yield the length of wellbore in two-phase flow.
This value
i s the input needed
to find the pressure drop in the two-phase flow zone. Two-Phase Pressure Drop The calculation for pressure drop in the two-phase flow zone i s compl icated; it requires correlations to compute the elevation pressure drop term and friction pressure drop term. These correlations are functions of the physical properties and relative volumes o f the steam and liquid water constituents of the fluid.
An iterative procedure is necessary
to complete the calculation; it is most easily done by a digital computer
10 program, There are many correlation coefficients for two-phase flow that exist in the technical literature. After consideration of several of the more prominent, those chosen for this edition of the design handbook are Hughmark for elevation pressure drop and Dukler, Case I I , for twophase friction pressure drop.
A decision was made to run a representative set of input conditions through the computer program and then present the output in graphic form. This method has two advantages: a large volume of data can be presented on a minimum amount of paper, and similar data sets with only one parameter change can be presented on the same graph for comparison purposes. The graphs included in the handbook each consist of eight (8) curves on a single set of axes.
The curves represent the results for inputs of
a specified diameter, two (2) mass flowrates and four (4) temperatures.
The mass flowrate, temperature and diameter have each been parameterized 2s
8 discrete
Val
ues. Thus a total of 64 two-phase we1 1 head pressure
graphs have been generated. The axes chosen as being the most convenient to use the data were Length of Two-Phase Zone as the abscissa and Wellhead Pressure as the ordinate. Wellhead pressure was chosen because it i s one of the output parameters of the handbook sequence; iength of two-phase
zone can be easily calculated once the single phase pressure drop is computed, and provides a most logical independent variable, since the pressure drop is a direct function of length o f the flow path.
OUTPUT There is an index at the start of Chapter I V to allow fast and easy
ocation of the two-phase Wellhead Pressure graphs, based on the
input parameters used in the single phase calculation. Once the proper
graph i s located, the user finds the length of two-phase zone (computed
11 as t h e r e s u l t of t h e s i n g e phase pressure drop) on the abscissa, f o l l o w s t h a t value v e r t i c a l l y t o
t s i n t e r s e c t i o n w i t h t h e proper curve, and reads
the corresponding Wellhead Pressure o f f the o r d i n a t e , Once t h e wellhead 'pressure i s found from the above-descr bed graphs, t h e wellhead temperature i s f i x e d due t o the saturated c o n d i t on o f t h e The wellhead temperature i s found from t h e graph o f s a t u r a t i o n
flow.
pressure-temperature r e l a t i o n s h i p s i n Chapter I V .
Q u a l i t y o f the geothermal
f l u i d , expressed as a'percent by weight o f the t o t a l f l o w ,
i s e a s i l y com-
puted using conservation o f energy and e n t h a l p i e s o f the f l u i d a t t h e f l a s h ~
horizon and a t t h e wellhead. ANALY S I S The a n a l y s i s o f t h e output o f t h i s handbook i s dependent on t h e use t o be made o f t h e geothermal f l u i d a f t e r e x t r a c t i o n .
w i l l be presented here.
A general methodology
Since i n most cases, some knowledge o f the r e s e r v o i r
i s a v a i l a b l e , t h e depth t o t h e producing zone and t h e production temperature can be f i x e d .
By varying w e l l diameter and mass f l o w r a t e inputs, a para-
m e t r i c s e t o f wellhead temperatures, pressures and q u a l i t i e s can be calculated.
An estimate of t h e number and s i z e o f w e l l s needed t o operate the
u s e r s ' intended process can now be made.
With t h i s information, cost
comparisons can be c a l c u l a t e d f o r t h e severa r a t e inputs used.
cases o f diameter and flow-
I f r e s e r v o i r c h a r a c t e r l s t cs a r e n o t w e l l defined,
a d d i t i o n a l cases w i t h changes i n depth and t mperature can be computed. Economic o p t i m i z a t i o n can be conducted by adding costs f o r t h e process i t s e l f as a f u n c t i o n o f f l u i d pressure and temperature a t t h e wellhead t o t h e w e l l costs as computed above. Long term w e l l operation can a l s o be ca culated, i f t h e pressure o f t h e r e s e r v o i r can be p r e d i c t e d a s a f u n c t i o n of e i t h e r time o r
12 cumulative production, The method used here depends on production pressure and temperature, so thst when standard reservoir engineering techniques are
applied, sufficient information can be obtained so that calculation of wellhead pressures and temperatures for future operation is possible. A final comment on the use of the output should be noted.
Because
of the simp1 Fying assumptions made and the complex nature of two phase flow, the we lhead conditions determined
via this handbook are approxima-
tions. This is why they are called estimates throughout the text. The output data have the most value when used to compare the relative merits of several proposed well configurations and the influence o f individual parameters on well performance.
13 1 1 1 . SAMPLES OF USE OF THE HANDBOOK PROCESS The Well Design Data Sheet i s introduced and i t s use explained i n t h i s chapter.
By f o l l o w i n g t h e step by step i n s t r u c t i o n s on the Well
Design Data Sheet, the user can determine the wellhead f l u i d conditions f o r any set o f input parameters t h a t l i e w i t h i n t h e range o f the param e t e r i z a t i o n noted i n Chapter 1 1 .
A blank Well Design Data Sheet (Fig. 2) t o
be reproduced and f i l l e d - i n by the user i s provided.
The f i r s t sample, us
d i s c r e t e values included i n t h e i n p u t parameterization, i s worked on a We1 Design Data Sheet and accompanied by t e x t explanation. i n t e r p o l a t i o n i s necessary i s a l s o given,
A second sample where
Also included i s a d e t a i l e d expla-
n a t i o n o f a method t o use when a change i n wellbore diameter i s encountered a f t e r the onset o f two-phase flow. The f l u i d p r o p e r t i e s necessary t o complete the s i n g l e phase pressure drop c a l c u l a t i o n s a r e presented i n Chapter I V . temperature and a r e shown i n grpphic form.
These p r o p e r t i e s vary w i t h
The graphs are marked t o show
t h e i r use i n o b t a i n i n g f l u i d p r o p e r t i e s f o r the sample c a l c u l a t i o n l a t e r i n t h i s chapter.
Reference t o t h e p r o p e r t i e s graphs a t the noted steps
i n t h e sample should help the user i n understanding t h e i r f u n c t i o n . Also contained i n Chapter I V are the graphs o f the two-phase flow pressure drop, presented as curves on Depth o f Two-Phase’Zone vs. Wellhead Pressure axes.
These are the data necessary t o compute the estimates o f
wellhead c o n d i t i o n s using the methodology o f t h i s handbook. used t o develop these curves were described e a r l i e r .
Calculations
It i s expected t h a t
b e t t e r c o r r e l a t i o n s f o r t h e two-phase pressure drop c a l c u l a t i o n w i l l be developed through l a b o r a t o r y and f i e i d experiments.
Improved graphs i n
t h e above described format w i l l be issued as replacements for t h e o r i g i n a l s i n t h i s handbook, and more accurate estimates f o r t h e output parameters
Figure 2. Symbol
Parameter
Well Design Data Sheet Units
Source
Wellbore Diameter (casing i n s i d e dia.)
D
inches
input
Depth t o Top o f Producing Zone
L
feet
input
1b/hr
input
OF
input
psia
input
~~~
Va 1ue
~
Mass Flow Rate Production Temperature
I
Tor
Production Pressure
PPr
S a t u r a t i o n Pressure a t Production Temperature ~
-~~~
'sat (T D r
I
psia
Graph P-4,
I
pg. 35
~~~
S i n g l e Phase Pressure Drop
PS
plP
I F APlp < 0
Well i s i n two phase f l o w i n producing zone
STOP
No f u r t h e r c a l c u l a t i o n can be made
L i q u i d Density
P
E l e v a t i o n Unl t Pressure Drop
IJ
Absolute V i s c o s l t y Reynolds Number
Graph P-1 , P. 32
psijft
Graph P-1, p. 3 2 , T
centlpoise
--
(E)
Graph P-2, p. 33 Re = (6.31607) Graph P-3, P.
--
f
S i n g l e Phase U n i t Pressure Drop
Equation :
lb/ft3
Re
Moody F r f c t i o n Factor
I
psi/ft
, Tpr
9
wA
jb
Tpr
Re
(equation)
1P
(E)
1P
=
(E)
e l ev
[I + (4.8377 x
I)-(
I
Figure 2. Symbo 1
Parameter Length o f S i n g l e Phase Zone
Wz11 Design Data Sheet (continued)
Units
ft
Va 1oe
Source L l p = APlP/(E) 1P
Length o f Two Phase Zone
IF LPp < 0
L2P
L2p =
L
- LlP
I
Well i s i n s i n g l e phase f l o w o n l y
Go t o Option
We1 1head Pressure *OUTPUT*
ft
@
below
'wh
psia
Two phase wellhead pressure graphs LA-1 through HD-8 (see index on pgs.30 6 311,
LzP OF
Wellhead Temperature *OUTPUT*
Twh
Wellhead L i q u f d Enthalpy
hRwh
BTW 1 b
L i q u i d Enthalpy a t FI ash Hor I zon
hEfh
BTU/ 1 b
Phase Change Enthalpy a t Wellhead Conditions
hQgwh
BTU/ 1b
Steam Q u a l i t y *OUTPUT* OPTION @ Wellhead Temperature *OUTPUT* We1 lhead Pressure *OUTPUT*
Q
Graph P-5,
P.
36, Tpr
I
by Weight
Twh
OF
'wh
psia
Twh
Steam Qual I t y = 0% f o r Slngle Phase Flow a t Wellhead
e
'pr
I I
16 can then be determined. SAMPLE WITH INPUT VALUES FROM THE DISCRETE PARAMETERIZATION Use of the Well Lesign Data Sheet is demonstrated here for an input data set chosen from the discrete values used in the construction of the two-phase wellhead pressure curves. The filled-in Data Sheet for this as Fig. 3.
sample is sh&n
Please refer to it as you follow the text.
Let us assume we know that the top of the producing zone is 6000 ft. below the surface, and that the production temperature of the fluid as it starts up the wellbore will be 45OoF.
Further, a reservoir engineer
has stated that at a flowrate of 500,000 lb/hr, the production pressure
(in the wellbore at the top of the producing zone) will be about 2280 There are plans to case the drilled well with 9 5/8" OD pipe
psia.
which hzs an inside diameter o f 9.063 inches.
These values should be
recorded, in the proper units, on the Sample Well Design Data Sheet, Fig. 3. Saturation pressure for the input production temperature is found
on Properties Graph P-4, page 35.
For the 450° used here, the saturation
pressure is 423 psia. When the pressure of the fluid rising up the wellbore drops to this value, boiling will start to occur in the fluid. This is by definition the flashing horizon and the top of the single phase flow zone in the well. APlp
e
Thus the available single phase pressure drop is Ppr
-
Psat;
for the sample case, APlP = 2280
-
423 = 1857 psi,
If the saturation
pressure is then more than the production pressure (i .e., APIP*'O),
then
the producing zone is in two-phase flow and the handbook cannot be used to produce estimates of wellhead conditions,
. , . _.._...
~
..~....... .
.
....l_l..____
.
.
~
F l g u r e 3.
~
.~
.
.
I.
.
.I
.. ...
......
_-
..--....-.^I
...
. ."
"".. ~"..
...._--._I
Sample Case w i t h D i s c r e t e P a r a m e t e r i z e d Input. Well Design Data S h e e t
Symbol
Parameter
Uni t s
Source
We1 l b o r e Diameter (casing inside dia.)
D
inches
input
Depth to Top of Producing Zone
L
feet
input
Mass Flow Rate
M
9.063 6000
I
P roduc t 1on Temperature
OF
Single Phase P r e s s u r e Drop
~~~
input
450"
input
psla
Psat(Tpr)
500,Or'-x7
i npu t
psia
PPr
Saturation Pressure a t P r o d u c t i o n Temperature
I I
1b/hr
Tp r
Productlon Pressure
Graph P-4, pg. 35
4-23
(Tp r 1
/&I57
3
PS i
plP
I F APlp
'tp
E
'pr-'sat
Well i s i n two phase flow i n producing zone
0
CON r / M U € -
No f u r t h e r c a l c u l a t i o n can be made
STOP
Liquid D e n s i t y
Val u e
1b / f t 3
Graph P-1, p. 3 2 , T ; ~
w
psilft c e n t i po i se
Graph P-1, Pa 3 2 , Tpr Graph P-2, p. 339 Tpr
Re
--
P
'
Elevation Unit P r e s s u r e Drop
5/. 4-
/AD\
Absolute V i s c o s i t y Reynolds Number
-
Re (6.31607)($,) Graph P-3, P- I
_-
f
Moody F r i c t i o n F a c t o r
0.357
L
,
~
2.7 Y /06 0.o/#
~~~
Single Phase Unit P r e s s u r e Drop
( e q u a t ion) I
Equation:
(g)1P = (g)e l e v
t
[I + (4.8377 x
I
(-)]
0.3607
--- - -
....
~
.
~
~~~
.
.
........
. .
.
~. ....
F i g u r e 3 (Continued) We1 1 Design Data Sheet (continued)
Parameter
Symbo 1
ft
Length o f S i n g l e Phase Zone
Va 1ue
Source
Units
Ev4-a
L l p = Ahp/(%) 1P
Length o f Two Phase Zone
Go t o Option
Wellhead Pressure *OUTPUT*
LfP
@
ft
L2p = L
- Llp
below
'wh
psia
Two phase wellhead pressure graphs LA-1 through HD-8 (see index on pgs.30 & 31 ) , L2D
Wellhead Temperature *OUTPUT*
Twh
Wellhead L i q u i d Enthalpy
hRwh
L i q u i d Enthalpy a t Flash Horizon Phase Change Enthalpy a t Wellhead Conditions Steam Q u a l i t y *OUTPUT* OPTION @ Wellhead Temperature *OUTPUT
*
We1 lhead Pressure *OUTPUT
*
hQgwh
Q Twh 'wh
Graph P-4, p.
35, Pwh
405
BTU/ 1b
Graph P-5,
P.
36, Tpr
4-3
BTU/ 1 b
Graph P-6, P.
37, Twh
0.17
OF BTU/ 1b
% ! by Weight
OF psia
Steam Q u a l i t y = 0%.for S i n g l e Phase Flow a t Wellhead
19 The first fluid properties needed in the single phase pressure drop calculation are the liquid density and the elevation unit pressure drop. Theseyvalues, as found on curves on Properties Graph P-1, page 32, are p =
51.4 lbs/ft3 and (AP/Ak)elev = .357 psi/ft., and should be listed in
the "Value" column of the sample Well Design Data Sheet, Fig. 3. Absolute viscosity is next determined from Properties Graph P-2, page 33, to be 0.12 centipoises, This figure is entered and then plugged into the Reynolds number equation presented on the next line of the Data Sheet, along with the mass flow rate and wellbore diameter previously iisted. The constant in the equation adjusts for units as given so that the product is dimensionless.
The equation to be used is
A Re = 6.31607 QJ
The Reynolds number found (Re = 2.9 x 106)
rovidas the necessary
input to find the Moody friction factor from Properties Graph P-3, page 3 4 .
The Graph of friction factor vs. Reynolds Number shows a range of friction factors due to the different diameters considered, with an average value plotted in the center of the rang
lue for this case was taken
from the "average" curve. The Moody
on factor Is found to be
f = 0.014 and i s noted on the sample Well
eslgn Data Sheet.
All necessary info phase unit pressu
able to calculate the single owing equation:
values are l i
in F g. 3. us
t calculator permits fast and accurate computa-
tion of the above parameter, whose value is ,3607 psi/ft for our sample case.
I
20
,
The length of the zone of single phase flow can now be computed using the following equation:
Substituting values listed on Fig. 3 and performing the division, the length i s found to be
Now the length of the two-phase flow zone
5148 ft.
can be computed, because the total well depth was an input parameter. This depth is also the location of the f1a.h L2p =
-
Llp = 6000
'horizon and is Siven by
- 5148,
which is 852 ft. for the sample case. When LIP is greater than the total well depth, L , the flow over the entire well depth remains single phase.
The wellhead temperature and
pressure are then found using formulae presented in Option A on the Well Design Data Sheet. The temperatureis unchanged due to the adiabatic wellbore assumption: Twe1 1 head
Tproduct ion
The pressure drop i s the product of the well depth and the single phase unit pressure drop; thus the wellhead pressure can be expressed as
-
The above equations are valid only when LPp is negative. Once the length of the two-phase zone is known, the wellhead pressure can be found on one of the 64 graphs presenting output of the two-phase flow computer program. tained in Table 2.
The Identification Key for these graphs is con-
The Two-Phase Flow Wellhead Pressure Graph Index,
pages 30-31, lists the locations by input parameter.
For the sample case
21
Table 2 Two Phase Flow Wellhead Pressure
Graph Identification Key
Product ion Temperature (Tpr)
r
Designation L
H
5000, 600°, 650°F 5500F)
Mass Flowrate (I?) 200,000 b/hr 300,000 b/hr
Designation
}
400,000 500,000 b/hr 600,000 800,000 b/hr
1,000,000 1 b/hr 1,200,000 lb/hr
-.
D
We1 lbore Casing Diameter (D)
6"
Designation
Outside Diameter ( 5.524'' ID)
1
7 518
(
7.125" ID)
2
8 518
( 8.097'l ID)
3
9 5/8
( 9.063" ID)
4
10 3/4
(10.192" ID)
5
1 1 3/4
(11.15"
ID)
6
13 318
(12.715" ID)
7
16
(1 5 375" ID)
8
Examples:
For h = 600,000 lb/hr, T = 400°F, D = 10 3/4" OD, curve i s found on Graph fC-5; For = 300,000 lb/hr, Tpr 550OF, D = curve i s found on Graph HA-2.
7 5/8" OD,
22
conditions: T = 45OoF yields "L" temperature designation; M = 500,000 Ib/hr, "Bll flowrate designation; and D = 9 5/811 OD, "4" diameter designaThus, the Graph to be used in the sample case i s LB-4.
tion.
has eight curves, four temperatures at each of two flowrates.
This Graph On the
T = 45OoF, M = 500,000 lb/hr curve, a length of 852 ft. corresponds to a wellhead pressure of 269 psia.
The value for wellhead pressure identi-
fied on this line of the Well Design Data Sheet i s one of the three output parameters. The second output parameter is the wellhead temperature, obtained from Properties Graph P-4 on page 35.
Two-phase flow at the wellhead
dictates that a saturation condition must exist, so that the temperature is fixed and known when the pressure is found, For the sample case, the we1 lhead temperature is 408OF. Wellhead steam quality (Q) i s a measure of the steam fraction of the wellhead fluid, by weight, expressed as a percent. output parameter of the handbook.
This i s the final
It is calculated by assuming constant
enthalpy in the wellbore, from the flash horizon to the wellhead. The fact that the fluid is 100% liquid at the flash horizon permits determination of enthalpy at that point.
Since there i s no loss of enthalpy,
the fluid at the surface must have an equivalent value on a per pound bas is.
The two-phase flow pressure/length curves (Graphs LA-1 through
HD-8) are used to find a wellhead pressure as detailed above.
Now a liqu,d
enthalpy (per pound) for wellhead conditions can be found from Properties Graph P-5, page 36, to be hawh = 3 8 3 . 5 BTU/lb,
From this same source,
enthalpy can be determined (using production temperature BTU/lb,
Entha py for phase change (heat of vaporization)
23 i s found from P r o p e r t i e s Graph P-6 on page 37; using t h e wellhead temperature,
gllwh t h i s value i s h quality i s
Q=
= 714 BTU/lb.
-
hRfh hkwh hQgwh
The energy balance t o determine steam
100
s u b s t i t u t i n g i n t h e values obtained above q u a l i y i s c a l c u l a t e d t o be
Q = 5.8% This completes t h e f i r s t sample c a l c u a t i o n . SAMPLE WITH INTERPOLATION
If t h e chosen values for e i t h e r t h e production temperature, Tpr,
or
the t o t a l mass f l o w r a t e ,
R,
z a t i o n i n Table 1, page
6, an i n t e r p o l a t i o n technique must be used t o f i n d
a r e not among those 1-isted i n the parameteri-
the process outputs of wellhead f l u i d conditions. . I t i s assumed t h a t enough standard p i p e
diameters a r e given t o avoid t h e need t o i n t e r p o l a t e .
The
i n t e r p o l a t i o n Sample Well Design Data Sheet, Fig. 4, demonstrates how tb handle such a case.
A l l i n p u t parameters remain t h e same as t h e previous sample, except t h a t t h e production temperature, Tpr,
has been r a i s e d t o 47OoF.
The s i n g l e
phase pressure drop c a l c u l a t i o n i s c a r r i e d o u t s i m i l a r t o t h e f i r s t sample. However, n o t e t h a t since t h e r e has been a change i n production temperature, t h e values of t h e f l u i d p r o p e r t i e s have a l s o changed,
Details o f the c a l -
c u l a t i o n a r e n o t presented here, but may be followed on Fig. 4. Once t h e l e n g t h of t h e two-phase zone has been determined (as t h e n a l step o f t h e s i n g l e phase c a l c u l a t i o n ) ,
i n t e r p o l a t i o n must begin.
near i n t e r p o l a t i o n i s used because i t i s simple, and t h e technique i s d e l y known,
The i n p u t production temperature l i e s between t h e parameterized
d i s c r e t e values of 45OoF and 50OoF.
So t h e proper Two-Phase Wellhead Pressure
..
.
Sample Case
F i g u r e 4.
Wi
t h I n t e r p o l a t i o n We1 1 Design Data Sheet.
Well Design Data Sheet Pa r ame t e r We1 l b o r e Diameter (casing i n s i d e dia.) Depth t o Top o f Producing Zone Mass F l o w Rate
Production Pressure
Source
D
Inches
i nput
L
feet
i nput
ri
1b/hr
input
psia
i nput
’pr
S a t u r a t i o n Pressure a t Production Temperature
, .
.
psia
‘sat (T p r
S i n g l e Phase Pressure Drop
I
PS 1
plP
Graph P-4,
STOP
No f u r t h e r c a l c u l a t i o n can be made
Elevation U n i t Pressure Drop
($)e1
Absolute V i s c o s i t y
ev
Reynolds Number
I
f
I
(E)
1P
(z)
elev
[1 + (4.8377 x
1765
Graph P-1,
_--
5 0 -3
0.35/
P. 32, Tpr
0. u-3
Graph P-2, p. 33 9 Tpr Re = (6.31607)
I
I)-(
3
5 1 5
pg. 35
psi/ft
S i n g l e Phase U n i t Pressure Drop
Equation :
500,0C2 c
Graph P-1, P. 32, Tpr
Re
Moody F r i c t i o n Factor
6000
Ib/ft3
centipoise
1.I
9.063
Ppr-Psat(Tpr)
Well i s i n t w o phase f l o w i n producing zone
P
Va 1ue
I
plp
I F BP1p < 0
L i q u i d Density
*
Uni t s
Symbol
3 - 0 8x
( 1 )
T , Re
Graph P-3, P- 5
I
IOLL’:”
0 -0/4
Figure
4
(Continued)
Well Design Data Sheet (continued) Pa r a mt e r
Symbo 1
Units
Length o f Single Phase Zone
ft
Length o f Two Phase Zone
L2P,
. ft
.
r
Go t o Option
@
Llp
Va 1ue
Source
-
Pp1P/(%)
4-374-
1P
-
L2p =
ioz 6
Llp
.
below ~~
We1 1 head Pressure *OUTPUT;\
'wh
psia
Two phase wellhead pressure graphs LA-1 through HD-8 (see index on pgs. 30 E 311,
339
L2P
We1 1 head Temperature *OUTPUT
Twh
*
Wellhead L i q u i d Enthalpy
hRWh
OF
BTU/ 1b
Graph p-5, P. 36, Twh Graph P-5,
, .
L i q u i d Enthalpy a t Flash Horizon
hRfh
BTU/ 1 b
Phase Change Enthalpy a t We1 lhead Condl t l o n s
hRgwh
BTU/ 1b
I Q I
% by Weight
Steam Qual I t y *OUTPUT* OPTION @ Wellhead Temperature *OUTPUTfc
Twh
We1 1 head Pressure *OUTPUTn
'wh
Steam Q u a l i t y
-
p. 36, Tpr
794 5.54
E' qwh ~
OF
psla
= T'
'wh 'wh
t3:
pr
Ppr
. 0% for Single Phase Flow a t Wellhead
- [(@l
OL]
P
26 Graphs are checked and the following pressures found for a two-phase zone
of 1026 feet:
45OoF:
Pwh = 252 psia
50OoF:
Pwh = 470 psia.
The interpolation multiplier is computed from the equation: x =
-
Tpr Tcooler fhotter - Tcooler
- 470-450 = - 5o0-450
o.4
Pwh for the desired TPr is found from an analogous equation: x = 'wh p500
-
'450 p450
rearranging terms and substituting numbers: Pwh
p450
4- X(P500
- P450) = 252 + 0.4 218)=
Thus the interpolated wellhead pressure is 339 ps a,
339 psia.
The other wellhead
parameters are calculated by following the remain ng steps on the Well Design Data Sheet. An analogous calculation can be made for mass f l w rates that are not in the discrete parameterization data set.
If both the total mass flowrate and production temperature values to be used in the calculation are not in the discrete parameterization data set, proceed as follows: 0
Compute the single phase pressure drop and find the length of the two-phase zone via the steps o f the Well Design Data Sheet.
0
Consider the discrete mass flowrate from the parameterization data set that is closest to, but less than, the actual value used in the problem. Obtain the Wellhead pressures using the Two-Phase Wellhead Pressure Graphs, from curves for the two temperatures from the discrete set that are closest to the input value, one greater than and one less than the actual input. Perform an interpolation following the above procedure to get a wellhead pressure that reflects the actual input production temperature, but is a function of the lower value discrete mass flowrate.
0
Perform a similar interpolation to that outlined above at the mass flow rate closest to, but areater than the actual value from the problem.
27
I
0
Perform a f i n a l i n t e r p o l a t i o n using the actual input mass f l o w r a t s a n d t h e two c l o s e s t mass flowrates from the d i s c r e t e set, w i t h t h e i r corresponding wellhead pressure values. These are t h e values computed i n the two previous steps. This f i n a l i n t e r p o l a t i o n gives a wellhead pressure t h a t has been corrected f o r both temperature and mass flowrates o u t s i d e the input d i s c r e t e parametetlzation.
0
Using t h e wellhead pressure found i n the l a s t step, f o l l o w the Design Data Sheet sequence t o o b t a i n the o t h e r wellhead f l u i d conditions.
The user should be aware t h a t l i n e a r i n t e r p o l a t i o n s are an approximation technique, and t h a t the r e s u l t s t h a t use i n t e r p o l a t i o n w i l l not be as accurate as those obtained d i r e c t l y from the d i s c r e t e parameterization i n p u t .
However,
the s i m p l i f y i n g assumptions made t o permit t h e production o f t h i s handbook compromise the absolute accuracy o f the r e s u l t s , so t h a t the i n t e r p o l a t i o n .material can be used as an estimate w i t h confidence. CHANGE I N WELLBORE DIAMETER
Calculations f o r a "telescoping" w e l l , one w i t h changes i n wellbore diameter, can be performed using t h e f o l l o w i n g sequence:. 0
Separate t h e t o t a l w e l l depth '(to the top o f t h e producing zone) i n t o Constant diameter segments: LA, LB, e t c .
0
Compute the pressure a t the top o f t h e bottom segment using the producing zone i n p u t parameters, f o l l o w i n g the sequence of the Well Design Data Sheet.
0
Moving up from t h e producing zone, use the pressure, temperat u r e , and f l o w r a t e values a t the top o f each segment as the input f o r t h e bottom of the succeeding segment.
There are two p o s s i b l e s i t u a t i o n s a t the s t a r t o f each new segment. The f i r s t i s t h a t t h e w e l l i s i n s i n g l e phase flow, i n which case t h e Well Design Data Sheet sequence i s used, w i t h pressure and temperature inputs s p e c i f i e d as those outputs o f t h e previous segment,
Secondly, i f t h e flow
i s two-phase a t the entrance t o a new segment, the key t o f i n d i n g the cond i t i o n s a t the top o f the subject segment i s t h a t the pressure a t the
28
bottom of that segment is known. I n the second case,
t is necessary to find an "equivalent length" of
che two-phase flow zone for the new diameter of the segment. Take the known pressure from the top of the previous segment as the ordinate on the proper Two-Phase Wellhead Pressure Graph.
Follow the constant pressure
line to its intersection with the correct curve for the given conditions and proceed vertically down to the corresponding Depth of Two-Phase Zone. This value is the equivalent length, defined as the length of wellbore of the new diameter that would be required to generate a pressure drop to reach the known pressure, if the flash horizon was located in the segment under study.
The length of the subject segment is then added to the "equiva-
lent length", and a new Wellhead Pressure i s found on the same graph.
This
new wellhead pressure in turn becomes the input pressure for the next segment. The treatment presented here assumes no pressure drop across a diameter change.
29 IV.
P r o p e r t i e s Graphs and Two-Phase Flow We1 head Pressure Graphs
Index P r o p e r t i e s Graphs Graph
P-1
Page
L i q u i d Density and E l e v a t i o n U n i t Pressure Drop a t S a t u r a t i o n Conditions
32
Graph P-2
Absolute V i s c o s i t y a t Saturation Conditions
33
Graph P-3
Moody F r i c t i o n Factor as a Function o f Reynolds Number
34
Graph P-4
S a t u r a t i o n Temperature-Pressure Re a t ionsh ips
35
Graph P-5
L i q u i d ' Enthalpy a t S a t u r a t i o n Cond t ions
36
Heat o f Vaporization a t Saturation Conditions
37
Graph
P-6 TWO
Flow Wellhead Pressure Graphs
(See Next Two Pages}
30
,
Index to Two-Phase Flow Wellhead Pressure Graphs
Temperat u re
Flowrate
Diameter
,
I
age
200,000 lb/hr 300,000 lb/hr Low Temperature
L
400,000 1 b/hr 500,000 1 b/hr
3OO0F 350°F 400zF 450 F SOOOF
600,000 lb/hr 800 ,000 lb/hr
Low Temperature
1,000,000 lb/hr 1,200,000 1 b/hr
NOTE:
To permit easier use o f Two-Ptiase Wellhead Pressure Graphs during interpolation, the curves for SOOOF appear on both
the Lo- and High Temperature graphs.
31 Two-Phase Flow We1 lhead Pressure Graphs (Continued) Temperature
I
1
D ia m e t e r
Page
I
i
I
I
200,000 b/hr 300,000 b/hr
I
iI
F 1 ow rate
High Temperature
1
400,000 1 b/hr 500,000 lb/hr
High Temperature
65
60
5s
50
G z W
a c W
k B
45
40
35
30
25
100
200
300
400
TEMPERATURE GRAPH P-l
500
600
OF
LIQUID DENSITY AND ELEVATION UNlT PRESSURE DROP AT SATURATION CON DIT ION S
c
TEMPERATURE
OF w W
GRAPH P-2 ABSOLUTE VISCOSITY AT SATURATION CONDITIONS
\
n
..
0
P
a
c
I
34
35
I-
'
'
a
1
1
f
.
.
.
I
.
,
.
I
,
,
.
I
,
,
I
I I
,
I
1
I 1 I ,
I
I I
'
I I I I
I
I I I I
I
2 TEMPERATURE
OF
GRAPH P-4 SATURATION TEMPERATURE-PRESSURE RELATIONSHIPS
36
0 3 P
TEMPERATURE OF
GRAPH P-5 LIQUID ENTHALPY AT SATURATION CONDITIONS
37
GRAPH P-6
HEAT OF V A P O R I Z A T I O N A T SATURATION C O N D I T I O N S
Legend
Diameter
A I T P ~ = ~ O O ~ F , 300,000 l b / h r 200,000 1 b/hr B: l p r =300°F, &l= CI fpr = 350° F , A = 300,000 1 b l hr 0: Tpr =35OOF, td z 200,000 t b / h r E: Tbr =40O0F, a z 300,0001 b/ hr
= 5.524
inches
38
F: Tor= 4OO0F, M = 200,000 l b / h r Tpr = 450°F, & =I 500,000 l b /hr H: Tpr =450°F, Q = 200,000 l b / h r 31 Tpr =500°F,P = 300,000 fb/hr K: T p r = 5 0 0 0 F , P = 200,000 l b / h r
G I
4
tn
n L
W
z
3
v)
tn W
a e 0
a W
I
J J W
DEPTH OF TWO PHASE ZONE, FT. GRAPH LA I : TWO PHASE WELLHEAD PRESSURE CURVES
Diameter = 7.125 inches At Tpr L 30O0Fl & LI 300,000 1 b/hr F: Tpr = 4OO0F, M = 200,000 lb/hr 200,000 1 b / hr G: Tp! * 4 W F , M = 300,000 l b l h r 8: Tpr =300°F, A = C* Tpr =350°F, 300,000 1 b/hr H: Tpr =450°F, IJ = 200,000 lb/hr 0: Tpr =35O*F, K l C 200,000 1 b/ hr 4% Tpr =50O0F1&4 = 300,000l b / h t Legend
E: Tpr +4OO0F, liC =
39
K: Tpr =5000F, & =I 200,000 lb/hr
300,000 1 b/ hr
800 I
,
...I
\
. .
I .
'
.
,
I
'
:
'
,
1
- - .
. ---
,
I
7-
I
I
I
I I I
,
'
:
'
I
I
I
I
.
:
I
I I
1
.
1
0
L
.
I
0 DEPTH
OF TWO PHASE ZONE, FT.
GRAPH LA-2: TWO PHASE WELLHEAD PRESSURE CURVES
Legend
40
Diameter = 8.097 inches
Ca Tbr =350°F, &l= 300,000 1 b/hr 0: Tar =35OoF, = 200,000 l b l h r rE: Tpr = 4 0 0 ° F , 300,000 1 b/ hr
.
H: Tpr = 4 5 0 * F , fi :: J * Tnr = 5 0 0 ° F , &4 =
200,000 lb/hr 300,000 lb/hr 200,000 lb/hr
a
cn a
c
W
a 3 cn cn W a Q,
0
a W r
J J
W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LA-3: TWO PHASE WELLHEAD PRESSURE CURVES
Legend
Diameter
A l T p r f 3 0 0 ° F , &f= 6: Tpr t300°F, M = C1 fpr s35O0F, &! f
300,000 l b / h r 2oC),OOO 1 b/hr 300,OOO 1 b/hr
=
41
9.063 inches FI Tort 4OO0F, M = G * Tpr,= 4SOOF, &4 L HI Tor =45OoF, h;r *
200,000 l b / h r
300,000l b / h r 200,000 l b / h r
800
cn a e w P
as w
I.
.J W
3%
V I
0
lobo
2doo
DEPTH OF TWO PHASE ZONE, FT. GRAPH LA- 4: TWO PHASE WELLHEAD PRESSURE CURVES
Diameter
Legend A: Tpr = SOOOF, &4 = 8: Tpr = 300°F , til = C: Tpr = 350° F , 1;1( = 0: Tpr = 3 S o F , til = E: Tar =4OO0F, =
300,000 200,000 300,000 200,000 300,000
1 b/hr 1 b / hr 1 b / hr 1 b/ hr 1 b/ hr
42 : 10.192
inches
F: Tprt 400°F, k
G: Tpi = 45OOF, H: Tpr = 4 5 0 ' F ,
= 200,000 l b / h r :
300,000 l b / h r
= 200,000 l b / h r
J: Tpr =500°F,64 = 300,000 l b / h r K: Tprr5000F, M = 200,000 l b / h r
e tn
Q. c
W
a
3
tn
m
W
a e n
Q W
I J
A
W
3
DEPTH
OF TWO PHASE ZONE, FT.
GRAPH LA-5. TWO PHASE WELLHEAD PRESSURE CURVES
i
Diameter
& = SO0,OOO l b / h r R= M=
200,000 1 b/hr 300,000 1 b/hr & =I 200,000 l b / h r &=I
= 11.60
43 inches
Fs Tp,r= 4OO0F, M = 200,000 l b / h r 6 : Tpr 4500 F, &4 : 200,000 l b /hr H: Tpr ~ 4 5 0 * F ,Id = 300,000l b / h r J * Tpr =500°F, P = 2OO,OOO l b / h r
300,0001 b/ hr
-ma e
c
W
c 2
m (0
W
a
e
n
a w
I
I. J
i
i
DEPTH OF TWO PHASE ZONE, FT. GRAPH LA-6: TWO PHASE WELLHEAD PRESSURE CURVES
44
-ma e
c
w
a
3 tn tn W
a e 0 Q
w I J
W
B
IO DEPTH OF TWO PHASE ZONE, FT. GRAPH LA-?: TWO PHASE WELLHEAD PRESSURE CURVES
Legend
Diameter
B* l p r =300°F, &4 = C' Tpr =3500F, fA = 0: Tpr =350°F, t4 = E: Tpr =400*F, &4 t
300,000 1 b / hr 200,Om 1 b/hr 300,000 1 b/ hr 200,000 1 b/ hr
45
= 15.375 inches
w = 300,000 l b / h r 3; Tpr = 5OOoF, rif = 200,000 1b/hr K: .Tplr50@F, hir = 300,000 lb/hr
H: Tpr =4SO°F,
I
c
W
K
3
cn
m w
a e P
a W
I
A A
V I
0
lobo 2doo DEPTH OF TWO PHASE ZONE, FT. GRAPH LA-8 TWO PHASE WELLHEAD PRESSURE CURVES
301 '0
46
w
a 3 cn cn w a e n
a W
I
J . J W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LB'I :TWO
PHASE WEUHEAO PRESSURE CURVES
47 Diameter
Le~cnd
AI T p r f 3 0 0 ° F , h = Bt Tpr =300°F,& =I C* Tpr *35O0F, &! E: 0: Tpr t3S0°F, t4 = E: Tpr =400°F,h;( L
800 I
I I
= 7.125
inches
400,000 1 b/hr 500,000 1 b/hr 400,000 1 b/ hr
Fl Tpt.' 4o0°F1 M = 4 ~ 0 , 0 0 0l b / h r G I Tpr = 4 5 P F , = 560,000l b / h r H: Tpr =45OoF, lh 400,000l b / h r Jr Tpr =500°F, P = 500,000 l b / h r
500,000l b / hr
K: Tpr t5000F,
500,000 l b / h r
-- .
th = 400,000 l b / h r
I
a I
,
600
a
m
e
c
w
a 3 cn m
400 Q
n a w
r
J J ..
DEPTH OF TWO PHASE ZONE, FT. GRAPH Le-2: TWO PHASE WELLHEAD PRESSURE CURVES
1
i
48
a cn
Q. L
W
a 3 cn cn Y a e 0
a W
I
J. J
W
DEPTH OF TWO PHASE ZONE, FT. GRAPH LB-3: TWO PHASE WELLHEAD PRESSURE
CURVES
Legend
Diameter
500,000 l b / h r 400,000 1 b/hr C* Tpr =S50°F, R 500, 0: Tpr t3500F, & e l 400,000 1b/hr E: Tpr =40O0F, U 500,000 1b/ hr A*Tpr'30OoF,
Q g
B: Tpr r300°F,
f
=
9.063 inches
FS T'r,' 40OoF, kl a 400,000 l b / h r Tpr = 45OOF, lh t 5 m O O O l b / h r Ht Tpr Kh90°F, &4 = 400,000 Ib/hr aJ1 Tpr L 500°F, 500,000 l b / h r Kc Tpr=5000F, P = 400,000 l b / h r
GI
800
DEPTH OF TWO PHASE ZONE, FT. GRAPH L6-4: TWO
PHASE WELLHEAD PRESSURE CURVES
49
I
53
6: Tpi =300°F,P = C: f p r 350' F, R * D: Tpr = S O oF , O = E: f ~ =400°F, , Pt
400,000 500,000 400,000 500,000
DEPTH OF TWO PHASE ZONE, FT. -name I e - c . .rum OUACC UIPI I
ueAn DPCCCIIDCPIIDVCC
51
DEPTH OF TWO PHASE ZONE, FT. GRAPH LB-6:TWO PHASE WELLHEAD PRESSURE CURVES
Legend
Diameter
A: Tpr = 300° F , P = B* Tpr s30O0F, M = C' Tpr =350.F, &! 8 0: Tpr *3506F, M =
E: Tpr =40O0F, 64 =
500,000 1 b l hr 400,000 1 b l h r 500,000 1 b i b 400,000 1 b l hr 500,000 1b l hr
=
52
12.175 inches FI Tprg 400°F, M = GI Tpr 4500F, M * H: Tpr g 45OoF, U = J' Tpr =50O0F, a;C = K: Tpr = 5000F, P =
400,000 l b l h r 500,000 l b l h r 400,000 l b l h r 500,000 l b l h r 400,000 l b l h r
DEPTH OF TWO PHASE ZONE, FT. GRAPH Le-? : TWO PHASE WELLHEAD PRESSURE CURVES
53
DEPTH OF TWO PHASE ZONE. FT.
GRAPH LB-8 :TWO PHASE WELLHEAD PRESSURE r, CURVES
54
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC- I : TWO PHASE WELLHEAD PRESSURE CURVES w
Diometer
Legend
A: Tpr 8: Tpr C* Tpr 0: Tpr E: Tpr
L
300*F, h
z30O0F, & l o =3508F, 641 tSSOOF, &4 g40O0F, &4 t
800,000 1 b / hr 600,000 1 b/hr
800,000l b l h r 600,000 l b / h r 800,000 1 b / hr
=
55
7.125 inches F * Tprz 4008F, M G: Tpr = 4500 F, td : H: Tpr +450°F, M = J : *Tpr =500°F, P = K:.'Tpr =5000F, & =
600,000 l b / h r 800,000 l b / h r 600,000 l b / h r 800,000 l b / h r 600,000 l b / h r
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-2: TWO PHASE WELLHEAD PRESSURE CURVES
6
4 . I I
cn e c
w
0:
2 tn
cn W a
e 0
a W
I
J J W
3
IO DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-3:TWO PHASE’WELLHEADPRESSURE CURVES
Legend
Diameter
= 9.063
inches
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-4: TWO PHASE WELLHEAD PRESSURE CURVES
57
Legend At Tpr 8: Tpr C* Tpr D: Tpr E: Tpr
Diornettr
=300°F, & = ~ 3 0 F, 0U ~= =350*F,li4 = =35OOF, ti! = =400°F, K4 f
800,000 1 b/hr
600,0001 b / hr 800,000 1 b/hr 600,0001 b/ hr 800,000 1 b/ hr
t
10.192 inches
Fi Tprs 4OO0F, M = 600,000 l b / h r G : Tpr * 450" F, t 800,000 1b /hr H: Tpr =450°F, = 600,000l b / h r Jt lpr =500°F, P = 800,000 I W h r K: Tpr =5000F, P = 600,000 lb/hr
-acn Q c
W
a 3 co m w
a Q
n
a W
I
J J W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-5 : TWO PHASE WELLHEAD PRESSURE CURVES
58
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-6: TWO PHASE WELLHEAD PRESSURE CURVES
Leiend
Oiometer
A: Tpr = 300' F, h = B: Tpr =300°F, G t
800,000 1 b / hr
C: Tpr = 35OoF, R 0: Tpr =35OoF, &
800,000 1 b / hr 600,000 1 b/ hr
= =
600,0001 b/hr
= 12.715
60
inches
FI Tprg QOOOF, IA
= 600,000
lb/hr
G: T p r = 4 5 0 0 F , M = 800,000 l b / h r H: Tpr =450°F, = 600,000l b l h r J: Tpr = 500°F, 64 = 800,000 1 b/ hr K: T p r = 5 0 0 0 F , P = 600,000 l b / h r
a
cn
CL L
W
a 3 cn rn W
a
CL
n
a
W
I
J
2
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-7 : TWO
PHASE WELLHEAD PRESSURE CURVES
Lcqcnd
Diameter
A * T p r = 3 0 O o F , bx B: Tpr 300' F , M t C: f p r e 5 0 ° F, &! t 0: Tpr z35O0F, Eic * E: Tpr t400°F,r;C I: f
800
a
~
__ ---
0
?
f
---L.-----?-
---*
1
& : 4
I I
,
F: Tpr= 4OO0F, k = 600,000 l b / h r G * Tpr 4500F, & t I 800,000 l b l h r H Z Tpr x 4 5 O 0 F , h;( = 600,000 l b / h r 3: Tpr f 5 0 0 ° F , P L 800,000 l b / h r K: Tpr = S O V F , IU = 600,000 l b l h r
800,000 l b / h r 600,000 1 b / hr 800,000 1 b / hr 600,000 1 b/ hr 800,000 l b / hr
-
61
= 15.375 inchcr
-2
lobo
r
I
__t
2000
DEPTH OF TWO PHASE ZONE, FT. GRAPH LC-8 TWO PHASE WELLHEAD PRESSURE CURVES
3000
DEPTH OF TWO PHASE ZONE, FT. GRAPH Dol: TWO PHASE WELLHEAD PRESSURE CURVES
A: Tpr=300°F, & = 8: Tpr 300°F , & = Cz Tor =350°F, A = 0: Tpr = 3 W F , M = E: T m =4W°F, f
63
Diameter = 7.125 inches
Legend
1,200,000 l b / h r I ,000,000 1 b/ hr 1,200,000 lb/hr I ,000,0001 b/ hr I,200,000 l b / hr
FI Tors 4OO0F, M = 1,000,000 lb/hr G: lpr * 45OOF, M * 1,200,000 lb/hr
N: T’r =45O0F, J r Tpr
* 5OO0F, Q
2 2
~,ooO,OOOlb/hr I,2OO,OOO 1 b/ hr
-cn
a
Q, c
W
E 3
cn cn W a
a. 0
a w
I
3 3 W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LO-2: TWO PHASE WELLHEAD PRESSURE CURVES
64 Legend
Diameter
AtTpr=30O0F, 8: Tpr = 300' F, h C: Tpr =350°F, I4 = D: Tpr = 3 W F , Ejr t E: Tmr =400°F, b = f
1,200,000 I b l h r I,O00,0001 b l hr 1,200,000 1 b/hr I ,OOO,OOO 1 b/ hr I ,200,000 1 b l hr
= 8.097 inchcr F: Tpr' 400°F, d G : Tpr = 450" F, M H: Tpr =450°F, fi
= 1,000,000 l b l h r t
1,200,000 1b l h r
= 1,000,000 I b / h r
J * Tpr g 5OO0F, fh = 1,200,000 lb/hr K: Tpr =5000F, P = 1,000,000 lb/hr
DEPTH OF TWO PHASE ZONE, FT. GRAPH LD-3: TWO PHASE WELLHEAD PRESSURE CURVES
Legend
Diameter
At Tpr t300°F, &I= 1,200,000 l b l h r 8: Tpr = 300' F, Itr I: I,000,000 1 b/ hr C: Tpr 350' F, M 1,200, D: Tpr = 3 W F , &4 = 1,000, E: TDr O4OO0F, &LI 1,200,000l b / h r
=
9.063 inches F' Tpr' 400°F, M = 1,000,000 l b / h r
GI Tpr = 45Oa F, &4 8 1,200,000 1b/hr F, M I,OOO,OOO1b / Rr F, &l= 1,200,000 1b / hr K: TPr=5000F, & =I1,000,000 l b / h r
a
. L
cn c
w
a 3 cn u3 W
QT
e 0
a W r: d
I . W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LO-4: TWO PHASE WELLHEAD PRESSURE CURVES
65
66 Diameter
Legend
A: Tar 8: Tpr C: Tpr 0: Tpr r
=
10.192 inches
300' F =300'F = 350' F ~350'F
3
DEPTH OF TWO PHASE ZONE, FT. CRhDU I
n-6.T W n PHALLISF W F U W F A O PRFSSLJRE CURVES
I
I
0
30
DEPTH OF TWO PHASE ZONE, FT. GRAPH LO-6: TWO PHASE WELLHEAD PRESSURE CURVES
Diometer = 12.715 inches
Legend
A: Tpr =300°F, h * B: Tpr 0 300*F, M t C: Tpr = 3 W F , ti4 = D: Tpr =3500F, t4 =
1,200,000 1 b/hr I,aoO,OOO 1 b / hr 1,200,000 1 blhr
1,000,0001 b/hr
68
FZ Tpr= 400°F, M = I,OOO,OOO l b / h r 1,200,000 1b /hr H: Tpr =450°F, a i,OOO,OOO l b / h r 3: Tpr = 5OO0F, a 1,200.000 l b / hr
G: Tpr = 4500 F, til
-coa 0, c
W
a 3 co co
3 Q P
a W r A A
W
3
0
0 DEPTH OF TWO PHASE ZONE, FT. GRAPH LO-7: TWO PHASE WELLHEAD PRESSURE CURVES
Legend
Oiame ter
15.375 inches
a
m
a
L
W
a
3 tn
cn a w
a 0
a
W'
I
I.
A
W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH LO-8. TWO PHASE WELLHEAD PRESSURE CURVES
69
70
-m
a
e
c
w
Q:
3 v,
m W
a Q
0
a
w
I
J J
s
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-I :TWO PHASE WELLHEAD PRESSURE CURVES
71 LEGEND
Diameter
A I Tpr= 5OO0F, B: Tprt 500°F, C* Tpr 55OoF, 02 Tpr m O ° F ,
&4
t
300,000l b / h r
t
200,000 l b / h r 300,000 1b/ hr 200,000 l b / h r
& lit &4
0
7.125 inches E: Tpr 6OO0F, &! F: Tpr :600°F, fd 0 : Tbr = 650°F, M H ITpr 0 650°F, riC
t
300,000l b / h r
= 200,000 l b / h r
=
,000 I b / h r ,000 1 b/ hr
-a v)
a. c
W E
3 tn tn W
a
e Q
a W
I
J I. W
9
0 0
1000
2000 DEPTH
3000
4000
5000
OF TWO PHASE ZONE, FT.
GRAPH HA-2: TWO PHASE WELLHEAD PRESSURE CURVES
6000
72
L
w
Q:
3
cn cn W a e P
a W
I
J J
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-~:TWO PHASE WELLHEAD PRESSURE CURVES
73 LEGEND Diameter A: Tpr* 500°F, Ih 300,000 l b l h r 8: Tpr=500°F, &l 200,000 l b l h r C' Tpr' 55OoF, R 300,000 l b l h r 0: Tpt=5SO0F, &4 200,000 l b l h r f
f
=
9.063 inches
E: Tpr = 6OO0F, Id = 300,000 l b / h r F: Tpr t60O0F, = 200,000 l b l h r 6 : Tpr s65O0F, t4 = ,000 1b / hr HITpr +650°F, M = ,000 1 b/ hr
800
600
a ... cn e
c
W
2
3
Cn 400 rn w
a e P
a W
I d
I.
s" I
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-4: TWO PHASE WELLHEAD PRESSURE CURVES
8
74
-tn
Q
e
c
w r
3
cn
m W
a
e 0
a W
I J
d W
%
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-5 :TWO PHASE WELLHEAD PRESSURE CURVES
75
DEPTH OF T W O PHASE ZONE, FT. GRAPH HA-6: TWO PHASE WELLHEAD PRESSURE CURVES
76
-v,
a
e
c
w
Q=
3 v, v, W Q= Q
X
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-7: TWO PHASE WELLHEAD PRESSURE CURVES
77 LEGEND
Oiometcr
A I Tpr=500°F, k4 t 2 0 0 ,000 lb/hr 8 : Tprz 5OO0F, &! g 3 0 0 ,000 lb/hr Ct Tpr=550°F, f4 = Z O O ,000 1b/hr 0: Tpr'55pF, g 3 0 0 ,000 lb/hr
= 15.375 inches El l p r s60O0F, fi=200,000 lb/hr
F: Tpr =60O0F, I4 =300,000 lb/hr G I Tpr g650°F, M t ,000 I b / hr H I Tpr =6500F,
L
,0001b/ hr
L
W
E
3
8 W
a
e
n a w I
1
J
2600
3000
4600
5600
DEPTH OF TWO PHASE ZONE, FT. GRAPH HA-8: TWO PHASE WELLHEAO PRESSURE CURVES
66(x)
78
L
cn
e c
W
r: 3
(0.
m W
a e
X
DEPTH OF TWO PHASE ZONE, FT. GRAPH HB-I :TWO PHASE WELLHEAD PRESSURE CURVES
79
X
DEPTH OF TWO PHASE ZONE, FT. GRAPH HB-2 :TWO PHASE WELLHEAD PRESSURE CURVES
DEPTH OF TWO PHASE ZONE, FT. GRAPH HB-3 :TWO PHASE WELLHEAD PRESSURE CURVES
81 LEGEND Diome9cr At TprC5OO0F, h * 500,000 l b / h r 8' lpr= 50O0F, = 400,000 l b l h r C I Tpr* 550°F, R = 500,UOO l b / h r
=
9.063 inches € 8
l p r t600°F, &I= 500,000 l b / h r
F: lp =600°F, r P = 400,000 lb/hr 01 lpr +650°F, P g ,000I b l h r ,000 1b/ hr
a cn
e c
w
DEPTH OF TWO PHASE ZONE, FT. GRAPH HB-4:TWO PHASE WELLHEAD PRESSURE CURVES
82
Q 0
m Q c
W
K
3
cn v)
W
a e P
a W r
. I . I
s
X
DEPTH OF TWO PHASE ZONE, FT. GRAPH H 6-51TWO PHASE WELLHEAD PRESSURE CURVES
a3
-
a. v)
e c
w Y
3
rn v)
w
K Q
n
a W r J
I.
I
DEPTH OF TWO PHASE ZONE, FT. GRAPH H8-6:TWOPHASE WELLHEAD PRESSURE CURVES
DEPTH
OF TWO PHASE ZONE, FT.
GRAPH He-7 :TWO PHASE WELLHEAD PRESSURE CURVES
I
0
2000
3000
4doO
5600
DEPTH OF TWO PHASE ZONE, FT. GRAPH HB’8TwO PHASE WELLHEAD PRESSURE
CURVES
86
DEPTH OF TWO PHASE ZONE, FT. GRAPH HC- I :TWO PHASE WELLHEAD PRESSURE CURVES
87
DEPTH OF TWO PHASE ZONE, FT. GRAPH HC-2:TWO PHASE WELLHEAD PRESSURE CURVES
88 LEGEND A: Tpr= 500°F, 8: TprL 5OO0F, C: Tpr=550°F, 0: Tpr = 5500 F,
Diameter
&! * 800,000 l b / h r kl = 600,000 l b / h r
M = 800,000 l b l h r &4 t 6 0 0,000 1b/ hr
= 8.097 inches E: Tpr 600°F, M =800,000 l b / h r F: Tpr z 600°F, tA =600,000 l b / h r 0 : Tpr t65O0F, M = ,000l b l h r H I Tpr =6500F, riC = ,0001b/ hr
600
Q v,
e
c
W
2
2
v) v)
400
W
a e P
a W
I
J J
s 200
0
IO00
2000
3000
4000
5000
DEPTH OF TWO PHASE ZONE, FT. GRAPH MC-3: TWO PHASE WELLHEAD PRESSURE CURVES
Sdoo
LEGEND A I Tpr= 500°F, 6: Tpr' 500°F, Ct Tprf 55OoF R Dt Tpr x 55OOF, );t
800,
R\ \\
Diornater = 9.063 inches I : 800.000 l b / h r € 8 Tpr =600°F, & =I600,000 l b / h r = 600,000 l b l h r F * Tpr =600°F, P4 t 600,000 l b / h r = 800,000 l b / h r 0 : Tpr = 65OoF, liR = ,000I b / h r 600,000 lb/hr H ITpr =650"F, IJ t ,000 1b/ hr 1
I
.,
I\ .
,
a cn e
c
w
'If
3
tn v)
w
a e 0
a w I
I.
A
W
?
DEPTH OF TWO PHASE ZONE, FT. GRAPH HG4:TWO PHASE WELLHEAD PRESSURE CURVES
,
8
i
90 LEGEND
Diometcr
A: Tpr= 5OO0F, & = 800,000 l b / h r 8: fpr= 500°F, = 600,000 l b / h r Cg Tpt 55OoF, t4 = 800,000 1b/ hr f
= 10.192 inches E: Tpr :6OO0F, h r 800,000 l b / h r
F: Tpr =600°F, ?4 = 600,000 l b / h r 6: Tpr =650°F, M 0 ,000 1b / hr ,000 1b/ hr
DEPTH OF TWO PHASE ZONE, FT. GRAPH HC-5:TWO PHASE WELLHEAD PRESSURE CURVES
LEGEND
biometer
A I Tpr”S0O0F, th 2 800,000 I b / h r 8 : TprC 500°F, k = 600,000 I b l h r i t Tpr=550°F, I;( * 800,000 lb/hr 0: Tar=550°F, = 600,00Olb/hr
=
11.150 .inches fpr =600°F, fi ~ 8 0 0 , 0 0 0 lb/hr F : Tpr =600°F, &=600,000 I lb/hr 0 : Tpr =650”F,M = ,000 I b / hr H:Tpr =650°F,li( = ,000 1 b/ hr
Ea
L
W U
3
cn cn W
o[:
e n
a W
I J J
$!
DEPTH OF TWO PHASE ZONE, FT. GRAPH HC-6: TWO PHASE WELLHEAD PRESSURE CURVES
LEGEND
Diorncier
A: Tpr' 500.F. & :800,000l b / h r 8 : Tar= 5OO0F, & 8I600,000 l b / h r 8 0 0,0001b/ hr 0: 6 r f 5 5 0 ° F , t 600pOO l b / h r
= 12.715 E: Tpr F: Tnr
inches ::6OO0F,
lh = 800,000 l b / h r
600°F, = 600,000 l b / h r =650°F, M = ,0001b I hr ,000 1b/ hr
z
800
600
-cn Q
e
c
W
z
3
cn 400 cn w a e 0
a
W
f
J J.
s 200
2000
3000
4000
5000
DEPTH OF TWO PHASE ZONE, FT. GRAPH HC-7:TWO PHASE WELLHEAD PRESSURE CURVES
93
c
w
2
3
rn tn W a
n 0
a
W
I
3
DEPTH OF T W O PHASE ZONE, FT. GRAPH HC-8:TWO PHASE WELLHEAD PRESSURE CURVES
94
j
c
W
z
'3
a e n
a W
I
J J
s
DEPTH OF TWO PHASE ZONE, FT. GRAPH HD-l :TWO PHASE WELLHEAD PRESSURE CURVES
95
X
96 LEGEND
800
A I Tprf50O0F, P = 1,200,000 B: Tpr 5OO0F, Q = l,OOO,000 Ca Tpr * 550' F , r;( = 1,2oO,OOO 0: Tpr 590' F , = I,MO,OOO I
1 1
=
Diameter
.,, ,
lb/hr 1b/ hr I b/ ht 1b/ hr
,
\ .
. I ,
.:
I
1 .
.
€8
Tpr
F8
Tpt
SOO*F, rSr =I,200,000Ib/hr
= 6OO0F, Q = I,OOO,OOO
1b/ hr
650° F, M 0 1,200,000 l b /hr H * Tpr = 6500 F, I4 = 1,000,0001 b/ hr
0 8 Tp, 1
I
n :
8.097 inches
t
.
I
!
.I
I
!
I
I
.
.
!
'
-
-tna
e
c
W
Y
3
tn
m W
a
e Q
a W
I
A A
Y
Id00
2000
.
3000
4600
5000
DEPTH OF TWO PHASE ZONE, FT. GRAPH HP-3:MO PHASE WELLHEAD PRESSURE CURVES
I
97
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH HD-4 :TWO PHASE WELLHEAD PRESSURE CURVES
a cn
Q c
W K
3
cn
tn W
a
n 0
a W
x A A
W
3
DEPTH OF TWO PHASE ZONE, FT. GRAPH HD-5:TWQ PHASE WELLHEAD PRESSURE CURVES
99
t 0
II
-,--+-
I
Id00
3000 4000 2000 DEPTH OF TWO PHASE ZONE, FT.
5000
GRAPH HD-6: TWO PHASE WELLHEAD PRESSURE CURVES
60-00
100
-m a
e
c
W
a
3
m
co W a a. 0
a
w I J J
W
3
X
DEPTH OF TWO PHASE ZONE, FT. GRAPH HD-7 :TWO PHASE WELLHEAD PRESSURE CURVES
!O 1 LEGEND
Diameter
=
15.375 inches
-a
u)
e
c
w
TT 3 v,
cn W a e 0
a
w
S
I.
J
W
3
DEPTH OF TWO PHASE ZONE, FT. U . s GOVERNMENT PRINTING OFFICE. 1982-546-085/3057
GRAPH HD-8 :TWO PHASE WELLHEAD PRESSURE CURVES
