Gilbert Charts

Flowing and Gas-lift Well Performance

ABSTRACT

The paper describes the tao-phase vertical-lift lunctlon, explains the hydraulics of natural flow, outlines t ~ o - p h a s e flow through orifices, sumnlarlzes methods for estimating individual well capabilities, and includes approximations for solutlon of natural- flow and gas-lltt problenls for tubing of the 1.66-, 1.90-, 2.375-, 2.875- and 3.50-ln. API sizes, and crude 011s in the gravlty range from 25 t o 40 API.

INTRODUCTION Advances I n knowledge of the diHerent lifting

methods do not lend theniselves to evaluation qulcli- ly or i n slmple econoniic ternis. I n the aggregate, however, they constitute the necessary b a s ~ s for in~proved l l f t ~ n g p o l i c ~ e s and profitabilities, wherever oil is r a ~ s e d .

Production by natural flow rightly tops the l lst of llftlng methods, inasmuch a s it produces more 011

than all other methods con~blned. It proceeds with n~ ln in~un~ cost In relatlve absence of operating difficulties; and 1s relinquished finally In an atnlosphere charged with regret, and supercharged with exple- t ives intended to fortify the conclusion that the stoppage 1s an irreversible act of Providence. Never- theless, production men have been haunted for years by the thought that a more defin~te knowledge of flowlng performance would suggest means of resum- ing flow after premature stoppages, permit more effective well control, more appropriate How-string selections, and serve In general to Increase the proportion of oil quantities economically recoverable by natural flow.

bevelopment of organized information on ve r t~ca l -

flow has been s o far a matter of slow growth. A pre- sentatlon in 1930 of the baslc theory by the late Professor boctor J . Versluys' prov~ded an initial impetus for current developments, but has been applied only to a liniited extent because of practical difficulties in evaluating factors which appear in the Versluys differential.

* N. V. De Bataafsche Petroleum Maatsch~pp~, The Hague, The Netherlands

t Presented at the sprlng meet~ng of the Pac~f ic Coast D ~ s t r ~ c t , D ~ v l s ~ o n of Product~on, Los Angeles, May 1954. ' References are at the end of the paper.

An Interesting attempt to solve the problem of two-phase vertical l ~ f t by testing flow through short (67-ft) tubes was reported in 1931 by 1. V. Moore and H , 1). Uilde.' Failure of this project to provide the deslred generalization seems attr~butable to use of tube lengths s o short that representative condl- tions were not attained. kemler and Poole,' in a paper on flow~ng wells presented before the American Petroleunl Institute I n 1936, developed a limited correlation between gas-llquid ratlo and pressure drop per unit of tublng length, and explained a nieth- od of estinratlng flowing Ilfe. The work of C. J. May and A. Laird4" resulted in vertical-l~ft peneraliza- tions well adapted to predlct results within a re- stricted range of condltlons. The interesting paper by Poettn~an and Carpenter6 appeared subsequent to the tinie of derivation of the material here presented.

"Gas-Llft Principles and Practices" by S. E'. Shaw,' the pioneer consultant on vertlcal flow, provides an lnterestlng discussion of gas-lift history and methods with correlations which, though limited in scope, were none the l e s s useful. Shaw's observation, that power lunctions may be applied in approximat~ng the relationships between nlininiuni gas- lift Intake pressures and glven liquid production rates, has been used here.

The excellent paper by L. C. Babsone added con- siderably to knowledge of vertical Bow, particularly in the range lor gas-llquld ratios greater than 2.0 Mcf per bbl. To a large extent the present paper i s a result of reviewing Babson's data and work after addlng a considerable fund of depth-pressure information involving gas-liquid ratios l e s s then 2.0 blcf per bbl. Thus, Shah, Babson, and the late L. N. R,lerrill mentloned by Babson, provided the prior hork nlainly used In the appended correlations of vertlcal flow.

It will be noted that no distinction is made here between gas-lift and natural flow. In the gas-lift range covered by Babson, n ~ i s t How and annular flow predominate and no perceptible diHerences are to be expected. hhere foam How exists , one would be led to expect son~ewhat steeper gradients for natural

FLOWING AND G A S L I F T WELL PERFORMANCE 127

flow than for gas-lift wlth the same total gas-l~quid

ratios, because for natural flow more of the gas would be in solution, and the ratios are small enough that the gas in solution could be an appreciable part 01 the total available. I n any case , i t may only be sald that no fimi differences between gas-lift and

two-phase natural flow have been observed; and the results here presented involving foam flow are derived from flowing-well data and would therefore tend to represent foam-flow gas requirements conserva- tively.

The present purposes are to explain flowing and gas-lift well performance i n the light of what is now known of vertical flow, and to provide procedures and empirical correlations which have been usefully applied over a period of years i n solution of prac-

tical problems. It i s believed that the paphical procedures suggested are ~ l d e l y adaptable. I 'he gradient data, however, should be used with care and

are oflered in the hope that they may encourage development of more specific data in forms readily adaptable to field use.

A PRIhlARY DISTINCTION To develop an understanding of the behavior of

flowing and gas-lift wells, l t is essential first to recognize that there i s one s e t of conditions affecting f l o ~ of gas-liquid mixtures into a bore hole, an en- tirely different se t of conditions affecting flow of mixtures from the bottom to the top of the well, and a third se t affecting flow through beans at the s u r - face. We may designate the first a s "inflow perform-

1 9 ance, the second a s "vert~cal-lift perforn~ance," and the third a s "bean performance."

Inflow Perfornlance

Knowledge of individual well inflow performance i s a basic necessity in equipping and operating 011 wells for n~aximum profit under any se t of imposed conditions.

Rigorous determination of the inflow performance of a well at any s ta te in i t s producing llfe would in- volve: 1. Measurement of the stat ic pressure in the well

at the midpoint of the producing interval. 2. Measurement of the mass rate of inflow of each

fluid phase corrected to midpoint conditions for each of a ser ies of steady operating pressures measured at the midpoint.

Fortunately, such detailed deternlinatlons are seldom necessary; but one or more very complete determinations in a particular field can prove helpful in de-

ciding what short-cuts and approximations are locally practicable.

The liquld inflow performance of a well at any stage in i t s decline may be defined by ~ t s stat ic pressure (in pounds per square inch) and maxirnunl inflow rate when the increment of inflow per unit of pressure or productivity index (PI, measured in bar- re ls per day per pound per square inch) i s a constant. The gas-liquid ratio (GLR measured in thousand cublc feet per barrel)may be, for practical p u r poses, constant. Under such simple conditions the inflow perforn~ance can be depicted a s shown in Fig. 1. Individual-well inflow-performance trends may be depicted a s shown in Fig. 2. Th i s latter type of graph i s useful in predicting both the timing and character of lifting changes needed to mantain production and implement the local reservoir policy. The relation between the midpoint pressure and the liquld inflow rate (inflow performance relationship, or IPH, a s mentioned later) i s not always a straight line a s shown in Fig. 1, but may be concave to the origin a s shown in Fig. 3. Even lf this curvature i s marked, it is posslble by study of a group of such curves from a given field tp develop a locally applicable nrethod of predicting the IPH from the well's stat ic pressure and a single drawdown deterniina- tion.

Gas-liquid ratio control i s a principal factor i n development of reservoir policy. Hatios in practice are affected by cumulated withdrawals; and, at any one stage of withdrawal, they are altected by production rates, a s has been pointed out by H. J. S u l l i ~ a n . ~ Generally, of all factors bearing upon future well performance, the gas-liquid ratio is the least predictable.

Lu Y i? 5 2000

z Z Lu 0 4 z w 3 1000 LU cd I-

a 2

200 400 boo 800

PRODUCTION IN BID

a

Fig. 1-Diagram of lnflaw Performance

128 W. E. GILBERT

@) STATIC PRESSURE @ GASILIOUID RATIO

MAXIMUM GROSS @ INFLOW RATE @(CUT Ctzii% CURVE)

. 0

CUMULATED OIL WITHDRAWALS

Fig. 2-Graph of Individual-well Inflow-performance

Trends

There have been instances of gas-oil ratio reduc- t ~ o n following a change in the tubing setting depth In flowing wells. However, the practice i s not recommended, especially i f it involves killing the well with water, inasmuch a s the change In tubing depth can have only a very minor effect of the drawdown opposite gas sands for a given liquid rate; and if the water reduces gas production, i t i s likely, at the same time, to reduce the well's future oil po- tential.

hater can be a useful agent In an oil reservoir; but on reaching the well bore, i t s usual tendency i s to mininilze flowing life, ultimate recoveries, and total profits. The operator i s fortunate when water production can be economically excluded. The type

MOO GASlLlOUlD RATIO = 1 5 MCFIBBL

2000

1 OOO

PRODUCTION IN BID

Fig. 3-Diagram of Inflow Performance with

Curved IPR

of watercut curve shown in F'lg. 1 generally indi- ca tes water influx predon~inantly from a relatively low-pressure source, and the cut curve in Fig. 3 a predominantly high-pressure source. Cut-cumulative curves such a s the one shown in Fig. 2, are of well-known value in estimating future oil recoveries fronr wet wells. -

In selecting the best operating gross rate for an individual wet well, it IS sometin~es helpful to plot the approximate water IPH from the gross IFH and two or three cuts a s indicated in E'ig. 4. However, if s p e c i d tes ts are necessary for this purpose, it i s desirable to remember that temporary use of abnor- nlally high inflow rates can induce a permanent in-

@ GROSSLIOUID IPR

DETERMINATIONS

3 CORRESPONDING WATER RATES O DEFINING WATER IPR

MAXIMUM GROSS

LIQUID INFLOW RATE

Fig. 4-Procedure for Outlining the Water IPR

crease in water productivity under some circuni- stances, e.g., if the water shut-off i s insecure, or if

there is a wide disparity between water and oil vis- cosit ies, gentle formation dips, and edge water close to the bore.

Lilfierential depletion i s progressive during sustained flowing periods wherever the ratio of lateral permeabilities to vertical permeabilities i s large; and interflow through the bore between producing layers takes place durlng any subsequent periods of shutdown unless a suitable mud i s spotted in the producing interval. Thus any water inflow from a relatively high-pressure source tends to seek out and enter the more depleted oil layers during a shutdown period, and with permanent injury in some fields to effective oil pernleabilities. After long pe-

FLOWING AND GAS-LIFT W E L L P E R F O R M A N C E 129

n o d s of flow, a two- or three-week shutdown can cause from 20 to 40 percent permanent reduction of the inflow capacity of a well tapping a depletion- type reservoir even if the water cut i s no greater than 5 percent. Thus, differential depletion i s a factor requiring close consideration in many fields if the operator's equity in operating wells i s to be pro- tected.

Generally, the rate of liquid inflow increases a s the operating pressure in a well i s reduced, and the absolute maximum'liquid inflow would result if zero absolute pressure could be maintained at the bottom of the well. Th i s condition, of course, cannot be attained, and leas t of all in a flowing well, because a pressure drop in the tubing from the bottom to the top of the well is necessary to sustain verti- :a1 flow. A large pressure at the bottom of a well facilitates vertical outflow but discourages lateral inflow. In this sense, the pressure requirements for inflow and those for vertical lift are opposed to one another, and, in particular cases , when an effective compromise can no longer be made by adjustment of controllable factors, flow must cease. For any steady flowing condition, the sum of 1 , the effective pressure dfop from the drainage radius to the bore, 2, the pressure drop i n the vertical column, and 3, the pressure drop across tbe bean (or orifice) at the surface is substantially equal to the difference between . the well's stat ic pressure and the flow-line pressure.

Vertical-lift Performance All we need know about two-phase vertical flow

i s how much pressure i s required to lift the well liquid a t a given rate from a given depth with a given gas-liquid ratio through tubing of a given size. This problem i s more complicated than the problem of single-phase flow in surface pipelines because we are dealing w ~ t h the flow of a gas-liquid mixture, and because the input pressure must be sufficient not only to overcome flow resistance in the pipe and the bean a t tbe surface, but must in addition be sufficient to support the total weight of the compress- ible mixture in the pipe. In single-phase horizontal flow, the total pressure drop for a given flow rate

can be represented a s so. many pounds per square inch per thousand feet of length. No such conven- ient can be used for vertical two-phase flow because the pressure drop per unit of length i s not constant, but increases with depth. For this reason, in proceeding to systematize field information on vertical flow for pressures l e s s than the bubble-point pressure, we find there i s a different

depth-pressure gradient for each s ize of pipe, each rate of liquid flow, and each gas-liquid ratio.*

Depth-Pressure Grad~ents

The depth-pressure gradient i s the basic unit of two-phase vertical flow, and solution of individual well problems i s largely a matter of having available a representative family of gradient curves cov- ering suitable ranges of tubing s izes , rates of liquid flow, and gas-liquid ratios.

h e are not concerned here with any detailed anal- yses of the physical phenomena which cause the pressure gradients observed or derived from practical field information. However, it is of interest to know that a single gradient curve represents a se- quence of different types of flow. I hus, starting a t the upper end of a gradient like that for 200 bbl per day in 2.875-111. tubing w ~ t h 1.0 Mcf per bbl gas- liquid ratio, a s shown at A in Fig. 5, mist flow will predominate a t the lowest pressures, modified progressively by an upwardly moving oil film which clings to the inside surface of the pipe and increases in thickness with depth. This film, combined with mist flow in the center of the pipe, has been de- scribed a s annular flow. A s relative depths Increase, the film becomes s o thick and wavy that it occa- sionally bridges across the section, resulting In slug f l o ~ . At st i l l greater depths, slug flow merges into foam flow, and this finally merges into single- phase flow a t the pressure beyond which all of the gas is in solution.

Fig. 5 illustrates the use of a gradient curve in determining the tubing pressure from the intake pressure, or the intake pressure from the tubing pressure, for a given production rate and ratio for a well of any depth. For instance, as shown a t t) in Fig. 5, 5,000- ft wells with 2.875-in. tubing producing 200 bbl per day with 1.0 Mcf per bbl will have an intake pressure of about 440 psi if the tubing pressure at the surface is one atmosphere (zero gage and, a s shown a t C, they will have an intake pressure of about 1,750 psi if the tubing pressure i s 800 psi. Similarly, as shown a t D in Fig. 5, an 8,000-ft well for the same conditions having an intake pressure of

*Grad~ents presumably are a l so affected by many other factors lncludlng 11qu1d surface tenslon, v ~ s c o s ~ t y and gravlty, flowlng temperatures, gas gravlty, and gas-l~quid s o l u b ~ l ~ t ~ e s . How- ever, there 1s a reasonably close correspondence between results whlch have been obta~ned In the 11ght-011 (25 to 40 API) fields of Long Beach, Santa Fe . Domlnguez, Ventura, Canal, and Ten Sect~on , and several forelgn fields, vv~thout ad~ustlng for such factors. Also, d has not been found necessary to cor- rect grad~ents for water cuts. However, the grad~ents are In- adequate to predlct the effects of emulsions.

130 W. E. GILBERT

2

4

6

8

1 0

1 2 PRESSURE

14

PRESSURE IN HUNDREDS OF P S 1

Fig. 5-Use of Gradient Curves

1,390 psi will have a tubing pressure of 200 psi. Thus by using the gradient for the desired production rate and ratlo and interpolating when necessary, we nlay estimate either the tublng pressure or the intake pressure in a well of any depth when one of these pressures i s known.

Empir~cal gradient curves for 2.875-111. tubing are glven in Fig. 23 through 27,*t and slmilar families of gadient curves for 1.66-, 1.90-, 2.375- and 3.50- in. tubing are given in Fig. 28, 30, 31, 32, and 33.*$ l 'he 2.875-1n. gradients are based upon correlation of data with gas-liquid ratios ranglng from 0.4 to 2.0 Mcf per bbl from 8,000-ft wells in Ten Section F ~ e l d , combined with Babson's generalizations in the gas- lift range. Errors attributable to the 2.875-in. curves for 100,200,400, and 600 bbl per day should not ex- ceed 15 percent. The gradients for 50 bbl per day in the 2.875-in. s lze and for 50, 100, 200,400, and 600 bbl per day In the other s i zes are based upon information which is far l e s s con~plete. However, they are offered In the belief that they reliably in- dicate the relative characteristics of each s ize and are not likely to lead to nl~sapplications if conser- vatively employed. Further, it may only be s a ~ d that they represent a fair correlation and interpretation of the 'lnformation readily available.

The Two-phase Vertical-lift Functlon Using the process outlined in Fig. 2, and a se t

of g r a d ~ e n t . c u ~ e s , such a s those on Fig. 23 through

*In each plate, group A includes gradients for gas-llquld ratios whlch are' less than the optimum, and group B includes gradients for ratlos greater than the optimum. The gradient for the optlmum gas-llquid ratlo (called optimum because it prc- vldes the lowest pressure for the given rate of flow) 1s at the bottom of group A and I S marked wlth an m o w pointing to the ratio. The grad~ents have been dlvided Into two groups slmply

to avold crossing of Ilnes.

t See p. 145-149, ~ n c l .

$ See p. 150, 154-157. incl.

27, the t ~ o - ~ h a s e funct~on for any particular depth and tubing-outlet pressure may be constructed. For example, confining attent~on to 8,000-ft wells, 2.875- in. tubing, and zero gage tubing pressure, the function may be represented either in terms of intake pressure and gas-liquid ratio, a s shown at A in Fig. 6, in terms of Intake pressure and production rate, a s shown at B in Fig. 6, or in terms of intake pressure, production rate, and gas-liqu~d ratio, a s shown a t C in Fig. 6. All three q a p h s represent equivalent information: At A i s the type of graph used by Babson; the fornl of illustration B is interesting because the ordinates and abcissae are the same a s those for the inflow performance (1PH)of a well, and the two types of data may thus be superimposed. They are cons~dered following in connection with estimates of the duration of flowing life. Several general characteristics of two-phase vertical flow may be observed at C In Fig. 6. In particular, i t may be noted that:

1. For any constant gas-liquid ratlo there i s a rate of flow which requires minimum intake pressure. Also, this rate of Bow for minimum pressure and the minimum pressure itself both increase a s the gas- liquid ratio i s decreased a s indicated by curve 1. (These observations are of Interest in connection with flowing wells because of the tendency of flow-

' ing wells to have a more or l e s s constant gas-liquid ratio a t any one tlme.)

2. For any constant rate of flow, there i s a gas- liquid ratio which prov~des minimum intake pressure. 1 his minimum intake pressure i s directly related to the rate of flow, while the gas-liquid ratio

for minimum intake pressure 1s inversely related to the rate of flow a s ~ndicated by curve 2. ( I h e s e o b servations are of interest in connection w ~ t h gas- lift wh~ch permits control of gas-liquid ratios.)

The form of the two-phase function i s largely the result of the Interaction of flow resistance *and s l ~ p - page of gas through the oil, the resistance factor being least important when slippage i s greatest and

vlce versa. It i s more or l e s s obvious that the column pressure, being the result of the weight of the mixture, i s greatest at low gas-liquid ratios. How- ever, i t i s l e s s obvious that for any gas-liquid ratio

and depth there i s a rate which requires minimum lifting pressure with lower rates requiring more lifting pressure because of slippage, and h~gher rates requiring more lifting pressure because of resistance. $

FLOWING AND G A S L I F T WELL PERFORMANCE 13 1

0 I 1 2 3 4 5

GAS I LIOUID RATIO IN M C F 1 B - LlOUlD PRODUCTION IN B I D ----a

Fig. 6-The Two-phase Vertical-lift Function for 2.875-in. Tubing Set at 8,000 F t (Tubing Pressure = Zero PSI Gage)

132 W. E. GILBERT

For the reader who finds difficulty with this s e t of facts, the following explanation may prove helpful:

a. Imagine for this purpose a 2,000-ft length of 2.875-in. API tubing mounted vertically on the face of a precipice in the Hocky Mountains with a wind-swept platform at ~ t s upper end where the reader may observe results, and a special-type pump station a t i t s lower end capable of con- tinuously injecting oil of, say, 0.85 gravlty and g a s with a constant ratlo of, say, 1.2 hlcf per bbl.

b. Taklng the i n ~ t l a l rate a s 0.01 bbl per day of oil with the 1.2 Mcf per bbl ratlo, the liquid level would appear a t the upper platforn~ after about 115 days (2,000 0.01 x 172.7 = 115.8). Out of the oil column the observer would see gas bub- bling a t the rate of about cu in. per s e c (1,200 x 0.01 x 1,728 + 1,440 x 60 = 0.24); and the pump at the lower end would be operating at an input pressure approximating the l ~ q u i d gradient pressure, amounting to 736 psi (2,000 x 0.433 x 0.85 = 736.1). kiost of the gas punlped Into the tubing durlng the 115-day period would have slipped out of the column by the time the level of the mixture reached the observation platform.

c. Now, I£ pumplng of the same mixture were maintained a t 400 bbl per day, because the l~qu ld alone would fill the pipe in l e s s than 45 min, (2,000 x 1,440 400 x 172.7 = 41.7+), there would be very llttle tlme for slippage of g a s through the oil and the 480 hlcf per day of gas (400 x 1.2 = 480) accompanying the oil would soon produce an oil mlst around the top of the pipe, the gas-oil volun~e ratio at that point belng about 213 volun~es per volume (480,000/400 x 5.614). The input pressure would be about 150 psi.

d. Last , with an in ject~on rate of 4,000 bbl per day, slippage would be obviated by extreme turbulence and the input pressure, increased by resistance, would be about 230 p s ~ .

Similarly, if we hold the liquid rate constant and increase the gas-llquid ratlo, the intake pressure decreases, from a starting point with zero gas when the pressure 1s the sum of the l lqu~d welght and the l i q u ~ d flow res~s tance , to a mlnlmum, and then increases steadily for greater ratios due to increasing resistance accon~panying higher fluid veloci t~es .

'1 he observations sun~marized in Par. 1 and 2 apply In general to two-phase ver t~cal flow from any

I Y1 rm 200 m 400

LIQUID PRODUCTION IN B / D

F i g . 7-comparison of Tubing Sizes for Vert ical - l i f t

from 5,000 F t wi th Z e r o Tubing Pressure

depth wlth an educter of any s l ze or type and any given outlet pressure.

l h e relative effects of the difierent tubing s l zes are indicated In Fig. 7 (which was constructed from the gradlent curves of Fig. 23-28,30-33). In general,

the smaller tubing s u e s offer the advantage of lower Intake pressures at comparatively low rates of flow, and therefore tend to prolong the flowing l ~ f e of low gas-l~quid ratio wells. The smaller s izes , however, limit rates of Bow, especially for the higher gas- liquid ratios.

Annular flow i s not treated here. However, i t may be mentioned that the poorer an annulus i s as a flow section for slngle-phase flow, the more effective i t will be for two-phase flow In minimlzlng gas s l ~ p p a ~ e and in improving gas utilization in the slippage range a s compared with a circular flow string of equal sect lond area.

Two-phase Bean Performance "Bean" i s the 011-country term for the orifice used

on the tublng outlet to control the production rate of a flowlng well. Product~on men are accustomed to

FLOWING AND G A S L I F T WELL PERFORMANCE

selecting bean s i z e s for particular wells on a trial- and-error bas is and no correlation for two-phase flow through beans has been generally applied.

The following approximation i s derived from reg- ularly reported daily individual well production data:

435 r0 546 B P = s 1.89

wherern: P = tubing outlet pressure, in psig r = gas-liquid ratio, in klcf per bbl

= gross liquid, i n bbl per day 5 = bean s ize , in sixty-fourths of an inch ' Approximate solutions for any one of the lour var-

iables when the other three are known, may be made by use of Fig. 29. Directions for use of this chart with examples are given on p. 151. The constant (435) used in the formula i s based upon Ten Section data with beans of the types shown in Fig. 29, the results of one sanipling from the Ten Section Field being shown in Fig. 8.

An error of '/,,,-in. in bean s i ze can effect an error of 5 to 20 percent in pressure estimates. In many cases , gas-liquid ratios are reported bnly to the nearest 50 or 100 cu ft per bbl and are frequently difficult to determine because of fluctuations which occur In many wells. Spot readings of pressure at heading wells are not representative of daily averages. For reasons of thls kind, no fornrula could be expected to maintain a 100 percent correspondence with observed data at individual wells even though it correctly correlated the variables involved.

As an exan~ple interpreting the forn~ula, the p e r formance of ''/,-in. beans 1 in. in length i s illustrated

13

6 15

9 1 1

18

7

ACCURACY 7 / -

0 20 40 60 80 100

PERCENT OF READINGS

Fig. 8-Indicated Range of Accuracy of

Bean-performance Formula (Ten Sect~on Data)

LlOUlD PRODUCTION IN B I D

Fig. 9-Performance of ''4, -in. Bean for Tubing

Pressures More than 70 Percent Greater than the

Lead-l ine Pressure

in Fig. 9. In the type of formula used, it i s assumed that actual mixture velocities through the bean ex- ceed the speed of sound, for which condition the downstream, or flow-line, pressure has no eflect upon the tubing outlet pressure (i.e., pressure on the upstream side of the bean). 1 hus, the formula applies for tubing pressures at leas t 70 percent greater than the line pressure. Fo; tublng pressures l e s s than 70 percent greater than the line pressure, the bean s ize indicated by the formula will be too small for the given conditions. fio study has been made of two-phase bean performance for tubing pres-. sures in the range from zero to 70 percent greater than line pressure. Field men usually try to avoid operation in this range because fluctuations of line pressure affect the well's operation. Flowing-well Performance

Individual well problems in natural flow may be analyzed quite simply by graphical means, a form which has general application being shown in Fig. 10. In this figure, curve A represents the inflow p e r formance of a well with tubinglntake pressures plotted against liquid production rates. The gradient curves B for 2.0 hlcf per bbl gas-liquid ratio were then plotted starting with the known intake pressures for 0 , 50, 100, 200, and 400 bbl per day. The intersections of these gradients at the surface establish the tubing pressures which the well will sustain, and the tubing-outlet performance may then be plotted a s shown by curve C . The depth vs. pressure diagram of Fig. 10 illustrates the part

134 W. E. GILBERT

played by gradients in flowlng-bell perforniance. liowever, curve C may be obtpned dlrectly iron, curve A by subtracting the total gradlent pressure for each of several rates of flow. Supenniposlng the perfornlance curve I) for a ''/,,-in. bean, we con- clude that the well should flow at about 96 bbl per day with a tublng pressure of about 850 psi. Con- s~der ing curves C and L), a s shown i n Fig. 11, i t will be seen that there are poss~b le equllibr~un~

eaamAL W U DATA

S I A K FUESlR€ # PSI = ZYI) nu INROW RATE IN BID = YX)

W l W U D RATK) IN MCFIBBL = 2 UOUDWGT INPSIPER 100 Fl =38

Fig. 10-Diagram of Flowing-well Performance

points, 1 and 2. Intersection 1 provides a stable flowing condition because, if a tendency develops to increase the flow rate, the bean imposes more pressure resistance than the well can sustain; and if a tendency develops to reduce the flow rate, the well develops a higher tubing pressure than the bean requires. In each of these cases a temporary displacement of the flowing rate generates a pressure differential which returns the well to ~ t s equi- libriumproducing condit~on. Intersection 2 i s an unstable equilibrium point because any temporary displacement brings into action a pressure di f fer ential which increases the displacement, and causes the well either to flow faster or to die, depending upon the direction of the initial displacenlent. This limited explanation assumes a constant gas-liquid

PRODUCTION IN BID

Fig. 11-Diagram illustrating Equilibrium Conditions at the Well Head

(For same w e l l as shown I n Fig. 10) ratlo. Both the tubing outlet curve C and the bean -

curve 13 change with each change in the gas-liquid ratio after the manner shown a t B in F'ig. 12, but for each ratio there IS a stable equil~brium point.

The relationship between bean s ize and production rates i s of the type shown at A in Fig. 12. Two similar curves derived from wells where several bean s izes were used over a short period of time (6 months or less) are shown In Fig. 13. Neither of these wells could be expected to maintain steady flow a t rates of l e s s than 50 bbl per day, although they both would produce satisfactorily at h~gher rates. The reason for th is limitation l ies in the fact that the differential pressure, available to increase product~on when the rate of flow temporarily drops below the stable equilibrium rate, progressively dlmlnishes a s the bean s ize i s reduced below the bean s ize which provides maximum tubing pressure. Thus, considering the bean-performance intersections with the tubing-pressure curve for 1,600 cu ft per bbl at B In Fig. 12, a ''/,,-in. bean provides

0 100 200 300 400

PRODUCTION IN B I D

Fig. 12-Effect of Gas-liquid Ratio on Equi l ibr im Production Rates


16 16

~ $ 1 , ~ y z l J

12

N ~ Z G g z a a z<* (+ u I 5 0 4 4

Ln

0 0 0 100 200 300 0 I00 200 300

PRODUCTION IN 0 I D PRODUCTION IN 0 I D

Fig. 13-Relationship Between Production and Bean Sizes

maximum tubing pressure; and for smaller beans, - -

large difl'erential pressures are available to prevent sustained increases of production rate, but the differential available to prevent decreases of production rate becomes sn~a l l e r a s the bean s lze i s reduced. For a 6/,-in. bean, the tubing and bean perforniance curves nearly coincide and reductions in rate of flow cannot be prevented. If thls s ize of bean were applied to the well represented, the well would "head up and die." Flow rates, below the practical minimum for one tublng s ize , can only be maintain- - ed by use of smaller tubing, or by flow~ng the well intermittently for short periods a t relatively high

rates. heedless to say, the most popular procedure in handllng wells with allotnlents too small to support flow with the existing tubing s ize i s to install nlechanical lift. Nhether or not this IS the best procedure depends upon the well's future capabilities a s judged from data summarized in the form indicated in Fig. 2.

FLOWING LIFE If future IPH's estimated froni a graph such a s

Fig. 2 are plotted for successive s tages of oil withdrawal a s shown in Fig. 14, and curves such a s those shown at B in Fig. 6 are superimposed, an estiniate can be made of flowing life. A procedure for this purpose was developed by h. J. hoodward.*

In Fig. 14, prepared by hlr. hoodward, the IPR's (shown a s straight l ines on the left side of the figure) and the gas-liquid ratio against cumulative withdrawals (shown a t A in the figure) provide the essential well data. A number of curves for the In- take pressures necessary to sustaln lift with 200 psi tubing pressure for a ser ies of gas-liquid ratios

*Shell 011 Company

2 875" TUBING AT 8000' 200 P S I TUBING PRESSURE

Fig. 14-Prediction of Flowing L i fe

136 W. E. GILBERT

Headrng Cycle: 1. Because of the bypassing of gas Into the annulus, the l lquid level IS slowly belng lowered, annulus oi l

IS belng displaced Into the tub~ng. 2. The wel l 1s st111 producing at a low rate and the tublng column IS heavy because gas 1s beingdlverted

into annulus and o i l from the annulus is belng dlverted Into the tubing. 3. The welght of the tubing column IS belng reduced because no further gas can be stored In the annulus.

T h ~ s further reduces the Intake pressure, and 4. Allows gas from the annulus to "blow around." For a short tlme the well 1s gas-lifted w ~ t h annulus

gas at a hlgh rate, and thls reduces the Intake pressure to ~ t s lowest value. The wel l gas is NOT belng used t o best advantage.

5. The extra annulus gas has been dissipated and fluid, because of the low Intake pressure, IS flowlng at a high rate Into both the tublng and the annulus. The tubing column IS becomlng heavler and the outflow rate IS d i m i n ~ s h i n ~ .

6. Fluld IS st111 flowlng Into the well at a faster rate than ~t will flow out of the wel l wi th the exlsting In- take pressure.

7. The rate of outflow IS again In balance wlth the rate of inflow, and bypassing of gas into the annulus starts repetltlon of the cycle.

Observatrons. Thls IS not an efficient type of flow because i t produces a large proportion of the o i l wlth a deficient

supply of gas and a small proportion of the o i l w ~ t h an excess supply of gas.

The usual practice of beanlng a well back t o a low rate of flow to avoid t h ~ s type of surging is not effi- c~ent , and In many Instances results in avoidable reduction of Income.

Thls type of flow IS characGr~s t~c of the latter part of the flowlng l ~ f e of wells in most areas, but is also characterlst~c of many relatively new low gas - l ~qu~d ratlo wells.

Heading actlon of thls klnd can be mlnirnlzed by use of tubing-casing packers, but where packers are not already ~nstalled, use of casing-actuated intermitters may be preferable.

Fig. 15-Unsteady Natural Flow

Headrng Cycle: 1. A t the start of the flowlng perlod, the tublng IS opened by the r is lng caslng pressure whlch actuates

the motor valve. The column of gas whlch has collected In the upper part of the tubing i s produced, and

the consequent reduct~on of pressure ensures flow of the fluld mixture In the tubing below th ls gas column.

2. The tubing pressure trends downward whlle fluld IS being displaced out of the annulus, and then 3. Rlses as annulus gas starts t o break around the foot of the tubing. 4. When the caslng pressure reaches the predetermined mlnlmum, the motor valve closes the tubing outlet,

but flow Into the we1 l continues wlth very l l t t le decrease In rate, both gas and l ~ q u l d flow lng Into the annulus. Tublng pressures contlnue t o r ise. The caslng pressure, whlch IS d ~ r e c t l y related t o the amount of gas stored In the annulus, a lso Increases In response to gas and l lquld enterlng the well.

When the casing pressure reaches the predetermined maxlmum, repet~ t ion of the cycle IS started by opening of the motor valve.

Observatrons: By regularizing flow, caslng-actuated lntermitters can be used to Increase the rate of flow and extend

the flowlng I l fe of wel ls when they reach the heading stage. lntermltters are not t o be recommended for wel ls whlch will produce more on the pump, but they are

recommendable: a. T o Increase the rate of flow of wel ls whlch have been beaned back t o avold heading. b. T o regularize and increase the flow of new low-ratlo wel ls unt l l Increase of gas rat los may permlt

steady flow at deslred rates. lntermltters have been used to flow wel ls whlch would not flow wrthout an ~ntermltter, wells w ~ t h water

cuts exceeding 50 percent and wel ls at rates exceeding 500 bbl per day. lntermitters have been misap- plied, and mostly by inexpert selection of bean slze and casing-pressure ranges. The bean should prefer- ably be as large as necessary t o ensure a continuous drop of casing pressure during the on-perlod (1 t o end

of 3) and no larger. The casing-pressure range must be large enough t o ensure a flow of gas around the

foot of the tublng, s lgna l~zed by a steady buildup In tublng pressure. A longer range IS unnecessary and often undes lrable.

Fig. 16-Intermitter Control of Natural F low

138 W. E. GILBERT

were superimposed over the IPR lines and the well's flowing progress was interpolated using the gas- liquid ratio data given. Rhen the well's progress curve becomes tangent to the IPR, flow must cease. By constructing sinlilar graphs for other tubing s izes , i t was concluded that this well would flow 120,000 bbl in 415 days with use of 3.5-in. tubing; 135,000 bbl i n 505 days with 2.875-in. tubing; and 265,000 bbl in 1,370 days with 2.375-111. tubing. Any serious errors in tubingsize selection can be avoided by applications of this procedure.

In connection with Howing life, it may be men- honed that observed rates of decline during natural flow are usually unreliable a s indices of the decline of well inflow capacities. Consequently, misappli- cations can result from assuming that flowing decline i s representative of the decline to be expected on mechanical Ilft. The reason for this l ies in the fact that flowing i s a high-rate lifting method and requires greater lifting pressures as rates are reduced. Examples can easily be drawn from practice. Iiowever, in the hypothetical case of Fig. 14, it will be seen that the well starts out flowing about 57 p e r cent (625~100/1,100) of i ts initial maximum-rate capacity, and at the end of i t s flowing life, i t i s only producing about 14 percent (75 x 100/540) of i t s residual maximum-rate capacity.

UNSTEADY FLOW A working knowledge of unsteady flow i s a nec-

essary tool in maintaining desired production rates and in avoiding unnecessary stoppages, particularly in the latter s tages of flowing life.

There are two principal sources of unsteady flow: 1, segregation of free g a s from liquid in the rising fluid column, and 2, segregation of free gas from liquid at the tubing intake.

Fornlatlon heading, which is evident in L a P a z F'ield, Venezuela, n ~ a y be excluded from usual consideration inasmuch a s it cannot occur unless the well i s tapping a fissured or cavernous reservoir.

Heading of the first type i s observable even in settled pumping wells operating wlth low-liquid volumetric-pump efficiencies and i s a relatively un- important phenomenon. It causes relatively small, and often irregular, pressure changes of short cy- clical duration and has little effect on the continu- ity of production except in very weak flowing wells. It may accentuate unsteadiness of the second type. Also, i ts presence makes tubing pressures inferior to casing pressures both a s indices of operation, and a s means of flow control.

Heading of the second type (sometimes called 6 6 annulus headingw) occurs when I, bubbles of free gas at the intake are b ~ g enough to escape entrain- ment ~ i t h the liquid entering the intake, and 2, the gas-liquid ratio i s materially sn~al ler than the gas- lift optimum for the average producing rate of the well. Fig. 15 provides diagrams illustrating heading of this type, and Eig. 16 illustrates the control function of an intermitter in this connection.

This type of intermitting does produce oil from the well head by "jerks," but it regularizes inflow, and with suitable adjustment, i t reduces the range of velocities through the liner screen a s compared with unregulated heading. A normally closed motor valve is preferable for operating a well at a low p e r centage of i t s full flowing capacity and a normally open valve should be used for n~axin~um-rate operation.

Casingtubing packers obviate annulus heading i f installed at the intake, but do not serve the function of an intermitter in regularizing production a t rates below the minimum stable-flow rate; and i f not installed when the well is completed, the danger of damaging the well by killing it with mud or water to install a packer may make alternative use of an intermitter more attractive. Incidentally, the only functlon of a packer in this case IS to gulde bubbles into the tubing, which fact may suggest new forms which are equally eflective and still permlt ready means of circulating to kill the well, if necessary, - without moving the tubing.

CASING AND TUBING PRESSURES hhen gas bubbles are large enough to escape en-

trainment with liquid entering the tubing, the annulus fills with gas and the casing pressure becomes a sensitive indicator of flowing performance. An empirical formula for estimating intake pressures from casing pressures i s given in Fig. 17. Bubble s i zes a t the intake, of course, cannot be measured directly. However, an engineer armed with simultaneous measurements of casing and intake pressures can easily determine whether or not the casingpressures of the wells in llis area are useful in estimating intake pressures. Gas gad ien t s are most likely to exist when gas-liquid ratios are on the high side and productivi- t ies are small. Two-phase gad ien t s are helpful in this connection, but are often l e s s accurate than casing-pressure data because they depend upon gas- liquid ratios which are l e s s reliable than pressure measurements.

FLOWING AND GAS-LIFT WELL PERFORMANCE 139

I N P S l A = TUBING DEPTH IN THOUSANDS

1 20

U P - - P

110

1 .oo 0 1 2 3 4 5 6 7 6 9

DEPTH IN THOUSANDS OF FEET

Fig. 17-Approximate Gas-gradient Relationship Between Casing Pressure at the Well Head and

Intake Pressure at Lower End of the Tubing

In many fields the IFH of a well may be estimated from knowledge of i t s stat ic pressure plus a representative casing pressure and the corresponding liquid-production rate, a s indicated in Fig. 18. For heading wells, the average casing pressure may be used. hs t imates of this type are in error on the con- servative side ~f the annulus contains liquid (~.e. , the true IPR will be larger than the estimated IPH). Thus, if casing pressures and stat ic pressures have been carefully measured and recorded, they can often be used to outline IPH trends in terms of withdrawals.

Generally, tubing and casing pressures merit attention both from engineers and operating personnel,

GIVEN AVG CSG PR = 1709 P S I AT 250 BID STATIC PR = M O O D31 GLR = 0 7 MCFIB TUBING. 2 375 INCH SET AT 8000 FT WELL DEPTH ezw n

ESTIMATE THE I P R

PROCEDURE 1 FROM FIG 17

Pq = 1 226 Pe = 1 226 (1709 + 15)

P* = 2115 PSlA

VI 2 CONNECT INTAKE PR = 21 00 P S l G 0. 2000 TO STATIC PR MAKING I P R ESTIMATE

Z

TUBING INTAKE)

200 400 600 800

PRODUCTION-RATE IN B I D

Fig. 18-Method of Estimating IPR's from the Static Pressure and a Casing Pressure

and there is much to be said In favor of accurate reporting and control of bean sizes.

Range-indicating pressure gages are beginning to be usefully applied, the thought being that flowing wells do not require gaging or other individual attention except when a change occurs i n the normal range of variation of thelr tubing and casing pressures. Hange readings are often conclusive a s in- d ices for operating control, and spot readings are not conclusive.

RESTARTING NATURAL FLOW Flowing wells are not improved by periods of

shutdown; and when they die, they are candidates for immediate attention. Even though flowing i s no longer the optlmum method, it i s sometimes desirable to restart a well a s a protective measure until final- lift equipment i s ready for operation.

Strong high-pressure high-productivity wells restart when the flow valve is opened; and a t the other end of the sca le , there are weak wells which can only be restarted by a procedure tailored to the requirements of the individual well and applied without unnecessary los s of time.

In connection with restarting, the following facts are often significant:

1. The gas-llquid ratio typical of the well may require two or three days of operation for full development after restarting because, under shutdown conditions, liquid produced into the well bore frequently invades the more active gas-producing layers and temporarily reduces effective gas p e r meabilities.

2. For wells without tubing-casing packers, i t is usually necessary to fill the annulus with gas at the desired intake pressure before stable flow can be re-established. 3. If the well d ies a s a result of heading action,

delay may diminish the possibility of successful restarting. Also, in critical cases , use of smaller tubing or use of a casing pressure-actuated i n t e r mitter may be necessary if i t is desired to prolong the well's flowing life.

Swabbing i s definitely inferior to use of a gas compressor for difficult restarting jobs because, with swabbing, the well ordinarily restarts with a considerable column of liquid still remaining in the annulus; and by the time the production crew has moved to another location, bypassing of gas pas t the intake loads the tubing with a heavy mixture from the annulus and the well dies. Incidentally, a s a well declines, reduction of the bean s i ze i s necessary to maintain stable flow. However, changes

140 W. E. GILBERT

must be made in small increments at weak wells because for each increase In Intake pressure an easily computed extra quantity of gas must be stored in the annulus before the well's full gas-l~quid ratio can be effectlve In the tubing for lifting at the lower - -

rate. Ignorance of this fact and lack of a readily available starting compressor result in premature relinquishment of natural flow In many cases.

GAS-LIFT APPLlCATIONS It i s st i l l true that no one method.of lift will pro-

vide optimunl results in all wells, and due process of rating wells and methods will always be d e s i r -

able to niainta~n the profit margins e s s e n t ~ a l in meet- ing demands for oil.

TOTAL G L R p$- PERFORMANCE RATE WITH FROM 5000 FT 2 875'

WlTH 50 PSI I TUBING PRESSURE (ii) \ I

PRODUCTION IN B I D

Fig. 19-Illustration of the Procedure Used for Maximum-rate Gas-lift Estimates

Gas 11ft i s primarily a h~gh-rate method and can be a final-lift method in wells tapping strong water- d r ~ v e reservoirs, as illustrated by experience in some Louisiana fields. It can have useful applications when allotted rates are n~aterially smaller than inflow capacities. Use of gas a s a means of liquid 11ft 1s always attended by impos~tion of some back . -

pressure against the formation, even when packers are used, and even when standing valves and con- centric or eccentric induction tubes are used. but i t must also be observed that formation back pressures are often unavoidable with the other forms of lift and especially when gas accompanies the oil produced. For this reason gas lift can be expected to find applications where the bore of the well is s o small a s to prevent effective gas-anchor ac~ ion . It i s also applicable when depth limits the relative capacities of other methods.

T o estimate the maximum-rate gas-lift possibili- t i e s of a well with a given IPR at a given tubing

100 200 400 600 loo0

PRODUCTION IN B I D

Fig. 20-Use of Log-log Paper for Extrapolations of

the Intake Pressures and Gas-liquid Ratios of Maximum-rate Gas L i f t

pressure, it i s only necessary to plot the intake pressure for each of a ser ies of rates. In each case , start on the optimum gradient (the one gradient in each g a p h marked with an arrow in Fig. 23-28, 30- 33J at the given tubing pressure, measure down from this point the depth of the well, and read the Intake pressure. A s shown in E'lg. 19, the resulting curve, A, outlines the highest-rate gas lift possible w ~ t h the given tubing s ize , tubing pressure, and depth; and the intersect~on of this curve w ~ t h the IPH gives the h ~ g h e s t rate and lowest intake pressure attain- able under the given condi t~ons in the particular well. By plotting the gas-liquid ratio for each gradient, an estimate, B, of the required total gas-liquid ratlo i s obtained from which the well's gas-l iqu~d

PRESSURE H P S I GLR IN MCFlB Ya 7- 1- 0 1 2 3 4 5 6 e

m

z Z lm g g " E

STIUNCS OF sun I N W ~

Fig. 21-Diagram Illustrating Some Flow and Gas-lift

Alternatives

(Gas-lift tub~ng pressure = 100 psi)

ratio i s subtracted to obtain the net gas-liquid ratio needed. Use of a higher or lower total gas-l~quld ratlo will increase the intake pressure and reduce the liquld-production rate. Both maxlmum-rate curves, such a s A in Fig. 19, and optimum gas-l~quid ratlo curves such a s the one shown in the figure, may be considered to be straight llnes on log-log paper when extrapolations are necessary, as shown in E'lg. 20. This observation does not hold for other grad~ents and their ratios; and, of course, any ex- trapolation of enlpirical data must be made advised-

ly. Flg. 21 illustrates some of the many gas-lift and

flow alternatives adaptable to a given well, and i s introduced a s an illustration of the type of graph~cal

' analysis which may be used. Such a well with a full string of 2.875-in. tubing would be nearlng the end of i t s flowing life, a s indicated by the smaller of the two tubing-pressure curves in graph C. It would flow strongly with use of a full string of 1.66-in.

Solution of well problems uslng combination strlngs can be made by adding gradients, using the same ratio for natural Bow or gas lift through the different s izes , and using the same pressure at the depth at - which a juncture between s izes takes place.

Any adequate discussion of flow valves would be beyond the intended scope of this paper. Flow valves have contributed greatly to the practical utility of gas lift. They are indispensable for starting against the high well pressures and for automatic restarting. Intermitter types with standing valves have been used for maintaining h~gher rates of flow than those poss~b le with straight gas lift In particular wells. The predictability of gas lift with flow valves i s not solely the responsibility of the valve manufacturer, but depends qea t ly upon the deference the operator has pald to determining well data of the type indicated in Fig. 2. However, a s better gradient data become available, improvements may be made in valve spacing, and both installation costs and the

The gas horsepower required by the gas-11ft user is:

Fig. 22-Chart Suggested for Estimating

tubing using a compressor for starting.Its maximum- rate gas-lift performance with a full string of each of three s i zes i s also shown in g a p h C and corres- pending gas requirements are shown in graph U. The input casing pressure for gas 11ft from 5,000 ft would be between the intake pressure and the static gas- gradient pressure shown. The well's maximum-rate gas-lift perfornlance with a 1,000-, 2,000-, 3,000-, or 4,000-ft string of 1.66-in. tubing inside 2.875-in. tubing i s 'shown in graph B. Graph A shows 2.875- in. gradients for 0.4 Mcf per bbl.

Tak~ng k = 7.25 for wet gas, t h ~ s formula may be

- proportion of total horsepower needed for startlng can be reduced. Incidentally, ~t seems likely that, with use of improved gradient data, a demand will develop for accurate determination of pressure losses through flow valves of the different types; and the exemplary data provided by one manufacturer for flow of gas through surface beans do not necessarily apply without modification to other types of orifices used in a tubing string.

In order to compare gas lift with other methods of lift In particular cases , the oil-country engineer

written:

wherern. M = Mcf per day at 14.7 PSI. It 1s here suggested that thls 1s the horsepower upon which quo- tatlons should be based w ~ t h the glven 7, pressure ratio; 2, Input gas temperature; and 3, Input pressure, and may be from 20 to 40 percent less than manufacturer's brake-horsepower ratings depending

upon the dev~ation from Boyle's law, the auxiliaries used, and the overall plant effic~ency atta~ned.

Gas-horsepower Requirements for Gas Lifting

142 W. E. GILBERT

stands in need of a ready means oi estimating horsepower requirements. P o s s ~ b l ~ a formula of the type given In Fig. 22 can be adapted to this purpose. Although n~anufacturers may regard this suggestion

a s an over-simplification, they also may be Inclined to agree that some simplificat~on would serve to pro- mote conlpressor s a l e s for gas lift In competition ~ i t h other lifting means. 1 he temperature of power gas, because of ~ t s low specific heat, i s usually controlled by well temperatures at points of appli-

- ~

cation, and usually the gas-rate requ~rement i s estimated at standard conditions.

CONCLUSION 1 he material presented here is ofleredas an i n t e r

in) report on a phase of production operations deserving uider attention than i t has been accorded in the past. It i s desired to thank the Shell Oil Com- pany for making the presentation possible, and particularly since this outline was con~pleted during the wr~ter ' s stay in their California area.

REFERENCES 'Versluys, J . klathematlcal Development of the Theory

of Flowing be l l s , Trans Am. Znst. Mtntng Met Engrs. (Petroleum Developnlent and Technology) 192 (1930). kloore, T. V. and Wllde, H. D: Experimental Measure- ments of Shppage In Flow through Vertical Plpes , Trans Anr. Znst Mrntng Met Engrs. (Petroleum Development and Technology) 296 (193 1). Kemler, Emory, and Poole, G. A. A Prellmlnary Inves- tlgatlon of Flowlng PJells,Dnllrng and Productton Prac- trce, 140 (1936). May, C. J and Laird, A. The Efficiency of Flowlng he l l s , J . Znst. Pe t Tech., 20, 214 (1934). kay, C. J Efficiency of F'lowlng 'Aells, Trans Am Znst Mrnrng Met Engrs (Petroleun~ Developnlent and Tech- nology) 114, 99 (1935). Poettmann, Fred H. and Carpenter, Paul G. The blulti- phase Flow of Gas, 011, and Uater through Vertlcal Flow S t r ~ n g s wlth Appllcatlon to the Deslgn of Gas-lift In- stallatlons,Drtllrng and Productton Practrce, 257 (1952). ' Shaw, S. F Gas-lrft Prrncrples and Practrces, Gulf

Publishing Company, Houston, Texas , 1939. 'Babson, E. C The Range of Appllcatlon of Gas-llft

Methods, Drtllrnk and Productron Practrce, 266 (1939). Sullivan, R. J. Gas-011 Ratlo Control In Flowing R'ells, Drrlltnh and Productron Practtce, 103 (1937).

DISCUSSION 'A. C. Sheldon ( 1 he Ohio Oil Company, L o s Ange- . . -

les)(written): 1 he author has a very useful tool for the solution of problems relative to flow of 011, gas, and water in a tubing string. In s o doing, he has assembled many pertinent facts, a s well a s helpful graphs. l 'hese should prove especially helpful to the engineer who i s confronted with the problem of design for a tubing string in a flowing orgas- lift well.

he oil industry IS accustomed to thinking of conservation in terms of barrels of liquids or material recovered, yet often fai ls to realize that the conservation of energy i s equally important. 1 he conservation of energy leads to a conservation of petroleum and increased recovery. 1 herefore, the conservation of nature's energy in producing oil becomes as important a s any other phase of conservation or eco- nomies.

I h e author briefly mentions the use of the "inflow performance relationship," or IPH, which cor- responds to the well-knonn "productivity index" or PI. In actual practice, the mass rate of inflow of

1s 1s each phase i s usually replaced by the PI. Th' a good approximat~on where the water cut is not large ( less than 25 percent) or the gas-oil ratio i s not excessive. What constitutes an excessive ratio for calculations in which P I i s substituted depends upon temperature, pressure, and fluid characteristics. Certainly, P I i s meaningless for calculations involving retrograde condensate wells which make significant volumes of water.

Cne question which occurred to nle is: Ahat effect has viscosity on the relationships developed7 It i s realized the Ten Sec t~on Field crude has low viscosity, in the range of 0.5 to 5 centlpolses within the flow string, depending upon temperature and composition. I should like to ask the author ~f he has any data showing the effect of viscosity on the charts prepared. \hat effect does viscosity have on the equation for the bean s i~e-pressure ;elation? hould the rapid change of slope in the viscosity- pressure curve at lower pressures explain the sen- sitivity of flow volume to changes in bean s ize at these pressures? Perhaps the onussion of a viscosity function in the bean sue-pressure equation would explain the author's point that the equation cannot be used at pressures l e s s than 70 percent greater than l ~ n e pressures. It w ~ l l be r ecogn i~ed that this i s the pressure range where bean s i ~ e i s most critical-a slight error often results in killing the well.

l'he author s ta tes ". . . rates of decline during natural flow are usually unreliable a s indices of the decline of well inflow capacities." l h i s difTiculty nlay be overcome by observing the decline in poten- tial or productive capacity with time.

Students of this will agree with the author that t h ~ s i s "a phase of production operations deserving wider attention than it has been accorded In the past." l h l s paper represents; a pra~seworthy cqntribution to the industry.

Rlr. Gilbert: T h e I P R and the P I a r e not equiva- lents . I h e IPR, a s used in t h i s paper, i s the re-

. .

la t ionship between intake pressure and liquid Inflow rate . T h e P I i s the first differential of the I P R in the spec ia l c a s e when the la t ter is a straight l ine, or i s s o nearly s t raight tha t i t s curvature may be ignored.

Very roughly, depth-pressure gradients some 15 percent heavier than those In the paper were found necessary for gas-011 ra t ios up t o 1 Mcf per bbl in one field; but in t h i s c a s e the oi l v i scos i ty i s a t l e a s t 1 0 0 t imes greater than that of T e n Section crude. I t i s bel ieved that v i scos i ty e f fec t s on flow through beans will prove very minor b e c a u s e of the ex i s tence of in tense turbulence. There i s a well- known formula, avai lable in any s tandard summary of flow of g a s e s through nozzles , which may be shown a s follows:

k being the ad iaba t ic constant , and p l / p o , the mini-

mum rat lo for which flow through noza les i s unaffect- ed by po, the downstream pressure. If k e q u a l s 1.25,

the cr i t ical ra t io i s about 1.8, compared with 1.7 used in the report. Thus , sugges ted u s e of upstream pressures exceeding the downstream pressures by a t l e a s t 7 0 percent i s b a s e d upon observat ion of field d a t a and rough consideration ot cr i t ical ra t ios (values of k for oil-laden g a s were not determined).

T h e dec l ine of the production ra te of a flowing well is greater than the decl ine of the well ' s inflow capacity, and the dispari ty i n c r e a s e s as flow con- t inues. A s Mr. Sheldon points out, i t i s preferable t o follow the well 's inflow capaci ty, which may b e plot ted in terms of time, or, bet ter s t i l l , in terms of oi l withdrawals, as indicated by curves 1 and 2 of Fig. 2.

T. H. Acres (Sunray Oil Corp., L o s Angeles) (written): l h i s paper is a n exce l len t a n a l y s i s and presentat ion of the fac tors affecting the behavior of flowing and gas-lift wel ls . I t i s t h e first treatment I have s e e n that recognizes n o dis t inct ion between g a s l i f t and natural flow; and, by s o doing, i t en- a b l e s one t o bet ter understand why natural Bow c e a s e s and how, by g a s lifting, the energy neces - s a r y for the well t o flow is augmented. T h e g a p h i - ca l methods and gradient d a t a presented provide means of predicting when the flowing l i fe will end

and a l s o provide means of calculat ing p r e s s u r e s and volumes of g a s necessary for optimum gas-lift operation.

T h e author points out that the gradient curves should be used with care. T h e s e a r e apparent ly the r e s u l t of the correlation of d a t a from many t e s t s In flowing and gas-lift we l l s modified and extended with information of other authors. k h e t h e r they a r e completely rel iable or not, they cer tainly provide a p i d e as t o t h e magnitude of p ressures and volumes of g a s required t o l i f t oil. T h e y further provide a con- venient pattern t o a n operator or engineer for ac- cumulating and present ing the r e s u l t s of h i s own well t e s t s .

I have severa l ques t ions tha t I should l ike t o a s k Mr. Gilbert.

1. In F ig . 2-Individual Well Inflow Performance -

Trend, w a s the productivity index omitted inten- t ional ly?

2. It i s s t a t e d that flowing w e l l s a re not improved by periods of shutdown. Where restar t ing is not a problem and the well i s c lean, d o you bel ieve some damage may resu l t?

3. In t h i s s tudy, the locat ion of the tublng intake with respec t t o the perforations must have had t o be considered many times. Was there any general conclusion indicated as to the optimum tubing location, i.e., a t the bottom of the perforations, top of the perforations, or a t some point above?

I h e author i s t o b e commended for a n excel lent paper. I bel leve he h a s had niuch of t h i s d a t a for some time, and I am g lad h i s company provided the time for him t o assemble it.

M. Gilbert: Answering Mr. Acres' quest ions:

1. Yes, the P I w a s intent ional ly omitted from Fig. 2 in recognition of the f a c t tha t IPR's frequently a r e curved. However, some engineers may prefer t o plot the PI ins tead of the maximum inflow ra te (curve 2) if the well 's I P R may b e taken t o be a straight line.

2. Yes, there a r e some poss ib i l i t i es that damage may resul t in shut t ing down even a c l e a n well which may be res ta r ted eas i ly . T h e dangers for short per iods of shutdown are usua l ly negligible. However, incipient cas ing l e a k s may become ac- t ive under shutdown condit ions ( l eaks , incidentally, which were s e a l e d off when t h e cas ing w a s t e s t e d with mud in the well). Also, under shutdown condit ions interflow wil l occur i n long perforated

144 W. E. GILBERT

lengths, with some degradation of ~ o t e n t i a l recovery. T h e s e a re fac tors b e s t judged under loca l conditions.

3. In general , whenever tubing-flow gradients a re lighter than g a d i e n t s in the l iner and cas ing for the same ra tes , i t is preferable t o s e t the tubing a s low a s i s cons i s ten t with safety, because the wel l will flow longer and a t higher r a t e s than would be the obtainable with a shal lower set t ing. How- ever , in clean wel l s with undersaturated crude there IS no s p e c i a l point in se t t lng the tubing below the depth where a l l the g a s remains in solution over the full range of desired operating rates .

I t is des i red t o thank Mr. Sheldon and Mr. Acres for their comments.

E.N. Kemler (University of Minnesota, Minneapolis) (written):* Flowing-well performance h a s not been given the at tent ion which i t s importance deserves . 1 h i s 1s indicated In part by the very meager biblio- graphy included in connection with hlr. Gilbert 's paper. Development of bet ter understanding of reservoir performance, together with more recen t b a s i c invest igat ions on multiphase flow should make i t poss lb le t o arrive a t a more rat ional approach t o t h e s tudy of flowing wells . T h e low c o s t of production by flowing, together with the advantages of postponing artificial l i f t a s long a s poss ib le t o permit more accura te evaluat ion of requirements and capaci ty of pumping equipment a s well as postpone- ment of the accompanying investment, would a l l contribute to making s t u d ~ e s which would prolong flowing l i fe most desirable . Mr. Gilbert 's paper i s a n outs tanding contribution to t h l s field and should l e a d to further s t u d i e s relating t o a rat ional approach t o the s tudy of flowing wells . Tubing and choke ~ n s t a l l a t i o n s In flowing wel l s a re deserving of the s a m e c o n s ~ d e r a t ~ o n with respec t t o des ign a s that given t o design of sucker-rod s tr ings. It should be expected tha t u s e of tapered tubing s t r ings , for example, would give bet ter flow condit ions than a uniform string.

T h i s paper represen ts a n outstanding contribution t o the l i terature of flowing-well performance. It

*Prepared following presentation of the paper.

should contribute to further development in t h i s long-neglected area.

Mr. Gilbert: I wlsh t o thank Dr. Kemler for h ~ s kind comments. If natural flow is in a s e n s e the "orphan child" among lifting methods, there may b e some significance in the fac t that flowing requ i res very l i t t le s p e c i a l e q u ~ p m e n t and consequent- l y h a s lacked t h e extra s t imulus of englneering attent ion accorded by the supply industry t o other methods of lift.

Diminishment of well IPR 's , and change of gas - liquid ra t ios in terms of withdrawal, a re fac tors tending to limit the pract ical ut i l i ty of tapered s tr ings. However, Insertion of a length of smaller tubing ins ide 3.5- or 2.875-in. tublng w ~ l l frequent- l y se rve to extend natural-flow production of a n al lot ted rate.

T h e methods of Poet tmann and Carpenter a re proving valuable in developing lmproved depth-pres- s u r e d a t a in readi ly u s a b l e form, although some difficulty h a s been experienced with ex tens ions into the pressure range below s a y 500-400 psi . Also, the a n a l y s i s of two-phase flow through b e a n s (chokes) given in the paper doubt less c a n be improved.

In the in te res t s of the oi l Industry, it i s t o be hoped that reference material concerning the dynam- i c s and economics of natural flow will b e consider- ab ly augmented over the next decade.

E.C. Babson (Union Oil Co. of Ca l~forn ia ,Ca lgary , Alberta, Canada)(written):* A s one who bas had a l i t t l e experience wlth the empirical approach t o gas- 11ft problems, I am impressed by the lnvest igat lon which i s summarized in hlr. Gilbert 's paper. T h ~ s paper ca r r ies the e m p ~ r i c a l a n a l y s i s of g a s l i f t performance far beyond any prevlous work, and I bel ieve i t may well prove t o be the definitive work on the sub jec t . It 1s probable that further refinements and ex tens ions of correlat ions c a n be made, but the paper covers almost completely the p r ~ n c l p l e s involv- e d In applying t h e s e d a t a t o p rac t ica l production problems

h%. Gilbert: I value highly both Mr. 13abson's opinion of the paper and the part h ~ s ear l ier work played in making it possible .


Fig. 23-Approximate Depth-pressure Gradients for 2.875-in. Tubing

W. E. GILBERT

GRADIENT PRESSURE IN PSI


FLOWING AND G A S L I ~ T ' WELL PERFORMANCE

GRADIENT PRESSURE I N PSI

Fig. 25-Approximate Depth-Pressure Gradients for 2.875-in. Tubing

W. E. GILBERT


FLOWING AND G A S L I F T WELL PERFORMANCE

GRADIENT PRESSURE IN PSI


FLOWING AND GASLIFT WELL PERFORMANCE

USE O F BEAN-PERFORMANCE CHART

A g a p h i c a l means of e s t ~ m a t i n g the bean performance is given in F ig . 29. F o u r var iab les are considered, and when three of t h e s e var iab les are known, the fourth may be est imated. In construc- tion, P a r t I of the chart represen ts the performance of a ''/,-in. bean and P a r t I1 i s simply a means of correcting resu l t s for other bean s i ~ e s . In solving for any one of the four variables , enter P a r t I if both the barrels per d a y and the g a s l i q u i d rat lo a re known; or enter P a r t I1 of the chart if the tubing pressure and bean s i z e a re known. I ' h e further procedure in solving for e a c h variable may be b e s t ex- plalned by examples.

1. Es t imate Gas-liquid Rat io or the G a s Rate

Suppose we have a well equipped with a '%,-in. bean operating with a tubing pressure of 720 p s i a t 200 bL1 per day. No differential recording meter h a s been ins ta l l edand a n es t imate of the g a s production i s desired.

Solutzon. F i r s t find in P a r t I1 of the chart, the intersect ion of the l ine for the 15 bean a t 720 psi ; go vert ical ly t o the s lan t ing 10-bean l ine and then horizontally t o the ver t i ca l 200 bbl per day l ine in P a r t I. At t h i s point the gas-liquid rat lo i s about 1.8 Mcf per bbl, from which the total g a s i s 360 Mcf per day (200 x 1.8).

2. Es t imate Production R a t e

After a bean change, a new well which showed a rat io of 1 ,400 cu f t per bbl on the prevlous gage, i s flowing through a 4 0 bean with 750 p s i tubing pressure. What i s the probable production ra te?

Solutzon: Enter P a r t I1 a t the intersect ion of the 40-bean and 750-psi l ines and go vert ical ly to the 1 0 line; then go hori tontal ly to 1.4 hlcf per bbl- the est imated production rate being found t o be 1,530 bbl per day.

3. Es t imate Tubing Pressure Es tab l i sh the performance of a 13 bean for 0.8 hlcf per bbl. Solutzon: Slnce the formula ind ica tes that there i s a straight-line relat ionship between tubing pres- s u r e and barrels per day, only one point need be establ ished. Thus , going h o r i ~ o n t a l l y from the intersect ion in P a r t I of the 0.8 rat io and, s a y , 200 bbl per day, t o the 10-bean l ine in P a r t I1 and thence vert ical ly to the 13-bean l ine, the pressure 1s found t o be 605 p s l and for any production rate with the 1 3 bean and 0.8 rat lo , the tubing pressure i n p s i is equal t o the barrels per day multiplied by 605/200 or 3.03.

4. Es t imate B e a n S ize

A well h a s been operating for a n extended period a t 200 bbl per day and 4.0 Mcf per bbl ratio. It is desired to reduce the rate t o 1 0 0 bbl per day and the tubing outlet performance curve Indicates tha t the tubing pressure a t th i s rate will be 1,800 psi . What s i z e bean should be used?

Sohtzon: Enter P a r t I and go horizontally from the intersect ion of the 1 0 0 bbl per day and 4.0 ra t io l i n e s t o the 10-bean l ine in P a r t I1 and thence vert ical ly t o the horizontal 1,800-psi line. An '4,- in. bean should be used.

152 W. E. GILBERT

PRODUCTION IN BID

Fig. 29-Bean-performance Chart

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Gilbert Charts

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