9 Coning of Oil, Gas, and Water

Any discussion of the coning problem usually refersto basic theoretical curves by Muskat and Chaney etal. for condition of homogeneous rocks (Figs. 9-1through 9-3). The curves are used to obtain a produc-tion rate, q, corresponding to a theoretical set of con-ditions that is corrected to field conditions using theequations shown on the proper figures. In a like man-

Production Ralesa! StarlWller ConingTop Open Interval is alTop at Pay.A 10%oftotalpaylsopen-ChaneyelalB 20% ollola] payJsopenC 30% 01 total pay is openo 40% 01 total payisopenE 50% ollolalpllyisopen-ChaneyetatF 50% oflotalp.8yisopen-Muska.1Dalareadfromlhlslheoretlcalcur;els

100 converted to field conditions by equation:q=.00333k.(Lpo,w) '(Irom curvej

,B

when system is oil and water.k=ellective permeabHily to oil, md.p = Density conlras!, gm/ccq:::: Oil product1on in STBlday,.=011 vi.cosily, cp

10 B:::: Oil RS/STB

The main assumptions madeara aslol:ews:(1) Ihereservoir rock is homogeneous(eilher isot,opicoranlsOlropic}; (:2) the~olume of the aquifer underlying fhe oilzone;s ~er)' sm"lI, so that it does notcontribute to reservoir energy; and (3)the gas cep expands afa very low rllte,so lhatHcan be assumed to be inCluasi-staticcondilions.

Production Rates at Starl Waler ConingTop Open Interval is at top 30% of Tolal PayA 10% of tOfal payis open-Chaney etal.B :20%olfolalpayisopenC 30% oltolalpaylsopeno 40% 01 lolaJ pay is openE 50%oll0lalpaylsopen

Waler Cone Height vs Critical RateTop of open i.ntervlll starts at30%'ortotal pay In oll-wllter & gas-watersYltems.Data from Chanl'!y

II

I

IThe relatedpreSSllre drop can be computedfrom the basIc flow equarlonl:Muskat: p,_p" '" 325(qI'B/Fkh)log(r,/r~)5.10Where Fallows for skin, partlal penetration,perforations. and similar restriclions to Ilowp,-p., = (141 (quB/klll [In(r'/r,l'';- s + 0,-.75]p,-p" = 141(q~B/kh) [InCUr,) -.75JEquations assume steady slile Ilow andthe .75 is omitted when depletlon absenl

Figure 9-1. Water coning in oil wells in homogeneous pay. (cour-tesy Petroleum Engineer, February 1978)

Muskat Equations,p-p.,=325(q"B/Fkh) log(r.lr,)q,=.00333 k.C:"-o .• )q curve-~::s--------

u:

" 100.c0U

~~"0

'"0>..:I:

Waler Cone HeIght vs Pressure Gradients, ]

Solid Iinaa from Mu.kal Fig. 5.25 - 1949Mu.kat UIoeS auumplions Such as well r.diusof ~'. fL, r. 01 500 ft., water density of.3gm/cm (.187 psi/fl.) andthes.e itemsmust be adjusted when diHerenllrom fieldvalues.

Theor,' and experience show thai conescan be controlled by low rates whichollen are uneconomical_ However, duringlale life most water drive reservoirsare produced at very high rates andhigh water cut to obtain maximum 011reco~ery. Production at low raleduring early lite then Is nolproper.

I

The main assumptions made are IS follow.:(1) the reservoir rock is homogeneous(either isotropic or anisotropic); (2) thevoiume 01 Ihe aquiler underlying the oilzone is very .mall, so that il does nolconlribute to reservoir energy; and (3) thegas ClIp expands at a very low rate, sothai il can be assumed to be in quasi·staflc conditions.

Figure 9-2. Water coning in oil wells in homogeneous pay. (cour-tesy Petroleum Engineer, February 1978)

Recovery eHlciency is reduced when 011 welsan inlUal gu cap. Recovery of 011 which IIadjacent to Ihe gu oil contact Is dlfflcuflat economic rales 01 oil production. GasInjection and completing well. below wateroil conlacl may be helpful when Itrong walerad~ance is •.••• ilable.

I

Data read trom this thaoratie.l curve Isconverted 10 field condllions when syslemi. oil and gas by following equation:

q, = 0.00167 k, {~_oo,gl '(from curve)---_.~. ---

Total oil colu~n 400ft.Top pre I. to GOC 160 fl.Perforatedinferval 40ft.Perll/total pay 10%GOC-T.P./total pay 40%'Curve 20,000

Gas Coning vs Critical RatesData from graphl by ChaneY

1:>. Top of open Interval I. al 20"W of 011 pay.nd 10% 01 011 pay I. perforatftd!

o Top of open Inl&fVal I. at 20% of 011 payand 40% 01 011 pay I. perfoTated.

- Top of open interv.lls al 40%'of oil payand 10% of oil p.y i. perforaled.

o Top 01 open Inlervall. al 40% of 011 p.yand 40% 01 011 pay I. perforated.

Figure 9-3. Gas coning in oil wells in homogeneous pay. (courtesyPetroleum Engineer, February 1978)

ner, data obtained from Chierici-Ciucci curves hasbeen crossplotted on log-log and semilog paper (Fig.9-4,5). They are referenced when pay has lower verti-cal than horizontal permeability. Values of IIJ readfrom the curves are used in an equation to obtainthe production rates applicable to conditions existingin a field.

"E ~ _~ = I pertorJted iE'_t~~val'"

~\ h Thickness of 011pay'..•.- = ,1

'7 = ,2

••• ...•.Z = ,3

'~ ~,.•. --- = A

O'~ .•.::-' '"::- - 8 =~=.o~, - -- h ~

\~ '- -- -- I

\.'\, -.•., [j =-~= .;) ~.•..•. h:" --,'-( - --~\ s =L.~ -, '. '- -,'\ --- ,\,1=)

~-- --" --

"" i'--. f--0 ' .•. -p- 'Ill'~ .•..•.., --.0, --- -- -- --'-..,r- :i 8 =~=2-, 0

..•.}..•.0 .... .•.•..

\~ -- -- -- --'a'\ 5=~=.1_"'-..,

p- I 0 I-

American Units

q = :3.07:3 x ICyl h~ ~ ~ 'V (r1h-' E, 8)B" !J-"

Figure 9-4. Cross plot of data for nonhomogeneous pays, (afterChierici and Ciucci, courtesy Petroleum Engineer, December 1978)

Several methods have been proposed to controlconing. Placing impermeable barriers to prevent verti-cal flow of fluids would be ideal. Unfortunately, mostreservoirs are deeper than about 1,500 ft, and frac-tures are vertical when fluids are injected at the highrates required to obtain a horizontal "pancake" ofthe injected liquids. In other words, nature preventsthe oil operator from attaining his objective. A verticalfracture probably will increase the coning possibilitysince \'ertical fractures usually do not seal effectivelyonce created.

Cones usually are not evaluated properly. Early andextensive coning is suggested by the forecast meth-ods, but such coning is not observed in field, probablybecause of a lower vertical permeability than that ob-tained from cores and logs.

Coning in a field being studied can also be modeled.

Unfortunately, the pay adjacent to the well-say,within 50 ft-is often difficult to describe in detail.Thin shale stringers and less-permeable hard streaksthat severely reduce the vertical permeability may notbe recognized adequately by studying cuttings, logs,or cores. Coning water and gas is a severe problemin many fields. Handling the added water and gascan be costly. Also, premature depletion of a gas capcan reduce recovery by wetting the original gas paywith oil. Production of secondary gas caps formedby vertical segregation of dissolved gas reduces pres-sure without obtaining the displacement effects asso-ciated with gas drive. When a very strong naturalwater drive is present, production at high rates re-sults in added oil recovery at abandonment. Reducingproduction rate to reduce coning does not appear at-tractive, as shown by Fig. 9-6.

For these conditions, an increase in the well densityat the locations of the last updip producing wellsshould be economical. Downdip wells when a strongedge-water drive is present do not contribute to ulti-mate recovery in homogeneous pays. Pays often arelenticular and are not connected-are not homoge-neous-so downdip wells and close overall spacingof wells may increase ultimate recovery as well as in-crease the overall rate of production. Unfortunately,water entry often is limited and must be supplementedon some pattern throughout the oil-bearing reservoir.A source of water capable of entry is necessary, andpermeability of pay must be sufficient to allow thenecessary water to move.

A decrease in well penetration results in higher oilrecovery. Minimum penetration permits the maxi-mum rate of water free production. Comparing thegraphs in Fig. 9-1 suggests a small, perforated intervalis best, and perforations somewhat below the top ofthe pay are not extremely harmful when flow capacityis adequate.

An increase in the gravity to viscous force ratioresults in a higher oil recovery.

Days, months or years are required for the coneto form and reach the point of incipient breakthroughinto the well. During this time, the well is producibleat rates in excess of the critical production rate. Ahigher rate increases the tendency toward a highercone, but a short early test does not evaluate the possi-bility of future coning problems.

The kh/kv term is the most critical term appearingin the coning equations. Also, coning is directly pro-portional to oil viscosity. Compressibility, well radius,and drainage radius are relatively unimportant in thesemisteady-state flow equations.

A well being swabbed or pumped intermittently

Coning of Oil, Gas, and Water

I \ I I 1 I 1E = b = Perforated interval

h Thickness of oil pay- \- -C) = ,1

-"""'- I-- v = ,2- = ,3 l-- -

~ .- •••••• -

r-- --.•. 6 = .4r--. .•..~----- --r-- -..-~100-.. -..... •... ~,-'..•--..--.r---- -~ -- ....-1:.::::..- ..• 1"_ •• r-- r- ;......... ",",- i..,,-•... '- -...., t" __

,-=,--~ ~-.•.- ...•- ""_, - } II'---, -r-:.: ••• ..... -~- I--. -.•.. -I-1:1 __ ~~. ~--~ ..•...- -- "'" - -.... [) - .5 I1-•••••• ....•.D~-'" ••••

""--•..., ~- ••• ,•.-...10-..... .-t-_ .... - -.. -r-- J_- 1""". - ..- "'1'-""""--- -- -.. -",,", -- -. -'.C~l.

1- r-- -.•.'( -- -, -- - • __ Ii-r::---- '-. '-- -~ ---. -- ~-r-- -."'-- ~ 1'0-- -- I"-- I~ ...- -,..,'- -- --.~-.--... - "". - E--- "-- - ....~ ...-.---r-- -.. -.1-_- - J_ - 1"" ._-- --r-- "'"- ----I'---- ••• 1--- -.- I- )- '-r •••• -- .- C\l- ..•_-. -- .... -,........•. -- '---,""-- "'"' -.l"_ 171'-_ -- --~. ,

Or- 0- - ••• -'""' ...- II-r--. -1-0 ••• ~r-- -~.--.. --I'---- ..•.---- --."'-. -~- ---. --•...... -,1-- ....•. -.1--r---- .- .•..•... ·w, .-I- -_/r---.... ,... --- .--;-~ - -.1"-II•... '-. w!-"""- II

,( ~I J

I I I

.1

8

7

6

5;.;",' 4

S 3~

Cross plot of data presented by Chierici and Ciucci in "ASystematic Study of Gas and Water Coning by Potenti-ometric Models", Journal of Petroleum Technology,Aug. 1964,

Notes:1. L se this CI'OSSp]ot \I' hen H,rtit:al and horizontal are

unequal. Refer to Continuous Tablps. PETRO-LEUM ENGINEER !:\TI':I(l'i.\T!ONAL, Fd)., HJ7<'\.

2. All methods, Muskat. Chaney and C'hieril'i, g-ivecomparable results \\'!wn permeability ratio is OIl<'.

:3. These curves usuall,l' al'l' not applil'able \\'!wn faultsOJ' tig-ht stringers sUt:h as thin shall's are pl'esent,

4. Corredions must IX' mac!l' for soml' typl'S of skins.

w w w

M"\iib~"±=* #Later woe ---- _ _LaterOriginal woe - - - - - - - - -

may pull in a cone during periods of high drawdown.Plugging back a well can be successful when the openinterval is long, particularly when a probable barrierto vertical flow is present in the well, such as a 5-10-ft shale stringer.

The density difference between oil and water issmall, and water quickly enters the well bore whena cement job is faulty or when a natural or man-madevertical fracture intersects the well bore if bottom wa-ter is present. The cement job may be repaired, butsealing the fracture is nearly impossible.

Often, a well in a coning situation will exhibit aninitial period of oil production followed by a rapidincrease in water after breakthrough. The water-oilratio should stabilize at some reasonably low value,probably less than 50%. The water is enteringthrough the lowest perforations or open interval whileoil enters through a large upper interval. The bottom

water will increase gradually as the water-oil contactincreases due to continued oil and water production.In contrast, water entering from the edge or flankswill increase much more gradually as fingers of waterarrive at the well. The water cut will gradually increasein both situations as the water fronts rise, and thewells will finally be produced with cuts in excess of90 % at high rates before reaching economic limitwhen a strong water source is present.

As in all testing, production at constant rate or atconstant pressure simplifies analysis of test data. Un-fortunately, field operation often is at an increasingtotal fluid rate, while oil production is constant.

The initial water cone can be lowered by reducingproduction rate. Since the water-invaded zone retainsexcess water as the cone seeks a lower level in equilib-rium with all forces, the method usually is not fol-lowed because of economics. Shutting in the well fora week or more is one way to confirm coning hasoccurred.

Water coning is difficult to control economicallyunless caused by a cement problem or unless a verticalbarrier is present within the well bore. Gas coningcan be more damaging, and controlling gas-oil ratiomay be economic when a pay is thick. Packers mayalso be useful.

Arthur's Method of Fingering and Coning of Water and Gas inHomogeneous Oil Sand*For the case of water or gas coning to a well wherethe penetration extends from one boundary of theoil sand to some distance from the static position ofthe water or gas, the solution may be obtained asfollows:

1. Determine the values of the potential ratio il</>/il</>e for various values of z from Figs. 9-7, 8, and 9and plot il</>/ il</>e vs. z/h. The value of </>~ is givenby Fig. 9-10 for the particular penetration of the prob-lem and for a well-radius parameter pw of 0.001.

For selected values of z/h, determine the valuesof </>z from Fig. 9-10. The value </>z is given as a func-tion of well penetration b/h and the relative distancebeyond the extremity of the well d/L. Determine </>for a reasonable value of drainage radius from Fig.9-11.

1.2

•Z 1.1•e;:;0 1.00II

~-.2 0.9

~C

~ 0.8.9

~C

~0.7

'00.~ 0.6([

\\\L

ASpherical flow \

(I)w rw-

(llW

rw

Figure 9-7. Correction factors for converting well velocity poten-tials. (after Arthur, courtesy JPT, @ SPE)

o Potential above dividing plane

{:, Potential below dividing plane

1230

.ta; 12.20

"1ij

.~C<D 12.100

(L

12.00<!>w

T

11.90

Figure 9-8. Solution of location of dividing plane and velocity poten-tial over well surface for case of simultaneous coning of water andgas. (after Arthur, courtesy JPT, © SPE)

2. Draw a tangent to the potential curve of fl<j>/fl<j>e vs. zlh from the point (fl<j>/ fl<j> = 1, zlh = 1).The value of zlh at the point of tangency representsthe maximum height y of a stable cone (ylh = 1 -zlh). Intersection of the tangent to the curve withthe value zlh = 0 gives the value expressed by:

(Llep) _ 1 _ gLlyhLlepe zlh=O LlP

3. From the graphically determined value of (fl<j>/fl<j>e)zlh=o, solve for flP, the maximum pressure differ-ential without coning:

P= gLlyh

1-(~:1Ih=o

0.6

~~-

0.5

~00(L

o."

r, ~ 500 tt

1.000 tt

Ie ~ 1.000 ft

Perforations totop of oil zone

Va;ueJl h-z at point of tangency givesmaximum equilibrium height of cone

Figure 9-9. Example of graphical solution of equilibrium heightof water cone and maximum pressure drawdown without water con-ing, for selected values of drainage radius. (after Arthur, courtesyJPT, © SPE)

Practical Reservoir Engineering

17

.:1016 =1-

:10e

15

14

13

12

11

10

0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0Well penetration b/h

Figure 9-10. Velocity potential distribution at well radius. (afterArthur, courtesy JPT, @ SPE)

600

400

200

.cs::: 100"0

0:0;QEwroQ.~::>-0~"CO'Wcit0

10

b = Well penetration, ft

h = Sand thickness, tt

Figure 9-11. Velocity potential at drainage radius. (after Arthur,courtesy JPT, @ SPE)

Q= volume rate of flowk= permeabilityr= radius, fth = sand thickness, ft

f-L = viscosity0/ = potential (velocity potential)P= pressure, Ib per sq in.

!!.p = pressure drawdown of producing well, Ib per sq in.Yo = density of oil

!!.y = difference in density between two fluidsg= acceleration of gravityz= distance of point from selected datum level, ftt= vertical distance of well from static water level, ft

e = angle of dip of sand body, degreesy= height of cone above the datum represented by the static

interface of the two fluids, fto/w = potential at well surface<p:" = potential at well surface for pu: = 0.001

<pz = potential at well radius and at depth z<Pc = potential at drainage radiusb = penetration of well in sand, ft

. bx= penetration parameter = 2h

zw= depth parameter = 2h

d. r

p = ra IUSparameter = 2h

q = fl ux density = 1In = natural logarithmC= correction of <p~ for value of pw other than 0.001d= distance from end of perforated interval of well to point z, ftL = distance from end of perforated interval of well to static inter-

face of the two flUids, ftg!!.y = difference in hydrostatic gradient at reservoir conditions be-

tween the two fluids involved, Ib per sq in. per ft

Coning Curves Proposed by Muskat and Wyckoff *

~.0

1 .c> 1,00010 0>

::le=;: .c

!<OJ- [lJ.0

8(l)c0

:i 0

~ :i0 100'ji 1.0 =

" '~

4 ~0; 0

'"~ 0'6 U)

(l) ~~ (ij(l) E5- 0,1 'x 10~

OJ::e

'xOJ:;;

Figs. 9-12 and 9-13 depict the maximum pressuredifferentials without cone breakthrough vs. penetra-tion devised by Muskat and Wyckoff. In both figures,the curves are under steady-state homogeneous-fluidflow without water-cone breakthrough as functionsof the well penetration for various oil-zone thicknesses(h), where:

well radius = V4 ftexternal-boundary radius = 500 ftwater-oil density contrast = 0.3 glcck/pJ3 assumed = 1k = permeability

* Material from Trans. AIME, 1935, @ SPE.

Figure 9-12. Maximum pressure differentials vs penetration. (afterMuskat and Wyckoff, @ SPE)

I-l = viscosity/3 = formation-volume factor

However, Fig. 9-13 should not be considered quan-titatively correct. Because of the higher concentra-tions of the pressure drop about the well bore inheterogeneous-flow systems, the critical pressure dif-ferentials for actual gas-drive oil-producing wellsshould be higher than those in Fig. 9-12. In estimatingthe corresponding maximal production rates fromFig. 9-13, account for the reduced values of k/JL/3,taken as 1 in Fig. 9-13, because of the effect of connatewater and free gas on k and of the gas evolutionon JL.

Figure 9-13. Maximum rates of flow vs penetration. (after MusKatand Wyckoff, @ SPE)

Coning Curves by Chaney et al.*Critical production rate curves were obtained fromboth mathematical and potentiometric analyzer analy-ses.

The curves show critical production rates in reser-voir barrels per day vs. the distance of the top ofthe perforated interval from the top of the sand orgas-oil contact. Curves are shown for sand thicknessesof 12.5, 25, 50, 75 and 100 ft, having drainage radiiof 1,000 ft. It should be emphasized that the termsand thickness refers to the actual oil-column thicknessor, in the case ofa gas reservoir, the actual gas-columnthickness.

A comparable set of critical production rates werecalculated for a drainage radius of 500 ft. Rates forthe 500-ft drainage radius ranged from 10 to 15%higher than those for the 1,000-ft radius. The 10 to15% figure varies according to the sand thickness andthe location of the perforations within the sand. Thefollowing assumed fluid and sand characteristics wereused:

Permeability = 1,000 mdViscosity of oil = 1 cpDensity difference between oil and water = 0.3

gleeDensity difference between oil and gas = 0.6 gl

cc

Therefore to use a rate obtained from these curves,it must be corrected for the actual values of the fluidand sand characteristics and also must be correctedto surface units. These corrections are taken into ac-count by the following equations:

Water-coning rates in on oil-water system:

Qc= 0.00333 Kc (Llyo,w) Qcurve, STB/d (9.3)/-Lo B

Water-coning rates in a gas-water system:

0.00333 Kc (Llyg,w) Q curve EdQc =---------- ,Mo,/-Lg V

Gas-coning rates in an oil-gas system:

0.00167 Kc (LlYo,g) Qeurve ST dQc= B ' BI/-Lo

Kc = specific permeability of the sand to oilor gas, md

/-Lo = viscosity of the oil, cp/-Lg = viscosity of the gas, cp

l1yo,w = density difference, glee, between the oiland water

I1Yo,g = density difference, glee, between the oiland gas

l1yg,w = density difference, glee, between the gasand water

B = formation volume factor which convertsreservoir units to stock tank units andmay be read from B curves

V= reservoir barrels occupied by 1 standardMef of gas as read from V curves

Q curve = critical production rate, res. bidQc = corrected critical production rate for well

in question

As an example, take the case of a 50-ft. oil columnhaving only a water-oil contact in the well and whichhas the middle 10ft of sand perforated. This wouldplace the top perforation 20 ft below the top of thesand. Referring to curve B on Fig. 9-14b, the maxi-

Position of static water table I,I Oil

i Well

~~/t'

Figure 9-14a. Coning curves. (after Arthur, courtesy JPT, © SPE,courtesy Chaney, Noble, Henson and Rice)

mum uncorrected water-free rate of production fromchis well would be 122 res. bid. This value would[hen be entered into Eq. 9.3, together with the correct\alues for permeability, viscosity, ete., to obtain the:orrected maximum water-free production rate forchis well.

If this well had a gas-oil contact and no oil-watercontact, the uncorrected maximum gas-free oil pro-duction rate would be 250 reservoir barrels per dayas read from curve b on Fig. 9-14b. This value wouldbe substituted in Eq. 9.5 to obtain the correct produc-tion rate.

100

~ ]3 ~?i

~100

g 2

"l' ~ca c

~ a0 10 ~" K"- K~ ~ 10B U

10o 20 40 60 80 100

Distance from top perforation to top of sand or gas-oil contact, ft

Figure 9-14b. Critical production rate curves. (1) Water-coning curves: A, 2.5-ft perforated interval; S, 5; C, 7.5; D, 10; E, 12.5. Gas-coning curves: a, 2.5-ft perforated interval; b, 5; c, 7.5; d, 10; e, 12.5. (2) Water-coning curves: A, 5-ft perforated interval; S, 10; C, 15;D, 20; E, 25. Gas-coning curves: a, 5-ft perforated interval; b, 10; c, 15; d, 20; e, 25. (3) Water-coning curves: A, 10-ft perforatedinterval; S, 20; C, 30; D, 40; E, 50. Gas-coning curves: a, 10-ft perforated interval; b, 20; c, 30; d, 40; e, 50. (after Chaney et al.,courtesy OGJ, May 1956)

Coning Curves of Chierici, Ciucci, and Pizzi*The critical production rate can be determined di-:-ectiy from equations in practical units:

-··.-here:qo = daily oil flow rate (m3/d or STB/d)a = constant (52.52 X 10-2 metric; 7.08 X 10-3

American)F1 = perforation correctionF2 = penetration correction

Fsk = skin correction

• This section from JPT, August 1964, © SPE.

q = 5.256 X IO-3h2 ~ kRO 'l'(rDe, E, 0)Bo /-Lo

0.1o 10 15 20 25

Distance from top perforation to top of sand or gas-oil contact, tt

where:q= m3/dh= meters

ilp = gm/cckRo =md/-Lo=cpEo = m3/m3

Practical Reservoir Engineering

q=STB/dh=ft

ap = gm/cckRo=mdJ-Lo = cpBo= bb/STB

The function 'l' has been determined within thefollowing ranges of its parameters:

reI€vo5 ,,:;;rDe =- - ,,:;;80h kRo

L0.07":;;0 = It ,,:;;0.9

Calculation of maximum water-free and gas-free oilproduction rate is requested. Based on 40-acre spac-ing, we get re = 745 ft. Therefore, one calculates,using Fig. 9-15:

745 !306rDe = 140 Y90 = 9.72

5009 = 140 = 0.357

30e=140=0.214

60ow= 140=0.429

~POg = 0.714 - 0.098 = 0.643 gm/cc~pwo = 1.092 - 0.741 =0.351 gm/cc

89 ~ ~h

LwOw =

h

be ~h

Figure 9-15. Water- and gas-coning systems in a homogeneousformation. (after Chierici, Ciucci, and Pizzi, courtesy JPT, August1964, © SPE)

On the diagram for rDe = 10 (Fig. 9-16), one reads:

for E = 0.214 and Og= 0.357, 'l'g=0.051

Fluids characteristics exist at reservoir conditions:density of oil po = 0.741 gm/cc, density of gas pg =0.098 gm/cc, density of water pw = 1.092 gm/cc, for-mation volume factor of oil Bo = 1.250 bbliSTB, andviscosity of oil J-Lo = 1.11 cpo

Therefore:

- -3 2 0.643 x ~qog-3.0n x 10 x 140 1.25 1.11

x 0.051 = 128 STB/d

and:

_ -3 20.351 X~qow - 3.073 X 10 X 140 1.25 1.11

X 0.065 = 89 STB/d

These calculations show that, in this case, waterconing is the limiting condition for the oil flow rate.The maximum oil production rate that the examplewell can give without water or free-gas productionis, therefore, 89 STB/d.

0,40

0.35 0.06C0.30

0.250.50 0.25 0.04C

Figure 9-16. Functions 4a and 4b for rDe= 10. (after Chierici,Ciucci, and Pizzi, courtesy JPT, August 1964, © SPE)

Trimble-Rose Method for Gas Wells*Field conditions are favorable for the application ofthe Muskat- Wyckoff theory at a field. When the theoryis combined in a computer program, a very usefultool is available for establishing water-free productionrates and for calculating reserves.

Calculated maximum efficient rates must be ad-justed periodically in the presence of a rising gas-water contact. Volumetric calculations of remaininggas in the different reservoir fault blocks can be usedin conjunction with geologic maps to determine thegas-water contact and have been satisfactory at thefield.

The most effective method of completion is by seg-regating each gas zone and perforating a small intervalin the top of each producing zone.

The gas flow rate for a partially penetrating well

b value.t::':::==.t:

':::OU')OLOOllh ...•..•. C\J(\J("')

II II II II II II.0.0 .0..0.0.0

Reservoir pressurePermeabilityExternal-boundary radius

1,000:2":;;:.,;"'5

'"":-'l100

b = footage perforated, ftD = distance from formation to cone

surface at r, fth = gas-sand thickness, ft

kg ~ permeability to gas at connatewater saturation, md

1o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Perforated interval/gas-sand thickness

Figure 9-17. Water-free gas rates for 1,500 psia. (after Trimbleand Rose, courtesy JPT, May 1977, @ SPE)

in an isotropic formation is given by:

_ O.000703kgh(P~ - pili) [b ( 7 ~w 7Tb)]qg - ----~~-~- - 1 + - cos-zTR/.Lg In (re/rw) h 2b 2h

This equation is modified for gas flow in field units.The unbracketed term is Darcy's law for radial flowof a gas in a sand thickness h. The term in bracketsaccounts for convergent flow from a sand of thicknessh to the perforation of length b.

This equation may be used to calculate an MER.A value of pw, the well pressure, is determined thatwill prevent water coning. The Muskat- Wyckoff equa-tion:

Reservoir pressure 2,000 psiaPermeability 100 mdExternal-boundary radius 1,000 ft

1 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0,9 1.0 1.1 1.2 1.3 1.4Perforated interval/gas-sand thickness

Figure 9-18. Water-free gas rates for 2,000 psia. (after Trimbleand Rose, courtesy JPT, May 1977, @ SPE)

b value======

~~~~gjgII II I! II II 11

.Q..Q ..0 ..D ..0 ..0Reservoir pressure 2,500 psiaPermeability 100 mdExternal-boundary radius 1,000 ft

o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4Perforated interval/gas-sand thickness

Figure 9-19. Water-free gas rates for 2,500 psia. (after Trimbleand Rose, courtesy JPT, May 1977, © SPE)

Sobocinski and Cornelius Method of Predicting WaterConing Time*The breakthrough curve on Fig. 9-20 representsthose conditions at which a water cone that buildsfrom static conditions will break into the well whenit is produced at a constant and uninterrupted rate.The basic buildup curve traces the apex of the watercone before water breakthrough, while the departurecurves describe the rise of the apex as it approachesthe well. It is interesting to note that the slope ofthe departure curve increases as it approaches thebreakthrough curve. This means the rise of the coneapex accelerates as the apex nears the well.

The four departure curves shown were obtainedfrom a limited amount of laboratory data. Departurecurves for other breakthrough times can be locatedby interpolation. The basic buildup and departure

* Material from jPT, May 1965, © SPE.

50

:E 4.0OJ'ij;.r::

OJc 3.00

""'"'OJC0'u;cOJE'6N

Figure 9-20. Dimensionless cone height vs dimensionless t,-~(after Sobocinski and Cornelius, courtesy JPT, May 1965, © S==-

:·..;rvesapply only to coning situations for which break-::-crough conditions fall on Fig. 9-20 (i.e., if for Z at~reakthrough, tv is less than 7.5).

1. Using Eq. 9.11, calculate the dimensionless cone.-_eight for breakthrough to determine whether break-::-crough will occur within the limits of Fig. 9-20, and,-= it will, where the departure curve will lie.

:2. Find the dimensionless time, tv, that corresponds::: the calculated Z for breakthrough.

3. Using Eq. 9-12, calculate t, the actual time of~~eakthrough in days.

-t. Determine the cone height at any time before_~eakthrough by assuming a cone height less than:-.e breakthrough height, by calculating Z from Eq."-11, by determining the corresponding tv from the~:.sic buildup and appropriate departure curves, and:'::-;allyby solving Eq. 9-12 for time, t.

Z = 0.00307 b.p kh h he (9.11)!Joo qo Bo

.6..p= water-oil density difference, gm/cc}-Lo = oil viscosity, cpkh = single-phase, horizontal permeability, mdh = oil zone thickness, ft

he = height of the apex of the water cone abovethe average water-oil contact, ft

go = oil production rate STB/dBo = oil formation volume factor res bbl/STB

_ 0.00137 b.p kh (l + Mrljttv ----------

!Joo cj> h Fk

where:t = time, days

</> = porosityFk = horizontal-to-vertical permeability ratio, kh/k"M= water-oil mobility ratio = }-Lo (kw)or/}-Lw (ka)we

where (kw )or is the effective permeability to wa-ter at residual oil saturation and (ka )wc is theeffective permeability to oil at connate watersaturation

a=0.5 for .vl< 1; 0.6 for 1 < M< 10.

Richardson et al.'s Control of Coning by Injecting Fluids*-=-~leconing of gas can be controlled in part by injec-:: In of oil as shown in Fig. 9-21. Muskat and 'Wyckoffz:.ve the following equation for approximating the:-:-.a.ximumrate at which a well can produce oil without::,mng:

_ 0.0246 ko b.p (h~ - h~)qo re

!Joo In-rw

:-. which go is the oil production rate in barrels per:as. When a circular horizontal barrier is present,-:le radius of that barrier is substituted into Eq. 9.13: :,r rw and the distance from the barrier to the bottom: f the oil zone is substituted for lip. (For anisotropic':.nds, he can be replaced by hev k,,/kh.)

Conditions favorable for control of coning are (1):_lick, permeable sands containing low-viscosity oils:':1d (2) a barrier with as large a radius as possible.

From a practical viewpoint, the size of the barrier-III usually be limited either by the distance between: erforations or by the rate at which liquid is injected:: form the barrier. Within the above constraints, it, frequently possible to approximate the performance

: = a fluid barrier by assuming that it is a fixed horizon-

Figure 9-21. Model for coning control by injection. (after Richard-son et al., courtesy JPT, September 1971, © SPE)

tal barrier having a radius equal to .6..h and locatedjust above the perforated interval. The correspondingoil production reference rate is then calculated bysubstituting .6..hof Fig. 9-21 into Eq. 9.13 in placeof rw:

go =0.0246 ~ Li.p (h~e - h~)re

/La In Li.h

Production rates with and without fluid injection arethen calculated using Eqs. 9.13 and 9.14.* The differ-ence between these two rates can then be used as ameasure of the incremental production rate thatwould be possible with oil injection. This increasecan rarely be achieved without coning some gas, butthe increased gas production should not be serious.

~ = 1 darcy}-to = 2.31 cppo = 54.3 Ib/cu ftpg=5.73 Ib/cu fthe = 32 fthp = 8 ft

6.h= 32 ft

* If desired, the more accurate method of Chaney et al. can beused for the case with no injection and this critical rate can bemultiplied by the ratio (In re/rw)/(In re/6.h) to obtain a closer esti-mate for the reference rate with liquid injection.

re = 1,024 ftrw = 1 ft

In 1024/1 = 6.93In 1024/32 = 3.476.93/3.4 7 = 2.0

Oil is injected into the upper perforations as shoh:-.in Fig. 9-21.

To find how much oil production rates can be iL-creased above the critical coning rate by injection~:liquid, solve using Eq. 9.13. The limiting gas-free C':.

production rate possible without liquid injection IS

(0.0246)(1.0)(54.3 - 5.7)(322 - 82)g-o- 2.31lnC,~24)

= 72.0 bid

By injecting oil, a liquid barrier having an effecri-,c:-radius of about 32 ft can be formed. The corresponc..ing production rate is now calculated to be 144 b/eor twice the previous rate. Thus, the model predic-a production increase of 72 bid should be possib>o:with only a moderate increase in the net GaR, a:·though it is not possible, using this simple mode:alone, to predict how much the GaR will increase

Shell Method of Controlling Coning by Perforating BelowWater Level**Perforating wells completed in a thin zone underlainby a very active strong water drive below the gas-water contact can be beneficial, as illustrated by thecalculations and field tests made by engineers withShell Oil. A drawback of the method is the extraamount of water that must be produced before asteady state is reached-not only during the initialproduction phase, but also after shut-in periods. Theratios of improvement would obviously have to bemodified for cases where the permeability is not uni-form, especially where there are shale lenses or frac-tures.

Z.

h",_a0.5:

2 4 6 8 10 20Water a;.-car thickness hw

Oil layer thickness ho

Figure 9-22. Improvement of oil production rate by perforar:-;below instead of at the oil-water contact. (courtesy Shell Oil Compan;