Water and Gas Coning

Coning is a term used to describe the mechanism underlying the upward

movement of water and/or the down movement of gas into the
perforations of a producing well. Coning can seriously impact the well
productivity and influence the degree of depletion and the overall
recovery efficiency of the oil reservoirs. The specific problems of water
and gas coning are listed below.

1- Costly added water and gas handling.

2- Reduced efficiency of the depletion mechanism.
3- The water is often corrosive and its disposal costly.
4- Loss of the total field overall recovery.

Delaying the encroachment and production of gas and water are

essentially the controlling factors in maximizing the field’s ultimate oil
recovery.

Coning primarily the result of movement of reservoir fluids in the

direction of least resistance, balanced by a tendency of the fluids to
maintain gravity equilibrium. The analysis may be made with respect to

either gas or water. Let the original condition of reservoir fluids exist as
shown schematically in figure (1-26), water underlying oil and gas
overlying oil.
 Figure (1-26), Original reservoir static condition

Production from the well would create pressure gradients that tend
to lower the gas-oil contact and elevate the water-oil contact in the
immediate vicinity of the well. Counterbalancing these flow gradients is
the tendency of the gas to remain above the oil zone because of its lower
density and of the water to remain below the oil zone because of its
higher density. These counterbalancing forces tend to deform the gas-oil
and water-oil contacts into a bell or cone shape as shown schematically in
figure (1-27).

Figure (1-27), Gas and Water coning

There are essentially three forces that may affect fluid flow
distributions a round the well-bores. These are:

1- Capillary forces.
2- Gravity forces.
3- Viscous forces.
Capillary forces usually have negligible effect on coning and will be
neglected. Gravity forces are directed in the vertical direction and arise
from fluid density difference.

Viscous forces refer to the pressure gradients associated fluid flow

through the reservoir as described by Darcy’s law. Therefore, at any
given time, there is a balance between gravitational and viscous forces at
points on and away from the well completion interval. When the dynamic
(viscous) forces at the well-bore exceed gravitational forces, a “cone”
will ultimately break into the well.

We can expand on the above basic visualization of coning by introducing

the concept of:

- Stable cone.
- Unstable cone
- Critical production rate.
If a well is produced at a constant rate and the pressure gradients in the
drainage system have become constant, a steady-state condition is
reached. If at this condition the dynamic forces at the well are less than
the gravity forces, then the water or gas cone that has formed will not
extend to the well. Moreover, the cone will neither advance nor recede,
thus establishing what is known as a stable cone. Conversely, if the
pressure in the system is an unsteady-state condition, then an unstable
cone will continue to advance until steady-state conditions prevail.

The critical production rate is the rate above which the flowing
pressure gradient at the well causes water (or gas) to cone into the well. It
is, therefore, the maximum rate of oil production without concurrent
production of the displacing phase by coning. At the critical rate, the
built-up cone is stable but is at a position of incipient breakthrough.

Defining the conditions for achieving the maximum water-free and/or

gas-free oil production rate is a difficult problem to solve. Engineers are
frequently faced with the following specific problems:

1- Predicting the maximum flow rate that can be assigned to a completed

well without the simultaneous production of water and/or free-gas.
2- Defining the optimum length and position of the interval to be
perforated in a well in order to obtain the maximum water and gas-
free production rate.
Critical rate Qoc is defined as the maximum allowable oil flow rate that
can be imposed on the well to avoid a cone breakthrough. The critical rate
would correspond to the development of a stable cone to an elevation just
below the bottom of the perforated interval in an oil-water system or to an
elevation just above the top of the perforated interval in a gas-oil system.

There are several empirical correlations that are commonly used to

predict the oil critical rate, including the correlations of:

1- Meyer and Gardner and Pirson Methods.

2- Craft and Hawkins Method.
3- Chaney Et AL. Method

1- Meyer and Gardner and Pirson Methods

Meyer, Gardner, and Pirson suggest that coning development is a

result of the radial flow of the oil and associated pressure sink around the
well-bore. In their derivations, Meyer, Gardner, and Pirson assume a
homogeneous system with a uniform permeability throughout the
reservoir, i.e., kh = kv. It should be pointed out that the ratio kh/kv is the
most critical term in evaluating and solving the coning problem. They
developed three separate correlations for determining the critical oil flow
rate:

- Gas coning
- Water coning
- Combined gas and water coning.

Gas coning

Consider the schematic illustration of the gas-coning problem shown

in figure (1-28).Meyer, Gardner, and Pirson correlated the critical oil
rate required to achieve a stable gas cone with the following well
penetration and fluid parameters:

- Difference in the oil and gas density.

- Depth Dt from the original gas-oil contact to the top of the
perforations.
- The oil column thickness h.
The well perforated interval h, in a gas-oil system, is essentially defined
as:

h=h–D

Figure (1-28), Gas coning

Meyer, Gardner, and Pirson propose the following expression for

determining the oil critical flow rate in a gas-oil system:

Summary of assumptions for gas-oil system:

1- Capillary forces usually have negligible effect on coning and

will be neglected.

2- No gas drive, that means GOR remain constant.

Ф = Potential = H

For any point, calculate H

Ф = gz + (Pg – Patm)/ ρgas …….. (1)

Ф = H*g → H = Ф/g

Hgas = z + Pg / (ρgas *g) ………. (2)

Hoil = z + Po / (ρoil *g) ………..(3)

Since Pc = zero i.e., Po = Pg (where Pc = Pg-Po = zero)

& Hg = constant (i.e., no gas drive).

For eg.(2) , solving for Pg →

(Hg – z) * ρg *g = Pg ..........(2-a)

& also eq.(3) becomes:-

(Ho – z) * ρo * g = Po ………(3-a)

Since Pc = zero → Po = Pg

Then eq.(2-a) = eq.(3-a)

(Hg – z ) ρg * g = (Ho – z) ρo * g ……….(4)

Solve eq. (4) for Ho

Ho = Hg * (ρg/ρo) + z [(ρo – ρg)/ρo] ……. (5)

Constant

Derivative equation (5) respect to Ho

dHo = [(ρo-ρg)/ρo] dz …….(6)

Darcy`s law Q = k A ΔP / μ L (for linear flow)'

Solving for oil flow:

Q → Qo

k → ko

L → dr

μ → μo

Radial area ↔ A = 2πrz

 z r

ΔP = ρo g dHo

Where P = ρ g H

Then Darcy's law →

Qo = 2π ρo g (ko/μo) z r (dHo/dr) ……. (7)

Substitute the value of (dHo) [i.e. eg.(6) in eq.(7)]

For radial flow

Qo = 2π (ρo – ρg) g (ko/μo) z r (dz/dr)

h
………. (8)

re ∫
(h-D)

∫
Qo max = r dr/r = 2π (ρo-ρg) g (ko/μo) z r z dz ……….. (9)
w

Qo max = π g [(ρo-ρg) / ln (re / rw)] (ko/μo) [h2 – (h-D)2]

…..(10)

Or in field units

Qo max = 0.001535 [(ρo-ρg)/ln(re/rw)] (ko/μoBo) [h2- (h-Dt)2] …(11)

Qo max = maximum oil production rata without gas coning (critical

rate), STB/day
ρo = oil density, gram/ cm³

ρg = gas density, gram/ cm³

re = drainage area radius, ft

rw= well-bore radius, ft

ko = oil permeability, md

μo = oil viscosity, cp

Bo = oil formation volume factor, bbl/STTB

h = thickness of oil zone (producing zone), ft

Dt = Depth from the original gas-oil contact to the top of the perforations,
ft

hp = Completion interval (Perforated interval), ft.

Example (1-1):

A vertical well is drilled in an oil reservoir overlaid by a gas cap.

The related well and reservoir data are given below:

Horizontal and vertical permeability, i.e., kh = kv = 110 md

Oil relative permeability, kro = 0.85

Oil density, ρo = 47.5 lb/ft³

Gas density, ρg = 5.1 lb/ft³

Oil viscosity, µo = 0.73 cp

Oil formation volume factor, Bo = 1.1 bbl/day

Oil column thickness, h = 40 ft

Perforated interval, hp = 15 ft

Depth from GOC to top of perforations, Dt = 25 ft

Well-bore radius, rw = 0.5 ft

Drainage radius, re = 660 ft

Using Meyer, Gardner, and Pirson relationships, calculate the critical

oil flow rate.

Solution

The critical oil flow rate for this gas-coning problem can be
determined by applying equation (11). The following two steps
summarize Meyer, Gardner, and Pirson methodology.

Step 1. calculate effective oil permeability, ko

ko = kro k = 0.85 * 110 = 93.5 md

Step 2. solve for Qoc by applying equation (11)

Qoc=Qo max=0.001535[((47.5/62.4)-
(5.1/62.4))/ln(660/0.25)](93.5/073*1.1) [402-(40-25)2]

Qoc=Qo max= 21.20 STB/day

Water Coning

Meyer, Gardner, and Pirson proposed a similar expression for

determining the critical oil rate in the water coning system shown
schematically in figure (1-29).

The proposed relationship has the following form:

Qo max = 0.001535 [(ρw-ρo)/ln(re/rw)] (ko/μoBo) [h2- -hp2] …(12)

 Figure (1-29), Water coning

Where:

ρw = water density, gram/ cm³

Db = Depth from the original water-oil contact to the bottom of the

perforations, ft

Example (1-2):

Resolve example (1-1) assuming that the oil zone is underlaid by

bottom water. The water density is given as 63.76 lb/ft. the well
completion interval is 15 ft as measured from the top of the
formation (no gas cap) to the bottom of the perforations.

Solution:

The critical oil flow rate for this water-coning problem can be
estimated by applying equation (12). The equation is designed to
determine the critical rate at which the water cone “touches” the
bottom of the well to give.

Qo max = 0.001535 [((63.76/62.4)-(47.5/62.4))/ ln(660/0.25)]

(93.5/0.73*1.1) [402- -152]

Qo max = 8.13 STB/day

Simultaneous Gas and Water coning

If the effective oil-pay thickness h is comprised between a gas cap

and a water zone (figure 1-30), the completion interval hp must be such as
to permit maximum oil-production rate without having gas and water
simultaneously produced by coning, gas breaking through at the top of
the interval and water at the bottom.

This case is of particular interest in the production from a thin

column underlaid by bottom water and overlaid by gas.

 Figure (1-30), The development of Gas and Water coning

For this combined gas and water coning, Pirson (1977) combined
equation (11) and (12) to produce the following simplified expression for
determining the maximum oil-flow rate without gas and water coning:

Qomax = Qow + Qog …. (13)

Qomax=0.001535(ko/μoBo)[(h2-hp2)/(ln(re/rw)]
[(ρw-ρo)((ρo-ρg)/(ρw-ρg))2+(ρo-ρg)(1-((ρo-ρg)/(ρw-ρg)))2 ]
….(14)
Example (1-3):

A vertical well is drilled in an oil reservoir that is overlaid by a gas

cap and underlaid by bottom water. Figure (1-31) shows an illustration of
the simultaneous gas and water coning.

Figure (1-31), Gas and Water coning problem (example, 1-3)

The following data are available:

Horizontal and vertical permeability, i.e., kh = kv = 110 md

Oil relative permeability, kro = 0.85

Oil effective permeability, ko = 93.5 md

Oil density, ρo = 47.5 lb/ft³

Water density, ρw= 63.76 lb/ft³

Gas density, ρg = 5.1 lb/ft³

Oil viscosity, µo = 0.73 cp

Oil formation volume factor, FVF, Bo = 1.1 bbl/day

Oil column thickness, h = 65 ft

Perforated interval, hp = 15 ft

Depth from GOC to top of perforations, Dt = 25 ft

Well-bore radius, rw = 0.5 ft

Drainage radius, re = 660 ft

Calculate the maximum permissible oil rate that can be imposed to avoid
cones breakthrough, i.e., water and gas coning.

Solution:

Apply equation (14) to solve for the simultaneous gas-and water

coning problem, to give:

Qomax =0.001535(93.5/0.73*1.1)[(652-152)/(ln(660/0.25)]
[((63.76/62.4)-(47.5/62.4))(((47.5/62.4)-(5.1/62.4))/((63.76/62.4)-
(5.1/62.4)))2+((47.5/62.4)-(5.1/62.4))(1-(((47.5/62.4)-
(5.1/62.4))/((63.76/62.4)-(5.1/62.4))))2 ]

Qomax = 17.1 STB/day

 Pirson derives a relationship for determining the optimum
placement of the desired hp feet of perforation in an oil zone with a gas
cap above and a water zone below. Pirson proposes that the optimum
distance Dt from the GOC to the top of the perforations can determined
from the following expressed:

Dt = (h – hp ) [ 1- ρo – ρg ] …..(15)

Ρw – ρg

Where the distance Dt is expressed in feet.

Example (1-4):

Using the data given in example (1-3), calculate the optimum

distance for the placement of the 15 foot perforations.

Solution:

Applying equation (15) gives:

Dt = (65 – 15 ) [ 1- 47.5 – 5.1 ] = 13.9 ft

63.76 – 5.1
Craft and Hawkins Method

In this method, the following empirical equation used to calculate

critical oil flow rate without water coning:

Qomax = 0.00708*((koh)/(μoBo))*((Pws-Pwf)/(ln(re/rw))*(PR) …(16)

PR = f [ 1+(7)*(rw/(2fh))½ * cos(f * 90º) ] ……(17)

Where:

PR = Productivity ratio

Pws = Static well pressure correct to middle of perforated interval (psi)

Pwf = Flowing well pressure at the middle of perforated interval (psi)

f = Partial penetration (hc/h)

ko = Oil permeability (md)

h = thickness of producing interval (ft)

ΔPmax = Maximum draw down pressure without water coning.

ΔPmax = 0.433 (ρw-ρo) Δhmax

Δhmax = Vertical distance between lower perforated interval and initial

oil water contact.

Example (1-5)

From this data:

(ρw-ρo) = 0.48 gm/cm³, ko = 1500 md, h = 16 ft, μo = 0.3 cp, Bo = 1.4

RB/STB, re = 1000 ft, rw = 0.25 ft, (Pws-Pwf) = 17 psi, f = 0.3125
(perforated upper part of oil production interval by 31.25 percent).

Calculate maximum production rate without water coning.

Solution:

From eq. (17) calculate (PR)

PR = 0.3125 [1+(7)*((0.25)/(2*0.3125*16))½ * cos(0.3125*90) ]

PR = 0.618

Then from eq. (16)

Qomax = 0.00708*((1500*16)/(0.3*1.4))*((17)/(ln(1000/0.25))*(0.618)

Qomax = 512 STB/DAY

Qomax must be reducing below 512 STB/DAY because maximum

flowing pressure drops without water coning equal:

ΔPmax = 0.433 * (0.48) *11

ΔPmax = 2.29 psi.

Chaney Et AL. Method

Chaney et al. (1956) developed a set of working curves for

determining oil critical flow rate. The authors proposed a set of working
graphs that were generated by using a potentiometric analyzer study and
applying the water coning mathematical theory.

The graphs, as shown in figures (1-32) through (1-36), were

generated using the following fluid and sand characteristics:

Drainage radius re = 1000 ft

Well-bore radius rw = 3 inch

Oil column thickness h = 12.5, 25, 50, 75 and 100 ft

Permeability k = 1000 md

Oil viscosity µo = 1 cp

ρw – ρo = 18.72 lb/ft³

ρo – ρg = 37.44 lb/ft³

The graphs are designed to determine the critical flow rate in oil-
water, gas-oil, and gas-water systems with fluid and rock properties as
listed above. The hypothetical rates as determined from the Chaney et al.
curves (designated as Qcurve), are corrected to account for the actual
reservoir rock and fluid properties by applying the following expressions:

In oil-water systems

Qoc = 0.5288 * 10-4 [ ko (ρw – ρo) ] Qcurve

µo Bo

In gas-water systems

Qgc = 0.5288 * 10-4 [ kg (ρw – ρg) ] Qcurve

µg Bg

In gas-oil systems

Qoc = 0.2676 * 10-4 [ ko (ρo – ρg) ] Qcurve

µo Bo

Where:
ρo = oil density, lb/ft³

ρw= water density, lb/ft³

ρg = gas density, lb/ft³

Qoc = critical oil flow rate, STB/day

ko = effective oil permeability, md

Bo = oil FVF, bbl/STB

Qgc = critical gas flow rate, Mscf/day

Bg = gas FVF, bbl/Mscf

Kg = effective gas permeability, md

Figure (1-32)
Figure (1-33)
Figure (1-33)
Figure (1-35)
Figure (1-36)
 Example (1-6)

In an oil-water system, the following fluid and sand data are

available:

Effective Oil permeability, ko = 93.5 md

Oil density, ρo = 47.5 lb/ft³

Water density, ρw = 63.76 lb/ft³

Oil viscosity, µo = 0.73 cp

Oil formation volume factor, Bo = 1.1 bbl/day

Oil column thickness, h = 50 ft

Perforated interval, hp = 15 ft

Well-bore radius, rw = 3 inch

Drainage radius, re = 1000 ft

Calculate the oil critical rate

Solution:

Step 1. Distance from the top of the perforations to top of the sand = 0

Step 2. Using figure (), for h = 50 ft, enter the graph with 0 and move
vertically to curve C to give”

Qcurve = 270 bbl/day

Step 3. Calculate critical oil rate from equation of oil-water system:

Qoc = 0.5288 * 10-4 [ 93.5 (63.76 – 47.5) ] * 270 = 27 STB/day.

1.1* 0.73

It should be pointed out that Chany`s method was developed for a

homogeneous, isotropic reservoir with kh = kv.