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Aspects of Gas Deliverability

ABSTRACT

WILLIAM HURST

WILLIAM

C GOODSON

RUSSelL

E

LEESER

MEMBERS AIME

Three aspects

of

gas deliverability are presented in this

paper.

The

first treats with the gas deliverability or avail

ability of a normal depletion-type dry gas field. Such

encompasses

not

only the period of stabilized constant

rate,

but

more

so, the tailings when a fixed abandon

ment

pressure is reached and the rate by necessity must

decline. A comprehensive work plot is offered, developed

from mathematics herein included, that removes the tria -

and-err r computatiol1S that attended such undertakings in

the past.

The second part treats with the discount factor of the

open flow potential constant from what is observed initially

in testing a gas well to what is evidenced when stabilization

is reached. This prevails in tight formations, such as the

Kansas Hugoton field which is offered as the example.

The means of establishing this factor are pressure build-up

curves which, as sustained by analytical deductions, repro

duce this entire period of transient flow under conditions

of a constant rate inflUX

Finally,

what

is offered in this paper

is

the deliverability

performance of an exceedingly rich gas condensate field

producing from a tight formation. The example shown is

the

nox

Bromide field in Oklahoma, producing from

the Bromide formations. The results are ominous, showing

early reduction in permeability to gas flow, due to the

retrograde condensate forming in the pore space, with

the attending early logging-up of these wells. The analytics

of lowered permeability are incorporated in the gas deliv

erability formula along with the PVT data that gives the

increased condensate liquid saturation as the gas flows to

the wellbore.

This paper would

not

be complete without a critique

offered at the end. With the

many

gas wells now in pro

duction

and

those that have completed their life, there has

been no factual information collected by any source as to

what constitutes that permeability range where a gas well

would be unimpaired in its gas deliverability by the pres

ence of rich condensate content,

and

the lowered range

where such would be harmful. This question confronts all

producers.

INTRODUCTION

Various aspects of gas deliverability are presented in

this paper that includes depletion-type reservoirs, deteriora-

Original manuscript received in Society of Petroleum Engineers office

Feb.

6, 1962.

Revised

manuscript

received

Jan. 24, 1963. Paper pr.e

sented

a t

Economics

and

Valuation Symposium, March

15-16, 1962,

In

Dallas,

Tex.

':'Now partner

in

Fraser, Goodson and

Willits, Dallas, Tex.

668

SPE 262

PETROLEUM CONSULTANT

HOUSTON TEX

REPUBLIC

NATURAL GAS

CO

DALLAS TEX

THE BRITISHAMERICAN OIL PRODUCING CO

DALLAS TEX

tion factor of the gas deliver ability

c o n s t a ~ t

and he

performance of a rich gas condensate reservOir producmg

from a tight sand. .

With respect to the presentation of gas

d e h v ~ r a b h t y

and its tailings for depletion-type gas ~ e s e r v O l r s one

notes that this is essentially the informatIOn offered .by

every gas transmission company and producer appearmg

before the Federal Power Commission for Letters of

Conveyance in the dedication of reserves. .

In

the ordinary procedure, as many engage upon t ~ I S

study, trial-and-error calculations are included, partic

ularly as apply to the tailings. For. many years one of

the writers has employed mathematical analyses to. per

form this step and avoid the complexities so assocIated.

In the preparation of this paper these analyses have been

amplified to include any slope n f o ~ . the open flow

potential relationship for which the taIlmgs can be de

termined from Fig. 1.

With reference to the deterioration

or

discount factor

of the open flow potential constant as such occurs in the

gas deliverability formula, this for the .most part has been

an unexplored subject. Although the Issue first a p p e ~ r e d

in the Kansas Hugoton field, where such was s u r m l ~ e d

but

only recently resolved, this situation of a deterioratIOn

of the gas deliverability constant

can

occur wherever dry

gas production from a tight sand is encountered.

The first concerted attacks upon this problem were the

presentations of Hurst' and Goodson' b e f o ~ e the ~ a n s a s

Corporation Commission to show that .translent. flUId flow

and unsteady-state flow formulas prevaIled. ThiS. ,:as .am

plified later before the Federal Power C?mm.lssIOn to

show that this deterioration factor could be IdentIfied from

pressure build-up curves. This has. been r e p o r ~ e d by

McMahon.' Its importance to the mdustry merIts the

review of these essential features in completing the pro

gram

on

the aspects of gas deliverability.

Finally, as illustrated here, for a low permeability for

mation such as the Knox Bromide field where the gas

is rich representing some 165 bbl of condensate

per

MMcf

'of

effluent gas, the gas deliver ability can be .of

limited extent in the life of the field, leaving substantial

amounts of condensate and gas unrecovered.

In

cases such

as this, gas cycling is mandatory. This is particularly e-

vealed by the fluid mechanics introduced here, employm.g

factual field as well as laboratory data, to show thiS

restriction upon gas deliverability.

PRESSURE DEPLETION

What will now be offered

is

the study

of

gas deliver-

lReferences given at end of

paper,

JOURN L OF PETROLEUM TECHNOLOGY

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ability or availability for a normal pressure depletion-type

dry gas reservoir.

Not

only is such information presented

before the Federal Power Commission, but it is of equal

importance in the evaluation of property in observing

yearly incomes.

In connection with such presentations, contractual agree

ments often stipulate that gas will be sold on a ratio

of

1 :8, meaning that 1 MMcf of gas will be produced each

day for every 8 billion cu ft of recoverable reserves ini

tially in place. This

is

usually to encompass a 20-year

period. Although this exact ratio is 1 :7,300, the use of

the smaller ratio is to include the tailings that represent

the decline in rate of gas production when a fixed BHP

is reached, or its abandonment pressure, that all told will

approximate this 20-year period.

With respect to the stabilized rate of gas production

over most of this time, no particular problem is involved,

as such is straight numerical calculations, contingent on

the accuracy of the reserves and the open flow potentials.

However, when the tailings are encountered with the

decline in the rate of gas production, problems do arise.

To

determine these production increments many use a

trial-and-error procedure, in which a rate is assumed

over one of the declining years; and such must be bal

anced by the total gas that could have been produced for

that year as evidenced by the decline in formation pressure

to reflect the corresponding pressure in the open flow

potential relationship to yield the rate involved.

Such is time consuming.

For

this reason a mathematical

procedure, based

on

the calculus, has been employed for

many years that automatically takes into account the

decline in formation pressure as represented by the mate

rial balance equation, and the lowering in rate incurred

as

associated with the open flow potential relationship.

With this paper in the offering, it was suggested that

this method be amplified to include any slope for the

open flow potential curve. Such is incorporated in the

graphical presentation shown in Fig. 1, and a brief de

scription of the analytics with a factual example follow.

With respect to any pressure depletion study treating

with the deliverability of gas, two basic equations are

involved; namely, the material balance of the gas voided

from the reservoir with its resulting reduction in formation

pressure, and the open flow potential relationship that

relates rate of gas production.

0.60

0.50

r f

PS/Pf,n)

\

/

/

V

/

I'

/ / ./

~ / v /

V

/

/

r

V

V

"

c

,%' ; ' "c Cc

/

/ i ~ < r

1

7

I

o ~

V I

~ ~ ~

I

I n=0.80 I---

--

....

~

~

t:::=

0

::::::::::

=

.......::::

0.40

0.30

0.20

0.10

o

1 0

0.5

0

In its simplest form, the material balance equation can

be

stated as

G p, - PF)

=

G

( I )

Pi

P

where G is the gas originally in place corrected to standard

conditions, and G

p

is the cumulative gas produced. The

pressures so identified are the initial pressure p with the

resulting formation pressure

PF,

for the voidage so in

curred. Where gas deviation factors are involved such will

be related for the conditions specified.

The second of these relationships is open flow potential

expressed as

qg =

C p/

-

Ps')

2)

which is determined from the plotting of p/ - Ps , abso

lute pressure squared difference of the prevailing forma

tion pressure and the flowing BHP PH vs the rate

of

gas

production expressed in MMcf/D, performed on a log-log

graph. The slope of n, which many consider for practical

purposes

as

equal to unity, is here specifically identified as

revealed by this plotting.

To proceed, the differentiation

of

Eq. 1, with respect to

time

t

in days, yields

G

dpF

dG

p

~ ~ - 3)

Pi dt dt

where the term on the right is nothing else but the open

flow potential for a single well, represented by Eq. 2,

but now multiplied by v the number

of

wells involved

in producing the field. This is expressed by the relation

ship

G dpF

C(

')

~ d =V P F P S .

p, t

(4)

and collecting those terms that will be manifested as

variables when a fixed abandonment bottom-hole flowing

pressure Ps is reached, give

- dp

vCp,dt

(p., - Ps')

-G--

5)

To recapitulate, while the field is producing at a stabil

ized or constant rate, both the formation pressure P. and

flowing BHP ps will decline as expressed by Eqs. 1 and 2.

However, when this fixed abandonment pressure

Ps

is

reached, still expressed in this symbolism

as

not to become

too involved in terminology, the lowered formation pres

sure

PFD

can be calculated that will still yield this stabil-

00

/

f PS/Pf,n) rl1

3

50

I

I

3

I

I

2

I

I

~ I ~

2

I

,

--

:::

8

r-

-:-::-=-t

i

--

n

=0.90J'l,. _

: : ~

~

I.

~ ~

.--

-

..-;:::.

I.

t:: :

: : : c

F---

-

00

50

00

50

00

n = 0.95 n = .00

O

50

0

o 0.05 0 10 0 15 0.20 0.25 0.30 0.35 0.40 0 45 0.50

0 55

0.60 0.65 0.70 0 75 0.80 0.85 0.90 0 95 1 00

P

s

I P

F

,

RATIO FLOWING

WELL

TO

FORMATION PRESSURE

VIr..

J-DEG. lNE

IN

GAS

DELIVERABlLITY WITH TIME.

JIJNIi , L963

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ized rate as expressed through Eq.

2.

This introduced in

1, gives the cumulative gas

G >

that will be produced

over this period

of

stabilization, which in turn divided by

this fixed rate for all producing wells gives that time

tn

that the tailings will start to occur.

Thus the introduction

of these limits in Eq. 5, yield

I

iF ,d

p

,

=vCp; t - t

n

).

6)

iF (PI'

- p, ) G

wherc

p