Ali F. Mangi Alta’ee

Lesson Outcomes

To explain the reserve estimation by DCA.

To describe the three types of decline curves

To apply the decline curve analysis for reserve estimation

RESERVES ESTIMATION

"reserves" means different things to different people.

• To the banker

• the amount of capital retained to meet probable future

demands.

• To the oil and gas operator

• the volumes of crude oil, natural gas, and associated products that

can be recovered profitably in the future from subsurface reservoirs.

Reserves (SPE & World of Petroleum Congress 1987)

• those quantities of petroleum which are anticipated to be commercially

recovered & marketable from known accumulations from a given date forward.

Who are the people in the industry interested to know about

reserves?

companies and individuals responsible for E&P and

operation of oil and gas properties

buyers and sellers of oil and gas properties

banks and other financial institutions involved in the

financing exploration, development, or purchase of oil

and gas properties

agencies with regulatory or taxation authority over oil

and gas operators

investors in oil and gas companies

potential reserves on undrilled prospects

proved, probable, and possible reserves on prospects being

developed

sizing and design of equipment

· opportunities for additional profit from well stimulation

Why are we concerned about reserve estimation?

Oil and gas reserves form an oil company’s main assets! • It is very important to quantify forms of reserves.

• Quantifying of reserves is a complex problem!

• limited data

• varying interpretation

Reserve estimation

•It is an on-going activity during exploration, development

planning, and during production.

Classification of Reserves

Proven reserves

discovered reserves that can be estimated with reasonable

certainty to be recoverable under current economic conditions,

technical conditions and government regulations.

Unproven reserves

those reserves that are based on data similar to that used in the

estimation of proven reserves but technical, contractual, economic

or regulatory uncertainties prevent these reserves from being

classified as proven.

Proven reserves:

1. Developed reserves are expected to be recovered from existing

wells

2. Undeveloped reserves are to be recovered from new wells in

undrilled acreage, deepening wells to different reservoirs

Unproven reserves:

1. Probable reserves are those that have a reasonable probability of

production with technology and profitablity close to those exist today

2. Possible reserves are those that are not yet discovered, but whose

existence is presumed with reasonable degree of probability.

ULTIMATE RESERVES = proven + probable + possible.

Considerations for proven reserve:

• Where significant data are available, particularly fluid production and reservoir

pressure data, and the reservoir drive is known.

• Where production and reservoir data are limited but the reservoir is analogous to

reservoirs in the immediate vicinity and same geologic horizon.

•Where such data are of sufficient quantity and quality to have established the

reservoir drive mechanism

•Where production and reservoir data are limited, but the estimate is supported by

a calculation of the hydrocarbons in place by the volumetric method.

Considerations for probable or possible reserve:

• Where significant production data are available, but the reservoir drive

mechanism is uncertain or the magnitude of the reservoir drive is uncertain.

•Where production and reservoir data are limited and there are no analogus

reservoirs in the immediate vicinity.

•Where production and reservoir data are limited and the estimate is not

supported by volumetric determinations.

Reserve status categories:

1. Developed reserves are reserves expected to be

recovered from existing wells including reserves behind

pipe.

2. Producing reserves are reserves to be recovered from

completion intervals open at the time of estimate and

producing to market.

3. Nonproducing reserves include shut-in and behind-pipe

reserves.

• Shut-in reserves are expected to be recovered

completion intervals open at the time of the estimate,

but which have not started producing, or were shut in

for market conditions of pipeline connections, or were

not capable of production for mechanical reasons and

the time when sales start is uncertain.

• Behind-pipe reserves are expected to be recovered

from zones behind casing in existing wells, which will

require additional completion work or a future

recompletion prior to start of production.

3. Undeveloped reserves are reserves expected to be

recovered

• From new wells on undrilled acreage

• From deepening existing wells to a different reservoir

• Where a relatively large expenditure is required.

Reserve status categories:

1. Analogy

• Employ no specific well information/ before a

well is drilled.

• Least accurate

• Dependent on proximity of similar reserves

2. Volumetric calculations

• Well been drilled/ log analysis/ information

obtained/ drainage area

• Subsurface contour map

METHODS OF RESERVE ESTIMATION

3. Material Balance equation

• Enough information available/ FDP has been well

planned & executed

• Reservoir is assumed homogeneous

4. Model study/ Reservoir simulation

• apply MBE/ reservoir broken up into small parts or

discreet elements.

5. Decline Curve analysis methods

• Extrapolation of the trend in performance/ most

widely used.

METHODS OF RESERVE ESTIMATION

Decline Curve Analysis

• Decline curve analysis is a graphical procedure used for analyzing

declining production rates and forecasting future performance of oil

and gas wells.

•Decline curve analysis is a basic tool for estimating recoverable

reserves. Conventional or basic decline curve analysis can be used

only when the production history is long enough that a trend can be

identified.

•Decline curves represent production from the reservoir under

"boundary dominated flow" conditions. This means that during the

early life of a well, while it is still in "transient flow" and the reservoir

boundaries have not been reached, decline curves should NOT be

expected to be applicable

•Decline curve analysis is not grounded in

fundamental theory but is based on empirical

observations of production decline.

•Three types of decline curves have been identified;

exponential, hyperbolic, and harmonic

•It is implicitly assumed, when using decline curve

analysis, the factors causing the historical decline

continue unchanged during the forecast period.

These factors include both reservoir conditions and

operating conditions.

Decline Curve Analysis

Decline Curve Analysis

Reservoir Conditions Operating Conditions

pressure depletion,

number of producing wells,

drive mechanism,

reservoir characteristics,

saturation changes, and

relative permeability

separator pressure,

tubing size,

choke setting,

workovers,

compression,

operating hours, and

artificial lift

•Good engineering practice demands that, whenever possible, decline

curve analysis should be reconciled with other indicators of reserves,

such as volumetric calculations, material balance, and recovery factors.

•It should be noted that decline curve analysis results in an estimate of

Recoverable Hydrocarbons, and NOT in Hydrocarbons-in-Place.

•Whereas the Hydrocarbons-in-Place are fixed by nature, the

Recoverable hydrocarbons are affected by the operating conditions. For

example a well producing from a reservoir containing 1BCF of gas-in-

place may recover either 0.7 BCF or 0.9 BCF, depending on whether or

not there is a compressor connected at the wellhead.

Decline Curve Analysis

Decline Curve Analysis

The following "decline curves" from production wells

are commonly used in the DCA:

Production rate vs. time.

Production rate vs. cumulative oil production.

Water cut vs. cumulative oil production.

Gas-oil ratio vs. cumulative production.

Percentage oil production vs. cumulative oil

production.

The (p/z) ratio vs. cumulative gas production.

Decline Curve Analysis

Different ways of data representation for decline curve analysis

Graphical representations of production data

•The rate is constant during the early life of the well.

•Thereafter, as the reservoir pressure is reduced, the rate begins to

decline.

Number of years

before abandonment Cumulative production

at time of abandonment

Percentage of oil or water-cut vs Cumulative Production

• When the value of the oil produced = the cost of disposing of the

produced water, we have reached the point of abandonment.

• In situations where the ultimate production rate is controlled by the

amount of water production.

• Reserves: the total production at the time of abandonment

•In bottom-water drive fields, we might plot the location of the oil-

water contact in the formation against cumulative oil production.

•Reserve: cumulative production when OWC reaches to the top of the

oil sand

OWC vs Cumulative Production

•As the OWC reaches the top of the sand, we know that we have

recovered the crude reserves for this well

•This plot is useful in cases where we know the expected total

gas to be produced.

Gp vs. Cumulative Oil Produced, Np

• Oil Reserve corresponds to the cut-off point of expected Gp

•This information provides an indication as to when the well will

reach its abandonment point.

Average Reservoir pressure, Pavg, vs Time

• Pressure build-up tests or observation well data are used for this plot.

Pavg, over the compressibility factor, z, vs. Gp

• The relationship is from the application of the gas law to a fixed volume

container & Material Balance Equation (MBE).

•The minimum producing rate is determined by the back-pressure

imposed on the well with or without surface compression.

•When the value or this limiting back-pressure is converted to a

value or average reservoir pressure, Pavg, divided by z and plotted

against cumulative production,

•An estimate of the ultimate predicable gas reserves may be

obtained

• Production rate is by far the most popular dependent

• It has the advantage of being readily available and easily

recorded.

• The production rate curves normally show a fairly smoothly

declining trend over extended periods when no major changes in

operating procedures are made and no stimulation treatments are

applied.

• The economic limit production rate

•When a production rate at which a well or field begins to lose

money if production continues. If we incorporate this value into

our rate versus time and rate versus cumulative production

curves, we can extrapolate each trend line to this cut-off point.

•We can determine the number of years the well or field will

produce profitably and the cumulative production at the time of

abandonment.

Relates production time

1. Exponential Production Decline

2. Hyperbolic Production Decline

3. Harmonic Production Decline

DECLINE CURVE ANALYSIS

Nearly all conventional decline-curve analysis is based on empirical

relationships of production rate versus time, given by Arps (1945) as

follows:

Where

qt = production rate at time t

qi = initial production rate stb/day

t = time, days

Di = initial decline rate, day −1

b = Arps’ decline-curve exponent

Exponential Decline

- the simplest type also known as constant percentage decline

q = qi e-Dt

where,

q producing rate at time t

qi initial rate, stb/day

D nominal decline fraction, 1/day

t time, days

Time

Lo

g R

ate

Production rate as a function of time: exponential decline

DECLINE CURVE ANALYSIS (cont’d)

1. Exponential decline

time not necessarily expressed in “day”. Any unit is

acceptable provided that other units must be consistent.

Conversion to other units can be done:

D1t1 = D2t2

note!!!: “Dt” term must be dimensionless

Re-expressing the Exponential Decline Curve in terms of

nominal decline fraction, D or time, t

q = qi e-Dt (1)

D = -[ln(q/qi)]/t (2)

t = -[ln(q/qi)]/D (3)

Exponential decline

Cumulative production, Np is defined as the integral from 0

t of qdt

t

qdt0

Np = (4)

= (qi - q)/D

Equation (4) can also be used to determine the nominal

decline fraction, D from the given production data.

D = (qi - q)/ Np (5)

Example 1

A well is expected to produce 70 Mstb recoverable reserves

and will be on exponential decline. The initial rate is estimated

to be 100 stb/day and the abandonment rate in this region is 5

stb/day. How long will the well last? Determine its annual

production.

Solution

q = qi e-Dt or t = -[ln(q/qi)] /D

given: Np = 70,000 stb and q = 5 stb, therefore need to find D?

D = (qi - q)/ Np = (100 - 5)stb per day / 70,000 stb = 0.001357 /day

D1t1 = D2t2

D1 = [D2t2]/t1

= (0.001357 per day)(365 days)/(1 year)

= 0.4954 per year

t = -[ln(q/qi)] /D = - [ln(5/100)]/ 0.4954 = 6.05 years

Annual Productions: exponential decline

Time Rate

(year) (stb/day) Cumulative Annual

(stb) (stb)

0 100.00 0 0

1 60.93 28,789 28,789

2 37.13 46,332 17,542

3 22.62 57,021 10,689

4 13.78 63,534 6,513

5 8.40 67,502 3,969

6 5.12 69,920 2,418

6.05 4.99 70,013 92

Production

100 [e(-0.4954 x 1)] [100-60.93]/ 0.001357 =28,789 - 0

2. Hyperbolic Decline

predicts a longer well life than is predicted by the exponential

decline model.

where,

b hyperbolic exponent . The value ranges from 0 to 1

Di initial nominal decline fraction, 1/time

Expressing in terms of other variables

Di = [(qi/q - 1]/(bt)

t = [(qi/q)b - 1] /(Dib)

integration of Di to obtain cumulative oil production

Di = {qib/[(1 - b) Np]} [qi

1-b - q1-b]

q = qi

[1 + bDit]1/b

integration of Di to obtain cumulative oil production

Np = {qib/[(1 - b) Di]} [qi

1-b - q1-b]

or expressing initial decline fraction in terms of Np.

Di = {qib/[(1 - b) Np]} [qi

1-b - q1-b]

Example 2

A well is expected to produce 70 Mstb recoverable reserves and

will be on hyperbolic decline with an exponent of 0.5. The initial

rate is estimated to be 100 stb/day and the abandonment rate in

this region is 5 stb/day. How long will the well last? Determine its

annual production.

Solution

Di = {qib/[(1 - b) Np]} [qi

1-b - q1-b]

={1000.5/[(1 - 0.5)(70,000)]} {1001 - 0.5 - - 51 - 0.5}

= 0.002218/day

= 0.8097/year

t = [(qi/q)b - 1] /(Dib)

= [(100/5)0.5 - 1] / [(0.8097)(0.5)] = 8.576 year

Time Rate

(year) (stb/day) Cumulative Annual

(stb) (stb)

0 100.00 0 0

1 50.67 25,983 25,983

2 30.54 40,341 14,358

3 20.39 49,450 9,109

4 14.58 55,743 6,293

5 10.94 60,352 4,609

6 8.51 63,872 3,520

7 6.80 66,649 2,777

8 5.57 68,896 2,247

8.576 5.00 70,005 1,109

Production

Annual Productions: hyperbolic decline

=100/ [(1 + 0.5(0.002218)(1)(365)](-1/0.5)

[(1000.5)/((1- 0.5)0.002218)] [(100(1-0.5) - 50.67(1-

0.5)]

3. Harmonic Decline

uncommon

predict longer time for recovery (i.e than exponential or

hyperbolic)

a special case of hyperbolic decline (exponent, b = 1)

q =

qi

[1 + Dit]

Np =

qi

Di

ln q

qi

Di =

qi

Np

ln q

qi

t = - 1 q

qi

Di

Cumulative Production,

(Integration of rate, q)

Initial Decline Fraction,

Flow rate, Time,

(production)

Example 3

A well is expected to produce 70 Mstb recoverable reserves

and will be on harmonic decline. The initial rate is estimated to

be 100 stb/day and the abandonment rate in this region is 5

stb/day. How long will the well last? Determine its annual

production.

Solution

Di =

qi

Np

ln q

qi

= (100 / 70,00) ln (100/5)

= 0.004280 per day

= 1.56 per year

t = - 1 q

qi

Di

= [(100 / 5) - 1 ]/1.56

= 12.16 year

Time Rate

(year) (stb/day) Cumulative Annual

(stb) (stb)

0 100.00 0 0

1 39.06 21,963 21,963

2 24.27 33,081 11,118

3 17.61 40,583 7,502

4 13.81 46,253 5,670

5 11.36 50,812 4,559

6 9.65 54,625 3,813

7 8.39 57,902 3,277

8 7.42 60,776 2,874

9 6.65 63,334 2,559

10 6.02 65,640 2,306

11 5.51 67,739 2,099

12 5.07 69,664 1,926

12.16 5.01 69,958 294

Production

100/[1 + (1.56)(1)]

Annual Productions: harmonic decline

=[100/0.00428] x ln(100/39.06)

Exponential, Hyperbolic and Harmonic Decline

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

exponential

hyperbolic

harmonic