7. Decline Curve Analysis

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

Why are we concerned about reserve estimation? 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 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.

Reserve status categories: 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.

METHODS OF RESERVE ESTIMATION 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.

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 •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 Reservoir Conditions

Operating Conditions

 pressure depletion,

 separator pressure,

 number of producing wells,

 tubing size,

 drive mechanism,

 choke setting,

 reservoir characteristics,

 workovers,

 saturation changes, and

 compression,

 relative permeability

 operating hours, and  artificial lift

Decline Curve Analysis •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-inplace 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 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

• In situations where the ultimate production rate is controlled by the amount of water production. • When the value of the oil produced = the cost of disposing of the produced water, we have reached the point of abandonment.

• Reserves: the total production at the time of abandonment

OWC vs Cumulative Production •In bottom-water drive fields, we might plot the location of the oilwater contact in the formation against cumulative oil production. •As the OWC reaches the top of the sand, we know that we have recovered the crude reserves for this well

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

Gp vs. Cumulative Oil Produced, Np

•This plot is useful in cases where we know the expected total gas to be produced. •This information provides an indication as to when the well will reach its abandonment point.

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

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.

DECLINE CURVE ANALYSIS

Relates production  time 1. Exponential Production Decline 2. Hyperbolic Production Decline

3. Harmonic Production Decline 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

Log Rate

Time 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 Np =



t

0

qdt

(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

D 1 t 1 = D 2t 2 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 (year)

Rate (stb/day)

0 1 2 3 4 5 6 6.05

100.00 60.93 37.13 22.62 13.78 8.40 5.12 4.99

100 [e(-0.4954 x 1)]

Production Cumulative Annual (stb) (stb) 0 0 28,789 28,789 46,332 17,542 57,021 10,689 63,534 6,513 67,502 3,969 69,920 2,418 70,013 92

[100-60.93]/ 0.001357

=28,789 - 0

2. Hyperbolic Decline

predicts a longer well life than is predicted by the exponential decline model. q =

qi [1 + bDit]1/b

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]} [qi1-b - q1-b]

integration of Di to obtain cumulative oil production

Np = {qib/[(1 - b) Di]} [qi1-b - q1-b] or expressing initial decline fraction in terms of Np.

Di = {qib/[(1 - b) Np]} [qi1-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]} [qi1-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

Annual Productions: hyperbolic decline

Time (year) 0 1 2 3 4 5 6 7 8 8.576

Rate (stb/day) 100.00 50.67 30.54 20.39 14.58 10.94 8.51 6.80 5.57 5.00

Production Cumulative Annual (stb) (stb) 0 0 25,983 25,983 40,341 14,358 49,450 9,109 55,743 6,293 60,352 4,609 63,872 3,520 66,649 2,777 68,896 2,247 70,005 1,109

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

[(1000.5)/((1- 0.5)0.002218)] [(100(1-0.5) - 50.67(10.5)]

3. Harmonic Decline

uncommon predict longer time for recovery (i.e than exponential or hyperbolic) a special case of hyperbolic decline (exponent, b = 1) Flow rate,

q =

qi Time,

t =

(production)

[1 + Dit]

qi q

-1

Di qi Cumulative Production,

Np =

(Integration of rate, q)

Initial Decline Fraction,

ln Di

qi Di =

ln Np

qi q

qi q

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.

Solutionq Di =

i

ln Np

qi

q

t =

qi

q

-1

Di

= (100 / 70,00) ln (100/5) = 0.004280 per day = 1.56 per year

= [(100 / 5) - 1 ]/1.56 = 12.16 year

Annual Productions: harmonic decline

Time (year)

Rate (stb/day)

0 1 2 3 4 5 6 7 8 9 10 11 12 12.16

100.00 39.06 24.27 17.61 13.81 11.36 9.65 8.39 7.42 6.65 6.02 5.51 5.07 5.01

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

Production Cumulative Annual (stb) (stb) 0 0 21,963 21,963 33,081 11,118 40,583 7,502 46,253 5,670 50,812 4,559 54,625 3,813 57,902 3,277 60,776 2,874 63,334 2,559 65,640 2,306 67,739 2,099 69,664 1,926 69,958 294 =[100/0.00428] x ln(100/39.06)

Exponential, Hyperbolic and Harmonic Decline 100.0 90.0

exponential

80.0 70.0 60.0 50.0

hyperbolic

40.0 30.0

harmonic

20.0 10.0 0.0 0

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