Decline Curve Analysis
Figure: A production record of an abandoned well and the causes of changes in production rate
DCA
Principle
• The principle of the decline curve method is to find a mathematical
relationship that fits the observed rate-time graph and then to
apply this relationship to extrapolate the graph in the future and
thus make predictions.
• Extrapolating the apparent trend until the economic limit assumes
that whatever causes controlled the trend of a curve in the past will
continue to govern its trend in the future in a uniform manner.
• This extrapolation procedure is therefore strictly of an empirical
nature and a mathematical expression of the trend based on
physical considerations of the reservoir can be set up only for a few
simple cases.
Purpose of Decline Curve Analysis (DCA)
Using Decline Curve Analysis (DCA) method, the followings can be determinedGIIP (matured field)
Prediction of Oil and Gas recovery
Reserves of a well with the economic analysis,
Economic production rate,
Remaining productive life of a well or the entire field.
Individual well flowing characteristics such as formation permeability, skin
Traditional DCA Analysis
• Production decline analysis is a traditional means of identifying well
production and predicting well performance based on real production data.
• DCA is a graphical procedure used for analyzing declining production rates.
A curve fit of past production performance is done using certain standard
curves. This curve fit is then extrapolated to predict potential future
performance.
• It 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 curve analysis is an Empirical Method (method based on
observations) that is commonly used the oil and gas Industry.
• DCA models are related to decline rate equation (Arps, 1945):
Assumptions and Limitations
Assumptions
1.
2.
3.
4.
Drainage Area is constant
Constant FBHP
Skin is not changing
PSS flow/ Boundary dominated flow. The production must have been stable
over the period being analyzed .
5. Not applicable for transient flow
6. change in production conditions (infield development wells could reduce the
current drainage area).
Limitations
• Any workover/ stimulation will affect the results
• A large number of data is required
• Correct production data is required
• Changing choke size will affect.
• Constant bottom hole pressure (BHP). If BHP changes, the character of
the well’s decline changes.
Factors Effect Decline Curve Analysis
•
•
Decline curves can be characterized by three factors
– Initial production rate or the rate at some particular time
– Curvature of the decline
– Rate of decline
These factors are a complex function of
– Reservoir parameters: porosity, permeability, thickness, fluid
saturations, fluid viscosities, relative permeability, reservoir size, well
spacing, compressibility, producing mechanism and fracturing
– Well bore parameters: hole diameter, formation damage, lifting
mechanism, solution gas, free gas, fluid level, completion interval and
mechanical conditions
– Surface handling facilities
The factors that affect the decline in gas production rate arei.
Reduction in average reservoir pressure
ii.
Increases in the field water cut in water drive fields
Decline Curves
Decline curve analysis is usually conducted graphically, and in order to
help in the interpretation.
• The equations are plotted in various combinations of "rate", "lograte", "time," and "cumulative production".
• The intent is to use the combination that will result in a straight line,
which then becomes easy to extrapolate for forecasting purposes.
•
The decline equations can also be used to forecast recoverable
reserves at specified abandonment rates.
Arps Decline Curves
Arps took many observations and concluded that the decline in the oil
production rate, qo, over time from actual oil reservoirs could be described
by the equations:
where the decline rate, D, is a time dependent function:
where
qi = initial oil rate (neglecting transient decline), volume/time
q = rate at time t, volume/time
Di = decline constant, time-1
b = decline exponent.
Arps Decline Curves
• D = continuous production decline rate at time t (1/time)
• If t = years: Da= annual continuous production decline rate (1/year)
• If t = months: Dm= monthly continuous production decline rate (1/month
Arps observed that production data can be fitted to equation with
qi, D, and the coefficient b, where b can represent:
1. exponential decline: b = 0
2. hyperbolic decline: 0 < b < 1
3. harmonic decline: b = 1.
With Arps Decline Curves
 Exponential Decline (b=0)
 Hyperbolic Decline (0<b<1)
 Harmonic Decline (b=1)
Exponential Decline (b=0)
If b=0,, D=Di=constant, and we can integrate
This equation is referred to as Exponential Decline because of the presence of
the exponential term. We can also develop a rate cumulative production
(qo−Np) relationship by noting that:
Multiplying by dt and integrating results in:
Exponential Decline (b=0)
It is used to make future well forecasts. It is a straight line in Np with a slope of −D
Exponential decline is most often associated with the Rock and Fluid Expansion Drive
Mechanism. In exponential decline, we have two parameters, qoi and D, with which to
match the field data.
First, if we know the Abandonment Rate for the reservoir or well, qo ab, (rate at
which the revenue from the oil sales would pay for the operating expenses of the
reservoir or well), then we would have:
The volume of oil that can be recovered from a reservoir or well with no regard to the
economics is called the Estimated Ultimate Recovery, or EUR, of the reservoir or well. We
can determine the EUR by simply allowing the rate from reservoir or well to decline to 0
STB/day production rate (infinite time). That is:
A semilog plot of rate vs time will result in a straight line if the production rate decline is
accurately approximated by the exponential model.
Abandonment time
For Gas
Abandonment time
Types of Decline
Nominal Decline
• Nominal Declines refer to the instantaneous decline rate .
• Nominal decline is a continuous function and it is the decline factor that is used in the
various mathematical equations relating to decline curve analysis.
•
For exponential decline it is a constant with time.
• The nominal decline factor d is defined as the negative slope of the curve
representing the natural logarithm of the production rate q vs. time t.
Effective decline
• Effective Decline
– the effective decline rate is a stepwise function where each step represents the
reported production.
- It is the drop in production rate from qi to q1 over a specific time period.
•De is the effective decline rate = the decline rate over a time period.
•De is a constant only for constant percentage or exponential decline.
•De decreases with time for hyperbolic and harmonic decline
Effective decline and Nominal decline
For exponential decline, the relationship between nominal and effective
decline factors can easily be derived. From the definition of effective
decline rate,
Applicability of Exponential Decline
• Types of reservoirs whose declines frequently follow the exponential
model are depletion drive:
1)
2)
3)
oil reservoirs above bubble point pressure,
oil reservoirs below bubble point pressure,
low pressure gas reservoirs.
Example
Using the data in figure,
• Estimate the production rate at the beginning of 2007 using both nominal and
effective decline factors, and compare the results with the field data.
• Estimate the cumulative production between 1/1/2007 to 1/1/2012
Solution
Assuming a time period of one year and using the endpoints of 2004, the effective decline
factor is
The nominal decline factor can be determined
using Eq
Using the nominal decline factor the production rate three
years later (beginning of 2007) is estimated to be:
Similarly, we can use the effective decline factor by recalling that the rate after each year
is only 69% of the previous year’s value.
Solution
The production rate at the beginning of 2012 is
Therefore the cumulative production becomes,
Hyperbolic Decline (0<b<1)
If b is in the range, 0<b<1, then the rate-time relationship:
While a second integration with respect to time results in the rate-cumulative
production relationship:
When the constant b is in the range 0<b<1, we refer to the resulting production decline
as Hyperbolic Decline. In hyperbolic decline, we have all three parameters, qoi, Di , and b
, with which to match the field data
Hyperbolic-decline curve analysis is much more complicated than
exponential or harmonic
Hyperbolic Decline (0<b<1)
Both the constants Di and b must be determined for a hyperbolic decline model.
Unfortunately, no direct linear plot can be made, and the two constants must be
determined by trial and error
Hyperbolic trial and error method to determine coefficients
Harmonic Decline (b=1)
If b=1, then the rate-time relationship:
While a second integration with respect to time results in the rate-cumulative production
relationship:
In harmonic decline, we have two parameters, qoi
and Di, with which to match the field data
Sometimes the production decline factor is not constant
but decreases proportional with the production rate. This
behavior is called harmonic decline and can be expressed
by:
Applicability of Harmonic Decline
Types of reservoirs that are sometimes best approximated
by the harmonic model are:
(1) edgewater drive in a viscous oil reservoir;
(2) depletion-drive oil reservoir near the final stages of its
life.
Therefore, a depletion-drive oil reservoir is sometimes best
modeled by exponential decline for most of its life, but by
harmonic decline for later stages.
• If the harmonic model had been used in Figure above
example, forecast the rate on 1/l/2012 from the rate on
1/l/2007,
a recovery between 1/l/2007 and 1/1/2012 of:
Comparison
This figure illustrates why harmonic decline leads to an infinite EUR – the production
can never achieve a zero rate and the area under the curve (Np) becomes infinite
Example
Cartesian Coordinate
Semi log
Cartesian Coordinate
Semi log
Production decline curves
Way of Decline Curve Analysis
1. Conventional analysis techniques
2. Production decline type curves
Advanced Decline Curve Analysis
Advanced Production Data
Analysis & Forecasting
Transient Flow
• Transient Flow – Flow within a reservoir has
not reached the reservoir boundaries.
Pseudo Steady State Flow
Pseudo Steady State (PSS) – Flow within a reservoir has reached the reservoir
boundaries. Boundary dominated flow.
No flow boundary
Steady State Flow
FETKOVICH DECLINE ANALYSIS
Fetkovich in 1980 laid the foundation for log (q) – loq(t) type curve matching by
combining both the transient and depletion solutions into a single graph .
This novel approach resulted in a systematic method of evaluating well and reservoir
properties and proved to be a powerful diagnostic tool.
To develop the type curve, new dimensionless terms were defined.
Definitions of Dimensionless Variables:
FETKOVICH DECLINE ANALYSIS
The steep-decline behavior (low reD value) during the transient flow period can be
attributed to either a successful well-stimulation; e.g., high negative skin, or to a small
drainage area. Conversely, a gentle decline suggests a damaged well and/or large drainage
area.
ADVANCED VARIABLE
RATES/PRESSURES
• The production decline analysis techniques of Arps and Fetkovich are
limited in that they do not account for variations in bottomhole flowing
pressure in the transient regime, and only account for such variations
empirically during boundary-dominated flow (by means of the empirical
depletion stems). In addition, changing pressure, volume, and
temperature (PVT) properties with reservoir pressure are not
considered for gas wells.
• Blasingame and his colleagues have developed a production decline method
that accounts for these phenomena.
• Blasingame’s improvements on the Fetkovich style of production decline
analysis are further enhanced by the introduction of two additional
typecurves which are plotted concurrently with the normalized rate
typecurve. These 'rate integral’ and 'rate integral derivative’ typecurves aid in
obtaining a more unique match. The derivation of these will be discussed in a
later section
Gas Reservoir
Exponential decline
(constant percentage decline)
For oil:
A plot of production rate versus cumulative production indicates a straight line trend
For Gas:
Abandonment time
Differentiating with respect to time
But
So
The nominal decline rate D   d (ln q)   1 dq
dt
q dt
Rate time relation
From the definition of the nominal decline rate
By integrating over time t
Rate cumulative relation
Taking logarithm
Example
Problem:01
constant percentage decline
Problem:02
constant percentage decline
Production Per Year
Harmonic decline
Differentiating with respect to time
Eliminating alpha from the above two equations
Rate time relation
Rate cumulative relation
Integrating the equation
We get
In terms of rate of production
Relation between nominal and effective decline
Abandonment time
Hyperbolic decline
When t=0
Putting the value of c in the above equation
(1)
Rate time relation
From
and
We get
(2)
Comparing equation 1 and 2 we get
b=0 yields constant percentage decline
b=1 yields harmonic decline
Thus the limits of the hyperbolic decline constant are
Rate cumulative relation
Abandonment time
Relation between nominal and effective decline
Curve fitting procedure
Problem:03
Q vs. t on semi log graph paper
Q vs. Gpd on semi log graph paper