USING MATLAB ONLY Decline curve analysis is a useful tool in

USING MATLAB ONLY:

Decline curve analysis is a useful tool in petroleum industry. There are three basic types of decline curves, including exponential decline, hyperbolic decline and harmonic decline. They are all empirical relationships of the rate decline (dq/dt) vs the rate (q, bbld) Exponential decline: (dq/dt)/q --D Hyperbolic decline: (dq/dt)/q (q/qi) *(-D) (0

Solution

Analysis Methods

Traditional

Background for Trad

itional Analysis

Decline curve analysis is

a graphical procedure us

ed for analyzing declining

production rates and

forecasting future perform

ance of oil and gas wells. A curve fi

t of past production performance is

done using certain st

andard curves. This curve fit is then ex

trapolated to predic

t potential future

performance. Decline curv

e analysis is a basic

tool for estimating

recoverable reserves.

Conventional or basic de

cline curve analysis can be used only wh

en the production

history is long

enough that a trend

can be identified.

Decline curve analysis is not

grounded in fundamental theory

but is based on empirical

observations of production decl

ine. Three types of decline

curves have been identified;

exponential, hyperbolic, and

harmonic. There are th

eoretical equivalents to these decline curves

(for example, it can be demons

trated that under cert

ain circumstances, such

as constant well

backpressure, equations of fl

uid flow through porous media

under \"boundary-dominated flow\"

conditions are equiva

lent to \"exponential\"

decline). However, decli

ne curve analysis is

fundamentally an empi

rical process based on hist

orical observations of we

ll performance. Because

of its empirical nature,

decline curve analysis is applied, as

deemed appropriate for any particular

situation, on single or multi-fluid

streams. For example,

in certain instances, t

he oil rate may exhibit

an exponential decline, while

in other situations it is

the total liquids (oil +

water) that exhibit the

exponential trend. Thus, in some

instances, the analysis is condu

cted on one fluid, sometimes on

the total fluids, sometimes on the ratio (for exam

ple Water-Oil-Ratio (WOR

) or even (WOR + 1)).

Since there is no overwhelming justif

ication for any single variable to

follow a particul

ar trend, the

practical approach to decline curv

e analysis is to choose

the variable (gas, oil,

oil + water, WOR,

WGR etc.) that results in a reco

gnizable trend, and

to use that decline curv

e to forecast future

performance.

It is implicitly assumed, when using decline cu

rve analysis, the factors

causing the historical

decline continue unchanged

during the forecast period. These

factors include both reservoir

conditions and operating cond

itions. Some of the re

servoir factors that af

fect the decline rate

include; pressure depletion

, number of producing well

s, drive mechanism, rese

rvoir characteristics,

saturation changes, and relative pe

rmeability. Operating c

onditions that influence the decline rate

are: separator pressure,

tubing size, choke

setting, workovers, compre

ssion, operating hours, and

artificial lift. As long

as these conditions do not

change, the trend in dec

line can be analyzed and

extrapolated to foreca

st future well performance. If thes

e conditions are altered, for example

through a well workover, then the

decline rate determi

ned pre-workover will

not be applicable to

the post-workover period.

When analyzing rate decline,

two sets of curves are

normally used. The flow ra

te is plotted against

either time or cumulati

ve production. Time is the most c

onvenient independent

variable because

extrapolation of rate-time graphs

can be directly used for pr

oduction forecasting and economic

evaluations. However, plots of

rate vs. cumulative production

have their own advantages; Not only

do they provide a di

rect estimate of the

ultimate recovery at

a specified economic

limit, but

will also

yield a more rigorous interpretation

in situations where t

he production is influe

nced by intermittent

operations.

Good engineering practice demands

that, whenever possible, decli

ne curve analysis should be

reconciled with other indicators of

reserves, such as volumetric ca

lculations, material balance, and

recovery factors. It should be

noted that decline cu

rve analysis results in

an estimate of

Recoverable Hydrocarbons, and NO

T in Hydrocarbons-in-Place.

Whereas the Hydrocarbons-in-

Place are fixed by nature, the Re

coverable 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 ther

e is a compressor connected at the

wellhead.

The following steps are taken for

exponential decline anal

ysis, and for predicting

future flow rates

and recoverable reserves:

Plot flow rate vs. time on a

semi-log plot (y-axis is logarithm

ic) and flow rate

vs. cumulative

production on a Cartesian (ari

thmetic coordinate) scale.

1.

Allowing for the fact that the ear

ly time data may not be

linear, fit a strai

ght line through the

linear portion of the data

, and determine the decline ra

te \"D\" from the slope (-

D

/2.303) of the

semi-log plot, or

directly from the slop

e (D) of the rate-cumul

ative production plot.

2.

Extrapolate to

q

=

q

E

to obtain the recove

rable hydrocarbons.

3.

Extrapolate to any specified ti

me or abandonment rate to obta

in a rate forecast and the

cumulative recoverable hydrocar

bons to that point in time.

4.

Production Decline Equations

Decline curve analysis is der

ived from empirical obser

vations of the producti

on performance of oil

and gas wells. Three types

of decline have been observed histor

ically: exponential, hyperbolic, and

harmonic.

Decline curves repres

ent production from the reservoi

r 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 b

een reached, decline curves

should NOT be expected to be

applicable. Typically, during transient

flow, the decline rate

is high, but it st

abilizes once boundary

dominated flow is reac

hed. For most wells this happens with

in a few months of production.

However, for low permeability wells (t

ight gas wells, in pa

rticular) transient flow

conditions can last

several years, and strictly spea

king, should not be analyzed by

decline curve methods until after

they have reac

hed stabilization.

All decline curve theory starts

from the definition of

the instantaneous or curr

ent decline rate (D) as

follows:

D is \"the fractional change in ra

te per unit time\", fr

equently expressed in \"%

per year\". In the

following diagram,

D = Slope/Rate.