We have discussed the advantages and drawbacks of type curves: • Advantages: One single curve can deal with a whole test • Drawbacks: log-log representation in type curve could not show small relative pressure variation THE DERIVATIVE Methods using the pressure derivative take advantage of the advantages of the type curve representation and counteract the drawbacks of the logatithmic representation These methods are based on an observed fact: in a well test the pressure variation is more significant than the pressure itself. This is illustrated by the fact that it is the slope of the semi-log straight lines that is used to get information on the reservoir in conventional methods
We have discussed the advantages and drawbacks of typecurves:
Advantages: One single curve can deal with a whole test Drawbacks:
log-log representation in type curve could not showsmall relative
pressure variation
THE DERIVATIVE
Methods using the pressure derivative take advantage of
theadvantages of the type curve representation and counteract
thedrawbacks of the logatithmic representationThese methods are
based on an observed fact: in a well test thepressure variation is
more significant than the pressure itself. Thisis illustrated by
the fact that it is the slope of the semi-log straightlines that is
used to get information on the reservoir inconventional methods
The pressure derivative as represented by D. Bourdet
iscalculated in relation to the time function of radial flow in
thetransient regime
PROPERTIES OF THE DERIVATIVE
The pressure derivative is expressed asfollows with the radial
flow time function:
All type curves thereforehave the 0.5 ordinatestraight line as
anasymptote during radialflow
WELLBORE STORAGE EFFECT
Pressure derivative is expressed by
Therefore, the derivative likethe pressure has as anasymptote
the unit slopestraight line that passesthrough the origin of
thecoordinates on a log-loggraph.
DIAGNOSIS
ANALYSIS WITH TYPE CURVESD. Bourdets type curves with a
derivative for homogeneousreservoirs are shown in figure below
where the set of curvessimilar to Gringartens with the addition of
the derivative of eachcurve
Derivative type curves have thefollowing remarkable
properties
ANALYSIS METHOD
VERTICAL MATCHING
VERTICAL + HORIZONTAL MATCHING
RESERVOIR KHPermeability is calculated based on thePermeability
is calculated based on thevalue P/st corresponding to
thestabilization of the derivativeThe value of this derivative
expressedin dimensionless term is known, it isequal to 0.5
WELLBORE STORAGE EFFECTWellbore storage can becalculated if the
coordinates of apoint located on the slope 1straight line are
known: p1 andt1
SKIN
The skin can be calculated ifthe coordinates of a pointlocated
on the semi-log straightline are known: ps, ts.
