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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.
CONCLUSIONS
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