Prssure Derivative For Drawdown Test

[amahaminer]

Hi all , i have a question in paper "Interpretation of Multirate Tests by the Pressure Derivative - I. Oil Reservoirs" SPE 53935 ,copy attached

in Example 1 when calculating :Prssure Derivative For Drawdown Test, i donot know the equation he used to get the highlighted results for derivative , could u help me with the equation.

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[vinomarky]

Are you sure it is a derivative? From the image, it is titled simply as "dp", with the units psi. If it were a derivative it would be psi/hr or psi/bbl or whatever the derivative was respect to

Edit: Had a quick look at the paper, and it does appear to be the derivative of the delta P wrt time (units dont seem to be correct). If I just use a simple linear slope between points I get similar numbers but not exactly the same, so dont know exactly how they are arriving at their derivative

ie first point I would get (938 - 883)/(1.5 - 1) = 110 vs 124, and second point I would get;
(965 - 938)/(1.89 - 1.5) = 69 vs 75

Perhaps they are using a derivative from a curve fit instead - try plotting up the dp's and dt's, fit an equation then take derivative of that equation and see what you get

[amahaminer]

Thanks vinomarky ,it seems reasonable

[ALFRE01]

Amahaminer, is there another methods of aproximation of the derivatives for greater accuracy, try to investigate about the "five-points" and "three-point" aproximation methods (or balanced difference quotient) in any Numerical Analysis book. This will produce a smooth derivative curve for easy analysis.