The Primary Pressure Derivative (Ppd) A New Diagnostic Tool In Well Test Interpretation
Authors: Mattar L. , Zaoral K. 
Published: March 2010

In well test interpretation, the derivative has traditionally been defined as the slope of the pressure with respect to the logarithm of lime. This paper defines a new diagnostic procedure called the Primary Pressure Derivative (PDD) which is the slope of the pressure-time curve (on cartesian coordinates).

The authors postulate that when a well is shut-in for a pressure build-up test, the pressure should rise Monotonically until it is finally static. This means that the Primary Pressure Derivative (PPD) should be a continuously decreasing function, until if becomes a zero when the well is fully built-up. However, wellbore related phenomena can cause the measured pressure to rise or fall independently of reservoir effects. One of the first functions of the well test analyst is to differentiate between wellbore dominated effects and reservoir fluid flow effects, and the PPD is presented as a very simple diagnostic tool to highlight the non-reservoir effects, so that pitfalls in interpretation can be avoided.

Introduction

The 1980s have been the decade of the derivative in the field of pressure transient analysis. This procedure was introduced by Bourdet et al(1). It consists of plotting the slope of the semilog plot (pressure vs log time) vs time, usually on a log-log scale, simultaneously with the regular type curve plot of the data. The derivative has two advantages:it makes type curve matching a more unique procedure;it identifies flow regimes more clearly and earlier than the type curve.

It has the disadvantage that a derivative "scatters" the data, and it, therefore, requires some son of smoothing algorithm. The derivative procedure should more properly have been named the semilog derivative SLD, because that is what it is, (dp/dlog t). The true derivative of pressure, by mathematical definition is dp/dt, and is the subject of this paper. The authors call it the Primary Pressure Derivative, (PPD), to avoid confusion with the semilog derivative SLD.

In their paper entitled "How Wellbore Transients Can Affect Pressure Transient Analysis", Mattar and Santo(2) illustrate that the pressure trend recorded on a pressure recorder can be significantly different from the trend inside of the reservoir, and can be misinterpreted as a reservoir effect instead of the wellbore effect that it is. The interaction of wellbore and reservoir can be very simple (downhole shut-in), or very complex (phase redistribution, changing liquid level, etc.). This paper presents a technique for identifying non-reservoir effects and, thus, avoiding misinterpretation.

Hypothesis

This hypothesis will be stated in simple physical terms first, and then in mathematical form.

No matter how complex the reservoir is - be it fractured, multilayered, bounded, multi-permeability, etc. - a build-Up will always look life curves A, B or C in Figure 1, never like curve, D, E or F in Figure 2, In other words, the build-up is always concave downward. If a build-Up is observed as in Figure 2, then the upward curvature is caused by a non-reservoir effect (changing wellbore storage, recorder malfunction, multiphase in the wellbore)."