Derivative Analysis Without Type Curves

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Abstract Modern type curve analysis involves matching the pressures and their semilog derivative on a set of dimensionless type curves, and selecting a match point. Using this point and a specified matching curve, reservoir parameters such as permeability, skin, fracture half length, fracture conductivity, etc., can be calculated. This paper shows that the same parameters can be obtained without having to use the type curves. In fact, only the semilog derivative of the data is needed on log-log coordinates. The various flow regimes such as wellbore storage, radial, linear, bilinear or spherical flow can be identified by their characteristic slopes (1, 0, 0.5, 0.25, -0.5). By simply placing a straight line with the appropriate slope on the (semilog) derivative points, all the required reservoir parameters can be calculated. This technique is, in actual fact, a combination in one single plot, of all the specialized analyses (which are traditionally done on their own individual scales, semilog, square-root, quad-root, cartesian). In addition to the semilog derivative data, it is advisable to superimpose a plot of PPD (Primary Pressure Derivative). This enables the analyst to differentiate between reservoir and wellbore effects, and thereby avoid some of the common pitfalls when using real (as opposed to synthetic) data. Introduction "Type Curve" analysis has been used in the field of hydrology since the mid 1930s. In the 1970s, type curves(2,3) were introduced to the petroleum industry, and in the early 1980s Bourdet et al.(1) added the "derivative," which helped in making type curve matching more unique. This article will explain how analysis of well test data can be achieved by using log-log plots and derivative, but without the need for "type curves." In order to understand this new procedure, a review of how type curve analysis works, will first be presented, and then extended to illustrate the new methods. Type Curve Matching: (The old way) The theory underlying type curve matching is fully explained in the ERCB (now AEUB) Gas Well Testing manual(2) and Earlougher(3). Basically the process consists of matching field data onto pre-selected dimensionless "type curves," and from the match point, calculating permeability, skin, wellbore storage constant, reservoir size, etc. Once a satisfactory match of the field data and the type curves has been obtained, a "match point" is chosen (any arbitrary point will do), and its coordinates read simultaneously from both the "type curve" scale and the "data" scale. From the coordinates of this arbitrary point, reservoir or wellbore characteristics can be calculated. For example to obtain permeability, read the vertical values ΔpD and Δp of the dimensionless type curve and of the data plot, at the selected common match point. From the definition of dimensionless pressure, the calculation of permeability is easily obtained as follows: Equation (available in full paper) In a similar manner, other variables can be calculated, once a match has been obtained. Traditional type curve analysis has two major drawbacks: