A common method in industry to correct pressure build-up data for producing time effects is use of Agarwal equivalent drawdown time (SPE 9289). But how does this correction affect the presentation of data and interpretation when performing well test analysis? It can be argued that a reasonable pressure match to a particular reservoir model can be achieved regardless of how the data is presented. An appropriate match can be quantified by goodness of fit criteria and the best match (model) selected on that basis. Because of the presence of non-unique solutions, it is difficult to know which flow geometry is most appropriate from the match alone. Future flow predictions will be effected by the selection an appropriate model with late time boundary conditions having the largest effect on forecasted volumes. The method presented in this paper will try to reduce the uncertainty when selecting a model to match the pressure behavior plus demonstrate that the Agarwal corrected and Horner corrected derivative are identical.
Agarwal equivalent draw-down time or Agarwal time (t e) has been used for a many years as a method to correct build-up data from producing time effects where the shut-in time is longer than the producing time. The correction here refers to changing the character or shape of the build-up derivative so that it more closely resembles the shape of the drawdown type curve. Changing the curve in this manner would allow the data to be matched to a set of draw-down type curves either manually or using a computer application. Now with advances in computer programs and algorithms, build-up type curves can be generated based on the flow history for any reservoir model. The data can be matched to a build-up type curve and the accuracy can be checked visually on the computer screen or qualitatively using best-fit statistical indicators. Unfortunately a solution is often non-unique with different models appearing to match the data each with a similar level of confidence.
Clues are required to select the most appropriate model for a particular well test. Most often the simplest model is selected but where questions of reservoir geometry are concerned the model will provide very different long-term production predictions. A simple case to demonstrate this would be a test where there is a slight upturn in the derivative at late times. Is this the result of a dual porosity system or near well boundaries? Other information is required to improve the confidence level in selecting the best model. This information can be from a variety of sources. Geological models will provide the type of trap and the potential location of boundaries. Rock type, depositional environment and facies information allows the selection of flow behavior either homogeneous, dual porosity or composite. A hydraulically fractured well suggests the use of a finite conductivity fracture model. Other information out side the well test may be available that further helps to identify an appropriate model.
Techniques are available using conventional plots of build-up and draw down data that also provide an indication of the appropriate type of flow model. Square root, quarter root, and Horner plots indicate the presence of linear, bi-linear and radial flow respectively. Straight lines on these plots are good indicators of the respective flow regimes. But in order for this flow regime to be valid, it must be identified on the log-log plot over the same time interval. The derivative has a specific behavior or character for each flow regime when presented as a drawdown type curve. Spherical flow, Radial flow, linear flow, bi-linear flow and pseudo-steady state all show straight lines with different slopes of -1/2, 0, 0.5, 0.25 and 1 respectively as a derivative plotted on a log-log scale. It is this character that is difficult to preserve when build-up data is used or build-up type curves are used. The solution is to some how correct the data to account for "producing time effects". The following is a recommended method to correct for producing time effects using the Radial flow equation.