Unified Analysis of Drawdown and Buildup Data for Physical Model Reservoir Flow With Producing Well at Center of Vertical Fracture

Summary A physical model of a gas reservoir having a vertical fracture with fracture half-length xf=0.0635 m was developed. The model is a right circular cylinder of latex concrete with the radius xe=0.305 m so that the xe/xf ratio is 4.8. The producing well is located at the center of the fracture. Experimental drawdown and buildup data taken from this reservoir were analyzed using available theoretical developments from the literature. The effect of pressure on permeability (the Klinkenberg effect) was included in the analysis. Simplex optimization was used in conjunction with unified (drawdown plus buildup) super-positioning to give fracture half-lengths of 0.0631 and 0.0635 m from two sets of experimental data. Corresponding values for permeability for these two sets of data were 0.0605×10−18 and 0.0624×10− m2, respectively, at a Klinkenberg coefficient of 5900 kPa. The fracture half-length and permeability are shown to be highly correlated. Thus, the results have more uncertainty than would be found in determining parameters by similar methods of analysis for an unfractured system. Bearing this in mind, the agreement between the known fracture half-length and values determined from the analysis of experimental data is excellent. Thus, we have demonstrated the utility of unified analysis as well as the ability to create an artificial fracture. Since the location of the model fracture relative to producing and observation wells is at the discretion of the designer, our model presents a unique opportunity to study various configuration which might be difficult to handle by mathematical modeling alone. Introduction Kurata Thermodynamics Laboratory personnel at the U. of Kansas have developed an apparatus which physically models the behavior of a gas well during drawdown and buildup conditions. This model allows acquisition of data from a porous medium of known characteristics under carefully controlled laboratory conditions. The comparison of these data with results from mathematical models permits checking and, if necessary, modifying the equations that describe flow in porous media. Breit et al.1 reported data obtained from such a model and described a unified method for analyzing drawdown and/or buildup data. Their unified method is an extension of that given by Odeh and Jones2 where the sandface rate becomes the afterflow rate after the well is shut in. We have found that it is possible to make a vertical fracture of known length and location relative to the producing well in the physical model reservoir. This paper presents data obtained from a physical model reservoir that contains a vertical fracture with the producing well located at the center of the fracture and an analysis of these data in terms of available theory.