Analytical Solutions for Hydraulic Fracture Diagnosis
This work presents old and new analytical solutions for hydraulic fracture diagnosis. The main body of this work is divided in two parts: Part I presents the main developments, theories and applications of pressure transient testing as a tool for hydraulic fracture diagnosis. Pressure transient analysis is an inverse process and therefore subject to uncertainties and uniqueness problems. Although the analysis of pressure data is nowadays fully computer automated which allows for faster, more accurate and more reliable interpretation and analysis it is found that the margin of error can still be quite large and new alternative methods need to be found in order to improve reliability of hydraulic fracture diagnosis. Part II offers a new method for hydraulic fracture diagnosis. Analytical solutions are developed for tracer response curves of: (1) conservative and/or reactive tracers in single-well push/pull tests, and (2) a conservative tracer that is contained in the fracture only. The hydraulic fracture is treated as linear flow with uniform flux fluid loss. It is found that concentration profiles collected during push/pull tests contain no diagnostic features if dispersion is neglected. It is, however, found that the produced concentration curve of a tracer that is contained within the fracture only, such as broken frac fluid residual compounds, can be used to give a good estimate of fracture area.