Radius of Investigation and its Generalization to Unconventional Reservoirs

The concept of radius of investigation is fundamental to well test analysis and is routinely used to design well tests and to understand the reservoir volume investigated. The radius of investigation can also be useful in identifying new well locations and planning, designing and optimizing hydraulic fractures in unconventional reservoirs. It has additional implications in estimating reserves and understanding stimulated reservoir volumes. There are many definitions of radius of investigation in the literature and Kuchuk (2009) summarized them recently. Although these definitions vary in detail, they all relate to the propagation of a pressure disturbance or impose thresholds on detectable pressure or rate changes. In this article we will focus on the definition proposed by Lee (1982). Lee defines the radius of investigation as the propagation distance of the “peak” pressure disturbance for an impulse source or sink. For simplified flow geometries and homogeneous reservoir conditions, the radius of investigation can be calculated analytically. However, such analytic solutions are severely limited for heterogeneous and fractured reservoirs, particularly for unconventional reservoirs with multistage hydraulic fractures. Generalization of the Concept How can we generalize the concept of radius of investigation to heterogeneous reservoir conditions including unconventional reservoirs with horizontal wells and multistage hydraulic fractures? For such general situations, it will be more appropriately called “the depth of investigation” rather than the radius of investigation. The simplest, not necessarily the most desirable, approach will be to use a numerical reservoir simulator. For example, we can simulate a constant rate drawdown test and observe the pressure response at every grid block in the simulation model. It is as if, we have distributed sensors throughout the reservoir. We can now compute the time derivative of the pressure at each grid block and note the time when the derivative reaches a maximum. We can then simply contour this “peak” arrival time at every grid block. Note that because the constant rate test corresponds to a step function (from 0 to Q), its derivative is an impulse function. Thus, by contouring the arrival time of the maximum of the pressure derivative, we are actually looking at the arrival time of the maximum of an impulse response as defined by Lee (1982). How well does the approach work? Fig. 1a shows the evolution of the radius of investigation for homogeneous radial flow using Lee’s analytic solution. Fig. 1b shows the radius of investigation obtained from numerical simulation. We have superimposed the analytic solution (black lines) on the results from the numerical simulation. We do see a close correspondence, although the numerical results have difficulties resolving the pressure transients away from the well. In spite of its limitations, the numerical approach is very general and can be applied to arbitrary reservoir and well conditions. The computation time and expenses, however, make the numerical simulation approach unfeasible for routine applications.