This paper presents a novel methodology for estimating an inflow profile in horizontal, hydraulically fractured wells. The methodology is based on the Péclet number theory applied to thermal flows in porous media. In the context of heat transfer, the Péclet number is defined as the ratio of heat transfer by convection to heat transfer by conduction and when applied to porous media the Péclet number provides a relationship between a temperature change and permeability. This concept will be applied to estimate the fracture permeability values based on the observed temperature change at each cluster along the lateral. Simulations of a horizontal, hydraulically fractured well are performed for a range of fracture permeabilities. From these simulations a relationship is developed between the temperature change at the sandface of each fracture and the fracture permeability. Using this relationship, or type curve, the permeability for each fracture is determined based on the observed temperature change at the fracture sandface. The observed temperatures normally are measured from distributed temperature sensing (DTS) fiber optic cable. A field example will be presented to illustrate the methodology in which temperatures were measured with DTS fiber optic cable placed on the outside of the production casing. Fracture permeability is the only adjustable parameter considered in this paper. This approach is computationally less intensive than most regression-based approaches.
The analysis of bottom-hole temperatures is increasingly being used in both production and stimulation operations. This is in recognition that temperatures contain information about the completion and reservoir. Analysis of bottom-hole flowing temperatures for a production well can provide estimates of layer flow rates, reservoir permeability, and possibly skin (Duru and Horne, 2011; Sui et al., 2008). In the case of hydraulically fractured, vertical completions, the estimation of fracture half-length, the fracture vertical extent and the proppant loading within the fracture can be inferred from the measurement and analysis of bottom-hole injection temperatures (Hoang et al., 2012; Wang and Bussear, 2011; Sierra et al., 2008). Additionally, the estimation of fracture fluid placement and the number of effective clusters can be determined from injection flowing bottom-hole temperatures in hydraulically fractured wells.
