Improved Distance-of-Investigation Model for Rate-Transient Analysis in a Heterogeneous Unconventional Reservoir with Nonstatic Properties

The concept of distance of investigation (DOI) has been widely applied in rate- and pressure-transient analysis for estimating reservoir properties and for optimizing hydraulic fracturing. Despite its successful application in conventional reservoirs, significant errors arise when extending the concept to unconventional reservoirs. This work aims to clearly demonstrate such errors when using the traditional square-root-of-time model for DOI calculations in unconventional reservoirs, and to develop new models to improve the DOI calculations. In this work, the following mechanisms in unconventional reservoirs are first incorporated into the calculation of DOI: (1) pressure-dependency of rock and fluid properties; (2) continuous/discontinuous spatial variation of reservoir properties. To achieve this, pseudo-pressure, pseudotime, and pseudodistance are introduced to linearize the diffusivity equation. Two novel methods are developed for calculating DOI: one using the concept of continuous succession of steady states, and the other using the concept of dynamic drainage area (DDA). Both models are verified using a series of fine-grid numerical simulations. A production-data-analysis workflow using the new DOI models is proposed to analytically characterize reservoir heterogeneity and fracture properties. The new DOI models compensate for the inability of the traditional square-root-of-time model to capture spatial and temporal variations of reservoir and fluid properties. The pressure-dependency of fluids and reservoirs (i.e., fluid density, fluid viscosity, rock permeability, and rock porosity) and reservoir heterogeneities (i.e., deterioration of reservoir quality from the primary fracture to the reservoir) can significantly retard the propagation of the DOI. Another important outcome of this work is to provide a practical and analytical approach to directly estimate the spatial heterogeneity from the production history of field cases.