| dc.description.abstract | Well test analysis is a critical tool for evaluation of well and reservoir performance. It is intrinsically an inversion methodology for reservoir parameter estimation and is closely related to the drainage volume evolution around the wellbore. Pressure transient analysis provides insight into our geometric understanding of the reservoir shape and volume, which helps us obtain a volume-averaged estimation of reservoir parameters from the interpretation of the flow regime in the porous media. Though straightforward, the conventional well test methodology can only help us interpret the flow mechanism in an analytic approach with simplified (homogeneous) models. When detailed reservoir information is required, numerical simulation needs to be employed to obtain grid-cell based reservoir parameters from integration of the well pressure or rate data.
To this end, we propose a semi-analytic methodology for simulation of fluid flow in the subsurface and interpretation of the grid-cell based reservoir parameters. It relies upon an asymptotic expansion to the pressure diffusivity equation based on the “diffusive time of flight” (DTOF) calculation, which transforms the three-dimensional diffusivity equation into a reduced one-dimensional formulation. The DTOF (τ) can be calculated from solving the Eikonal equation using the fast marching method (FMM).
In this dissertation, we first discuss the formulation of the drainage volume using the DTOF and prove its relationship with the well test derivative. Different orders of drainage volume discretization schemes in the near-well region are analyzed and combined into a hybrid version, which includes an analytic formulation at the well cell
and ensures sufficiently accurate transient pressure behavior at early times of simulation. Similarly, a hybrid version of cumulative pore volume discretization is used for the DTOF-based transient flow simulation and proves to be able to generate stable and consistent solutions in general heterogeneous porous media.
The second part of this dissertation focuses on exposition of an inverse modeling methodology that can be used to estimate grid-cell based reservoir parameters by integrating pressure transient data into the geologic model. The well test derivative is inversely related to the drainage volume and is treated as the well observation. Its analytic sensitivity coefficients with respect to reservoir parameters are formulated and included into a penalized objective function for inversion. This inversion technique leads to a computational speed orders of magnitude faster than conventional sensitivity-based inverse modeling approaches that would require numerical perturbations.
Finally, we propose a FMM that can be used for reservoir models with faulted corner point grids (CPG). The local Eikonal solution is formulated in a quadratic equation for the DTOF, the coefficients of which are formulated explicitly. This new FMM for CPG applies for general anisotropic heterogeneous media and is easy to implement on triangular and tetrahedral meshes, which constitute the unit CPG. Complex geometric features including the faults and pinch-outs are taken into account when the new FMM is designed. | en |
