Masanori Kurihara's dissertation
by
Masanori Kurihara, Ph.D.
University of Texas at Austin, 1995
Supervisors: Larry W. Lake
Gary A. Pope
Tracer test results can be analyzed to characterize flow through permeable media.
Usually this is carried out by history matching with numerical models. However, a
conventional streamline model, using line source and sink solutions, can be applied
only to two dimensional (2D) areal geometry. Use of a numerical simulator for this
purpose is limited because of numerical artifacts and large calculation time.
We have developed a semianalytical three dimensional (3D) streamline model (UTSTREAM)
for use with a steady-state velocity field. This model is based on the assumption
that each directional velocity component varies linearly within a gridblock. This
assumption allows analytical expressions of streamline trajectories and transit times
of tracer particles along streamlines.
Furthermore, the model incorporates the sub-programs that solve the
convection-diffusion (C-D) equation with longitudinal and transverse dispersion,
using newly introduced equivalent parameters that can convert a three phase problem
to an equivalent single phase problem.
The results of several test runs with and without dispersion showed good agreement
with analytical solutions and UTCHEM results, and that the model requires quite small calculation time.
As an application of the 3D streamline model, interwell tracer tests were simulated
for characterizing residual hydrocarbon (HC) in a subsurface water zone.
Sensitivities of the effluent partitioning tracer response were investigated for the
reservoir parameters, including HC volumes, HC locations and completion intervals,
that showed promise to successfully detect residual HC.
UTSTREAM was next applied to the estimation of permeability fields and residual HC
saturation distributions through automatic history matching with tracer test results.
The program developed for this purpose, which incorporates the 3D streamline model
and a program that stochastically generates permeability fields by the matrix
decomposition method (MDM), solves the nonlinear least square problem by the hybrid
methods of the Quasi-Newton, Levenverg-Marquardt and steepest descent. Although it
is very difficult to obtain a unique solution for inversion problems in general,
several trials were made to obtain the exact solution.
Finally UTSTREAM was used to scale up fine grid permeability to a coarse grid system.
As a result of the investigation of the tortuosity of streamlines drawn by UTSTREAM,
it was revealed that the effective permeability of a coarse gridblock can be
expressed as a function of the dimensionless parameters including a dimensionless
correlation length, effective aspect ratio and a newly defined effective correlation
length ratio. The effective permeability obtained from this relationship could be
successfully applied to a scale up problem.
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