Amini, Shahram (2007-12). Development and application of the method of distributed volumetric sources to the problem of unsteady-state. Doctoral Dissertation.
This work introduces the method of Distributed Volumetric Sources (DVS) to solve the transient and
pseudosteady-state flow of fluids in a rectilinear reservoir with closed boundaries. The development and
validation of the DVS solution for simple well/fracture configurations and its extension to predict the
pressure and productivity behavior of complex well/fracture systems are the primary objectives of this
In its simplest form, the DVS method is based on the calculation of the response for a closed rectilinear
system to an instantaneous change in a rectilinear, uniform volumetric source inside the reservoir.
Integration of this response over the time provides us with the solution to a continuous change (constantrate
pressure response). Using the traditional material balance equations and the DVS pressure response
of the system, we can calculate the productivity index of the system in both transient and pseudosteadystate
flow periods, which enables us to predict the production behavior over the life of the well/reservoir.
Solutions for more complex situations, such as sources with infinite or finite-conductivity (i.e., a fracture),
are provided using discretization of the source. This work considers the case of a complex system with a
horizontal well intersecting multiple transverse fractures as an example to show the ability (and flexibility)
of the new method. The DVS solution method provides accurate solutions for complex well/fracture
configurations -- which will help engineers to design and implement optimum well completions.
The DVS solutions has been validated by comparing to existing analytical solutions (where applicable), as
well as to numerical (simulation) solutions. In all cases the DVS solution was successfully validated -- at
least in a practical sense -- specifically in terms of the accuracy and precision of the DVS solution. As the
DVS method is approximate (at early times), there are small discrepancies which are of little or no
practical consequence. In terms of computation times, because of its analytic nature, the DVS method is
not always optimal in terms of speed for certain problems, but the DVS approach is similar in computation
speed with commercial reservoir simulation programs.