Summary
This paper discusses new techniques for the modeling and simulation of
naturally fractured reservoirs with dual-porosity models. Most of the existing
dual-porosity models idealize matrix-fracture interaction by assuming
orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady
state flow. More importantly, a direct generalization of single-phase flow
equations is used to model multiphase flow, which can lead to significant
inaccuracies in multiphase flow-behavior predictions. In this work, many of
these existing limitations are removed in order to arrive at a transfer
function more representative of real reservoirs.
Firstly, combining the differential form of the single-phase transfer
function with analytical solutions of the pressure-diffusion equation, an
analytical form for a shape factor for transient pressure diffusion is derived
to corroborate its time dependence. Further, a pseudosteady shape factor for
rhombic fracture systems is also derived and its effect on matrix-fracture mass
transfer demonstrated. Finally, a general numerical technique to calculate the
shape factor for any arbitrary shape of the matrix block (i.e., nonorthogonal
fractures) is proposed. This technique also accounts for both transient and
pseudosteady-state pressure behavior. The results were verified against
fine-grid single-porosity models and were found to be in excellent
agreement.
Secondly, it is shown that the current form of the transfer function used in
reservoir simulators does not fully account for the main mechanisms governing
multiphase flow. A complete definition of the differential form of the transfer
function for two-phase flow is derived and combined with the governing
equations for pressure and saturation diffusion to arrive at a modified form of
the transfer function for two-phase flow. The new transfer function accurately
takes into account pressure diffusion (fluid expansion) and saturation
diffusion (imbibition), which are the two main mechanisms driving multiphase
matrix-fracture mass transfer. New shape factors for saturation diffusion are
defined. It is shown that the prediction of wetting-phase imbibition using the
current form of the transfer function can be quite inaccurate, which might have
significant consequences from the perspective of reservoir management.
Fine-grid single-porosity models are used to verify the validity of the new
transfer function. The results from single-block dual-porosity models and the
corresponding single-porosity fine-grid models were in good agreement.
Introduction
A naturally fractured reservoir (NFR) can be defined as a reservoir that
contains a connected network of fractures (planar discontinuities) created by
natural processes such as diastrophism and volume shrinkage (Ordonez et al.
2001). Fractured petroleum reservoirs represent over 20% of the world's oil and
gas reserves (Saidi 1983), but are, however, among the most complicated class
of reservoirs. A typical example is the Circle Ridge fractured reservoir
located on the Wind River Reservation in Wyoming, U.S.. This reservoir has been
in production for more than 50 years but the total oil recovery until now has
been less than 15% (www.fracturedreservoirs.com 2000).
It is undeniable that reservoir characterization, modeling, and simulation
of naturally fractured reservoirs present unique challenges that differentiate
them from conventional, single-porosity reservoirs. Not only do the intrinsic
characteristics of the fractures, as well as the matrix, have to be
characterized, but the interaction between matrix blocks and surrounding
fractures must also be modeled accurately. Further, most of the major NFRs have
active aquifers associated with them, or would eventually be subjected to some
kind of secondary recovery process such as waterflooding (German 2002),
implying that it is essential to have a good understanding of the physics of
multiphase flow for such reservoirs. This complexity of naturally fractured
reservoirs necessitates the need for their accurate representation from a
modeling and simulation perspective, such that production and recovery from
such reservoirs be predicted and optimized.
© 2006. Society of Petroleum Engineers
View full textPDF
(
2,494 KB
)
History
- Original manuscript received:
6 June 2004
- Revised manuscript received:
21 December 2005
- Manuscript approved:
11 March 2006
- Version of record:
20 September 2006
View Cart
