Summary
It is well established within the industry that injection of (produced)
water almost always takes place under fracturing conditions. Particularly when
large volumes of very contaminated water are injected—either for voidage
replacement or disposal—large fractures may be induced over time.
This paper aims to provide a methodology for injection-falloff (IFO) test
analysis of fractured (produced) water-injection wells. Some essential elements
of IFO for fractured water injectors include the closing fracture, (early)
transient elliptical reservoir-fluid flow, finite fracture conductivity, and
fracture face skin.
An exact semianalytical solution is presented to the fully transient
elliptical fluid-flow equation around a closing fracture with finite
conductivity, fracture face skin, and multiple mobility zones in the reservoir
surrounding the fracture. This solution also captures the case that during
closure, the fracture is generally shrinking from adjacent geological layers
under higher in-situ stress. Based on this solution, type curves of the
dimensionless bottomhole pressure as a function of dimensionless time are
provided, covering both the period during fracture closure/shrinkage and the
period after fracture closure. The shape of these type curves is studied as a
function of the different relevant parameters, in particular the fracture
compliance, the height of in-situ stress contrasts, fracture face skin,
fracture closure time, and injection period. It is shown how the fracture
length and height and the degree of fracture containment (in combination with
the heights of the stress contrasts) can be derived from these types of curves.
It is also demonstrated that the analyses based on the storage flow and linear
formation flow regimes need to be integrated into one analysis method to obtain
consistent results.
Finally, the concepts developed in this paper are applied to a number of
field examples, in which the dimensions and degree of containment of the
induced fractures are derived from the analysis of the IFO data.
Introduction
IFO test analysis offers one of the cheapest ways to determine the
dimensions of induced fractures. Unfortunately, hardly any work has been
carried out to date to provide a methodology for interpreting the
pressure-transient data of fractured water-injection wells. This contrasts with
the vast amount of work that has been carried out in the area of
pressure-transient analysis for wells with propped fractures. Both
pressure-transient tests during hydraulic fracture stimulation (called
“minifrac tests”; see Ref. 1) and pressure-transient tests during production
after stimulation (i.e., buildup tests; see Refs. 2 through 5) have been
studied extensively. The theories as developed in Refs. 1 through 5 by now are
well-accepted “textbook” methodologies.
This paper deals with the subject of pressure-falloff analysis on fractured
water-injection wells. In this area, the situation is entirely different from
the one above in the sense that until recently, there existed no practical
methodology dedicated to pressure-falloff analysis on fractured water
injectors.
The very limited interest in falloff-test analysis on fractured water
injectors may well be related to the fact that historically, most operators
have been unaware that their water injectors are fractured. Only in recent
years has this situation started to change. Unfortunately, one of the
consequences of the lack of a dedicated method of analysis is that falloff
tests on injectors are generally interpreted in the wrong way, even if one
realizes that they are fractured. Typically, such interpretations lead to
wellbore-storage coefficients that can be up to orders of magnitude too high,
and to fracture lengths based only on analysis of the linear formation flow
period (see Ref. 10).
The objective of our study is to fill the gap as described above (i.e., to
provide a dedicated interpretation methodology for falloff tests on fractured
water injectors). In a recent paper, we presented a novel interpretation
methodology for falloff tests on fractured water injectors. This methodology is
based on exact 2D solutions to the problem of pressure falloff around fractured
water injectors for different boundary conditions. The most important step
forward of Ref. 6 is that it allows the determination of fracture length from a
consistent combined analysis of the storage and linear-to-pseudoradial
formation flow periods, and of fracture height from a consistent combined
analysis of the storage and pseudoradial flow periods. Thus, uncertainties in
the determination of fracture dimensions from falloff-test analysis are
reduced.
In the course of analyzing a variety of field cases, we found, based on the
signature of field falloff-test data, that in many cases, the induced fractures
must have penetrated into adjacent higher-stress zones. Therefore, the
methodology as developed in Ref. 6 was extended to cater to this effect, with
the objective being to enable derivation of local in-situ stress contrasts from
falloff-test interpretation. This extension forms the main subject of the
current paper.
The paper is organized as follows. The next section presents the
pressure-transient solution for a closing and shrinking water-injection
fracture, including a brief recap of the main concepts presented in Ref. 6. The
third section presents in some detail the shape of the pressure-transient type
curves for a closing/shrinking fracture as a function of the different relevant
parameters, such as the fracture compliance and the height of in-situ stress
contrasts. Subsequently, this method is applied to four field examples.
Finally, the last section presents our conclusions.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
16 February 2004
- Revised manuscript received:
21 June 2005
- Manuscript approved:
25 June 2005
- Version of record:
15 October 2005
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