Summary
Reservoir formations are often very heterogeneous and fluid flow is strongly
determined by their permeability structure. Thus, when a scale inhibitor (SI)
slug is injected into the formation in a squeeze treatment, fluid placement is
an important issue. To design successful squeeze treatments, we wish to control
where the fluid package is placed in the near-well reservoir formation. In
recent work (Sorbie and Mackay 2005), we went “back to basics” on the issue of
viscous SI slug placement. That is, we re-derived the analytical expressions
that describe placement in linear and radial layered systems for unit mobility
and viscous fluids. Although these equations are quite well known, we applied
them in a novel manner to describe scale inhibitor placement. We also
demonstrated the implications of these equations on how we should analyze
placement both in the laboratory and by numerical modeling before we apply a
scale inhibitor squeeze. An analysis of viscosified SI applications for linear
and radial systems was presented both with and without crossflow between the
reservoir layers.
In this previous work, we assumed that the fluid being used to viscosify the
SI slug was Newtonian(Sorbie and Mackay 2005). However, the question has been
raised concerning what the effect would be if a non-Newtonian fluid was used
instead. We mainly consider the effect of shear thinning, although our analysis
is generally applicable if the non-Newtonian flow rate and effective viscosity
function is known. We address the questions: Does the shear thinning behavior
result in more placements into the higher or lower permeability layer (in
addition to the effect of simple viscosification)? Can the shear thinning
effect be used to design improved squeeze treatment?
Background and Introduction
Chemical SIs have long been applied in downhole “squeeze” treatments to
prevent mineral scale formation(Miles 1970; Vetter 1973; Meyers et al 1985;
King and Warden 1989; Yuan et al. 1993; Boreng et al 1994; Sorbie et al. 1994).
In a homogeneous reservoir layer, adsorption may be the only retention
mechanism governing the SI return from the well. However, reservoir formations
are rarely homogeneous but are made up of highly heterogeneous rocks which may
have a layered or more complex structure as determined by various
sedimentological, structural, and diagenetic factors(Weber 1982). Here we will
consider only layered systems where the various layers have different
permeabilities, k (and porosities, f) in the near-well formation. In such
systems, SI placement within the formation is an additional aspect of a squeeze
treatment that must be considered because this may affect the SI returns.
Scale inhibitors are typically applied as aqueous solutions at
concentrations, in the range 10,000 to 150,000 ppm. These solutions usually
have a viscosity (m) close to that of an injection brine; (i.e., ~1 cP at 20oC
and 0.3 cP at 100oC). Therefore, apart from a slight temperature effect, the
injected brine displaces formation water (FW) at unit mobility. Also, for
lighter oils, a unit mobility displacement is often involved although viscosity
and relative permeability effects may be more important in heavier oils. In
unit mobility injection into a heterogeneous layered linear or radial system,
as shown schematically in Fig. 1, the fluid placement into layer i is governed
solely by the (kh)i product. That is, injecting fluid at a total volumetric
flow rate of QT into an N-layer system of the type shown in Fig. 1, then flow
into layer i, Qi, is given by:
Figure (1)
It can easily be shown that this is true for unit mobility displacement in a
linear or a radial system with or without crossflow. However, this well
established result might foster the belief that linear and radial systems are
also very similar under viscous slug injection with and without crossflow and
this is not the case.
In recent years, the use of viscosified slugs of SI has been proposed to
change the placement pattern in a “favorable” manner (Mackay et al. 1998;
Feasey et al. 2004; Mackay and Al-Mayahi 2003; Jordan et al. 1999). In this
context, “favorable” may mean to place the SI slug entirely in the high
permeability layer from which the water is being produced. However, it may also
mean that we wish to place the inhibitor slug in the lower permeability layers
where it may be “stored” and flow back to the well more slowly because of the
reduced flows from these layers. Whatever our intention, we must clearly
understand the fluid mechanics of viscous slug placement in heterogeneous
systems to achieve the effects we are after (i.e., most of the SI slug in the
high k or low k layer).
At this point, we note that viscosified solutions or other types of
“diverter” may also be injected to modify the relative flows in the wellbore
and near-well formation in long horizontal wells(Mackay et al. 1998; Feasey et
al. 2004; Mackay and Al-Mayahi 2003; Jordan et al. 1999). Viscous fluids are
also used in a similar manner in viscous acidizing where the central intention
is to “present the treatment fluid evenly to the face of the formation”.
However, we will not consider intra-wellbore effects in this paper. We are
primarily concerned with the fluid mechanics in layered heterogeneous
formations both with and without crossflow for linear and radial systems. These
layered systems may have N-layers but for simplicity, we consider only 2, as in
the simple schematics in Fig.1.
Most results here can be generalized quite easily to multi-layer systems. In
our previous paper, we described both analytical and numerical result for
viscous SI placement using a Newtonian fluid (Sorbie and Mackay 2005). Here, we
generalize these results to where a non-Newtonian (shear-thinning) fluid is
used to viscosify the SI slug to “help” in the placement.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
16 March 2006
- Meeting paper published:
30 May 2006
- Revised manuscript received:
20 December 2006
- Manuscript approved:
5 January 2007
- Version of record:
20 November 2007
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