Summary
The membrane efficiency of shales is usually measured in the laboratory
using pressure-transmission techniques that can be very time consuming and
require shale core samples that may not be available. These tests also
require special high-pressure equipment and cannot be conducted at the
rigsite.
This paper presents a quick and relatively easy method for obtaining the
membrane efficiency of shale cuttings (or cores) through
electrochemical-potential measurements. The electrochemical test measures the
voltage drop across shales that are in contact with fluids of different
salinities. The measured voltage drop is used to calculate the shale’s ion
selectivity, which reflects the shale’s ability to restrict ion flow (membrane
potential). Data are presented to show the influence of ion type and ion
concentration, shale permeability, and cation exchange capacity (CEC) on the
ion selectivity. It was found that the shale membrane efficiency is well
correlated with the membrane potential. The membrane potential is shown to be
proportional to the ratio of the CEC and to the permeability of shales. A
higher CEC/k ratio correlates very well with higher ion selectivity. The
rigsite-measured ion selectivity can be correlated with the
spontaneous-potential (SP) curves in the well.
The rapid determination of shale membrane efficiency using shale drill
cuttings allows chemical interactions between shales and water-based fluids to
be taken into account in wellbore-stability calculations without the need for
shale core samples.
Introduction
When two aqueous solutions with different ionic concentrations are separated
by a porous medium that is permeable to cations and anions, an electrical
potential develops. This is because of differences in ionic mobility (diffusion
rate). Generally, smaller ions have higher mobilities than larger ones and
multivalent ions have a lower mobility than monovalent ions (because of their
larger diameters when hydrated). Differences in ionic mobility can be
attributed to the hydrated-ion size for each type of ion. Sodium ions have a
larger hydrated-ion size than chloride ions. Thus, chloride ions move faster
than sodium ions, and as a result, a diffusion potential develops across any
interface across which a concentration gradient is imposed.
The magnitude of this diffusion potential (or liquid junction potential)
depends on the difference between the transport number of cations and anions
and the ratio of the ionic activities on both sides of the membrane as
follows:
…..……….(1)
where t+ and t- are the transport
numbers of the cation and anion, respectively, in bulk solutions, R is
the universal gas constant, T is the absolute temperature, F is
the Faraday constant, and a1 and a2 are
the ionic activities.
When two solutions of different concentrations are separated by a shale, a
modified diffusion potential develops because the shale allows cations to pass
while restricting anions. Therefore, shales are considered to be ion-selective
membranes that selectively allow cations to move through while restricting
anions. Since the diffusion potential is a measure of the shale’s ability to
restrict anion movement, it can be used to deduce the shale’s membrane
efficiency.
Background and Past Work
Ion-selective membranes yield a modified diffusion potential, whereas
nonselective membranes yield a diffusion potential. If the ion-selective
membrane completely blocks the passage of the co-ions, the charge transport is
entirely because of the counter ions. This type of membrane is referred as a
perfect ion-selective membrane. The maximum possible potential difference, that
can be generated by a perfect ion-selective membrane is given by the Nernst
expression as follows:
……..……………..(2)
The Nernst equation is a special case of the liquid-junction expression, Eq.
1. For this type of membrane, the co-ion transport number is zero while the
counter-ion transport number is unity.
Shales contain negatively charged clay particles. The negative charges on
the clay surfaces tend to facilitate the movement of positive ions, and
restrict the negative ions (Lomba et al. 2000). Sherwood (1995) pointed out
that ion exchange plays an important role affecting not only the rates of
transport of ions, but also the mechanical and swelling properties of the
shale. van der Zwaag (1995) measured electrochemical potentials across shale
samples under different loads and atmospheric conditions. The main objective of
his experimental work was to determine shale membrane efficiency through the
evaluation of ion-transference numbers.
Jin and Sharma (1994) presented a formula that related shaley-sand
conductivity to the membrane-potential. In their work, they showed that
membrane potential measurements can be closely correlated with the CEC of the
rock. Lomba et al. (2000) conducted experiments to evaluate membrane
efficiencies of native shales by measuring the electrochemical potential across
the shale samples. The experiment involved placing shale samples between two
fluids of different concentrations. The electrical-potential difference was
measured and then converted to a membrane efficiency. They showed that the
composition of the interstitial pore fluid in shales plays a determining role
on the electrochemical potential and, in some cases, the behavior of the shale
is close to the expected behavior of a perfect cation-selective membrane.
They developed mathematical models that estimate shale membrane efficiencies
and modified diffusion potential on the basis of the shale and drilling-fluid
physical parameters. It is important to note that the membrane efficiency
calculated by Lomba et al. (2000) was based on comparing the actual diffusion
potential of shale to the maximum expected diffusion potential.
While the previously mentioned studies measured the diffusion potential of
shale, no attempts were made to relate the measured diffusion potential to the
membrane efficiency. In addition, the factors that control the diffusion
potential (ion selectivity) of shale were not investigated thoroughly.
In this work, we measured diffusion potential (ion selectivity) of shales
following the same test matrix used for the membrane-efficiency test. This is
done to correlate the ion selectivity of shale to its membrane efficiency so
that our electrochemical test can be used to infer shale membrane efficiency.
Moreover, we have studied the dependence of the ion selectivity on ion type and
concentration and on shale permeability and shale CEC. We believe that these
are the most important factors that control the ion selectivity and membrane
efficiency of a shale.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
7 September 2005
- Revised manuscript received:
16 April 2006
- Manuscript approved:
25 May 2007
- Version of record:
20 September 2007
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