Download Estimation of pressure and saturation changes from 4D

Estimation of pressure and saturation
changes from 4D seismic AVO and
time-shift analysis
Enhanced Oil Recovery processes have considerable
impact on a reservoir’sphysical characteristics.
4D seismic inversion presents an efficient tool for
quantifying changes in a reservoir’s dynamic properties.
Landro (2001) proposed a simple method for detecting
changes in rock properties from AVO data.
However this inversion algorithm is prone to great
uncertainty. We present here an inversion scheme
based on a modified form of Landro’s equations and
extended with a third equation that relates the P-wave
time-shift to fluid properties changes. The combined
information from amplitudes and travel times can
quantify the changes in the rock properties with fairly
high accuracy. The methodology was tested on a
synthetic field case.
a.
b.
c.
Figure 1. a. Cost function for the solution proposed by Landro; b. Cost function for the solution obtained from a system of three linear equations; c. Cost
function for the solution obtained from a system of three quadratic equations.
Review of Landro’s method
Landro (2001) proposed an elegant procedure to express changes in seismic amplitude
attributes as a function of variation in reservoir saturation and pressure. The expressions
are based on the Smith and Gidlow (1987) PP reflection coefficient equation, which reads:
with kα, lα, mα, kβ, lβ, etc., being the regression coefficients of empirical curves, θ the angle
of incidence, ΔS the change in fluid saturation and ΔP the change in net pressure. Splitting
this expression into the seismic attributes intercept (R0) and gradient (G) leads to a system
that can be explicitly solved for changes in saturation and pressure.
Extension of Landro’s method using
the time-shift as a constraint
The system of equations proposed in Landro
(2001) was extended with an additional
equation expressing the PP-wave time-shift
as a function of changes in pressure (ΔP) and
in saturation (ΔS), defined as:
where D is the reservoir thickness. Explicit
expressions for ΔP and ΔS were found by
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a.
b.
Figure 2. a. Reservoir saturation after two years of production; b. Reservoir pore pressure after two years of production.
solving the system composed by the approximations of change in
vertical reflectivity (ΔR0), change in gradient reflectivity (ΔG) and PPwave time-shift (ΔTpp). The non-linear system was solved with a
Gauss-Newton algorithm. The results were compared to the changes
in pressure and saturation obtained
by solving the system using linearised equations and with Landro’s
method, which does not incorporate the time-shift.
Since approximations were used, estimation of the unknowns can
never be exact (except for the zero perturbation case). The error,
expressed as a cost function, can be quantified as the square root
of the squared differences in saturation and pressure change,
normalised over the dynamic range of each variable:
Costfunc=
In Figures 1a through 1c the cost function has been calculated over
the entire region of interest; in general, the quadratic approximations
present the minimum cost function (i.e., the most accurate solution).
a.
Results
Time-lapse seismic data were analysed as a way of comparing the
estimations of changes in reservoir fluid properties. The basis was
a synthetic 15 × 25 × 11 gridblock, sandy, heterogeneous reservoir.
(Each cell is cubic with sides of 10 m.) A water injector well was
placed in the centre of the reservoir, and four producers in the corners.
Initial water and oil saturation were 10% and 90%, respectively, and
pore pressure was 40 MPa; fluid properties are initially homogeneous.
4D seismic data was modelled before and after two years of production.
The reservoir saturation (a) and pressure (b) after two years of
production are plotted in Figures 2a and 2b.
Figures 3a and 3b show the changes in AVO coefficients after two
years of production.
The predominant changes in pressure explain why G changes more
than R0. We also determined the time-shift, shown in Figure4.
b.
Figure 3a. Change in R0 after two years of production; b. Change in G
after two years of production.
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Figure 4. Time-shift at the reservoir bottom: red corresponds to the
maximum time-shift of 1 ms.
a.
b.
Figure 5. a. Differences between the true average ΔP and the ΔP estimated by Landro’s algorithm for
all the CDPs; b. Differences between the true average ΔP and the ΔP estimated by the linear equation
system for all the CDPs; c. Differences between the true average ΔP and the ΔP estimated by the
quadratic equation system for all the CDPs.
The quadratic approximations, making use of the supplementary
information from PP-wave travel time and of a second order
approximation in both variables, better estimate the vertically
averaged pressure variation.
Conclusions
A 4D seismic inversion scheme based on a modified form of Landro’s
equations and extended with a third equation is proposed; the latter
equation expresses the time-shift induced by P-wave velocity changes
as a function of pore pressure and saturation changes. The method
was tested on a synthetic reservoir. The results showed an
improvement of the ΔP and ΔS estimation with respect to Landro’s
method. The next step is to use the inversion results together with
the production data in a data assimilation scheme (Leeuwenburgh
et al., submitted to 70th EAGE Conference & Exhibition).
c.
Information
Mario Trani
T +31 15 278 61 34
F +31 15 278 11 89
E [email protected]
Rob Arts
T +31 30 256 46 38
F +31 30 256 46 05
E [email protected]
Olwijn Leeuwenburgh
T +31 30 256 45 17
F +31 30 256 46 05
E [email protected]
Jan Brouwer
T +31 30 256 49 57
F +31 30 256 46 05
E [email protected]
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