The Monte-Carlo simulation of wells (i.e., 1-D stratigraphic profiles with
measured physical properties) using a combination of geological knowledge can
be used in seismic lateral prediction studies (Wood and Curtis,
2004; De Groot et al., 1996). The simulation
of realistic synthetic reflection sequences or of lithological sequences has
been studied by Sherrif (1992), Barnes and
Tarantola (1993), Walden (1993) and Kerner
and Harris (1994) because of the potential benefit in seismic reservoir
characterization applications (De Groot et al., 1996).
The Monte Carlo method is a procedure that involves sampling based on probabilities
to approximate the solution of mathematical or physical in a statistical way
(De Groot et al., 1996; Vazquez-Prada
et al., 2002). Monte- Carlo models are used for a variety of different
problems (Musson, 1999; Yang et al.,
2000; Santini et al., 2004; Przybilla
and Korn, 2008). In geoscientific applications, the method is used e.g.,
for reserves and porosity estimations and for prospect evaluations.
The Monte-Carlo-model utilized in this study is a computer program designed
to simulate a two-spike seismic P-wave reflection event and generate seismic
amplitude attributes for the event. Three layers consisting of upper bounding
shale, laminated sand and lower bounding shale define the model. Average
values (and in some instances a statistical variance) of the parameters
controlling the elastic properties of each layer are given as inputs.
The given distribution functions are randomly sampled to generate an ensemble
of two-spike events. For each event offset-dependent synthetic seismograms
are generated using Zoeppritz equations to model the angle-dependent reflection
coefficients and convolving with specified wavelet.
GENERIC MONTE-CARLO MODEL
The geology of the Gulf of Mexico (GoM) deepwater environment is similar
to that of the Niger Delta Slope (Fig. 1). Information
is presently inadequate on the Niger Delta deepwater environment because
few wells are available. The Gulf of Mexico data, where available, could
therefore be utilized as a generic model for the understanding of the
Niger Delta Slope geology and hence its petrophysical and seismic attributes.
In this study therefore, Monte-Carlo simulation of a well log from the
deepwater Gulf of Mexico is undertaken as a control to enhance the understanding
of the petrophysical crossplots in the Niger Delta Slope. Shallow and
deep Monte-Carlo models were generated using SAVIORTM.
The regressions generated in the study area in the Niger Delta Slope environment
(Oladapo and Adetola, 2005) were used for the model while
Harvie-Braunsdrof fluid method was utilized for reservoir fluid properties.
Fourier velocity was also adopted as velocity function for the models. It was
observed that salinity, temperature and pressure variations had trivial influence
on the model results. The data utilised for the crossplots generated in this
study were acquired from Buit-1 well within the Niger Delta Slope. A typical
seismic section from the study area showing horizons of interest is shown in Fig. 2.
||Geological sketch map of Niger Delta complex (Short
and Stauble, 1967) showing the deepwater location of the study area
|| A seismic section from the Niger Delta Slope
The generic model obtained from Gulf of Mexico well log generated for the combined
horizons evaluated include AVO L-M (or A-B) (Bortfeld, 1961;
Shuey, 1985) crossplot shown in Fig. 3a.
The L-M crossplots are typical of brine sand (pink plots), residual hydrocarbon
(light orange) and commercial hydrocarbon (red) models. The brine model forms
the background trend. Abnormally high background normal (Bn) values characterised
the residual hydrocarbon models. Unconsolidated gas sand formations may exhibit
such abnormal characteristics. Similar AVO crossplots may therefore typify the shallow reservoir sand
formations of the Niger Delta Slope.
The 1-D composite synthetic section generated from the AVO crossplot
of Fig. 3a is presented in Fig. 3b.
This plot shows three models i.e., brine, residual hydrocarbon and commercial
hydrocarbon. All the three models are characterised by decrease in Vp
and density as hydrocarbon saturation increases. In contrast the Vs,
stack amplitude, intercept (L) amplitude and half gradient (M/2) values
show increase in value as hydrocarbon saturation increases. The synthetic
seismogram exhibits amplitude increase with offset on residual and commercial
hydrocarbon models while no amplitude variation was displayed on the brine
The composite AVO crossplot of Fig. 3c reveals that
AVO crossplot could be a robust tool for mapping deep reservoirs. The
background normal vectors for the residual hydrocarbon models are very
low compared with similar reservoirs at shallow levels. In contrast the
background normal values for the commercial hydrocarbon are much higher
than for the residual hydrocarbon. Such results could enhance interpretation
of AVO analysis. However, the depth adopted for this model may not exist
within the Niger Delta Slope.
||(a) AVO crossplot of GOM shallow reservoir model, (b)
1-D synthetic seismogram from AVO crossplot of shallow Gulf of Mexico
model and (c) AVO crossplot for the Gulf of Mexico deep model
MONTE-CARLO MODEL WITHIN THE STUDY AREA
AA horizon: The Monte-Carlo model of AA horizon resulted in the generation
of AVO crossplots (L-M) and synthetics. In brine saturated AA model, separation
of residual and commercial HC on L-M crossplot could not be achieved (Fig.
4a, b). In the residual hydrocarbon model of Fig. 4c,
little separation of residual and commercial hydrocarbon models was obtained
on the class III quadrant (Rutherford and Williams, 1989;
Castagna et al., 1998). Variation in background
normal vector also characterised the crossplot. The much desired AA model is
presented in Fig. 4d where commercial (red plots), residual
(yellow plots) and brine (pink) are assumed present in the presence of whitening
noise. The separation is well defined with a near-constant background vector
for residual and commercial hydrocarbon.
The AA horizon L-M crossplot real model is shown in Fig. 5a.
The incoherent orientations of the crossplots point to the fact that the AA
horizon is possibly unconsolidated.
(a) AVO crossplot of Buit AA brine sands model, (b)
AVO crossplot of Buit AA brine sands model + noise, (c) AVO crossplot
of Buit AA residual HC sands model and (d) AVO crossplot of Buit AA
commercial hydrocarbon sands model
||(a) AVO crossplot of Buit AA as encountered and (b)
AVO synthetic of Buit AA generated from AVO crossplot
(a) AVO crossplot of brine saturated Buit BB model,
(b) AVO crossplot of Buit BB commercial hydrocarbon model, (c) AVO
crossplot of Buit BB horizon as encountered and (d) AVO synthetic
of Buit-BB horizon as encountered
The synthetic seismogram generated from
the L-M plot is shown in Fig. 5b. The plot shows three models
in one plot: brine, residual hydrocarbon and commercial hydrocarbon. Figure
5b shows no perceptible amplitude variation with offset on all the models.
BB horizon: Two Monte-Carlo models generated for the BB horizon
are brine saturated model and commercial hydrocarbon saturated model.
The brine saturated model typically plotted on the hard sand (hard kick)
quadrant (Fig. 6a). In contrast, the commercial hydrocarbon
model (Fig. 6b) is plotted on quadrant III (soft kick).
Complete separation of oil sands from gas sands seems unfeasible in the
model. Net to gross associated problems may be responsible for any scatter
in the real plot as seen in the model.
Figure 6c is the L-M crossplot of the encountered
BB horizon. Most of the commercial hydrocarbon plots and some of the residual
hydrocarbon plots fall on quadrant III (bright spot quadrant).
(a) AVO crossplot of brine saturated Buit-CC model as
encountered, (b) AVO crossplot of commercial hydrocarbon saturated
Buit-CC model and (c) AVO crossplot of commercial hydrocarbon saturated
Buit-CC model + noise
||(a) AVO crossplot of brine saturated Buit-DD model and
(b) AVO crossplot of commercial hydrocarbon saturated Buit DD model
the BB L-M crossplot is diagnostic of hydrocarbon-saturated horizon with
some lithology variations within the horizon.
The synthetic seismic generated for the BB horizon (real model) (Fig.
6d) exhibits positive AVO response (soft kick) on the commercial hydrocarbon
CC horizon: The brine saturated model of the L-M crossplot for
the CC horizon model plotted mostly on hard sand quadrant (Fig.
7a). Conversely, presumed commercial hydrocarbon saturated CC is split
between the hard sand and soft sand quadrants with low background normal
values (Fig. 7b, c). Distinction between commercial
hydrocarbon and residual hydrocarbon AVO attributes is somehow difficult
to obtain, as the cloud of crossplots does not enhance good separation.
DD horizon: The DD horizon is similar to the deep model of the
Gulf of Mexico and hence exhibits similar crossplot. For gassmann substituted
brine sand DD model, the crossplot (Fig. 8a) typifies
a general background trend that would exist for the petrophysical crossplot
of the horizon. The brine sand in these instances the yellow and pink
plots, forms the background trend plot for the horizon. Any deviation
from the trend may have been caused by the presence of a lighter fluid
presumably hydrocarbon. Lithology changes may also cause such difference.
A commercial hydrocarbon model is shown in Fig. 8b.
A separation is observed in the plots of commercial hydrocarbon (red),
residual (yellow) and brine (pink). However, the separation is not as
distinctive as what obtained at the shallower levels. Notwith standing,
the red plots still appeared clearly on quadrant III (bright spot possible).
Even in the presence of noise (Fig. 6c) the distinction
The AA horizon is typified by incoherent orientations of AVO crossplots.
The horizon is thus presumed unconsolidated. The synthetic seismogram
generated shows no perceptible amplitude variation with offset on all
AVO crossplot of the encountered BB horizon show that most of the commercial
hydrocarbon plots and some of the residual hydrocarbon plots fall on quadrant
III (bright spot quadrant). Synthetic seismic generated for BB horizon
exhibits positive AVO response (soft kick) on the commercial hydrocarbon
model. A similar but marginal response was obtained on brine saturated
Brine saturated model of the AVO crossplot for CC horizon model plotted
mostly on hard sand quadrant. Conversely, presumed commercial hydrocarbon
saturated CC is split between the hard sand and soft sand quadrants with
low background normal values.
The DD horizon is similar to the deep model of the Gulf of Mexico and
hence exhibits similar crossplot.
Curiously, high background normal (Bn) characterized residual hydrocarbon
models while unconsolidated gas sand horizons exhibit anomalous characteristics.
The Monte-Carlo models obtained from the Gulf of Mexico well MC-522wc
and the variety of models generated from Buit-1 well data of Niger Delta
Slope can aid in understanding the AVO attribute crossplots. The AVO crossplot
obtained from the Monte-Carlo model could be a robust tool for mapping
reservoirs within the Niger Delta Slope.