joint stochastic inversion of petrophysical logs and 3d ... · of seismic amplitude in terms of...

SPWLA 46th Annual Logging Symposium, June 26-29, 2005

JOINT STOCHASTIC INVERSION OF PETROPHYSICAL LOGS AND 3D PRE-STACK SEISMIC DATA TO ASSESS THE SPATIAL CONTINUITY OF FLUID UNITS AWAY FROM WELLS: APPLICATION TO A GULF-

OF-MEXICO DEEPWATER HYDROCARBON RESERVOIR

A. Contreras and C. Torres-Verdin, The University of Texas at Austin, W. Chesters and K. Kvien, Fugro-Jason Rotterdam, and M.Globe, Anadarko Petroleum Corporation

Copyright 2005, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. This paper was prepared for presentation at the SPWLA 46th Annual Logging Symposium held in New Orleans, Louisiana, United States, June 26-29, 2005. ABSTRACT This paper describes a novel methodology to integrate well logs and 3D pre-stack seismic data. The objective is to assess lateral continuity and spatial extent of lithology and fluid units penetrated by a well. Pre-stack seismic data were used to fill the spatial gap between sparse well locations since they embody the degrees of freedom necesary to uniquely interpret lateral variations of seismic amplitude in terms of variations of litho-facies and petrophysical properties. The proposed approach is based on a stochastic global inversion method that concomitantly honors the well logs and multiple angle stacks of seismic amplitude data. Inversion results consist of 3D spatial distributions of acoustic properties, litho-facies, and petrophysical parameters between wells that exhibit a vertical resolution intermediate between that of well logs and 3D seismic data. Examples of the application of this technique are shown using high-quality 3D seismic data acquired in the deepwater Gulf of Mexico. Reservoir units consist of stacked turbidite sands. Conventional petrophysical interpretation based on well logs and rock-core data was performed for 7 wells. Petrophysical and litho-facies logs were constructed and correlated with elastic parameters inferred from P- and S-wave sonic logs to assess the sensitivity of elastic parameters to variations in porosity and fluid saturation. Both petrophysical logs and elastic-petrophysical correlation cross-plots, together with four angle stacks of pre-stack seismic amplitude data, were entered to the stochastic inversion algorithm to produce 3D distributions of litho-facies, porosity, permeability, and fluid saturation. Results successfully describe the spatial continuity of sand units and of their porosity, permeability, and saturating fluids away from wells, showing the

efficiency of the technique for quantitative integration of well logs and pre-stack seismic data. INTRODUCTION Anadarko's Marco Polo deepwater development project is located in Green Canyon Block 608 in the Gulf of Mexico, approximately 175 miles south of New Orleans, in a 4300' water depth environment (Fig. 1). Hydrocarbon production originates from reservoirs consisting of Tertiary deepwater sand deposits. This paper considers a small portion of the Marco Polo Field where hydrocarbon-bearing sand units pertain to the “M” series and are buried at depths between 11500 and 12500 ft (Figs. 2 and 3). The overall “M” series consists of sandy turbidite reservoir deposits interbedded and separated by muddy debris flows. These reservoir intervals are interpreted as stacked, progradational lobes within an overall fan complex. The massive and planar stratified sands exhibit excellent interparticle porosity. Rock-core measurements indicate excellent intrinsic properties: 30%+ porosity, and 100-4000 millidarcies of nominal permeability. The purpose of this research is to assess the lateral continuity and spatial extent of M-series lithology and fluid units penetrated by wells by using pre-stack seismic data. Well logs exhibit a radial length of investigation shorter than 3 m and hence provide limited indication of lateral extent and continuity of reservoir flow units. In the past, post-stack seismic data have been used to fill the spatial gap between sparse well locations. However, post-stack seismic data respond to acoustic impedance (the product of bulk density and P-wave velocity) and, therefore, cannot always uniquely discriminate between spatial variations of porosity, thickness, shale concentration, and fluid saturation. Pre-stack seismic data, on the other hand, are sensitive to S-wave velocity and bulk density in addition to P-wave velocity. This provides additional degrees of freedom to uniquely interpret lateral variations of seismic amplitude in terms of variations of petrophysical properties and flow-unit thickness.

1


(a) Deterministic inversion techniques have been successfully used for reservoir delineation and lithology/fluid characterization in the study area; however high-resolution 3D lithologic and petrophysical models are required to build static reservoir models and accurately assess the spatial continuity of fluid units away from wells. In an effort to simulate elastic and petrophysical properties in the inter-well region of the reservoirs in the Marco Polo Field and improve the vertical resolution of the reservoir models, we resorted to integration of 3D pre-stack time migrated seismic amplitude data with well logs based on a novel geostatistical inversion technique.

We first conducted a standard petrophysical analysis to compute curves of porosity, permeability, and water saturation, and then applied Amplitude-Versus-Angle (AVA) stochastic inversion to generate high-resolution spatial distributions of elastic properties and litholotypes. Subsequently, we co-simulated petrophysical models of porosity, permeability, and water saturation from the inversion results using multivariate statistics. Finally, we assessed the reliability of the results through a detailed sensitivity analysis on the inversion parameters and diverse quality control tests.

C

D

N

B

A

(b)

A B

Marco Polo Block 608

N

Fig. 1. Geographic location of the Marco Polo Field. Anadarko's Marco Polo deepwater development project is located in Green Canyon Block 608 in the Gulf of Mexico.

Fig. 2. (a) Basemap of the Marco Polo Field with well locations and time horizon (top of the M-10 reservoir). (b) Seismic cross-section in time with two control wells in lithotype color-code to show the extent of the reservoir interval.

2


PETROPHYSICAL ANALYSIS

tandard petrophysical evaluation techniques were

he methodology used for petrophysical analysis

) Generation of volume of shale (Vsh) curves from

) Density porosity computation for a dual mineral

) Vsh-correction of density and neutron porosity logs.

) Effective porosity computation from average of

) Simultaneous computation of effective water

process;

) Generation of irreducible water saturation curves.

ty nd irreducible water saturation curves using the Tixier

ata were consistently used throughout the rocess to calibrate and validate computed curves.

y combining multiple lithology-sensitive logs such as

detailed crossplot analysis was performed to orroborate the existence of natural correlations

Fig. 3. Example of wireline logs describing the characteris w Density, P- and S- velocity values across the

Sapplied to generate curves of volume of shale, effective porosity, effective water saturation, and permeability. Tconsisted of the following 7 steps: (1gamma ray logs using Larionov’s equation for Tertiary clastic rocks. (2(sand-matrix, shale) and single fluid (brine) model. (3 (4Vsh-corrected density and neutron porosity logs. (5saturation and fluid-corrected effective porosity using the Simandoux model and the dual mineral (sand-matrix, shale) and dual fluid (brine, hydrocarbon) porosity model through an iterative optimization

tic lo

hydrocarbon-bearing “M-series” sands. (6 (7) Permeability computation from effective porosiamodel. Core dpFigure 4 shows an example of the porosity, water saturation, and permeability results for well control # 1. Additionally, lithotype (sand/shale) logs were generated bvolume-of-shale, density, p-wave velocity, and s-wave velocity. Finally, a cbetween acoustic and petrophysical variables (Figs. 5 and 6).

3


(a) Effective Porosity and Water Saturation Logs

) Permeability Log (b

Fig. 4. Example of curves generated from the

etrophysical analysis. (a) Porosity (red) and water

) P-Velocity vs. Porosity (a

(b) S-Velocity vs. Porosity

psaturation (blue); (b) Permeability. Blue dots represent core data.

(c) Density vs. Porosity

Shales

Sands

Shales

Sands

ShalesSands

Fi

f correlations between acoustic and petrophysical

g. 5. Crossplot analysis corroborating the existenceovariables: (a) Vp vs. Porosity, (b) Vs vs. Porosity, and (c) Density vs, Porosity. Color-code represents volume-of-shale (Vsh).

4


(a) P-Velocity vs. Water Saturation

(b)

S-Velocity vs. Water Saturation

(b) Density vs. Water Saturation

HC-Sands

Fi

f correlations between acoustic and petrophysical ariables: (a) Vp vs. Sw, (b) Vs vs. Sw, and (c) Density

order to prepare the 3D pre-stack seismic data for

r partial angle stacks using a velocity

inverted with well logs using a novel ochastic inversion algorithm, which is based on the

e 1-ms micro-layering to be nforced by the inversion results. Input data consisted

) 3D istributions of acoustic properties (P-velocity, S-

d at ms) and deterministic inversion results generated

lithotype models can be multaneously generated with the inverted acoustic

g. 6. Crossplot analysis corroborating the existenceovvs, Sw. Color-code represents volume-of-shale (Vsh).

PRE-STACK STOCHASTIC INVERSION Instochastic inversion the time-migrated gathers were

Shales +

Water-Sands

organized into foufunction. Time shift corrections were additionally applied to the stacks in order to reduce the effect of event misalignment due to processing problems such as residual NMO. Subsequently, these partial angle stacks were simultaneously

HC-Sands stMarkov Chain Monte Carlo (MCMC) (Gilks et al., 1996) and Multigrig Monte Carlo (MGMC) (Goodman et al., 1989) methods, combining the Gauss random field conceptual model underlying traditional geostatistics with iterative local updates inherent to nonlinear optimization. The stochastic inversion uses a stratigraphic/structural framework to define th

Shales +

Water-Sands HC-Sands

eof: (1) four partial angle stacks and angle-dependent wavelets for the following angle ranges: (6-16), (16-26), (26-36), and (36-46) degrees; (2) lithotype, P-velocity, S-velocity, and density logs, and (3) well-log generated geostatistical information in the form of variograms and histograms of properties (Fig. 7). Figures 8 to 10 show the results of the AVA stochastic inversion, consisting of high-resolution (1 msd

s Shale velocity, and density), and lithotypes (sand/shale). Figure 11 is a comparison between the high-resolution stochastically derived acoustic impedance (sample

Water-Sands

1using a constrained sparse spike inversion (CSSI) algorithm (sampled at 4 ms). One important characteristic of this novel stochastic inversion technique is that siproperties, which are the controlling variables that govern the lithologic simulation. Such simulation of lithotypes is based on 3D joint PDF’s of acoustic properties (P-velocity, S-velocity, and density) defined for each specific lithology from well log data (Fig. 12).

5


(a) Near angle seismic and extracted wavelet (6-16°)

6

used for inversion.

(b) Mid angle seismic and extracted wavelet (16-26°)

(c) Far angle seismic and extracted wavelet (26-36°)

(d) UltraFar seismic and extracted wavelet (36-46°)

A B

M-Series Sands

a

ty

Fig. 7. Input data for pre-stack stochastic inversion: (a) Lithotype logs, (b) Mid PAS nd wavelet 16-26° with P-vel (c) Far PAS and w 6° with S-velocity logs, and (d) UltraFar PAS and wavelet 36-46° with Densi Black horizons describe the stratigraphic model

avelet 26-3 Near partocity logs,

logs.

ial angle stack (PAS) and wavelet 6-16° with

Time (ms)

Near (6-16°)

Time (ms)

Time (ms)

Time (ms)

Mid (16-26°)

Far (26-36°)

Ultra Far (26-36°)

Sand Shale


(a) P-Velocity

(b)

sto(c

(b)

sto(c

S-Velocity

S-Velocity

(c) Density (c) Density

pre-stackcity, and

ew of on

pre-stackcity, and

ew of on

Fig. 8. Elastic properties derived from

chastic inversion: (a) P-Velocity, (b) S-Velo) Density. This example s the 3D vi

Fig. 8. Elastic properties derived from

chastic inversion: (a) P-Velocity, (b) S-Velo) Density. This example s the 3D vishowshow lyly

one internal microlayer associated to the uppermost sand reservoir (M-10). The spatial coverage is approximately 4 km2.

(a) P-Velocity

one internal microlayer associated to the uppermost sand reservoir (M-10). The spatial coverage is approximately 4 km2.

(a) P-Velocity C D

M-Series Sands

(b) S-Velocity

D

C

(c) Density

Fig. 9. Cross-section of the acoustic properties derived from pre-stack stochastic inversion: (a) P-Velocity, (S-Velocity, and (c) Density. e color-scale is the same

b) Th

as in Fig. 7. Sand intervals are represented by relatively low values of the three elastic properties.

7


(a)

D

C

(b)

DC

(c)

Fig. 10. Lithology distributions derived from the pre-stack stochastic inversion: (a) 3D view of one interna

icrolayer associated to the uppermost sand reserv r l

m oi(M-10); (b) 2D line intersecting wells # 1 and 1st1 as shown in Fig 8a; and (c) 3D view of the filtered sand distribution (yellow geobodies) corresponding to the M-10 reservoir (mean of 6 realizations).

(a)

(b)

(c)

Well-Log P-Impedance (g/cc*m/s)

Stochastic

GR

GR

C

D

Fig. 11. Deresults: (a)

verted P-iminlocation. Dewhereas stocms.

8

Deterministic

terministic versus stochastic inversion inverted P-impedance cross-sections; (b) pedance pseudo logs extracted at a well

terministic results are sampled at 4 ms hastic inversion results are sampled at 1


CO-SIMULATION OF PETROPHYSICAL PROPERTIES

etrophysical properties from post-stack seismic inversion results consists of co-simulation of

the clusters ssociated with each lithofacies appear as three-

basis of assumptions about the ultidimensional joint distribution of all the properties

r saturation) ere generated via co-simulation from the AVA

ility distributions of acoustic properties enerated from well log sample histograms and used for

the clusters ssociated with each lithofacies appear as three-

basis of assumptions about the ultidimensional joint distribution of all the properties

r saturation) ere generated via co-simulation from the AVA

ility distributions of acoustic properties enerated from well log sample histograms and used for

Conventional approaches for generating 3D distributions of p

a

one petrophysical property (i.e. porosity) from the inverted acoustic property (i.e. P-impedance) by establishing a geostatistical correlation between them. However, pre-stack stochastic inversion results consist of three elastic properties (P-velocity, S-velocity, and density), which are in turn, dependent on medium physical properties such as lithology, porosity, and pore fluid content (Castagna and Backus, 1988). This provides additional degrees of freedom to generate improved statistical relationships between more than one acoustic and petrophysical property. When cross-plotting three properties (such as P-velocity, S-velocity, and porosity)

s consist of three elastic properties (P-velocity, S-velocity, and density), which are in turn, dependent on medium physical properties such as lithology, porosity, and pore fluid content (Castagna and Backus, 1988). This provides additional degrees of freedom to generate improved statistical relationships between more than one acoustic and petrophysical property. When cross-plotting three properties (such as P-velocity, S-velocity, and porosity) aadimensional clouds, comprising samples from a 3D joint distribution. Projecting this distribution onto the sides of the diagram would yield the 2D joint distributions (for P-velocity/S-velocity, P-velocity/porosity, and S-velocity/porosity); information is lost in the projection, and it is not necessarily possible to reconstruct the 3D distribution even from the full set of 2D distributions. In other words, there are correlations between the three properties which are not captured in the correlations between the three pairs, just as correlations between two properties are not captured in their 1D histograms. Our approach consists of performing reservoir characterization on the

dimensional clouds, comprising samples from a 3D joint distribution. Projecting this distribution onto the sides of the diagram would yield the 2D joint distributions (for P-velocity/S-velocity, P-velocity/porosity, and S-velocity/porosity); information is lost in the projection, and it is not necessarily possible to reconstruct the 3D distribution even from the full set of 2D distributions. In other words, there are correlations between the three properties which are not captured in the correlations between the three pairs, just as correlations between two properties are not captured in their 1D histograms. Our approach consists of performing reservoir characterization on the mminvolved (elastic and petrophysical), rather than about their individual histograms or pairwise cross-plots. The more precisely we can represent the true shape of the joint distribution, the more accurate and less uncertain our predictions will be. For example, we may be able to make a better porosity prediction for a reservoir if we take into account both P-velocity and S-velocity, than if we derive porosity from either velocity on its own. And we will be able to image the sands better if we can rule out unlikely combinations of sand Vp, Vs, and ρ, than if we look separately at Vp vs Vs and Vs vs ρ. The 3D spatial distributions of the main petrophysical properties (porosity, permeability, and wate

involved (elastic and petrophysical), rather than about their individual histograms or pairwise cross-plots. The more precisely we can represent the true shape of the joint distribution, the more accurate and less uncertain our predictions will be. For example, we may be able to make a better porosity prediction for a reservoir if we take into account both P-velocity and S-velocity, than if we derive porosity from either velocity on its own. And we will be able to image the sands better if we can rule out unlikely combinations of sand Vp, Vs, and ρ, than if we look separately at Vp vs Vs and Vs vs ρ. The 3D spatial distributions of the main petrophysical properties (porosity, permeability, and watewwstochastic inversion results (P-velocity, S-velocity, and density) using this multivariate statistics approach. The methodology consisted of generating well log 1D sample histograms for each elastic and petrophysical

property and then combining the information into layer- and lithotype-dependent multidimensional joint distributions, in order to capture all the relationships nd correlations between the 6 properties (P-velocity,

S-velocity, density, porosity, permeability, and water saturation). Figure 12 is an example of the multidimensional (3D) joint probab

stochastic inversion results (P-velocity, S-velocity, and density) using this multivariate statistics approach. The methodology consisted of generating well log 1D sample histograms for each elastic and petrophysical

property and then combining the information into layer- and lithotype-dependent multidimensional joint distributions, in order to capture all the relationships and correlations between the 6 properties (P-velocity, S-velocity, density, porosity, permeability, and water saturation). Figure 12 is an example of the multidimensional (3D) joint probabggpre-stack stochastic inversion. The same approach is used for petrophysical co-simulation but integrating 3 acoustic and 3 petrophysical variables (6D joint PDF’s), the results are shown in Figs. 13 and 14.

pre-stack stochastic inversion. The same approach is used for petrophysical co-simulation but integrating 3 acoustic and 3 petrophysical variables (6D joint PDF’s), the results are shown in Figs. 13 and 14.

(a)

(b)

Fig. 12. Example of lithotype-dependen

ultidimensiona ns generated from ell log data: (a) Vp-Density Joint PDF (2D

Vp_Vs Joint PDF

t

Vp_ρ Joint PDF

m l joint distributiowhistogram) derived from 1D sample histograms ; (b) 3D Joint PDF of acoustic properties: P-Velocity (Vp), S-Velocity (Vs), and Density (ρ).

9


(a) Porosity (φ)

(b) Permeability (k)

o-simulated petrophysical properties for the ability, and (c)

water saturation. This example shows the 3D view of only one internal microlayer associated with the M-10 reservoir. The spatial coverage is approximately 4 km2.

Permeability (k)

Fig. 14. Geobody extraction of co-simulated petrophysical properties for the M-10 reservoir: (a) geobodies represent areas with porosity higher than 20% (right) and 30% (left), (b) areas with permeability higher than 1500 mD, and (c) areas with water saturation lower than 20 %. Different colors represent individual non-connected geobodies.

(a) Porosity (φ)

(b)

(c) Water Saturation (Sw)

(c) Water Saturation (Sw)

Fig. 13.

φ > 20 %

Sw < 20 %

k > 1500 mD

φ > 30 %

CM-10 reservoir: (a) porosity, (b) perme

10


EVALUATION OF RESULTS

In order to evaluate the reliability of the results, several sensitivity analysis and quality control tests where performed. Initially, synthetic seismic data generated from well logs where used to assess the effect of data quality and inversion parameters on the inversion results. 3D volumes of acoustic properties (Vp, Vs, and density) where generated from well-log data, and subsequently used to generate synthetic part e stacks through the Knott-Zoeppritz eq , convolution wit ndent wavelets synthetic random noise. Inversion ee synthetic data clearly produced the mo results (high cross-correlation between input and inverted acoustic volumes); a sensitivity analysis on angle ranges showed that availability of far angles is crucial for accurate reconstruction of S-velocity and density. Another sensitivity analysis on inversion parameters was performed using post-stack seismic data. Parameters analyzed included: variogram type, variogram vertical/lateral range, lithotype fraction, noise level, wavelet, and seed value for different

alizations. This study evidenced that v ation on the d the inversion

sults (Figs. 15-16) and the selection of optimal inversion parameters can be achieved by using criteria such as the highest real/synthetic seismic cross-correlations (low residuals) and property distributions that follow the shape of seismic amplitude anomalies. Additionally, well blind tests were performed to compare litho-type simulations generated using post-stack data (only dependent on P-Impedance) and those obtained from pre-stack data (jointly conditioned by P-Velocity, S-Velocity, and density). Figures 17a shows that litho-type realizatio sing either post- or pre-stack seismic dat ilar when all the available well log information is included in the inpu

owever, well blind tests (Fig 17b) show that litho-typ ore accurately

constructed from pre-stack inversion, and the lateral extent of the sands for the case of pre-stack results is less affected by the exclusion of well log data in the input. The results of the sensitivity analysis and blind tests also evidence that the thickest sand units (with thickness above seismic resolution) are better reconstructed in blind tests and less affected by changes in inversion parameters. Porosity co-simulations using 2D, and 4D correlations where compared to assess the effect of including

e ,

e ll

e three acoustic properties (Vp, Vs, and density) for

relationships between Vp, Vs, and density on thporosity predictions (Figs. 18-19). 2D joint distributionsconsist of single relationships between Vp and PorosityVs and Porosity, and Density and Porosity, whereas 4Djoint distributions consist of simultaneous relationshipamong Vp, Vs, density, and porosity. The most accurate porosity predictions were obtained when using 4D PDF’s (Fig. 20). Finally, blind well test where performed to validate thacoustic and petrophysic t known welocations. These tests evi version of pre-stack seismic data is capable of reconstructing acoustic

roperties at well locations; and the simultaneous use o

ial angluations

g noise-frre accurate

al results adence that inh angle-depe , and addin

of

ari

p f thco-simulation of petrophysical properties such as porosity is a reliable approach (Fig. 21). (a) Variogram lateral range = 500m.

reinversion parameters slightly affectere

(b) Variogram lateral range = 1000m.

ns generated ua are very sim

t;eh

distributions at well locations are mre

Fig. 15. Sensitivity analysis on the inversion parameter “Variogram lateral range”: (a) Lithotype section obtained using a variogram lateral range of 500 m., (b) Lithotype section obtained using a variogram lateral range of 1000 m. Inversion results are clearly affected by the variogram lateral range; however, the lateral extent and geometry of the thickest sand bodies remain almost invariant.

11


(a) Lithotype Fraction = 5% Sand / 95% Shale

(b) Lithotype Fraction = 25% Sand / 75% Shale

Fig. 16. Sensitivity analysis on the inversion parameter “Lithotype Fraction”: (a) Lithotype section obtained rom a 5% Sand /f 95% Shale distribution, (b) Lithotype

) Normal Tests (using well # 1) (a

section obtained from a 25% Sand / 75% Shale distribution. Inversion results are clearly affected by the lithotype fraction parameter; however, the lateral extent and geometry of the thickest sand bodies remain almost constant and mainly thin sands are added when increasing the sand/shale ratio.

(b) Blind Tests (excluding well # 1)

Post-Stack derived

Pre-Stack derived

g. 17. Litho-types distributions obtained from Post-re-stack seismic inversion: (a) Normal tests

cluding well # 1 as input data for the inversion); (b)

Post-Stack derived

Pre-Stack derived

Fiand P(inBlind Tests (excluding well # 1 from input data). Blind tests show that litho-type distributions on well # 1 are better reconstructed from pre-stack inversion. Also, the lateral extent of the sands (normal vs. blind test) is more consistent for the case of pre-stack results.

12


φ - Vp (a)

Fig. 18. Co-simulation test # 1: Porosity from only P-Velocity. (a) Porosity-Vp joint PDF used for co-simulation; (b) e extracted M-10 reservoir geododies associated with porosity values higher than 25%.

e extracted M-10 reservoir geododies associated with porosity values higher than 25%.

3D view showing thng th

(b)

(

(a) C

φ - Vs

φ - Vp

(b)

Porosity from Vp

(c) φ > 25 % φ - ρ

d)

Porosity from Vp, Vs, ρ

Fig. 19. Results of the co-simulation test # 2: Porosity from P-Velocity, S-Velocity, and Density. (a), (b), (c)joint PDF’s used for co-simulation (Porosity-P-Velocity, Porosity-S-Velocity, and Porosity-Density respectively) ; (d) 3D view showing the extracted M-10 reservoir geododies associated with porosity valueshigher than 25%.

φ > 25 %

13


Fig. 20. Well blind test associated with the porosity co-

mulations shown in Figs. 18 and 19: (a) Porosity mulation from only Vp (blue curve); (b) porosity mulation from Vp, Vs, and ρ (green curve). The red urve represents the real porosity log computed at the ell location. The inclusion of Vs, and ρ has clearly proved the porosity simulation results.

sisisicwim

(a) (b)

Fig. 21 Porosity co-simulation tests in section view: (a) normal test (including the well as input for the co-simulation); (b) blind test (well porosity log not used for co-simulation). Thick and high porosity sands are better co-simulated. Notice that the lateral extent o e

s is not affected by the petrophysical co-simula on.

CO By sto ta and well lo uity and s nits penet hat three ac ack seis rally relat s of free o-

The key for accurate extrapolation of petrophysical variables away from well logs consists of (1) generate reliable volumes of acoustic properties from high-quality pre-stack seismic data, and (2) establishing precise multidimensional correlations between acoustic and petrophysical variables at well locations that can be use to guide the petrophysical co-simul inverted acoustic volumes. Pre-stack stochastic i ults ar y sensitive to inversion parameters such as v

teral range and lithotype fraction, however good

ed by slight changes in inversio rameters. Definition of accurate multidimensional correlations between acoustic and petrophysical properties will depend on the quality of the well log data and petrophysical estimations, as well as on the clear existence of natural correlations among such variables in the study area. A ly, the accuracy of the results is directly pro to the res ty of the sand units, i.e. the best results are obtained for reservoirs with thickness above seismic resolution, and characterized by clean- high porosity sands. Finally, pre-stack seismic data has proven to be more effective than post-stack seismic data for assessing the lateral continuity and spatial extent of lithology and fluid units penetrated by a well; and for co-simulation of petrophysical properties in the inter-well area. This is attributed to the amplitude-versus-angle (AVA)

formation preserved in pre-stack seismic data which

(a) (b)

φ from Vp, Vs, ρ

φ from only Vp

NCLUSIONS

chastically integrating pre-stack seismic dags it is possible to assess the lateral continpatial extent of lithologic and fluid u

rated by a well. This is attributed to the fact toustic properties can be inverted from pre-st

mic data (Vp, Vs, density) which are natued to lithology and fluids. Additional degreedom are then available for more accurate clations of petrophysical properties via multiv

statistics. simu ariate

ations from

e relativelariogram

nversion res

laquality seismic data and availability of enough angle ranges remains crucial to capture amplitude variations with angle which result on accurate inversion of elastic properties, and subsequent petrophysical predictions. Additionally, sensitivity analysis and blind tests indicate that thick sands are better reconstructed from inversion and less affect

n pa

ccordingportional ervoir-quali

inallows the inversion of three acoustic properties (Vp, Vs, and Rho), increasing the degrees of freedom for co-simulation of petrophysical properties.

f thtisand

14


15

he authors would like to thank Anadarko Petroleum orporation for providing the data set used for this

research study. A note o l gratitude goes to Fugro-Jason for their u ricted technical and software support. This wo was supported by UT Austin Research Consortiu Formation Evaluation, jointly sponsored by Anad Petroleum Corporation,

er Atlas, BP, ConocoPhillips, ExxonMobil, Halliburton Energy Serv e Mexican Institute for

roleum, Occidental Petr eum, Petrobras, Precision Energy Services, Sc berger, Statoil, Shell

ternational E&P, and

REFERENCES Castagna, J., and Backus, M , 1993, Offset dependent reflectivity – Theory and practice of AVO analysis:Society of Exploration Geophysics, p. 3-135. Gilks, W., Richardson, S., and Spiegelhalter, D., 96,

arkov Chain Monte Carlo in practice: Chapm

HORS

and Geosystems Engineering, where he has

Fugro-Jason, Anadarko

um and Geosystems Engineering f The University of Texas at Austin, where he

ACKNOWLEDGMENTS

TC

f snrestrk

m onarko

ices, thol

hlum TOTAL.

.

pecia

Bak

Pet

In

19an & M

Hall/Crc, p. 45-54. Goodman, J., and Sokal, A., 1989, Multigrid Monte Carlo method. Conceptual foundations: Physical Review D, volume 40, p. 2035-2071.

BOUT THE AUTA Arturo Contreras received a B.S. degree in Geophysical Engineering from the Central University of Venezuela in 1999. During 2000 he held the position of Lecturer for the Department of Geophysics of the same university. In 2001, he joined the PhD program of the Department of Geological Sciences at the University of Texas at Austin, and since 2002 he has been working for the UT-Austin Research Consortium on Formation Evaluation at the Department of

etroleumPheld the positions of Teaching Assistant of Fundamental of Well Logging and Graduate Research Assistant on Integrated Reservoir Characterization and Seismic Inversion. The work presented in is this paper is part of his PhD dissertation research which is jointly supported by the UT-Austin Department of Geological Sciences, the UT-Austin Formation Evaluation Consortium at The Department of Petroleum and

eosystems Engineering, GPetroleum Corporation, and PDVSA.

Carlos Torres-Verdín received a PhD in Engineering Geoscience from the University of California, Berkeley, in 1991. During 1991–1997 he held the position of Research Scientist with Schlumberger-Doll Research. From 1997–1999, he was Reservoir Specialist and Technology Champion with YPF (Buenos Aires, Argentina). Since 1999, he has been with the Department of Petroleocurrently holds the position of Associate Professor. He conducts research on borehole geophysics, formation evaluation, and integrated reservoir characterization. Torres-Verdín has served as Guest Editor for Radio Science, and is currently a member of the Editorial Board of the Journal of Electromagnetic Waves and Applications, and an associate editor for Petrophysics (SPWLA) and the SPE Journal.

joint stochastic inversion of petrophysical logs and 3d ... · of seismic amplitude in terms of...

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