Rock Physics Perturbational Modeling: Carbonate case study, an intracratonic basin Northwest/Saharan Africa

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1 Rock Physics Perturbational Modeling: Carbonate case study, an intracratonic basin Northwest/Saharan Africa Franklin Ruiz, Carlos Cobos, Marcelo Benabentos, Beatriz Chacon, and Roberto Varade, Luis Gairifo, Mercedes Socas, Nidal El Hafiz, and Iman Suripto Abstract We present an innovative methodology to conduct a rock-physics based perturbational modeling of synthetic seismograms appropriate for tight reservoir rocks. It consists of perturbing the rock s fluid and solid constituent volumes at each well-log depth, and estimating the elastic properties of the perturbed rock. The properties of the mineral constituents and their uncertainties are known fairly well and are kept constant along the entire depth interval. The fluid properties are changed as physical conditions vary. The properties of the perturbed rocks are estimated using an appropriate effective medium approximation. The properties can be upscaled to seismic wavelengths and synthetic CMPgathers can be calculated and compared with measured gathers at well locations. The simulated gathers can be used to interpret measured gathers, in terms of rock fabric parameters. Meticulous perturbations allow us to produce a set of seismic signatures and crossplots of elastic properties, as each model parameter is changed, mimicking properties away from well locations. This approach can be used to better select suitable seismic attributes techniques to be applied in the area. In this scenario, expectations for hydrocarbon discovery and quantification increase. This approach was applied successfully to a carbonate well data set from an intracratonic basin northwest-saharan, Africa. Introduction We present an approach to conduct a rock-physics based perturbational modeling of synthetic seismograms appropriate for tight sandstone and carbonate rocks. The methodology consists of perturbing the volumetric fractions of the rock s fluid and solid constituents at each well log depth, and estimating the elastic properties of the new created rock: the perturbed hypothetical rock. The perturbation of the volumes is achieved without changing the type of microstructure or rock fabric. The elastic properties of the solid constituents and their uncertainties are known fairly well and are kept constant in the entire depth interval. The elastic properties of the fluids are changed as physical conditions vary. The elastic properties of the perturbed rocks are estimated using an appropriate effective medium approximation, which is consistent with the studied rock microstructure. The elastic properties of the new hypothetical rocks can be upscaled to seismic wavelengths, and synthetic CMP gathers can be calculated and compared with measured seismic gathers at well locations. The simulated gathers can be used to interpret measured gathers, previously conditioned for AVO and inversion analysis, in terms of rock fabric parameters and/or physical conditions (e.g. fluids, cracks, mineralogy, diagenesis, pore pressure, and stresses) that control the character of the seismic wavefield. During the modeling, layer thickness effects are also considered after up-scaling the elastic to seismic wavelengths. Meticulous perturbations to the hypothetical rock s constituents allow us to produce a set of seismic signatures and crossplots (templates) of elastic properties and AVO parameters, as each fluid and mineral constituent, porosity, and physical conditions are varied away from well locations. In this scenario, the expectations for hydrocarbon discovery and quantification increase, as well as a reliable technique to optimize the site-specific selection of the appropriate

2 seismic attributes technique to be used in seismic reservoir characterization projects. Our goal is to estimate seismic signatures and/or associate measured seismic data away from the well, with variations in the type and amount of pore space fluids and minerals. We apply this methodology to a well data set from an intracratonic basin northwest-saharan, Africa. The reservoir rock consists of a well-cemented, brittle, and fine to medium crystalline, white to light grey limestone. To estimate the elastic properties of these rocks, we use the soft porosity model (SPM). SPM treats the well cemented carbonate matrix as a continuous solid with embedded low concentrations of stiff (rounded pores) and soft pores (crack like pores). In tight rocks, if pores have high aspect ratios (rounded), the elastic moduli of the rock mineral matrix often dominates those of the bulk rock (Ruiz and Dvorkin, 20), but if the rock has low aspect ratio pores (crack like pores), this is not necessarily true. The magnitude of the effect of crack-like pores (soft pores) on the rock elastic properties will not only depend on the cracks density and aspect ratios, but also on the compressibility of pore fluids. We assume that the solid grains and pores are randomly oriented and randomly positioned, and that the P- and S-sonic wavelengths (~3 ft) are much greater than grains and pores dimensions. Soft Model (SPM) To estimate the elastic moduli of tight rock we use the soft-porosity model (Ruiz and Cheng, 20), which is based on the multimineral version of the self-consistent approximation (Berryman, 1995). SPM consists on dividing the rock pore space (total porosity) into two pore spaces: the soft-pore space (soft-porosity) and the stiff pore space (stiff-porosity). In the SPM, the soft-porosity ( soft ) is defined as the volumetric fraction of soft inclusions with a fixed aspect ratio = 0.01 and the stiff-porosity ) as the volumetric fraction of spherical inclusions with a fixed = 1. The methodology ( stiff consists of matching well log sonic data with the theoretical-velocities to determine the soft porosity required to accomplish this match. This methodology looks for the elastic equivalency between the hypothetical rock model and measured data. If such elastic equivalency can be established for all log data points in the studied depth interval, it is possible to identify an idealized physical analogue to real rock that can be used as a tool of extrapolation, interpolation, prediction of seismic signature, and interpretation of seismic data. Case Study: Low porosity Intracratonic Basin Carbonate We use a well data set an intracratonic basin northwest-saharan, Africa. The stratigraphic column in the studied area consists of rocks that vary from Cambrian-Ordovician to Quaternary. The available well-logs were edited, spliced, and conditioned (Figure 1), before proceeding with the rock physics analysis. Information on mineral type and volumetric fractions, pore types and connectivity, textural characteristics and grain size of the studied rock samples were obtained using X-ray diffraction and petrographic analysis. The laboratory data are used to calibrate the petrophysical estimated volumetric fractions of minerals and fluids (at well-log scale). The rock images, at the micro-scale, allow us to choose an appropriately idealized microstructure that captures most features of the real rock. Once the microstructure is selected, we look for an appropriate effective medium approximation which is consistent with the chosen microstructure. This theory allows us to estimate the elastic properties of the hypothetical rock with known constituents and microstructure. The studied limestones comprise mixtures of calcareous fragments together with local replacive dolomites. Dolomite is coarsely crystalline and occurs as variably sized crystal. Well logs show that physical properties change over small intervals, which is a characteristic of fine heterogeneities in the subsurface formations. The total porosity varies from 0.5 % - 3% with an approximate average value of 1.% approximately. Water saturation is estimated using the dual water model, obtaining values and ranges from 0 to 0%. Clays, quartz, calcite and dolomite average content values are %, 9%, 5% and 2%, respectively.

3 Figure 1 From left to right: Volumetric fractions of minerals and fluids; fluid saturations; total porosity T ; soft-porosity soft ; measured (black) and theoretical (red) V p velocities; predicted Vs velocities estimated from V p ; measured (black) and theoretical (red) density. Vs velocities were not available, so they are predicted using the soft porosity model. In the modeling, the stiff- and soft-pore spaces are filled with a fluid with an effective bulk modulus, given by the harmonic average of bulk moduli of the brine and gas phases, respectively. Figure 1 shows the predicted V, the calculated (z) and a comparison of the theoretical and measured densities. s soft Rock physics perturbational modeling The rock physics perturbational modeling is achieved by varying the volume of selected rock s constituents within specific ranges and estimating the elastic properties of the perturbed rock using the soft-porosity model. Pore pressure, stresses, and temperature may be also varied. The range of variation of each model parameter is selected based on the variability of the parameter along the well or in the studied area. In this study, we perturb the following rock s parameters: volume of quartz and dolomite; fluid type; and stiff porosity. We also model the effect of random micro-cracks by adding cracks to the rock and estimating the elastic properties of the new hypothetical cracked rock. Fluid substitution is conducted by filling soft- and stiff-pores with a single effective fluid. The results of the perturbational modeling are shown by cross plotting the P- and S-wave acoustic impedances, Ip and Is, respectively, versus Poisson s ratio (PR) or density. The theoretical data are compared with the measured data in the Ip-PR, Is-PR, and Ip-density planes (Figure 2). The five perturbed parameters are varied as follows: (I) Increase the in situ quartz volume by 20% and reduce all other mineral volumes proportionally. We observe that an increase in quartz volume up to 20% causes a small increase in acoustic impedances, but a significant decrease in Poisson s ratio and density. (II) Increase the in situ dolomite volume by 20% and reduce all other mineral volumetric fractions proportionally. An

4 increase in dolomite volume up to 20% causes a small increase in acoustic impedances, as well as a small increase in Poisson s ratio and density. (III) Increase the in situ total porosity by increasing the stiff-porosity by % and reducing all mineral volumetric fractions proportionally. An increase in stiffporosity up to % causes a significant decrease in acoustic impedances, and density, but Poisson s ratio remain constant. (IV) Fluid substitution is conducted by: a) replacing the in situ fluids with mixture of 80% gas and 20% brine, and b) replacing the in situ fluids with pure brine. The saturations in the mixture are kept constant with depth. Replacing in situ fluids by gas causes a significant decrease in acoustic impedances, as well as a significant decrease in Poisson s ratio and density. (V) Add cracks (oblate spheroids) with aspect ratio and crack density 0.1. The cracks are filled with in situ fluids. The bottom row of Figure 2 shows the measured data colorcoded by brine saturation (Sw). It also shows the changes on elastic properties when adding cracks. Notice that the gas-filled cracks cause a much larger effect on the elastic properties than the brine-filled cracks. When we add cracks filled with brine, the acoustic impedance remain constant, but Poisson s ratio increases slightly. When we add cracks filled with gas the acoustic impedances, and also Poisson s ratio decreases considerably. The aspect ratios used for quartz and dolomite grains are 1 and for clay minerals is 0.2. When a specific mineral is perturbed, we keep porosity and saturations constant and only rebalance the volumetric fractions of minerals. The perturbation procedure may change depending on the specific diagenetic process we wish to take into account. For instance, we can increase calcite and reduce dolomite proportionally, keeping constant the volume of other minerals, mimicking calcite-dolomite conversion. It is important to consider that a diagenetic process may change the rock microstructure, so if necessary, during the perturbational modeling, the selected idealized microstructure may be changed, and in consequence, the corresponding effective medium approximation. Conclusions We propose an approach to conduct rock physics based perturbational modeling of synthetic seismic data. The meticulous perturbations to the hypothetical rock s constituents allowed us to produce a set of crossplots and seismic signatures showing the behavior of elastic properties, as each fluid and mineral constituent, porosity, and physical conditions are varied away from well locations. This new and innovative methodology is determinant in setting realistic expectations for reserve discovery and quantification in the studied area, as well as a valuable methodology to optimize the site-specific selection of seismic attributes to be used in seismic reservoir characterization projects.

5 % Stiff Is (km/s g/cc ) +% Stiff Ip (km/s g/cc ) +% Stiff Gas Effect Brine Effect Measured Cracks w ith Gas Cracks w ith Brine Poisson ratio Is (km/s g/cc ) 8 Gas Effect Brine Effect Measured Gas Effect Brine Effect Measured Sg Cracks w ith Gas Cracks w ith Brine Poisson ratio Ip (km/s g/cc ) Density (g/cc) Figure 2. First column: P-impedance (Ip) versus Poisson s ratio. Second Column: S-impedance (Is) versus Poisson s ratio. Third column: P-impedance versus density. From top to bottom, rows are a comparison between measured and perturbed properties when adding: 20% quartz, 20% dolomite; and % stiff porosity; and when replacing in-situ fluids with gas or brine; and when adding cracks with aspect ratios 0.00 and crack density 0.1. In the bottom row the measured data is colorcoded by water saturation (Sg). The arrows indicate the trend the data follows after the perturbation. All green symbols correspond to data after achieving perturbations and black s to measured data. References Berryman, J.G. [1995] Mixture theories for rock properties. In: American Geophysical Union Handbook of Physical Constants, edited by T. J. Ahrens, AGU, New York, Ruiz, F. and Cheng, A. [20] A rock physics model for tight gas sand. The Leading Edge, 29, Ruiz, F. and Dvorkin, J. [20] DEM and SC estimations of elastic moduli of complex rock matrix using composites as analogs. Society of Exploration Geophysicists Extended Abstracts 29, Cracks