Fluid Substitution Model to Generate Synthetic Seisic Attributes: FluidSub.exe Sahyun Hong and Clayton V. Deutsch Geostatistical data integration is a ature research field and any of algoriths have been developed in petroleu reservoir odeling. Seisic data and its derived attributes are widely used secondary variables. The selected data integration algorith ust be tested and evaluated using control data before applying with real data. However, it is not easy to acquire real seisic data and its derived attributes such as acoustic ipedance and seisic velocity. One can generate priary data, e.g., porosity by unconditional siulation, and then generate acoustic ipedance being negative correlated to the siulated porosity. This is a purely statistical generation of secondary variable with no physical relation. This short note is for introducing fluid substitution odel to provide synthetic seisic attributes based on physical odel. Gassann equation is a representative fluid substitution odel and it provides P-wave velocity, acoustic ipedance and seisic trace given porosity, fluid saturation and rock type. Synthetic data generation progra fluidsub.exe is provided as well. Introduction Secondary data integration has been an active area in odern petroleu reservoir odeling. Well data is a direct easureent on petrophysical properties, however, it is collected sparsely in horizontal direction. Secondary data is an indirect easureent, but it contains reservoir property inforation with lateral continuity in ost petroleu applications. Seisic attributes such as aplitude, acoustic ipedance and P- /S-wave velocity or their ratio, are widely used secondary variables in reservoir odeling. Incorporation of priary and secondary data is able to provide plausible reservoir odeling with less uncertainty. Many geostatistical techniques have been developed to integrate seisic secondary data. They are needed to be evaluated using test data before applying in the field. Access to a real seisic data, however, is difficult in case of attepting to test new ethodology. Besides, real data does not allow users to test several data conditions, e.g., different level of noise and data correlation between priary and secondary. Controlled or synthetic data ight be a good test exaple before applying to real case. One can evaluate his/her proposed algorith and perfor sensitivity analysis using synthetic data. In this note, we introduced process and sall progra to generate seisic attributes which is based on well-known physical odel. Gassann s fluid substitution odel is adopted as a physical odel. The Gassann fluid substitution odel requires porosity, fluids saturation, fraction of shale as input paraeters, then P-wave velocity, P-wave ipedance, seisic traces are generated as output seisic attributes. Figure-1 scheatically illustrates the process of testing data integration algorith using synthetic data. Gassann s Fluid Substitution Equation Fluid substitution is an iportant part of the rock physics, which provides a way to identify fluid saturated rock. The Gassann equation is a widely used odel as fluid substitution. Elastic rock properties change with porosity, fluid type and saturation, rock ineral fraction change. Gassann equation generates seisic responses based on changed elastic rock properties resulting fro various reservoir rock conditions. The Gassann theory allows us to calculate P-wave velocity V P 1000 = sat in /sec (1) ρ sat Density of the porous fluid saturated rock obeys the ixing law: ρ = ρ (1 φ) + ρ φ (2) sat f 204-1
where the quantities are: φ porosity in fraction ρ ρ f pure ineral density in g/cc pore fluid ixture density in g/cc Provided that different types of fluids are saturated density of fluid ixture can be obtained by cobining fluid saturation fraction and fluid density such as, ρ = Soρ + Swρ + Sgρ (3) f o w g where So, Sw and Sg are fractional fluid saturation of oil, water and gas. sat is a P-wave bulk odulus of fluid saturated rock, which is obtained by: + Q d sat = + Q in Pa (4) where, is P-wave odulus of rock foring ineral (possibly ixture of different inerals) in Pa. is derived fro pure ineral bulk odulus (in Pa) and shear odulus (in Pa) 4 = K + μ in Pa (5) 3 where, K pure ineral bulk odulus in Pa μ pure ineral shear odulus in Pa There is rare case where single rock foring ineral is doinant over the reservoir. More than two rock inerals are ixed. For exaple sandstone is often inter-layered with shale and ain ineral coponents of sandstone and shale are quartz and clay, respective. Of course, two rock inerals have different elastic properties resulting in different odulus. Thus, ineral bulk and shear odulus are derived fro inverse proportion of pure ineral odulus K 1 and K 2, K C 1 C = + K K 1 1 1 2 1 in Pa (6)-a C 1 C μ = + μ μ 1 1 1 2 1 in Pa where C 1 and C 2 are fraction of ineral 1 and 2. d in equation (4) is bulk odulus of dry porous rock frae and it is estiated in ters of ineral odulus and porosity as following, (6)-b c ( a+ bφ ) (7) d User input paraeters a, b and c are free paraeters to adjust the relation between d and. It can be obtained by lab experients. Q ter in equation (4) is related to fluid bulk odulus, which is derived by, 204-2
Q = K ( ) f d φ( K ) f (8) K f is pore fluid ixture bulk odulus in Pa. Multiple types of fluids are saturated then K f is weighted su by fluid bulk odulus and its fractional saturation. 1 So S S w g = + + (9) K K K K f o w g There is no doubt physical paraeters of fluids and inerals depend on reservoir conditions. For exaple, density of oil is affected by reservoir teperature, pressure, oil gravity ( API) and gas specific gravity. Density of water depends on teperature, pressure and salinity. Those paraeters are currently hard-coded in the source code; however, one can use the reservoir teperature, pressure, salinity, oil and gas specific gravity as input paraeters in fluidsub.exe progra. Workflow Given inforation: 1. Reservoir pressure, teperature, salinity, oil and gas specific gravity (hard coded in the progra) 2. Mineral bulk odulus in Pa (K ) 3. Mineral shear odulus in Pa (μ ) 4. Mineral density in g/cc (ρ ) 5. Fluid bulk odulus in Pa (K o,k w,k g ) 6. Fractional fluid saturation (S o,s w,s g ) 7. Fluid density in g/cc (ρ o, ρ w, ρ g ) 8. Fractional porosity 9. Calibration paraeters (a,b,c) Calculate: 1. Pore fluid ixture density (ρ f ) using equation (3) 2. Saturated rock density (ρ sat ) using equation (2) 3. P-wave odulus of rock foring ineral ( ) using equation (5) 4. Bulk odulus of dry porous rock frae ( d ) using equation (7) 5. Pore fluid ixture bulk odulus (K f ) using equation (9) 6. Q ter using equation (8) 7. Bulk odulus of fluid saturated rock ( sat ) using equation (4) 8. P-wave velocity using equation (1) 9. P-wave acoustic ipedance by V p (step 8) ρ sat (step 2) Final resulting seisic attributes are P-wave velocity and acoustic ipedance. To generate seisic trace, acoustic ipedance should be convolved with pre-defined wavelet function like as Ricker wavelet. This convolution process is not ipleented in fluidsub.exe progra. Given ineral bulk and shear odulus depends on the reservoir rock type. Quartz ineral is doinant in sandstone reservoir. Clay ineral is abundant in shaly reservoir. Quartz and clay inerals are interblended between clean sand and shaly 204-3
reservoir. fluidsub.exe progra considers the reservoir between sand and shaly reservoir depending on the fraction of vshale. Thus, pure bulk odulus of quart (clean sand) and clay ineral (shale) are used to calculate equation (6)-a and (6)-b depending on vshale fraction. In equation (6)-a and (6)-b, subscript 1 and 2 are illite and quartz ineral, respectively. Illite was chosen as doinant clay ineral in shaly rock. Hard coded ineral odulus and ineral densities are following: K in Pa μ in Pa ρ in g/cc Quartz 37900 44300 2.65 Illite 76800 32000 2.71 Figure-2 shows the paraeter file to fluidsub.exe progra. Porosity, vshale and fluid saturation are input files (line 5 line 7). Line 12 ipleents the controlled noise level. Gaussian rando noise will be added in the resulting seisic attributes unless this value is set as 0. Porosity Fluid sat. Vshale Gassann theory P-wave Ip P-wave vel. Seisic Trace Unconditional siulation Sapling for priary well data Treat as several secondary data Test Data Integration Algorith Figure-1: The process of testing data integration algorith using synthetic seisic data generated by physical odel 204-4
Figure-2: Paraeter file for the fluidsub.exe progra Nuerical Results Porosity, water saturation and vshale data were generated by 50 50 50 grids. Correlation aong input variables are shown Figure-3. It is noted that correlation between porosity and clay, and porosity and water saturation is negative. Water saturation is positively correlated to vshale. P-wave velocity and P-wave ipedance were produced using the input variables and paraeters (without additive rando noise). Figure-4 illustrates the input variables and resulting P-wave ipedance. 50 vertical grids were averaged to create 2-D ap. It should be physically ensured that correlation between P-wave velocity and porosity, porosity and ipedance. In rock physics, P-wave velocity is positively correlated with porosity and ipedance is negatively correlated with porosity. Figure-5 shows the correlation between input porosity and seisic attributes. They have clear negative correlation due to no interrupting by rando noise. Conclusions Fluid substitution odel is considered to generate synthetic seisic attribute based on physical odel. Gassann equation was ipleented in fluidsub.exe progra. As input variables, porosity, fluid saturation and vshale data (previously prepared by siulation or kriging) are used in the progra. Resulting seisic attributes are seisic wave velocity (P-wave), acoustic ipedance and seisic trace. Rando noise can be added with user defined noise level. References Liner, C. L., 2004, Eleents of 3D Seisology, PennWell, Tulsa, Oklahoa. Mavko, G., Mukerji, T. and Dvorkin, J., 1998, Rock Physics Handbook, Cabridge University Press. 204-5
Figure-3: Correlation between input variables (Porosity, water saturation, vshale fraction) 204-6
Figure-4: Input variables and resulting seisic attribute. Vertically averaged P-wave ipedance is shown in the right. 204-7
Figure-5: Correlation between seisic attributes and porosity 204-8