An Accurate Estimation of Shear Wave Velocity Using Well Logging Data for Khasib Carbonate Reservoir-Amara Oil Field

Shear and compressional wave velocities, coupled with other petrophysical data, are vital in determining the dynamic modules magnitude in geomechanical studies and hydrocarbon reservoir characterization. But, due to field practices and high running cost, shear wave velocity may not available in all wells. In this paper, a statistical multivariate regression method is presented to predict the shear wave velocity for Khasib formation Amara oil fields located in SouthEast of Iraq using well log compressional wave velocity, neutron porosity and density. The accuracy of the proposed correlation have been compared to other correlations. The results show that, the presented model provides accurate estimates of shear wave velocity with correlation coefficient of about unity than other currently available methods.

However, most of previous attempts to predict the Vs of a field case consider the determination coefficient as a sufficient criterion to evaluate the accuracy of the empirical model, which may not always capture the total variation of rock independent variables.
Recentstudies have proved and shown the capability of using artificial intelligence modeling and fuzzy logic over empirical and statistical correlations to predict Vs from Vp and other well log data such as neutron porosity and bulk density as an input data, ( Zoveidavianpoor, 2017; Tariq In this study, an attempt is made to predict accurate Vs for Amara oil field, this field is selective due to its drilling stability and production problem.

DATA ANALYSIS AND METHODOLGY:
This study presents multivariate regression analysis using SPSS softwarethat is used to develop new correlation to predict shear waves and among effective petrophysical properties of a productive carbonate (limestone) section of South East Iraq (Amara field -Khasib formation). The Khasib Formation is considered one of the important reservoirs in the Misan oilfields. The development of empirical models in which the measurable well logs can provide an estimation of Vs will also be outlined. Data analysis is used to ensure that the relationship between input data and the outcome function is logical. Sonic wave data can be determined using logs or core plugs, Fig. 1 shows the variation histograms with a statistical evaluation of the log dataset, which contains 80 data values for Vp, Vs, porosity, Resistivity and gamma ray, and 80 data points for bulk density.

MODEL DEVELOPMENT
This work done in one reservoir of the South-East Iraq, Amara field -Khasib formation, where, shear wave velocity available. Dipole Sonic Imagers (DSI) run in wells 2 for measuring the shear wave velocity.
The main lithology of Amara field -Khasib formation is carbonate rocks "Limestone". Therefore, the ability of the introduced equation to predict the shear wave velocity is a check in interest reservoir.

USE OF RELATION BETWEEN S -WAVE VELOCITYAND P-WAVEVELOCITY
By using the Simple regression, the calculated Vs can be described as a linear model with Vp as shown in Eq. (9): = + So as, Statistical method was used to obtain an equation to calculate Vs with better correlation coefficient. At first, only Vp from sonic log was used as input data. In this way the best equation is as follow: UsingEq. 10, the shear wave velocity has been predicted and compared with the real values of shear wave velocity as shown in Fig.5. Eq. 10 has one input parameter (Vp) and R² for this equation is approximately 1. Figure 5. The relation between measured and predicted Vs in AM-2 using Eq. 10.

MULTIPLE REGRESSION METHOD
Regression analysis is a statistics process used to develop a mathematical correlation for determinate the unknown variables based on known variables, (Pallant, 2013, Salal and Khudair, 2019). In this study, multiple regression method in SPSS software was used to predict Vs from well logs data, such as, NPHI, RHOB, GR, Rt and P-wave velocity. So that, first, investigate the Where, NPHI is neutron porosity expressed as a fraction, RHOB is bulk density in gm/cc, Vp and Vs are compressional and shear wave velocity, respectively in km/s, GR in API and Rt true formation resistivity in ohm.m. In multiple regression model, the use of available wells data could be useable in other wells. The magnitude of the input variables affecting on Vs are given by their degree of contribution to the Vs, which is determined by the multivariate regression analysis. Contribution factors are (0.05, 0.520, 0.003, 0.0001, 4.401E-6, and -9.114E-6 respectively.). It can be seen that the essential affecting variables in the presented correlation are the Vp, NPHI, and RHOB that play significant roles in Vs accuracy. The weakest variables are GR and true formation resistivity, which means that they must be taken out of the model. The new model was fitted again and the following equation was obtained: Eq. 12 became as: The suggested equation could beas follow: = + * + * + * ( + ) 2 + * ρbc + g * (ρbc + h) 2 (14) The statistical process made by SPSS software, shows that Eq. (14) can be written using the coefficients of dependent parameters as follow: Where Vs and Vp in (km/s).

ERROR ANALYSIS
Two criteria were used to evaluate the accuracy of this correlation compared to five correlations.

RESULTS AND DISCUSSION
Estimated Vs using the Eq. 18 shows excellent match with measured Vs (Fig. 7) with R² about 0.9997. Fig.8 presents the computed shear wave velocity using Eq. 15and core shear wave velocity versus depth for AM-2. Multiple regression method presents robust correlation to predict shear wave velocity from well log data. The multiple regressions of the presented variablesshow a strong correlation among (Vs) values predicted from well logging data.  The results show that statistical method performs better estimates than empirical models, which can be used only to obtain an order of magnitude for shear wave velocity. Checking the relation between the output parameter (Vs) and input parameters (RHOB, NPHI and Vp), shear wave velocity predicted in well Am-3. Fig. 9shows the relation between measured and predicted S-wave velocity values in well Am-3.

CONCLUSIONS
1-Presents more accurate correlation to estimate shear wave velocity in Khasib reservoir Eastern South of Iraq Amara oil field using conventional well log data. 2-It is validated that well logging data are useable to predict the shear wave velocity, due to continuous and actual values of these parameters.
3-The sonic log is a major input data of regression. It is observed that the most important variable to this regression, which considers as intrinsic properties of rock such as the P-wave velocity (Vp), NPHI, and RHOB that play significant roles in the statistical model. 4-It has been clearly demonstrated that the shear wave velocity can be estimated from P-wave velocity, porosity and density if the dipole sonic log is not available.