PUBLICATIONS. Geochemistry, Geophysics, Geosystems

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1 PUBLICATIONS Geochemistry, Geophysics, Geosystems RESEARCH ARTICLE Key Points: Regression model has been developed to estimate pore pressure Model predicted values have been implemented in other wells Overpressure zone is detected Correspondence to: R. Chatterjee, Citation: Singha, D. K., and R. Chatterjee (2014), Detection of overpressure zones and a statistical model for pore pressure estimation from well logs in the Krishna-Godavari Basin, India, Geochem. Geophys. Geosyst., 15, , doi:. Received 19 NOV 2013 Accepted 1 FEB 2014 Accepted article online 7 FEB 2014 Published online 11 APR 2014 Detection of overpressure zones and a statistical model for pore pressure estimation from well logs in the Krishna-Godavari Basin, India Dip Kumar Singha 1 and Rima Chatterjee 1 1 Department of Applied Geophysics, Indian School of Mines, Dhanbad, Jharkhand, India Abstract Abnormally high pressures, measured by repeat formation tester (RFT) and detected by well log data from 10 wells in the Krishna-Godavari (K-G) Basin, occur in the Vadaparru of Miocene and Raghavapuram of Early Cretaceous age. Overpressures generated by disequilibrium compaction, and pore pressures have been estimated using the conventional Eaton sonic equation with an exponent of 3.0. The observed abnormal pore pressure gradient ranges from to MPa/km, whereas fracture pressure gradient varies from to MPa/km. The magnitude of vertical stress (S v )hasa gradient from to MPa/km. The minimum horizontal principal stress (S h ) magnitude is found to vary from 64 to 77% of the S v in normally pressured to overpressured sediments. A multiple linear regression model with a squared multiple correlation coefficient (R 2 ) of 0.94 is proposed for pore pressure prediction from gamma ray, density and sonic logs to focus on efficient drilling operations and to prevent borehole instability. The statistical model has been calibrated with the RFT data from five wells covering about 3400 sq. km area of the onshore K-G Basin. The model predicted pore pressure values are in close agreement with the actual RFT data for another four wells including a well in the offshore K-G Basin. Hence, the proposed regression model may be useful for predicting pore pressure from other well logs in the K-G Basin. 1. Introduction Pore pressure prediction is an essential requirement in any producing sedimentary basin to ensure safe drilling operations and it is a fundamental input into well design, particularly the selection of casing points [Law and Spencer, 1998; Sayers et al., 2002]. Pore pressure has been estimated from seismic velocities (i.e., predrill) [Sayers et al., 2002] as well as from changes in sonic velocity or resistivity logs [Mouchet and Mitchell, 1989; Bell, 2002; Sarker and Batzle, 2008]. Many sedimentary basins throughout the world exhibit abovehydrostatic fluid pressure [Xie et al., 2001; Zahid and Uddin, 2005; Osborne and Swarbrick, 1997; Tingay et al., 2009]. In the drilling phase, an accurate pore-pressure prediction and the ability to update and revise predictions quickly can be vital for safe and economic drilling. For example, a major cause of cost overruns in deep water drilling is due to stuck pipes and lost circulation of drilling fluids, resulting in costly lost rig time. Estimates of proper pore pressure and fracture pressure are also essential for an optimized casing program design and for avoiding well control problems, such as blowouts [Dutta, 2002]. There are many causes for overpressures in sedimentary basins such as disequilibrium compaction, tectonic compression, hydrocarbon generation, aquathermal expansion, mineral dehydration, mineral transformation, vertical fluid movement, and hydrocarbon buoyancy [Osborne and Swarbrick, 1997; Fleming et al., 1998; Bowers, 2002; Chopra and Huffman, 2006; Sarker and Batzle, 2008; Zhang, 2011]. Overpressures generated by disequilibrium compaction are associated with anomalously high sediment porosities (undercompaction) and are thus more readily detectable in sonic log [Sayers et al., 2002; Tingay et al., 2009]. In this paper, we shall focus on the prediction of pore pressure and fracture pressure by understanding the mechanism of overpressure generation in the K-G Basin, a petroliferous basin located at the eastern continental margin of India (ECMI). The main objectives of this study are (a) to compute pore pressure from sonic travel time, (b) to detect overpressure zones in about 10 wells covering 4700 sq. km of the onshore K-G Basin (Figure 1), (c) to compute fracture pressure, (d) to compute in situ stresses, and (e) finally, to propose a statistical model for estimating pore pressure based on clay content, sonic travel time, and vertical stress obtained from gamma ray, sonic, and density logs. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1009

2 Figure 1. Illustrates the tectonic map and location of 10 wells in the oil and gas fields of K-G Basin [after Sastri et al., 1973, 1981; Rao, 2001]. 2. Study Area The K-G Basin, producing oil and gas is located at midportion of ECMI. It holds large number of structures and trap which have been identified for drilling in the onland and offshore parts of the basin [Rao, 2001]. This basin is subdivided into three subbasins namely Krishna, west Godavari, and east Godavari which are separated by Bapatla and Tanuku horsts, respectively (Figure 1) [Sastri et al., 1973, 1981]. West Godavari subbasin is further subdivided into the Gudivada, Bantumilli grabens separated by Kaza-Kaikalur horst. The Mandapeta graben and Kavitam-Draksharama high are situated on either side of Tanuku horst in the east Godavari subbasin. The geologic traversing subbasins such as: Krishna-west Godavari-east Godavari to offshore is showing the overall sediment deposition with geologic age (Figure 2) (R. Venkatarengan et al., Lithostratigraphy of Indian petroliferous basin, Document VIII: Krishna-Godavari Basin, unpublished report, pp. 1 27, KDM Inst. Pet. Explor. ONGC, Dehradun, India, 1993). The grabens are filled up dominantly by Mesozoic sediments which constitute the rift fill sequence tilted landward [Biswas, 1993]. During the Mesozoic the sedimentation was fluvial. The sedimentation pattern changed in the Tertiary. Two major rivers, the Godavari and Krishna supply the clastic sediments to sea shore initiating deltaic processes [Biswas, 1993]. Various sedimentation rates ranging from 0.07 mm/yr to more than 2 mm/yr are reported in the K-G Basin [Rao and Mani, 1993; Raju et al., 1994; Mazumdar et al., 2009]. High sedimentation at rates (>1 mm/yr) generate overpressure in many sedimentary basins around the world [Rubey and Hubbert, 1959;Fertl, 1976]. Subsidence and sedimentation played a dominant role in overpressure development in K-G Basin. When low-permeability sediments are rapidly loaded, pore fluids cannot escape, and the fluids bear some of the overlying sediment load. In this situation, a pore pressure exceeding the hydrostatic high pressure (overpressure) develops. Few parts of east Godavari as well as west Godavari subbasins of K-G Basin are suffering complex geology and overpressure zone during the well drilling [Jain et al., 2012]. The 10 wells drilled in the K-G Basin covering an area of 5100 sq. km distributed at the MDP, END, RAN, KAV gas fields located at east Godavari and at the MDH, SUR gas fields of west Godavari subbasins including one well at shallow K-G offshore namely, KY are available for delineation of overpressure zone SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1010

3 Figure 2. Displaying the generalized geologic section from K-G onshore to offshore. The Formations are shown with geologic ages (after R. Venkatarengan et al., unpublished report, 1993). (OPZ) (Figure 1). The two wells such as: KM and KR are located in the MDH and SUR fields, respectively, whereas KA well is located about 3 km away from MDH field. The wells KG, KS, and KK are situated near to the RAN field and the well KV is located at the KAV field closer to the K-G coast. The wells KD and KE are located at the MDP and END fields, respectively. The wells KM, KA, and KR at the west Godavari subbasin have penetrated sedimentary formations such as: Raghavapuram at bottom, followed by Tirupati Sandstone, Razole volcanics, and Nimmakuru Sandstone at top, ageing Early Cretaceous to Paleocene age [Rao, 2001]. The wells KG, KS, and KK penetrate Vadaparru at bottom followed by Matsyapuri Sandstone and Godavari clay at top, ranging in age from Eocene to Pleistocene. The well KV has penetrated the sediments of Raghavapuram overlain by Tirupati Sandstone. The wells KE and KD penetrate the formations like Kommugudem Formation at bottom followed by Mandapeta Sandstone, Gollapalli Sandstone, Raghavapuram, Tirupati Sandstone, Razole volcanics, and Rajahmumdry Sandstone at top ageing from Permo-Carboniferous to Miocene age [Rao, 2001; Gupta, 2006; Chatterjee, 2008]. Figure 3a is showing the log correlation through the gamma ray (GR) and deep resistivity logs (laterolog deep, LLD) for seven wells (KR, KA, KM, KV, KK, KS, and KG) indicating Formation tops under the section M-N, whereas Figure 3b is showing the well correlation results for two wells namely KD and KE in Mandapeta graben. Previous authors have reported that the overpressure at the ECMI has been generated in the lowpermeability sediment or in the sediment, bounded by low-permeability media [Roy et al., 2010]. The knowledge of pore pressure and fracture pressure during the exploration phase of K-G Basin is required to study the hydrocarbon trap seals, mapping of migration pathways, analyzing trap configurations, basin geometry and calibrations for basin modeling [Chopra and Huffman, 2006]. 3. Detection of OPZ and Pore Pressure Estimation During deposition of sediments in the K-G Basin, with the increase in vertical stress (S V ), the pore fluid escape from pore spaces as for compaction. In a sand/shale sequence as observed in the wells of K-G Basin, the low permeability, e.g., clay prevents the escape of pore fluids at rates sufficient to keep up with the rate of increase in vertical stress. The pore fluid begins to carry a large part of the load and pore fluid pressure will increase. This process is referred to as undercompaction or compaction disequilibrium and is being understood overpressure mechanism to explain and quantify overpressure in the K-G Basin [Chopra and Huffman, 2006; Roy et al., 2010]. Previously, Chatterjee et al. [2011] describe that the high-rate deposition and transportation of sediment under ECMI is responsible for developing of overpressure in which excess fluid gets trapped in the low-permeable formation such as Vadaparru in the east Godavari subbasin and in the offshore basin also. For delineation of OPZ for 10 wells under study, deviations from normal compaction trend (NCT) in travel time from sonic logs have been observed for seven wells on onshore K-G Basin. NCT represents optimum fitted linear data in the low permeable zone (shale) as shown in Figures 4a and 4b for two wells namely, KA and KG in the west and east Godavari subbasins, respectively. Figure 4c is showing the NCT for the well KD in Mandapeta graben. There is a little deviation from NCT as observed from well KD. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1011

4 Figure 3. Showing well log correlation (a) for section M-N and (b) for wells KD and KE. GR in API unit, and LLD in ohm m. Top of the Formation are identified and correlated through the gamma ray and resistivity logs. Volume of shale (Vsh) has been computed from natural gamma ray logs using equation (1) for 10 wells. The observed sonic travel time against shale has been considered for computation of NCT. The sonic and density porosities have been derived from the following equations. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1012

5 Figure 4. Displays normal compaction trend (NCT) and top of overpressure zone (OPZ) and porosities derived from sonic and density logs for well (a) KA, (b) KG, and (c) KD. Three wells have penetrated the sedimentary formations (Fm.) with age are shown in this figure. RGM, Raghavapuram; TRP, Tirupati; RZL, Razole; NMK, Nimmakurru; VDR, Vadaparru; MTS, Matsyapuri; GDR, Godavari; and GLP, Golapalli. Vsh 5 ðgr 2GR min Þ=ðGR max 2GR min Þ (1) where GR 5 gamma ray log reading at any depth, GR min 5 minimum gamma ray reading, and GR max 5 maximum gamma ray reading. Density derived porosity ðu d Þ 5 ðq ma2q log Þ ðq ma 2q fluid Þ (2) q ma 5 matrix density point gm/cc, q fluid 5 density of fluid5 1 gm/cc, and q log 5 Log density data of rock in gm/cc. Sonic derived porosity [after Wyllie et al., 1956, 1958] ðu s Þ 5 1 ðdt 2DT ma Þ C p ðdt f 2DT ma Þ (3) In uncompacted sand, the travel time in overlying shale indicates values more than 100 microsec/ft. Therefore, compaction correction (c p ) is required for estimation of corrected porosity. The compaction correction is further estimated as c p 5 DT shale 100 ; it varies from 1 to 1.82, AA 5 matrix travel time in limestone microsec/ft, DT f 5 travel time in fluid microsec/ft, and DT shale 5 travel time in overlying shale. Top of the OPZ is detected from the departure from NCT as well as from the separation between density and sonic porosities. Figure 4 is showing the porosity trend of normal compacted and under compacted shale formations. The crossplotting porosities derived from sonic travel time and density logs with depth for three wells such as: KA, KG, and KD are shown in Figure 4. The top of OPZ as detected from seven wells are listed in Table 1. Overpressure zone is not detected in well KY. Figure 4c illustrates the NCT against in the well KD but separation between density and sonic porosities is not observed. Excess of pore pressure is observed in the well KD and KE because of lithology variation in the Raghavapuram. This may not be developed due to differential compaction. Overpressure formations as delineated from seven wells under study when compared with a normally pressured section at the same depth exhibit higher porosities and higher sonic travel time (DT). The knowledge of vertical stress in the K-G Basin is required to compute pore pressure and fracture pressures from Eaton s sonic equation [Eaton, 1972] and Matthews-Kelly s equation [Matthews and Kelly, 1967], SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1013

6 Table 1. Lists the Top of OPZ, S v Gradient, PP Gradient, FP Gradient, S h Gradient, S h /S v and Porosities for 10 Wells in K-G Basin Predicted FP Gradient (MPa/km) S h Gradient (MPa/km) S h /Sv Porosity (Fraction) In OPZ Formation Predicted PP Gradient (MPa/km) In OPZ In Normal Pressured Sediment In Normal Pressured Sediment In Normal Pressured Sediment ud us Name Wells Top of OPZ (m) S v Gradient (MPa/km) In OPZ In OPZ In OPZ KR Raghavapuram KA Raghavapuram KM Raghavapuram KV Raghavapuram KK Vadaparru KS Vadaparru KG Vadaparru KD KE KY Geologic Age Early Cretaceous Early Cretaceous Early Cretaceous Early Cretaceous Late Eocene- Miocene Late Eocene- Miocene Late Eocene- Miocene respectively. Vertical stress (S v ) is calculated using bulk density of the rock which is force per unit area applied by load of rock above the point of measurement. The required equation given by Plumb et al. [1991] is S v 5 ð z 0 q ðþgdz z (4) where z is depth at point of measurement, q(z) is the bulk density of the rock which is function of the depth, and g is the acceleration of gravity. The pore pressure (PP) has been calculated using Eaton s [Eaton, 1972] sonic equation PP 5 S v ðs v PhÞ 3 ðdtn =DTÞ 3 (5) The fracture pressures (FP) have been determined from Matthews-Kelly s equation [Matthews and Kelly, 1967]. FP 5K i 3ðS v 2 PP Þ1 PP (6) K i 5 matrix stress coefficient 5 S h /S v, where S h 5 minimum horizontal stress calculated from the equation [Whitehead et al., 1987; Engelder and Fischer, 1994; Hillis, 2000] S h 5PP 1r ðs v PP Þ=ð12rÞ (7) where r is Poisson s ratio of the rock in the K-G Basin ranging from 0.24 to 0.28 [Chatterjee and Mukhopadhyay, 2002]. Ph 5 hydrostatic pressure ð Ð z 0q gdzþ, where q 5 average mud density which is constant, DTn 5 sonic travel time in low-permeable zone calculated from NCT trend, DT 5 observed sonic travel time. Hydrostatic pressure gradient is taken as 10 MPa/km for the 10 wells in this basin. The estimated S V, PP, FP, and S h from the respective equations (4 7) as well as actual PP obtained from RFT, Leak-off Test (LOT) data at selected depth intervals for above mentioned three wells are displayed in Figure 5. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1014

7 Figure 5. Displays hydrostatic pressure (Ph), pore pressure (PP), mud weight (MW), minimum horizontal stress (S h ), fracture pressure (FP), and vertical stress (S v ) for wells (a) KA, (b) KG, and (c) KD, respectively. Leak-off test (LOT) and repeat formation tester (RFT) values are provided at selected depths. 1, Ph; 2, PP; 3, MW; 4, S h ; 5, FP; and 6, S v. The minimum horizontal stress magnitude for these 10 wells in K-G Basin has been determined from the poroelastic equation [Whitehead et al., 1987; Engelder and Fischer, 1994] though it can be directly estimated by evaluating leak-off tests (LOTs) [Brent and Alvin, 2010] results performed on the selected wells at selected depths. The gradient S V for these 10 well is found to vary between MPa/km in well KG and MPa/ km in well KD. Figure 5 displays the variation of Ph, PP, S h, FP, and S V with depth for three wells under the east and west Godavari subbasins. The few values of LOT data are also plotted along with S h and FP for three wells in this Figure 5. The LOT data matches reasonably well with the estimated S h values for these wells. It is observed from this analysis that the Vadaparru in east Godavari subbasin and Raghavapuram in west Godavari subbasin have been characterized by high PP gradient. Table 1 lists the top of OPZ, S V gradient, predicted PP gradient, FP gradient, S h, and Formations with age for 10 wells. The gradient of PP varies in the overpressure zone (OPZ) from to MPa/km, whereas the gradient of FP ranges MPa/ km for these seven wells. It is also observed from Table 1 that the ratio of S h /S V ranges from 0.64 to 0.68 at the normal pressured sediment, whereas it is increased and varies from 0.70 to 0.77 at the overpressured sediments. Mud weight (MW) values are also plotted with the PP values. Mud weight values shown in the three wells of Figure 5 lying in the MW window. The PP gradient increases from west Godavari subbasin to coastal part of the east Godavari subbasin. This is due to the rich sediment deposition along with the increase of vertical stress. It is observed as well as known from the previous studies that sand units in the overpressured Formations like in Raghavapuram and Vadaparru s contain gas [Rao, 2001]. Therefore, the delineation of OPZ in this area will be helpful for gas migration as well as borehole stability studies during depleting the reservoirs in these gas fields. To maintain the stability of a well in the K-G Basin, proper MW can be estimated from PP studies. Selection of MW for pressure control requires knowledge of PP and FP gradients. PP gradient defines the lower limit of MW, while FP defines the upper limit of MW [Tan and Willoughby, 1993; Wang et al., 2008]. The OPZ generated by disequilibrium compaction is most detectable because this zone is associated with higher porosity in the sediment of K-G Basin and the sonic and density derived porosities are being separated from one another. The overpressures, which occur mostly in the sediments from Cretaceous to Miocene age, have 4 km of thickness deposited in fluvio-deltaic conditions pointing toward a comparatively higher rate of sedimentation [Biswas, 1993; Rao et al., 1994]. The double overpressure configuration lies primarily in the KS, KK, and KG wells located near the RNG field, Amalapuram area. The single overpressure configuration lies primarily in the west Godavari subbasin. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1015

8 Table 2. Range of Response and Independent Variables for Estimating Pore Pressure Using Multiple Linear Regression Analysis Wells Depth Interval (m) RFT(MPa) DT (microsec/ft) S v (MPa) Vsh (fraction) KA KM KK KG KD The overpressure tops in Table 1 and overpressure horizons show three important characteristics: (a) the distribution of the pressure coefficient (abnormal pressure/normal hydrostatic pressure) is not uniform. There are many low overpressure zones against a background of high overpressure, (b) the pressure coefficient near the gas fields like RZL and RNG is greater than the pressure coefficient observed in the SUR and MDH field, and (c) the maximum pressure coefficient of 1.31 is observed in the well KV near RZL field. There is a low overpressure interval between the high overpressure zones in these wells. The analysis of well logs like density, neutron porosity logs indicate gas bearing zones above the OPZ in wells KV, KS, KK, and KG in Matsyapuri Sandstone in east Godavari subbasin. The gas bearing zones are seen at the sand lenses inside the overpressured Raghavapuram s in wells KA, KR, and KM of west Godavari subbasin. Normally pressured Raghavapram shale acts as a seal of gas bearing reservoirs at Gollapalli and Mandapeta Sandstones in the KE and KD wells. Overpressure in the formation controls hydrocarbon accumulation, because of its strong sealing capacity [Li et al., 2008]. The overpressure existing in the formation can drive hydrocarbon migration from the source rock to the traps [Tang and Lerche, 1993; Hao et al., 2002]. Strong overpressure (pressure coefficient greater than 1.8) can also fracture the formation and drive the sandstone intrusion into the shale, and causes the formation of the sand injectites that create new areas for hydrocarbon exploration and production [Shi et al., 2013; Hurst et al., 2011]. Well log data reveal sand lenses in the Raghavapuram Formation. Therefore, due to presence of OPZ, an accurate determination of pore pressure is essential for designing stable boreholes and an optimized casing program before drilling through depleted reservoirs [Bell, 1990; Hillis, 2000]. 4. Multiple Regression Analysis for Estimation of Pore Pressure As described in the foregoing section regarding the delineation of OPZ in sand/shale sequences of K-G Basin, the properties of shale vary more than as a function of pressure than do sands [Lindsay and Towner, 2001]. Pore pressure is a critical parameter in rock property and reflectivity models because of its disproportionate influence on the elastic properties of the shale cap rock [Ebrom et al., 2003; Sarker and Batzle, 2008]. An independent estimate of pore pressure is needed to estimate selection of MW when models are made for prospects away from well control. It is observed that the PP varies with velocity, shale content and vertical stress [Eberhart-Phillips et al., 1989; Hillis, 2000; Vernik and Kachanov, 2010]. It is observed from the previous PP analysis that PP prediction is dependent on sonic travel time, lithology and vertical stress. Actual pore pressure has been considered from RFT for the five wells namely KA, KM, KK, KG, and KD covering an area of 3400 sq. km of K-G onshore. Multiple linear regression model is proposed for a response variable like RFT using three independent variables: Sv, DT, and Vsh for the above mentioned five wells distributed in the K-G onshore. Table 2 is listing the well name, depth interval, RFT, DT, S v, and Vsh for the multiple regression statistical analysis and is showing the range of values for the dependent and independent variables. Analysis of variance (ANOVA), a technique analyzes the relationship between a dependent variable and three independent variables using IBM SPSS Statistical Software, version The ANOVA model is the simplest linear statistical model with independent variables. The independent variables namely, S v, DT, and Vsh are three different groups in this analysis. The ANOVA one-way approach has been adopted with group means m i for i 5 1, 2, 3 and variance. The ANOVA calculations for multiple regressions as shown in Table 3, the model degrees of freedom (df) are equal to 3, the error (residual) degrees of freedom, i.e., the df for residual are equal to 40 and the total degrees of freedom are 43. The null hypothesis for ANOVA [Koch and Link, 1970] states that m 1 5 m 2 5 m 3 5 0, and the alternative hypothesis simply states that at least one of the parameters m j 5 0, j 5 1, 2, 3. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1016

9 Table 3. ANOVA Results ANOVA a Model Sum of Squares df Mean Square F Significance 1 Regression b Residual Total a Dependent Variable: RFT. b Predictors: (Constant), Vsh, DT, S v. Table 4. Model Summary Model Summary Model R RSquare Adjusted R Square Standard Error of the Estimate a a Predictors: (Constant), Vsh, DT, S v. In Table 3, the F statistic is equal to / The distribution is F (3, 40), and the probability of observing a value greater than or equal to is less than because significance (sig.) of this test has value of There is strong evidence that m 1 is not equal to zero. The ratio between sum of squares for regression model (SSM) and total Sum of squares (SST), i.e., SSM/ SST 5 R 2 is known as the squared multiple correlation coefficient (Table 4). Therefore, R / This is the proportion of variance in the dependent variable (RFT) which can be explained by the independent variables. This is an overall measure of the strength of association and does not reflect the extent to which any particular independent variable is associated with the dependent variable. R is the square root of R-Squared and is the correlation between the observed and predicted values of dependent variable. Adjusted R-squared in Table 4 is computed using the formula 1 ((1 R 2 ) 3 (N 2 1))/(N )) where N is 43. Standard error of the estimate is referred to as the root mean squared error. It is the square root of the mean square for the residuals in Table 3. The general test in the ANOVA model [Gelman, 2005] examines the null hypothesis that all of the group means are equal. Rejecting this hypothesis means that at least one difference of two means is not zero. To find out the specific difference, or in finding out which of the differences is significantly different from zero, t test is performed to compare individual means. Here we use linear regression, which associates the two variables through an unstandardized coefficient. This can easily be generalized to multiple regressions, where we consider several covariates at the same time to try to understand their joint relationship to the outcome. In this linear regression model, the estimated raw or unstandardized regression coefficient for a predictor variable (referred to as B in Table 5) is interpreted as the change in the predicted value of the dependent variable for a one unit increase in the predictor variable. Thus, a B coefficient of 1.0 would indicate that for every unit increase in the predictor, the predicted value of the dependent variable also increases by one unit. The intercept or constant term (Table 5) gives the predicted value of the dependent variable when all predictors are set to zero. The constant coefficient is this simple mean of group means. Table 5. Coefficients From Multiple Regression Analysis Unstandardized Coefficients Coefficients a Standardized Coefficients Model B Standard Error Beta t Significance 1 (Constant) S v DT Vsh a Dependent Variable: RFT. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1017

10 Figure 6. The regression plot between model predicted pore pressure and actual pore pressure (RFT), combining data from wells KY, KE, KS, and KR. Confidence intervals (CIs) with 95% confidence level are shown with the best fit regression line. Influence of each predictor is reflected by knowing the values of standardized coefficient, beta as well as the p value, i.e., significance (sig.) for each predictor (Table 5). The beta value is a measure of how strongly each predictor variable influences the dependent variable. The beta is measured in units of standard deviation. For example, a beta value of of S v indicates that a change of one standard deviation in the predictor variable (say, S V ) will result in a change of standard deviations in the dependent variable. Thus, the higher the beta value the greater the impact of the predictor variable on the dependent variable. Prediction of PP at any depth through the multiple regression analysis with FP may provide indicate proper selection of MW as well as detection OPZ in these wells. The linear regression model for computation of PP is PP predicted 529: :662 3 Sv 1 0:044 3 DT 2 0:824 3 Vsh with R 2 5 0:94 (8) The newly established equation (8) has been used to compute PP for rest of four wells for testing of models under study. The model is not tested for well KV due to nonavailability of RFT values. Figure 6 is illustrating the regression results between the predicted PP and actual PP (RFT) for wells KY, KE, KS, and KR with R and confidence intervals (CIs) with 95% confidence level. The predicted PP is excellently matched with selected RFT values. The new PP model is now applied for these wells for computation of PP with depth. Figure 7 is showing the hydrostatic pressure and predicted pore pressure variation with depth for these wells. The pressure variations are plotted with the standard deviation (sd) as error bars in this figure. Top of OPZs are distinctly visible at depths 1350 m for well KE, 1425 m for well KS, and 1750 m for well KR, Figure 7. Displays the hydrostatic pressure and variation of model predicted pore pressure with depth for wells (a) KY, (b) KE, (c) KS, and (d) KR, respectively. Error bars are showing the standard deviation (sd) for the predicted pore pressure values. SINGHA AND CHATTERJEE VC American Geophysical Union. All Rights Reserved. 1018

11 respectively. The top of OPZ has not been noticed in well KY while above-hydrostatic pressure zone is observed below 1200 m till drilled depth. The OPZs, identified from the model predicted pore pressure curves are closely matched with the deviation as observed from NCT of wells KS and KR (Table 1) whereas it is not clearly detected from NCT in wells KE and KY. 5. Conclusions The OPZ generated by disequilibrium compaction is most detectable because this zone is associated with higher porosity. The sonic and density derived porosities are to found to be separated from one another in OPZ. The pressure coefficients indicate that there is widespread overpressure under the study area of K-G Basin with maximum pressure coefficient of The vertical stress, horizontal stress, pore pressures, and fracture pressures have been predicted from 10 wells of K-G Basin. Overpressure zones are detected as departure from NCT in sonic travel time for seven wells. Delineation of OPZ in the K-G Basin indicates the increase of PP gradient from onshore to coastal areas. The development of OPZ toward offshore direction is in close agreement with the previous PP studies of K-G offshore wells [Chatterjee et al., 2011]. The observed abnormal PP gradient in seven wells ranges from to MPa/km, whereas FP gradient varies from MPa/km in normal pressured sediment to MPa/km in overpressured sediments these wells. Vertical stress gradient is observed to vary from 21 to MPa/km. The S h magnitude is found to vary from 64 to 77% of the S V in normally pressured to overpressured sediments. A new statistical multiple regression model capable of estimating pore pressure has been proposed from well log data with R 2 of The predicted PP have been compared with the actual PP (RFT) values for four wells in K-G Basin other than the wells used for regression modeling. The model predicted PP indicates the top of OPZ and matches fairly well with the NCT-derived PP values. The pore pressure models proposed by Eaton [1972, 1975], Zhang [2011] primarily involve depth dependent normal compaction trendline and overburden stress and are assisted either by resistivity or sonic travel time or formation porosity. Bower s method suggested the pore pressure model from sonic velocity and effective stress with presumed calibration constant [Bowers, 1995]. The new statistical model provides a much easier way to compute pore pressure handling overburden stress, sonic travel time and volume of shale without using normal compaction trend. The prediction of PP and FP would be estimating MW at selected depth intervals which will be further helpful to study the reservoir depletion effects, to prevent wellbore collapse, borehole breakdown; sand production, and reservoir compaction induced casing failure. Acknowledgments Authors are thankful to ONGC for providing us the well log data and geologic information. Ministry of Earth Science (MoES/P.O. 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