Abstract
This work has been developed to classify sand and shale from seven wells in the Cauvery basin using a multilayered feedforward neural network (MLFN) model. Seven wells distributed over 5100 km2 of this basin have been utilized for analysis of conventional well logs and reservoir characterization. Hydrocarbon bearing sediments of Andimadam, Bhuvanagiri, Nannilam and Niravi formations of the Cauvery basin are evaluated in terms of shaliness, cementation factor, porosity, water saturation, and permeability. Pickett plot has been applied to investigate the cementation factor, formation water resistivity, permeability. The cementation factor (m) varies from 1.31 to 1.86 in these formations, whereas permeability varies from 0.01 to 400 md. Very good quality reservoir exists in the Bhuvanagiri formation with high permeability 300–400 md, whereas a good quality reservoir is occurring in Niravi, Nannilam and Andimadam formations with hydrocarbon saturation 60–70%.
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1 Introduction
Identification of hydrocarbon bearing zone and estimation of the petrophysical parameters associated with it, namely, water saturation, the volume of shale, cementation factor, porosity, and permeability are essential for the determination of flow unit. The physical properties of sediments like natural radioactivity, resistivity, density, compressional/shear sonic travel time, neutron porosity commonly measured through geophysical logging, are used for identification of fluid and lithology of hydrocarbon bearing sand reservoir (Singha and Chatterjee 2017; Das and Chatterjee 2018). Several authors have classified mud-rocks, siliciclastic, coal and coal proxi parameters from conventional well logs using the neural network (Baldwin et al. 1990; Bhatt and Helle 2002; Maiti et al. 2007; Schmitt et al. 2013; Ghosh et al. 2016). The available geophysical log responses are observed in wells at the Cauvery basin. The purpose of this study is to classify the hydrocarbon bearing zone, water bearing zone and shale using a multilayered feedforward neural network (MLFN) model. We have further estimated the cementation factor, porosity, permeability and water saturation of hydrocarbon bearing zones of wells drilled in this basin.
Typically conventional logs (such as density, neutron and sonic logs) are used to estimate porosity, but permeability estimation requires the study of core samples. However, in the absence of core data, well log data may be used for the computation of permeability. Pickett plot (resistivity vs. porosity) is generally used to characterize the behaviour of reservoir flow units (Martin et al. 1997; Aguilera and Aguilera 2002; El-Khadrag et al. 2014). Sanyal and Ellithorpe (1978) and Greengold (1986) had demonstrated computation of the cementation factor (m) from the Pickett plot. This paper describes the MLFN model for the identification of hydrocarbon bearing zones and the uses of Pickett plot (Aguilera 2001) for computation of reservoir parameters such as the cementation factor, formation water resistivity, water saturation, permeability from eight wells of Cauvery basin.
2 Study area
The Cauvery basin extending along the east coast of India, has been formed as a pericratonic rift basin due to fragmentation of Gondwanaland during drifting of India–Sri Lanka landmass system away from Antarctica/Australia plate in Late Jurassic/Early Cretaceous (Prabhakar and Zutshi 1993; Saha et al. 2008; Phaye et al. 2011). The basin exhibits a series of parallel horsts and grabens structures trending NE–SW direction formed due to rifting (figure 1). Exploratory drilling in this basin revealed more than 6 km thick deep marine clastic sediments of Mesozoic and Cenozoic age with multiple reservoirs holding commercial hydrocarbon. The generalized lithostratigraphy of the Cauvery basin interpreted from the available seismic section with age varying from Pre-Cambrian to Miocene is shown in figure 2 (Venkatarengan et al. 1993). Eight wells: CBV, CPT, CKL, CMT, CNL, CPV, CKP and CKK are distributed covering 5100 km2 area of the Cauvery basin (figure 1). The well log correlation using gamma ray and resistivity logs (Rider 2002; Eichkitz et al. 2009) through seven wells: CBV, CPT, CKL, CMT, CNL, CKP and CKK across section AA′ is shown in figure 3 (Choudhury et al. 2015). Top of formations are marked on the basis of gamma ray and deep resistivity log characteristics.
3 Well log analysis
Geological formations such as: Andimadam, Sattapadi Shale, Bhuvanagiri, Kudavasal Shale, Nannilam, Portonovo Shale, Kamalapuram, Karaikal Shale, Niravi Sandstone of age ranging from Lower Cretaceous to Middle Miocene as described in figure 2 are evaluated using conventional well log analysis. Multimineral lithologies consisting of sandstone, limestone, dolomite and shale exist in the sediments penetrated through eight wells under the study area. Gamma ray logs measure the radioactivity of formations in the well which indicates the presence of clay mineral, oil source rock, organic matter and shale in reservoir rock (Schlumberger 1972). Sandstones (hydrocarbon or water bearing), have a low concentration of radioactive elements thus registering a low gamma ray count. The gamma ray (GR) values in these hydrocarbon bearing zones of wells CMT, CKK, CBV, CNL, CPV and CPT range from 20.39 to 70 API.
Resistivity is the property of a material or substance to resist the flow of electric current through material (Schlumberger 1972). Three types of resistivity logs are available which are, flushed zone resistivity (micro spherically focussed, MSFL), shallow resistivity (laterolog shallow, LLS) and deep resistivity (laterolog deep, LLD). LLD and LLS logs show a higher value than MSFL logs in hydrocarbon bearing zones. The deep resistivity log response in hydrocarbon bearing zones as observed from six wells ranges from 4.0 to 874.0 Ωm. As gas concentration increases, the separation between MSFL and LLD/LLS also increases. In the case of water saturation, all resistivity curves coincide with each other.
Density log is strongly affected by the presence of gas and records the lowest density values in gas saturated sand. The neutron porosity tool accounts for the amount of hydrogen present in the formation. In clean sandstone formations, where porosity is filled with water or oil, the neutron log measures liquid-filled porosity. Neutron log response becomes high in shale because of the presence of clay bound water, whereas it shows a very low value in gas saturated sand.
The gas bearing zone is indicated when the neutron porosity is less than the density porosity in a porous and permeable zone. This separation between neutron and density, termed as a crossover, is an indicator of gas bearing zones in clean sand (Bateman 1985). The crossover effect becomes smaller suggesting the presence of oil saturated sand. Water saturated sand is represented by overlaying of neutron and density logs (Singha and Chatterjee 2017; Das and Chatterjee 2018). The typical well log responses for water bearing zone, hydrocarbon saturated zone and shale are illustrated through figure 4(a and b) for wells CMT and CNL, respectively. The hydrocarbon bearing zones are delineated from neutron-density crossover and the separation between deep (RD), shallow (RS) and flushed zone (Rxo) resistivity logs. The multilayered neural network approach is to be used for identification of hydrocarbon bearing zone, water bearing zone and shale from seven wells under study area.
4 Multilayered Feed Forward Neural Network (MLFN) approach for identification of reservoir, water saturated zone and shale
Cross plotting techniques are available for identification of fluids and lithology using conventional logs for selected depth intervals (Singha and Chatterjee 2017; Das and Chatterjee 2018; Gogoi and Chatterjee 2019). Here, our aim is to identify hydrocarbon bearing zones from seven wells for depth intervals varying from 300 to 3800 m. A quick look or cross plotting technique will be tedious and time consuming for identifying hydrocarbon bearing zones using conventional well log responses.
Estimation of lithology from well logs in heterogeneous formation is difficult to solve by the quick look interpretation method (Masoudi et al. 2011). Artificial neural network (ANN) tool has been successfully utilized for the determination of lithology using the transformation between well logs (Lim 2005; Singha et al. 2014; Chatterjee et al. 2016; Ghosh et al. 2016).
MLFN is a special arrangement of ANN that is the most precise method for solving the non-linear classification of lithology and bed boundaries identification problems (Maiti et al. 2007). In general, the architecture of an MLFN consists of one input layer, one output layer and at least one or two intermediate hidden layers between the input and output layer (Hampson et al. 2001). Here an MLFN model is created using geophysical log data, such as: GR, RD (Rt), flushed zone resistivity (Rxo), bulk density (Rhob) and neutron porosity (Phin) as input parameters. Water saturated zone, hydrocarbon bearing zone and shale are considered as output parameters with double hidden layers (Masters 1994). In a fully connected MLFN, neurons of each layer are connected to the neurons of the next layer through some weight (Chatterjee et al. 2016; Ghosh et al. 2016). As shown in figure 5, the input layer constitutes of the input data for the nodes in hidden layers and output data of this hidden layer constitutes the input data for the output layer. Nodes are not connected within the same layer. For the training of the MLFN model, three lithocodes (10, 20 and 30) are assigned to hydrocarbon bearing zone, water bearing zone and shale, respectively, as output layers (Maiti et al. 2007; Ghosh et al. 2016). The selected depth intervals for two wells, CMT and CNL are used to train the model. The training dataset of 98 depth points have been chosen from depth intervals: 400–1700 m from well CMT, 2000–3700 m from well CNL, respectively. The selected depth intervals for two wells, CMT and CNL are used to train the model. Hydrocarbon bearing zone, water bearing zone and shale are identified from log responses in these depth intervals (figure 4a and b). Hydrocarbon bearing zone is identified from 566.5 to 570.5 m in well CMT as well as from 2085 to 2112 m in well CNL. Water bearing zone is identified from 960 to 985 m in well CMT as well as from 2169 to 2175 m in well CNL. Shale is identified from 554 to 564 m in well CMT as well as from 3380 to 3389 m in well CNL. Table 1 shows the range of log responses for three lithocodes to train the MLFN model.
The network is trained with known lithocodes to develop an optimal set of weights between nodes (Chatterjee et al. 2016; Ghosh et al. 2016). The back-propagation algorithm (Dayoff 1990; Paul et al. 2018) uses a training pattern in which the first step is the forward propagation step followed by the back-propagation step. The parameter at the output layer has been computed using the back-propagation technique as given below:
where Y is the output parameter, x is the input parameter, α and β are the connecting weights, \( n_{1} \) is the dimension of the input vector, and \( n_{2} \) is the number of hidden neurons. \( \alpha_{0} \) and \( \beta_{oj} \) are called the bias weights. The thresholding function \( \left( f \right) \) applied at the hidden node is typically a sigmoid function.
The general form of sigmoid function is
It squeezes its input (i.e., a) to a value between 0 and 1.
The problem of estimating the weights has been considered a nonlinear optimization problem, where the objective is to minimize the sum-squared error (SSE) between the observed lithocode and the MLFN predicted lithocode.
where, n is the number of observations, xi is the value of the ith observation and \( \bar{x} \) is the mean of observations.
To initialize the hidden layer weights, SSE for a trial model is computed by repeating steps for 1000 epochs with 16 hidden nodes at the two hidden layers. The lowest value of SSE is chosen for the selection of weights to optimize the MLFN model (Paul et al. 2018). The network is trained with 70% of the total available data, then validated with the remaining 20% and then tested on 10% data using IBM SPSS version 21 software. The training dataset accounts for 70% of the entire dataset and is used to calculate errors and adjust connection weights and bias of network. The overtraining or over-fitting effect is avoided by using the validation dataset. Figure 6(a and b) displays the SSE vs. epoch for training and validation dataset. It is observed that the training error reaches a minimum at 600 epoch and then increases, whereas validation is minimum at 600 epoch and then starts undulating. Since it becomes minimum at 600 epoch, so the training is optimized with 600 epoch with 16 hidden nodes. Therefore, two hidden layers each consisting of 16 individual nodes with 600 epoch are best suited to present identification problems as dictated by well log data. Figure 6(c) presents the relation between observed lithocode and predicted lithocode with the goodness-of-fit (R2 = 0.98) for training the MLFN model. Training dataset and MLFN predicted lithology for selected depth intervals of two wells: CNL (2050–2170 m) and CMT (530–600 m) are shown in figure 6(d). Testing dataset and MLFN predicted lithology for selected depth intervals of two wells: CPV (2540–2580 m) and CKK (1730–1800 m) are shown in figure 6(e).
Accuracy of prediction is justified with figure 6(c–e). A very good match is observed between the observed lithology and MLFN predicted lithology with excellent R2 of 0.98 of the trained the MLFN model. Figure 6(d and e) indicate the MLFN predicted lithology corresponding to the log responses for training and testing wells with the observed lithology respectively.
The trained MLFN model is applied to the five wells for identification of hydrocarbon bearing zones for total depth interval varying from 300 to 3800 m. The model predicted results are listed in table 2. Figure 7(a) shows the MLFN predicted output for well CKK; figure 7(b–d) are the output for well CPV; figure 7(e) is for well CBV, for specific depth intervals (figure 7). Hydrocarbon bearing zones are identified in four wells namely; CKK, CPV, CBV and CPT. Hydrocarbon bearing zones are not detected in well CKP.
5 Estimation of petrophysical parameters
5.1 Pickett plot
Pickett plot has been used for computation of cementation factor and reservoir parameters of hydrocarbon-bearing formations penetrated through six wells; CBV, CPT, CMT, CNL, CPV and CKK in the Cauvery basin.
Water saturation computation for clean sand requires cementation factor (m), formation water resistivity (Rw), tortuosity (a) and saturation exponent (n). Therefore, the Pickett plot has been utilized obtaining aRw and m from porosity, deep resistivity logs for all six wells. Rw values are calculated from the spontaneous potential (SP) log for the selected intervals of six wells. This value is used for estimating ‘a’ in table 3. Water saturation is computed with the estimated aRw and m from the Pickett plot for each well. For estimation of petrophysical constant like cementation factor (m) and reservoir parameters such as permeability is discussed through a well CKK below:
Pickett plot is generated using Archie’s formulae (Archie 1942). Rearranging the Archie equation we get
where the resistivity index = I and saturation exponent = n.
where
and a is tortuosity and Φt = total porosity. Rt = RD, R0 = resistivity of formation with 100% water saturation.
Equations (5 and 6) are combined to yield
where, Rw is the formation water resistivity.
Equation (7) (Pickett 1966) leads to
which is a straight line on log–log graph paper with slope (–m) and intercept (aRw).
An example from a well CKK in Bhuvanagiri formation is shown in figure 8. The intercept is shown in this figure with total porosity (Φt) = 1. According to Pickett (1973), the saturation exponent ‘n’ which is a function of water saturation equals the value of porosity exponents ‘m’. Water saturation lines varying from 25 to 100% are drawn in this plot. Table 3 lists the value of Rw, m for hydrocarbon bearing zones of six wells.
5.2 Permeability
The ability of rock to allow fluids to flow through interconnected pore space is termed as permeability (K). The irreducible water saturation (Swi) is expressed as (Morries and Biggs 1967):
where Swi is the irreducible water saturation.
The irreducible water saturation has been expressed in terms of total porosity and effective porosity (Aguilera 1990) as:
After incorporating into equation (7) the true resistivity in terms of permeability is written as (Aguilera 1990):
By taking logarithm on both sides for gas bearing zones in well CKK, equation (11b) is written as:
From equation (12), by plotting Rt vs. Φt on log–log graph paper, the relation results a straight line with a slope equal to (–3n – m) with a constant aRw and permeability. Since m = n, the slope equals (–4m). The intercept of a straight line with 100% porosity indicates aRw (79/K1/2)−n. The line of constant permeability equals to 0.01 to 500 md is drawn by computing Rt from equation (11).
The parallel lines of permeability ranging from 0.01 to 500 md are shown in figure 9.
5.3 Estimation of volume of shale, porosity and water saturation
Hydrocarbon bearing zones are available in six wells under the study are of the Cauvery basin. Petrophysical parameters are estimated from six wells holding hydrocarbon bearing sediments, namely, CBV, CMT, CNL, CPV, CPT and CKK (figure 1). Table 4 shows the depth intervals of hydrocarbon bearing sediments from Niravai Sandstone aging Upper Oligocene to Andimadam formation of Lower Cretaceous from six wells. The thickness of hydrocarbon bearing zones ranges from 1 to 19 m. Table 4 lists the values of petrophysical parameters of oil and gas bearing zones like effective porosity Φeff, the volume of shale (Vsh) and water saturation (Sw) of six wells in the Cauvery basin. The volume of shale and effective porosity (Φeff) are estimated from the following equations (Fertl and Frost 1980):
where GR = gamma ray log reading at any depth, GRmin = minimum gamma ray reading, and GRmax = maximum gamma ray reading. GRmin varies from 17 to 26 API and GRmax from 142 to 182 API in six wells.
We have assumed clean sand when Vsh ≤ 6% for computation of water saturation using Archie’s law (Archie 1942).
6 Results and discussion
Hydrocarbon (HC) bearing zones are represented by the crossover between density and neutron porosity logs characterising high resistivity with low gamma ray value. Water saturation zones are represented as coinciding density and neutron porosity logs with low gamma ray and Rt value. Shale zones are represented by high neutron porosity (approx. 40%), low resistivity value with high gamma ray value. In general, the MLFN predicted model detects the water bearing, HC bearing zones and shale. The model is not able to detect other lithologies such as limestone or dolomites in these wells. There is a very good match between MLFN predicted HC bearing zones and quick look log interpretation at depths: 1950–2070 m in well CKK. Well CPV has shown very good match with the log data and MLFN predicted HC bearing zones namely; 1649.5–1651.5, 3090–3091.5, 3279.5–3281 and 3336.6–3380.8 m. Well CBV has shown good match with the log data and MLFN predicted HC bearing zones namely, 3408.3–3410, 3433–3434.7 m. MLFN predicted hydrocarbon bearing zones are listed for well CPT in table 2.
The cementation factor used in Archie’s relation is an important parameter for the computation of water saturation. Its value generally varies from 1.3 to 3.1 depending on both reservoir and geological parameters (Salem and Chilingarian 1999; Tabibi and Emadi 2003). The lithologies of the selected hydrocarbon bearing zones of six wells are listed in table 3. The HC bearing zones are occurring in geological formations such as: Andimadam to Niravi Sandstone aging Lower Cretaceous to Upper Oligocene (table 4). The volume of shale in these zones is varying between 0 and 6%. Clean sands are assumed with Vsh less than 5–6%. Effective porosity and water saturation ranges from 10–33% and 12–60%, respectively. Cementation factor (m) in three wells, namely; CKK, CBV and CPV in Bhuvanagiri formation aging Lower Cretaceous to Upper Cretaceous ranges from 1.31 to 1.75 with porosity 10–24%. Oil bearing zones identified in wells CMT and CNL penetrated through Niravi Sandstone followed by Nannilam formation of Upper Oligocene to Upper Cretaceous characterize m varying from 1.55 to 1.80 with porosity 18–33%, respectively. Oil bearing sand layer in well CPT belonging to Nannilam and Bhuvanagiri formations of Upper Cretaceous indicates varying m of 1.56 to 1.86 with 18–30% porosity. Andimadam formation of Lower Cretaceous penetrated by a well CPV indicates m of 1.55 with the porosity of 11–19% whereas other penetrated gas and oil bearing zones in Bhuvanagiri and Nannilam formations are characterized by low m of 1.31. The value of m is found to be 1.8–1.86 in high porous sands and 1.31 in low porous sands. Permeability ranges from 0.01 to 400 md of these wells. Low permeability is observed in oil well CPV and the highest permeability is observed in gas well CKK, respectively.
Several publications are available to predict the petrophysical parameters: porosity, permeability, water saturation, the volume of shale, lithofacies using neural network modelling (Anifowose et al. 2016; Gogoi and Chatterjee 2019). The key findings of this paper are to detect HC zones from well log data and to estimate shale volume, porosity, water saturation and permeability for these HC zones. The porosity, permeability and volume shale values of sandstone reservoirs in Andimadam, Bhuvanagiri, Nannilam and Niravi formations are adequate to hold sufficient hydrocarbon. These reservoir characteristics tend to improve significantly as sedimentation proceeds basinwards. Very good quality reservoir characterizing with porosity 20–22% and permeability of 300–400 md exists in well CKK of Bhuvanagiri formation.
Petrophysical analyses are crucial to reservoir modelling because the physical parameters of rocks provide a reference for delineating reservoir and non-reservoir distributions (El sayed et al. 1993; Bornard et al. 2005). Reservoir characterization has been carried out using conventional well log data of Abu Madi Formation in Abu Madi and El Qar’a fields, Nile delta Egypt to predict information about porosity, the volume of shale and hydrocarbon saturation (Mahmoud et al. 2017). Petrophysical parameters had been calculated using well log data in Krishna–Godavari and Upper Assam basin (Das and Chatterjee 2018; Gogoi and Chatterjee 2019). Reservoir discrimination and characterization of its lithology along with its fluid-content in reservoirs of Cauvery basins uses quantitative techniques of log studies. These factors along with seismic data will discriminate the reservoirs and non-reservoirs under the study area. However, the identification of HC zones from well log data using MLFN modelling in the Cauvery basin would be useful as a tool for the classification of lithology and HC zones for other sedimentary basins of India. These studies would further be implemented for reservoir modelling in addition with seismic data (Datta Gupta et al. 2012).
7 Conclusions
This paper reveals the ability of MLFN modelling in the classification of lithology from well log data. Complex lithologies consisting of sandstone, limestone, dolomite and shale exist in these sediments penetrated through the wells. The methodology discussed demonstrates the classification of sands in terms of hydrocarbon and water bearing zones along with shale using MLFN model from two training wells. The MLFN model is tested for identification of HC zones for the other four wells, CKK, CPV, CBV and CPT. MLFN model is not used for well CKL as it lacks neutron porosity data. Out of the seven wells, HC zones are identified from six wells using the MLFN model. Petrophysical parameters are obtained from these zones. Pickett plot technique is found to be useful for the computation of cementation factor, formation water resistivity, tortuosity, saturation exponent and permeability from well log data. The thickness of 30 HC zones in six wells varies from 1 to 19 m. Clean sands are interpreted in terms of effective porosity and water saturation estimation. Sand with high porosity (30–33%) present in wells CMT and CPT shows a higher m (1.8–1.86) whereas sand with low porosity (~11%) in well CPV indicates a low m of 1.31. The petrophysical analysis shows that the reservoir in Bhuvanagiri formation is of very good quality with hydrocarbon saturation ranging from 40 to 88%, the volume of shale between 0 and 6% followed by a good quality reservoir in Niravi, Nannillam and Andimadam formations with hydrocarbon saturation 60–70%. In the Petroleum industry, this method is suitable and plays a substantial role in lithology classification in the exploration stage.
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We are sincerely thankful to ONGC for providing the well log data for academic and research work.
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Pandey, A.K., Chatterjee, R. & Choudhury, B. Application of neural network modelling for classifying hydrocarbon bearing zone, water bearing zone and shale with estimation of petrophysical parameters in Cauvery basin, India. J Earth Syst Sci 129, 33 (2020). https://doi.org/10.1007/s12040-019-1285-4
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DOI: https://doi.org/10.1007/s12040-019-1285-4