Permeability is an important petrophysical parameter of hydrocarbon reservoirs for oil and gas production. Formation perme- ability is often measured in the laboratory test using core samples. However, when few core samples are available to calculate the permeability in the field, estimation of permeability becomes a challenging task. In study area, the Chandmari field of upper Assam-Arakan basin with the availability of only seven core samples and conventional logs such as density, porosity, resistivity and gamma ray data from few wells, the estimation of permeability becomes a difficult task. Therefore, in the present study an attempt is made to estimate the permeability from well log and core data using Buckles’ method approach in Langpar and Lakadong + Therria sanstone reservoir of Eocene–Paleocene geologic age in the field under the assumption and geological support that reservoirs in the study area are clean sand having very less shale control and are homogenous reservoir with little/no heterogeneity. In this study, petrophysical evaluation from log data and that from core data are integrated for the analysis of the reservoir characteristics. The relationship between porosity and water saturation which is required to distinguish mobile from capillary bound water or irreducible water saturation is used to estimate the irreducible water saturation. The estimated irreducible water saturation which is an essential parameter for water cut and permeability estimation is used for estimating the permeability in the field. The estimated permeability in the reservoirs using Buckles’ method ranging from 1500 to 4554.38 mD is well matched with the permeability estimated from core sample. The estimated permeability results suggest that the oil reservoir has the higher permeability than the gas reservoir. The permeability esti- mation relationship can further be used for the estimation of permeability in the inter-well region of Chandmari oil field. Keywords Buckles’ number · Porosity · Permeability · Well log · Core data · Assam-Arakan basin Introduction can be predicted using empirical relationships, capillary models and hydraulic radius theories (e.g. Scheidegger An oil/gas reservoir is a heterogeneous geological structure 1953, 1954, 1974; Bear 1972; Houpeurt 1974). It usually having large inherent complexity properties (Verma et al. increases with the size of pores in sandstone reservoirs, but 2012). Basic reservoir properties such as porosity, perme- it is complicated for carbonate reservoirs (Abdideh et al. ability and hydrocarbon saturation are directly linked to 2013). Both the permeability and porosity of a rock is result the storage capacity, fluid flow capacity, type of rock and of depositional and diagenetic factors that combine grain amount of hydrocarbon in pore volume, respectively (Verma size, pore geometry and grain distribution (Mortensen et al. et al. 2012; Singha and Chatterjee 2014; Chatterjee and 1998). Sometimes, sand or/and sandstone reservoir contains Mukhopadhyay 2002). The permeability is an important and the high permeability for the coarser grain at a low poros- primary rock property to access the fluid movement within ity and the presence of fine grain causes the low perme - the reservoir. It is the most difficult property to determine ability at the high porosity (Mortensen et al. 1998; Nelson and predict. The permeability value for a single-fluid flow 1994; Beard and Weyl 1973; Holmes et al. 2009). Many investigators (Archie 1942; Tixier 1949; Wyllie and Rose 1950; Pirson 1963; Timur 1968; Coats and Dumanoir 1974; * N. P. Singh Schlumberger Ltd 1987; Kapadia and Menzie 1985; Bloch email@example.com 1991; Ahmad et al. 1991) attempted to capture the relation Department of Geophysics, Institute of Sciences, Banaras of permeability function with model. However, these studies Hindu University, Varanasi, Uttar-Pradesh 221 005, India Vol.:(0123456789) 1 3 298 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 only contributed to the better understanding of the factor conditional average or expectation of permeability (Draper controlling permeability but not the actual relationship. They and Smith 1981; Wendt et al. 1986; Yao and Holditch 1993; demonstrated that it is only an illusion that a ‘universal’ rela- Doveton 1994). The newest method, called virtual meas- tion between permeability and variables from wireline logs urement (McCormak 1991; Wiener 1991; Osborne 1992; can be found (Mohaghegh et al. 1997). The permeability Mohaghegh et al. 1994a, b), makes use of artificial neural value of the rock is frequently measured by core data in the and fuzzy logic as model-free function estimator and flexible laboratory experiment considering various apparatuses and tool that can learn the pattern of permeability distribution in different pressure and time conditions (Behnoud far et al. a particular field. These methods which solely use data for 2017; Tadayoni and Valadkhani 2012; Holmes et al. 2012). the permeability calculation do not perform adequately once The empirical method which uses certain core data such new data are used (Mohaghegh et al. 1997). The ability of as effective porosity and water saturation to predict perme- virtual measurement to predict permeability values for entire ability values in the entire wells is somewhat realistic in wells without prior exposure to log/core data and ability to the sense that it makes calibration/comparison/matching of learn from external and then generalize the learning to solve the predicted and core data values and is categorized as a new problem set it apart from all methods using solely log direct method of permeability prediction. Artificial neural data for this purpose. networks have been widely applied to estimate the reser- The Assam-Arakan basin in India is one of the most voir permeability from the petrophysical data and well logs petroliferous basins producing oil and gas commercially. In (Jamshidian et al. 2015; Aminian and Ameri 2005). A com- the present study, an attempt is made to predict the permea- parison of nonparametric approaches, namely the alternat- bility in the inter-well region of Chandmari oil field of upper ing conditional expectations (ACE), generalized additive Assam-Arakan basin using few well log and core sample method (GAM) and neural network (NNET), have shown data. Buckles’ equation with the help of Willy-Rose relation that ACE is better than other two (Rafik and Kamel 2016). and Timur’s constant has been used to predict permeabil- There are various indirect methods for determining perme- ity values using two well log data (Well-A and Well-B) for ability using geophysical well log data, but their results are Langpar and Lakadong + Therria (Lk + Th) sandstone reser- often unsatisfactory (Mohaghegh et al. 1997; Molnar et al. voir of Eocene–Paleocene age in the upper part of the basin 1994). The regression method which is based on statisti- (Fig. 1). The predicted permeability of the two wells is vali- cal method of deterministic formulation tries to predict a dated by the few core samples for selected depth intervals, Fig. 1 Geological map of upper Assam-Arakan; study area is marked by black circle near Chandmari region. (After Mandal and Dasgupta 2013) 1 3 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 299 and on basis of that a relation has been established with Barua 2010). The structure is composed by few numbers the porosity data derived from the core sample. The prime of minor faults dipping in both the north and south direc- importance of this study is that once the basic porosity, tions and trending almost parallel to the main fault. These water saturation and permeability relations are established minor faults are trending nearly parallel to the main fault. using the core data, the same relations can further be used The generalized stratigraphic succession in the study in other wells from the same reservoir where core data are area is given in Fig. 2. The main reservoir rocks are the not available. Sylhet formation (Eocene), Kopili formation inter-bedded sandstones (Late Eocene–Oligocene), Tura (basal) marine sandstones and Surma Group alluvial sandstone reservoirs Geological setting (Mandal and Dasgupta 2013). The most productive reser- voirs in the upper basin are the Barail (Oligocene–Mio- This upper part of Assam-Arakan basin is bounded by cene) sands and the Tipam group (Miocene) massive sand- Himalayan orogenic belt in the north, a thrust belt in stones. Other formations are Girujan (Miocene), Namsang the southern side, Mishimi hills in northeastern side and (Pliocene) and Siwalik/Dhekiajuli (Recent) (Balan et al. the shield of Mikir hills in the west (Pahari et al. 2008; 1995; Mandal and Dasgupta 2013). Langpar formation Sekhar Deb and Barua 2010). A Basement High trends (Paleocene) is followed by the basement at Pre-Cambrian found parallel to River Brahmaputra where thirteen wells age. Lakadong + Therria sand reservoir of Sylhet forma- have been drilled by national oil companies. Sedimentary tion and Langpar formation have been found in the area. sequences ranging in age from Late Mesozoic to Cenozoic The main hydrocarbon potential is confined to the Langpar are exposed in the Assam-Arakan basin (Balan et al. 1995; formation and the lower part of Sylhet formation (Laka- Mandal and Dasgupta 2013). The study area, Chandmari dong + Therria units). These formations constitute fine- to oil field is located in the crested part of Basement high and coarser-grained sandstone and occasionally coal deposit bounded by two NE-SW-trending major faults in the north- and limestone/calcareous band with thickness varying ern and southern sides of the structure (Sekhar Deb and from 140 to 170 m (Sekhar Deb and Barua 2010). Fig. 2 Generalized stratigraphic formation of the upper Assam-Arakan basin. (After Sekhar Deb and Barua 2010) 1 3 300 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 where V is the volume of clay and C is Buckles’ constant. Methodology cl If irreducible water saturation is fixed, the permeabil - ity is calculated using the formula (Eq. 4) given by Wyllie The several empirical methods have been constructed based and Rose (1950). Since the reservoir is Lanpor and Laka- on the correlation between porosity, irreducible water satu- dong + Therria sandstone formation, we used Timur (1968) ration, and permeability (Tixier 1949; Timur 1968; Coats values of constants for sandstone in the generalized equation and Dumanoir 1974; Coates and Denoo 1981). However, the of Wyllie and Rose (1950) which is also known as Timur’s relationships between porosity and irreducible water satu- parameters, as follows. ration are best described by Buckles 1965, Chilingar et al. P = 3400 (For Oil), 340 (For Gas), Q = 4.4, R = 2.0 1972 and Doveton 1994. Buckles’ proposed that porosity and irreducible water saturation are hyperbolically related as follows (Buckles 1965). Results and discussion Φ× S = C wi (1) The above relation (Eq. 1) can be linearized to The well log data for this study are shown in Figs. 3 and 4. The curve on track 4 depicts the intergranular porosity (pur- log S = log C − log (2) wi ple color) calculated from the ELAN Plus volumetric analysis where is the porosity, S is irreducible water saturation, wi (using Techlog (GeoFrame) ELANPlus modules of Schlum- and C is a constant whose magnitude is related to the rock berger) and core data (blue color), respectively. ELAN Plus type. gives the quantitative petrophysical analysis of multi-mineral The simplest quantitative method of permeability pre- lithology using a number of optimized simultaneous equations diction from logs with the support of core studies has been and models. It is different from the traditional petrophysical keyed to empirical equations of the type analysis because it solves a set of equations to estimate the volume of each formation component first. Then, it measures (3) K = PΦ the properties such as porosity, water saturation, volume of where P and Q are constants determined from core meas- shale from the derived volumes and does not compute the for- urements and applied to log measurements of porosity to mation properties from a number of fixed formulas step by generate predictions of permeability (K). step (Schlumberger 2013). The intergranular porosity curve Wyllie and Rose (1950) proposed an empirical equation (PIGN), water saturation and clay volume (V ) have been CL which is modification of the Carman–Kozeny (1937) equa- determined by carrying out petrophysical interpretation of tion that substituted irreducible water saturation for the spe- wireline log data. The default values of Timur’s parameters cific area term. As the specific surface area is quite difficult recommended for sandstones are modified after calibrating to measure directly by conventional methods and therefore it it with the available core data in both the wells individually. is linked with pore size, this in turn controls the irreducible Following good match of porosity curve with the core data, water saturation. Buckles’ constant has been determined corresponding to both the Langpar and Lk + Th reservoirs separately. The Lk + Th K = P (4) R formation is having the finer sandstone, whereas the deeper wir Langpar sandstone reservoir is relatively coarser. The esti- mated values of Buckles’ number in both reservoirs support The equation functions as a powerful surrogate variable the fact that Buckles’ number increases for finer-grained rocks. for specific surface area, and this accounts for the improve- The log curve on track 5 shows the derived permeability using ment in permeability estimates when incorporated with Wyllie and Rose (1950) formula and core data, respectively, porosity. The constants R and Q are measured from core whereas the ELAN Plus volume is presented on the last track measurements and then applied to well log data. This is one 6 (Figs. 3, 4). The crossplot between porosities values derived of the oldest permeability estimation methods available and from density log (on X-axis) and ELAN interpretation (Y-axis) is reliable when calibrated to core data. are analyzed, and a straight line curve is drawn to fit the data In hydrocarbon zones above the transition zone, irreducible points. The crossplot between the porosities estimated from water saturation is taken equal to water saturation ( S ) values two different inputs show a very good correlation coefficient, from any shale-corrected method. Below the hydrocarbon 91% in Well-A (Fig. 5) and 73% in Well-B (Fig. 6). A liner zone (i.e. in the water and transition zone), we calculate the relationship between porosity derived from density log and irreducible water saturation using the following formula. effective porosity obtained from ELAN interpretation using C conventional petrophysical software (Techlog, Schlumberger) S = wir (5) which is also calibrated with the core data, is established and 1 − V cl is shown in Figs. 5 and 6 for both the Well-A and Well-B, 1 3 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 301 Fig. 3 ELAN interpretation and permeability prediction in Well-A respectively. This relationship can further be utilized for pre- 3.2 (PIGN) KINT = 3400 ∗ (7) dicting the permeability in another well in the same area where 2.2 wir core data are not available. The sets of equations used for per- meability calculation in both the wells are as follows. Well‑B Well‑A The reservoir sand interval in Well-B is 3820–3830 m (Lk + Th reservoir) and 3872–3892 m (Langpar reservoir), The reservoir sand interval in Well-A is 3900–3921 m with the shale break and volume of shale average (< 10%) in the ranges respectively. The well is producing gas from Langpar as well as LK + Th reservoirs of Eocene age, and having volume 3915–3915.3 m and 3918.8–3919.2 m. Hence, it is considered as a clean sand reservoir. Well-A produces oil from Langpar of shale less than 10% is treated as a clean reservoir. The following sets of equation and parameters are used for the formation of Eocene age. The following sets of equation and parameters are used for the permeability calculation in Well-A. permeability calculation in Well-B. C = 0.03 (for Lk + Th reservoir), 0.02 (for Langpar C = 0.02, P = 3400, Q = 3.2, R = 2.2 Here, few changes in abbreviations, PIGN.IN = , VCL. formation) P = 3400, Q = 3.2, R = 2.4 IN = V and KINT = K CL PIGN 3.2 (PIGN) S = C (6) wir KINT = 3400 ∗ (1 − V (8) 2.4 CL wir 1 3 302 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 Fig. 4 ELAN interpretation and permeability prediction in Well-B Fig. 5 Crossplot between porosities derived from density and ELAN interpretation in Well-A 1 3 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 303 Fig. 6 Crossplot between poros- ity derived from density and ELAN interpretation in Well-B in good agreement with each other. The goodness of fit (R ) shows a significant value of 0.70. On basis of this, an equation has been established which can be further applied to calculate permeability of the reservoir where enough well data are not available. As both the permeability and porosity of a rock is result of depositional and diagenetic factors that combine grain size, pore geometry and grain distribution (Mortensen et al. 1998), sometimes reservoir contains high permeability for coarser grain at low poros- ity and fine grain causes low permeability at high porosity (Mortensen et al. 1998; Beard and Weyl 1973). The gas sands have the lower permeability and higher porosity, whereas the oil sands have the higher permeability and lower porosity as shown in Fig. 8. The gas sands in Well-A are located at the depth interval of 3872–3892 m followed by the oil sand at depth of 3900 m. The Langpar reservoir is relatively coarser in grain size than the Lk + Th reservoir causing its higher permeability and comparatively lower Fig. 7 Crossplot between predicted permeability from Buckles’ porosity than Lk + Th reservoir. approach and core permeability for the Well-A and Well-B at selected depth intervals Conclusion Permeability relation This paper presents a case study of permeability predic- tion from wireline logging and core data from Assam- The permeability measured from core data and that pre- Arakan basin. Applicability and suitability of empirical dicted from Buckles’ method approach for Langpar res- methods for permeability prediction using wireline log ervoir and Lk + Th reservoir in both the wells at selected and core data are tested, and the suitable one is applied depth intervals are shown in Fig. 7, which are found to be for the purpose. The empirical relationship has allowed 1 3 304 Journal of Petroleum Exploration and Production Technology (2019) 9:297–305 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( htt p://c r ea t ive co - mmons .org/licen ses/by/4.0/), which permits unrestricted use, distri- bution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. References Abdideh M, Birgani NB, Amanipoor H (2013) Estimating the reser- voir permeability and fracture density using petrophysical logs in Marun oil field (SW Iran). Pet Sci Technol 31(10):1048– 1056. https ://doi.org/10.1080/10916 466.2010.53680 6 Ahmad U, Crary SF, Coates GR (1991) Permeability estimation: the various sources and their interrelationships. 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