A Comparative Study on Appraisal of Lithological Boundaries and Litho-Models Using Well Log Data at Bhogpara Oil Field in Assam of NE India

Introduction

Discrimination of bed boundary, well correlation and precise measurement of thin beds are the necessary steps involved in reservoir characterization. Generally, the geophysical well log data are used in finding the lithological boundary and petro-physical properties of the formation. Well-log responses are the continuous measurement of petrophysical properties of formation through which the well is drilled. At present, in oil industry spontaneous potential (SP), gamma ray (GR), resistivity (latero-log deep (LLD)), P-wave velocity, bulk density (RHOB) log responses are used for bed boundary detection [1]. In this study only SP, GR, and LLD wire-line log responses having a sampling interval of 0.1 m are used for lithological boundary detection. As well log data register the petrophysical properties of the heterogeneous sub-surface at a particular sampling interval, thus, well log response can be treated as a non-stationary signal [2]. Traditionally, different interpreters use their experience of well logging and geological knowledge of the area. However, different interpreters may sometimes provide dissimilar outcomes from the same data set with same geological condition [3]. According to the quicklook interpretation technique, sudden changes took place in the wireline log data may infer the changes in the lithological layers [4].

Researchers have documented a few non-traditional techniques to interpret rock layer boundaries through the use of wavelet transform-based approaches [2, 5]. However, these wavelet-based techniques are able to discriminate thick lithological layers of the order of 30 m or more. Fang, et al. [6] proposed a technique based on the improved dynamic time warping (IDTW) for stratigraphic correlation using wireline logs. Additionally, in the E&P industry to validate the traditional log interpretation results, core data is not always available for the entire depth section of the drill site, even core recovery is also a difficult task. Though nowadays using the advanced borehole imaging tools like Formation Micro-Scanner (FMS) and Full-bore Formation Micro-Imager (FMI) made by Schlumberger, have the capability to detect bed boundaries in centimeter scales [7]. In petroleum industry, due to cost management, these expensive logs (FMS and FMI) were run only for some specific interest in a particular zone of the reservoir. Therefore, we have to look forward for some unconventional way of interpretation, that may be able to discriminate the lithological boundaries in an automated manner with higher accuracy.

The intention of present study is to find out the plausible thick and thin beds from conventional routine wire log data. Additionally, this technique can provide a general assessment of bed boundary successions of the studied region in more robust manner with less computation time and cost. Numerous techniques and workflows have been recommended and accomplished on bed boundary detection using well log data by applying the Walsh transform, i.e., basically the signal (well log data) passed through Walsh low pass filter [8]. Further researchers used Walsh transform for automated bed boundary detection [9, 10] and log analysis [11]. Walsh transform is also used in other field of geosciences, like, identifying fracture time-frequency analysis of well logs [12], gravity applications [13, 14] and resistivity filtering [15] etc.

In present study, initially the quick look interpretation approach was used on the GR log response to assessed the possible bed boundaries. Subsequently, these beds were correlated among the wells and a traditional lithological model was built-up. In order to obtain the bed boundaries more explicitly, Walsh transform and boundary picking algorithm were applied on available aforesaid wireline logs, as well as a lithological model was proposed on the basis of Walsh picking boundaries.

Walsh Filters and Bed Boundary Detection Algorithm

Walsh transform are a set of complete and orthogonal function of non-sinusoidal waveform. In contrast to sinusoidal waveforms whose amplitudes may assume any value between +1 to -1 [16]. Walsh functions assume only discrete amplitudes that provide the kernel function of the Walsh transform. Because of this special nature of the kernel computation of Walsh transform of a signal is simpler and faster than the Fourier transform. Analogous to the frequency in Fourier analysis, Harmuth [17] has introduced the concept of the generalized frequency in Walsh transform called sequency. Sequency is defined as half of the average number of zero crossing in unit interval (time or space). The unit for sequency is zeros per second (zps). The complete set of Walsh function can be derived through the difference equation as [16],

$$\text{wal}(2k+1) = \left( -1 \right)^{\frac{1}{2}-\frac{1}{4}} \left( \text{wal}(k, 2k+1) + \left( -1 \right)^{\frac{1}{2}-\frac{1}{4}} \text{wal}(k, 2k) \right) \text{for } -\frac{1}{2} \leq x \leq \frac{1}{2} \quad (1)$$

$$= 0 \quad \text{for } -\frac{1}{2} > x > \frac{1}{2} \quad (2)$$

where, $q = 0$ or 1 and $k=0, 1, 2, \ldots$ correspond to the sequence of the Walsh functions. Walsh functions are subdivided into even and odd functions called cosine like Walsh function denoted as Cal (i, t) and sine like Walsh function denoted as Sal (i, t) respectively. i.e.,

$$\text{Cal}(k, x) = \text{wal}(2k, x) \quad (3)$$

and $$\text{Sal}(k, x) = \text{wal}(2k+1, x) \quad (4)$$

A function $f(x)$ defined in the interval $(-1/2, 1/2)$ and satisfying Dirichlet’s conditions can be represented by an infinite series of Walsh functions as [16],

$$f(x) = \sum_{k=0}^{\infty} F(k) \text{wal}(k, x) \quad (5)$$

where,

$$F(k) = \int_{-1/2}^{1/2} f(x) \text{wal}(k, x) \text{d}x \quad (6)$$

For eventually spaced sequence {x(i)} of N number of data sets discrete Walsh Transform is required, is defined as,

1 ,

1 − $$ ) = \frac {1}{N} \sum_ {i = 0} ^ {N - 1} x (i) \operatorname {w a l} (k, i) \tag {7} $$ N ( ) ( ) ( ) i x i wal k i N X k

0 and x(i) can be obtained as,

1 − $$ ) = \sum_ {k = 0} ^ {N - 1} \mathrm {X} (\mathrm {k}) \operatorname {w a l} (\mathrm {k}, \mathrm {i}) \tag {8} $$ N ( ) ( ) ( )

0 , k X k wal k i x i Discrete Walsh transform is mathematically correct, but computational efficiency is found to be less while considering a large data points for analysis due to N2 operations are involved. Thus in practical case, Fast Walsh transform is used that reduces the number of operations to 2 Nlog N . The Walsh transform is found to be superior mathematical tool, having no Gibbs phenomena [18] and no need to choose any special window in time domain. In Walsh filter, the filter coefficients are set to either 0 or 1 [17]. Thus, for Walsh low pass filtering, all sequencies above a certain threshold are multiplied by 0 or 1 [14]. Rock boundary detection was carried out by Walsh low pass versions of well data [8]. Similar algorithms were also applied to detect bed boundary by Maiti and Tiwari [9]. Lanning and Johnson [8] used the depth that corresponds to the initial point of log data as first boundary value. Instead of that it is called as mean boundary value. In present study, the modified methodology has been used. Walsh low pass version of wireline logs, i.e., step functions of the studied logs are considered for modified methodology. Initially, we computed the absolute magnitude difference between present and the mean of the previous values for all previous steps until last boundary was detected. These absolute differences were calculated for all log data simultaneously. Further, each of them was multiplied by a weight value and results are summed up to compute the Walsh pick value. This Walsh pick value is a non-dimensional quantity that measures the amount of change took place simultaneously on all low pass versions of the log data. The term Walsh pick values are compared with another non-dimensional number called “Walsh check” (carefully assigned by the interpreter). This Check is conditioned in a such way that, if Walsh pick is greater or equal to the Walsh check value, then the depth at the beginning of the step is detected as a bed boundary, or else this indicates no new boundary is present in that depth location, and further we go for the repetition of the procedure for the entire studied depth section.

Case Study

The Assam-Arakan basin is situated in the north-eastern part of India and on the basis of production, this basin is categorized as a Category-I basin. The basin covers an area about 116000 sq. km. The detailed map of this area and well locations are shown in Figure 1. The SP, GR, LLD logs responses are taken for analysis from well-2, well-3, well-4, well-7, well-13 are represented in Figures 2-6, respectively. According to the geology of the Bhogpara area, we selected the depth ranges associated with the Lakadong + Therria formation at the studied wells, as it is the main petroliferous sector of the Bhogpara oil field, belongs to the late Palaeocene epoch.

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Discussion

To identify the rock boundaries in an automated manner, we implemented the modified Walsh based bed boundary detection technique proposed by Maiti and Tiwari [9], which was originally introduced by Lanning and Johnson [8]. We implemented the Walsh based bed boundary detection technique on the wireline logs associated with the Bhogpara oil field of Assam-Arakan basin. Initially, the conventional bed boundaries are demarcated using the GR log data only, afterwards, using these traditionally demarcated boundaries, we computed the 3D lithological model. Further, the Walsh boundary picking technique was applied to the GR, SP and LLD logs to obtain the possible bed boundaries more precisely. It is clearly seen that the Walsh detected boundaries are well corroborated with the conventionally demarcated boundaries in addition to a few thin beds using Walsh transform-based technique. Walsh transform technique has added advantage to the traditional interpretation technique, i.e., it can identify the finest bed that was very difficult to be recognized in traditional interpretation. Therefore, the proposed non-conventional model shows more number of beds and it represents the lithological succession with higher precision as compared to the conventional model. Thus, if this type of non-conventional interpretation is carried out in parallel with the traditional one, we may have less chance of misinterpretation and this approach will be able to generate more accurate lithological model in any study area.

Here we have used only three conventional logs such as gamma ray, laterolog deep resistivity and self-potential logs, However, in addition to the aforesaid logs, oil industry people generally use bulk density, photoelectric factor and neutron porosity logs to find out the rock layers more accurately [1]. Additionally, the self-potential log data is not recorded in marine sediments [4]. Therefore, to interpret rock layer boundaries, researchers must use gamma ray, laterolog deep resistivity, bulk density, neutron porosity and photoelectric factor simultaneously to achieve best and geologically meaningful result.

However, in this technique, the detected bed boundary is ‘weight’ and ‘check value’ dependent and these values are assigned by interpreter. Thus, the number of detected boundaries can be controlled by changing the ‘weight’ and ‘check’ values. Therefore, interpreter must have to choose the ‘weight’ and ‘check’ values in such a way that, at least a few numbers of the Walsh picking boundaries are more or less well corroborated with conventionally interpreted boundaries or the boundaries derived from the core information. Thus, the interpreter has to be careful while choosing the values of ‘weight’ and ‘check’ in order to get geologically meaningful results.

The borehole image logs identify the thin bed in centimeters scale [7], but these are very costly and usually measure specific depth of interest instead of whole depths of a particular well. Therefore, instead of using borehole image logs, Walsh boundary detection techniques can be used for assessing the bed boundary distribution of any reservoir using routine wireline logs.

Conclusions

We have analysed the gamma ray, self-potential and laterolog deep resistivity logs associated with the five wells (well2, well-3, well-4, well-7 and well-13) of Bhogpara oil field in the Assam-Arakan basin. The step length obtained from the Walsh low pass version is 3.29 m for the well- 2 and well-13, and 3.09 m for well-3, well-4 and well- 7, respectively. The Walsh-derived bed boundaries are corroborated with the traditionally estimated boundaries quite accurately. Additionally, the present approach of bed boundary detection could delineate thin beds of the order of ~3 m from the gamma ray, self-potential and laterolog deep resistivity logs. Whereas, the bed boundary, derived through the traditional (quicklook) interpretation of gamma ray, is ~5 m. Therefore, the litho-model derived from the Walsh technique shows finer distribution of rock strata and their continuation throughout the wells under study than the litho-model established based on the bed boundaries derived based on traditional interpretation. We must mention that the number of detected boundaries using Walsh-based approach depends on weights and ‘check’ values. Thus, interpreter should carefully assign the weights and ‘check’ values to achieve geologically meaningful results. Thus, the practical implementation of the Walsh based boundary detection technique to the wireline logs is an efficient, automated and trustworthy technique to demarcate the rock layer boundaries of a hydrocarbon reservoir. Moreover, the Walsh based technique allows multiple logs simultaneously to achieve higher accuracy and hence escapes tedious task involved in traditional or quick-look interpretation. This technique also facilitates the generalized appraisal of distribution of rock layers from conventional logs by avoiding unnecessarily use of expansive image logs. The technique is also one of the robust techniques to find out rock layers based on simultaneous blockiness changes of the logs, when we don’t have any a-priori core information or rock layers.

Acknowledgments

First author is thankful to the Director, Wadia Institute of Himalaya Geology, Dehradun for permission to publish this work. We are grateful to the Oil India Limited (OIL), Duliajan, Assam and GM, Geology and reservoir section of this company, who allowed us to use their well-log data. Our special gratitude to Mr. S. Rath, Former Director (Exploration & Operations), OIL for his kind initiative to support this research with data of OIL. The author also acknowledges the anonymous reviewers for improving the manuscript. KS also acknowledges SERB-DST for providing him with the JC Bose National Fellowship.