EXTINCIÓN DE DERECHOS MINEROS

Neural networks have a long history, going back at least to the early 1940’s. Neural networks have been applied in a wide variety of fields. One of the principle advantages of a neural network is its ability to discover patterns in data, which may be imperceptible to the human brain or standard statistical methods. The most frequently used type of neural network is a feed forward neural network using a back-propagation learning algorithm, due to it is popularity and simplicity. In a typical neural data processing procedure, the database is divided into two separate portions called training and test datasets. The training dataset is used to develop the desired network. In this process (depending on the paradigm that is being used) the desired output in the training set is used to help the network learn by adjusting the weights between its neurons or processing elements.

Neural networks can help engineers and researchers by addressing some fundamental petroleum engineering problems that conventional computing has been unable to solve. Petroleum engineering may benefit from neural networks on occasions when engineering data for design and interpretations are less than adequate, such as old fields. Lack of adequate data may also be encountered because of the high cost of coring, well testing, and so on. Neural networks have proved to be valuable pattern–recognition tools. They are capable of finding highly complex patterns within large amounts of data. A relevant example is well log interpretation. It is generally accepted that there is more information embedded in well logs than meets the eye. Determining, predicting, or estimating formation permeability without actual laboratory measurement of the cores (or minimal cores) or interruption in production for well test data collection has been a fundamental problem for petroleum engineers. Neural networks can potentially help predict reservoir parameters using minimal training data.

A neural network is a generalised numerical tool which enables the correlation or linking of one set of data called the 'input' to another set called the 'output'. It is assumed that the input and output may be related in some way, although it is not necessary to know this relationship. Rather a known set of data, called the 'training dataset', containing both input

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and output for a number of different cases is used to teach the neural network to recognise any association which may exist. Therefore, the training dataset is said to comprise a number of 'patterns' each of which is a list of the inputs and outputs. The values of the input data are applied into an array of 'input neurons'. Each of these is connected to a variable number of neurons in a 'hidden layer' and the value of each input is transmitted through a connection into these hidden neurons where they are combined. In turn each neuron in the hidden layer communicates a signal to an 'output neuron' which represents a specific output value. In fact, there may be more than one hidden layer of neurons and the number of neurons in each layer may be different, although they will all be inter-connected to the neurons of adjacent layers. Importantly, the signals which are transferred between neurons in a network are modified by multiplying the value by a 'weight' which is associated with each connection. The different connections have different weights and these, therefore, determine the influence a particular neuron has on a particular output of the network. During training both input and output are known. With the input data, the connection weights are adjusted so that the neural network will give output values which match as closely as possible the real output values in the training dataset. When this training process is complete, the values of the weights are fixed. At this point these weights have essentially encoded the intelligence of the training dataset into the neural network. The neural network is then able to predict further outputs on the basis of information supplied as input along with the weights that were determined in the training process.

Osborne (1992) first introduced back-propagation neural networks for permeability prediction from wireline logs. Following this several other studies have been published (Mohaghegh et al., 1995; Wong et al., 1997; Arpat et al., 1998; Jamialahmadi and Javadpour, 2000; Helle et al., 2001). All previous studies have used wireline logs in conjunction with core plug data to train the neural network. In the present study some SCAL parameters on core plugs were measured in the laboratory in the Libyan Petroleum Institute (LPI). Part of the data was used for the neural network training datasets, and part of it was used to test the neural predictions in the test datasets. The work presented is new as very few previous studies have attempted to predict SCAL parameters such as true resistivity, resistivity index, saturation exponent, water saturation, and Amott-Harvey Index from neural networks using minimal core training data.

4 1.2 Fundamental Reservoir Rock Properties

For any reservoir rock there are two key petrophysical parameters. The first is the capacity of the rock to store fluid, namely porosity. The second is connectivity of the pore space, which allows fluid to flow through the rock, namely permeability. Routine core analysis defines the porosity and permeability magnitude and distribution. SCAL complements this routine data, and furnishes information that allows calculation of static fluid distribution as well as dynamic flow performance of a well or reservoir. Moreover, a special core analysis program can assist in defining the most favourable recovery technique to maximize oil recovery and profitability. Downhole log interpretation is considerably enhanced by a SCAL program through the measurement of electrical and acoustic properties of reservoir rocks and fluid saturations from displacement experiments (capillary pressure and relative permeability data). The objectives of performing a SCAL program are to achieve an accurate representation of the reservoir rock characteristics, information that is necessary for reliable reservoir engineering calculations and modelling.

The amount of hydrocarbon reserves is one of the most important parameters in the decision making process in developing a reservoir. The estimation of hydrocarbon reserve is strongly dependent of electric log data and on the value of saturation exponent (n) used. The interpretation of the electrical (resistivity) logging data is based on Archie’s law. Resistivity logging is the most widely used method of identifying hydrocarbon intervals in the wellbore. The standard method of relating oil saturation in clay-free reservoirs to electrical resistivity is based on Archie’s saturation equation (Archie 1942):

t S_w n

Ro R

RI   --- (1.1)

where the resistivity index, RI , is equal to the ratio of the resistivity of the sample (Rt) at

brine saturation (Sw) over the resistivity of the sample at one hundred percent brine

saturation (Ro). The resistivity index is related to the saturation of the sample and the

saturation exponent (n). The saturation exponent must be determined by experimental core analysis. The standard technique for determining the saturation exponent involves measurments on cleaned cores, usually with air as the non-wetting phase and brine as wetting phase. This air/brine system is only representative of the drainage conditions in

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strongly water wet situations. When oil displaced by water, for instance during water flooding, different distributions of fluid may prevail at the pore scale due to hysteresis effects controlled by pore geometries, initial saturation and wettability distribution at the pore scale. When the rock is compacted as a result of overburden pressure, the matrix is under stress and porosity decreases as a result of compaction, and the cementation factor will change.

Rocks can be classified based on their pore geometry as intergranular or non intergranular. Pore size and pore throat size varies regularly through the rock. Rasmus (1987) studied the effect of pore geometry on reservoir rock resistivity. He modelled mathematically the effect of vuggy pore geometry on rock resistivity. His model results showed that the resistivity of the fully saturated rock is relatively insensitive to the secondary vuggy porosity. In partially saturated rocks, the resistivity of partially saturated rocks is insensitive to the vuggy pore system if the vugs are oil wet. The Archie saturation exponent tends to increase as a result of increasing water saturation caused by a vuggy pore system, since the water occupies the middle of the vugs in an oil-wet vuggy system forming discontinuous droplets. These isolated water droplets do not contribute to the electrical conduction but give rise to water saturation, and, in turn, the saturation exponent will increase. In water-wet systems, as oil continuous to invade the pore system, the water volume decreases dramatically compared to the increase in resistivity, resulting in a lower water saturation and saturation exponent.

Wettability plays a major role in controlling the distribution of fluids within the pore space inside a rock. Keller (1953) presented evidence that the saturation exponent could be substantially different from the usually assumed value of 2.0. He found that Archie’s saturation exponent (n) varies from 1.5 to 11.7 for the same rock, depending on how the cores were treated. For the same water saturation, the resistivity of an oil reservoir can vary by a thousand times for different wetting conditions. The wettability of sandstone cores was altered from water-wet to oil-wet conditions by using various chemical treatments. Keller concluded that the wettability played a great role in the fluid distribution within the rock space. By changing the relative position of the conducting fluid with respect to the rock surface, the electric behaviour of the fluid-filled sandstone would also change.

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