Oil Reservoir Properties Estimation By Fuzzy-Neural Networks
Memoirs of the Faculty of Engineering, Kyushu University, Vol.67, No.3, September 2007Oil Reservoir Properties Estimation by Fuzzy-Neural NetworksbyTrong Long HO* and Sachio EHARA†(Received August 16, 2007)AbstractPorosity and permeability are two fundamental reservoir propertieswhich relate to the amount of fluid contained in a reservoir and itsability to flow. These properties have a significant impact on petroleumfields operations and reservoir management. Up to now, more thantwenty reservoirs have been found in basement rocks all over the world,which were known as un-usual reservoir. They were named un-usualreservoir because of the small number are compared with clastic andcarbonate reservoirs. Study on basement reservoir always is difficulttask, especially estimation of reservoir properties due to complex natureof the geological model. In this paper, we suggest an efficient method todetermine reservoir properties from well log by using fuzzy logic andneural networks. The ranking technique based on fuzzy logic is used fornoise rejection of training data for neural networks. By learning thenonlinear relationship between selected well logs and coremeasurements, the neural network can perform a nonlineartransformation to predict porosity or permeability with high accuracy.The approach is demonstrated with an application to the well data inA2-VD prospect, Southern offshore Vietnam. The results show that thistechnique can make more accurate and reliable reservoir propertiesestimation than conventional computing methods. The study plays animportant role in projects of development of basement reservoirs in thefuture.Keywords: Porosity, Permeability, Fuzzy logic, Artificial neural networks, Welllog, Basement reservoir, A2-VD prospect1.IntroductionVietnam is one of the countries having oil in basement rock. Hydrocarbons were found infractured basement rock in more than twenty basins all over the world. Such basins are found in*†Graduate Student, Department of Earth Resources EngineeringProfessor, Department of Earth Resources Engineering
118T.L. HO and S. EHARAAlgeria, Argentina, Brazil, Canada, Chile, China, Egypt, India, Indonesia, Russia, United Kingdom,United States and Vietnam (Sircar, 2004). In Vietnam, basement reservoirs are major reservoirswhich are providing over 90% of the production rate. Therefore, the basement reservoir has becomean attractive target and has been paid a great attention for investigation.However, because of complex nature of the geological model and the small number of fracturedreservoirs compared with clastic and carbonate reservoirs over the world, the researches on thebasement reservoir are still limited and the understanding of the basement reservoir is also difficult.Such reservoir was named an “unusual reservoir”.The area that forms the scope of this study lies in the southern offshore Vietnam, Cuu Longbasin, which is ranked first among petroleum potential basins (Fig. 1). Because of its rich lacustrinesource rock and unusual fractured basement reservoir, it has become well known not only inVietnam but also in South-East Asia. The Cuu Long basin is a Tertiary rift basin on the southernshelf of Vietnam. It covers an area of approximately 25,000 km2 (250 km x 100 km). The basin wasformed during the rifting in Early Oligocene. Late Oligocene to Early Miocene inversionintensified the fracturing of basement and made it an excellent reservoir.Basement rock of the Cuu Long basin includes magmatic rocks such as granite, granodiorite,quarzt-diortie, monzodiorite, diorite, and meta-sediments; in them, granite is the basement rock ofA2-VD prospect (Dong et al., 2001). The outstanding feature of the petroleum system in this basinis the combination of the Oligocene source rocks with the Mesozoic basement reservoir (Dien,2001). Many descriptions and analysis of this type of basement reservoir showed that the porosityof the basement reservoir consisted mainly of fractures and vug-cavities due to various processessuch as tectonic activities, weathering, hydrothermal and volumetric shrinkage of cooling magma.(Dong et al., 1991, 1994, 1998, 1999; San et al.,1997; Vinh, 1999, Dien, 2001). Among them, thetectonic activity and the hydrothermal processes are practically the main factors that control theporosity of the fracture systems. Recent studies (Cuong, 2001; Schmidt, 2003) proved that thecompression event that occurred during Late Oligocene reactivated the pre-existing faults/fracturesand created effective porosity inside the basement.Basin analysis and evolution of basement highs showed that the most effective porosity of thebasement reservoirs has a relationship with many factors relating to the basement highs andsurrounding sedimentary sequences. This special combination consists of the volumetric shrinkagedue to the diagenesis of the Paleogene sedimentary sequences distributed in grabens up-lap slopesof basement highs, the breakable of rigid-brittle and non-bedding basement highs on thehangingbranch of fault systems, and the accumulated capping-mass of Miocene to Quaternarysediments on top the basement high (i.e. the highest area of the basement). The break of buriedcrystalline basement rocks has lead to the formation of a series of fractures and vugs with diverseshape and size in the environment where there was no filling sedimentary materials and water. Thisis the most effective porosity type of the basement reservoirs in Cuu Long basin.Permeability of the basement reservoir in Cuu Long basin is mainly influenced by fracturesystem, and the high permeability zone is related to fracture zone and shows the fracturedevelopment area. Therefore, porosity and permeability are two key parameters of the A2-VDprospect in Vietnam. They are very valuable information for reservoir simulation and developingplans of the prospect in the future. In this paper we will present a method to predict porosity andpermeability in basement rock from well log data by using fuzzy logic and neural network, and acase study in the A2-VD prospect, southern offshore Vietnam.
Oil Reservoir Properties Estimation by Fuzzy-Neural Networks119Fig. 1 Location of the studied area.2.Fuzzy-Neural Networks RecognitionFuzzy logic was first developed by Zadeh (1988) in the mid-1960s for representing uncertainand imprecise knowledge. It provides an approximate but effective means of describing thebehavior of systems that are too complex, ill-defined, or not easily analyzed mathematically. Fuzzyvariables are processed using a system called a fuzzy logic controller. It involves fuzzification,fuzzy inference, and defuzzification. The fuzzification process converts a crisp input value to afuzzy value. The fuzzy inference is responsible for drawing conclusions from the knowledge base.The defuzzification process converts the fuzzy control actions into a crisp control action.When anything becomes too complex to fully understand, it becomes uncertain. The morecomplex something is, the more inexact or "fuzzier" it will be. Fuzzy logic provides a very preciseapproach for dealing with uncertainty which grows out of the complexity of human behavior.Among fuzzy logic techniques, fuzzy ranking is a tool to select variables that are globally related, itallows ranking the level of the globally relationships. Fuzzy ranking is known as a very efficienttool for removing noise of data by evaluating globally relationship between variables.One of the most successfully applications of artificial neural network is pattern recognition, butthe limitation of the neural networks is that their success strongly depends on noise of training dataset. Therefore, in this study, we suppose to use fuzzy ranking to reject noise from training data setof the neural network, which is called fuzzy-neural network. The fundamental idea of thefuzzy-neural network approach is shown in Fig. 2.
120T.L. HO and S. EHARARankingRank.1 Rank.2 Rank.3 Rank.4 Rank.5 Rank.6Selection best inputs for NNDendriteSomaAxonNode lNeural NetworkFig. 2 Fundamental of the fuzzy-neural network.Consider a data pair (x, y) where x is the event and y is the reaction. The problem is to predict ywhen x changes slightly, in a neighbourhood close to x. The fuzzy membership function of (x, y)gives a local prediction of y, according to the information from only (x, y). The fuzzification of thedata is done with Gaussian function. Fuzzy membership function is defined as follows; x x 2 Fi ( x ) exp i . y i , b (1)where b defines the shape of the fuzzy membership curves and is about 10% of data set range. Afuzzy curve function is used to rank noisy data. The fuzzy curve function gives a global predictiony because it consists of the sum of the local predictions (fuzzy membership functions). Fuzzy curvefunction FC(x) is defined as follows;n Fi ( x )FC ( x ) i 1n.(2) Fi ( x ) / y ii 1The two fuzzy curves resulting from defuzzification of the fuzzified data in Fig. 3 are shown inFig. 4 (Weiss et al., 2001). As seen in Fig. 4, the random data set has a no-slope dashed best-fit linewhile the random data set plus the x0.5 trend has a best-fit line that has a range of about 0.85. Therange of fuzzy curves can be used to identify related variables in noisy data sets and rank the inputvariables for further analysis. The selected well logs then can serve as inputs to regression or neuralnetwork to develop multivariate correlations with core measurements. Such fuzzy membershipfunctions have been obtained with the help of a Matlab toolbox for Fuzzy logic (The MathWorks,2000).
Oil Reservoir Properties Estimation by Fuzzy-Neural Networks121Fig. 3 Conventional cross plot of data sets. (a) A random data set (0–1), and (b) A random dataset plus a square root trend (red and green lines are two fuzzy membership functions of (xi , yi )).Fig. 4 Fuzzy curves FC(x) generated from data sets resulting from defuzzification of thefuzzified data in Fig. 3. (a) A random data set (0–1), and (b) A random data set plus a square roottrend.Artificial Neural Networks (ANNs) have been successfully used in a variety of relatedpetroleum engineering applications such as reservoir characterization, optimal design ofstimulation treatments, and optimization of field operations (Mohaghegh, 2000; Tamhane et al.,2000). Many researchers have used ANNs for porosity and permeability estimation anddemonstrated very good results obtained from the method (Aminzadeh et al., 2000; Lim, 2005;
122T.L. HO and S. EHARAAminzadeh and Brouwer, 2006). Particularly, most of the successful studies of geophysicalproblems used the multilayer perceptron (MLP) neural network model which is the most popularamong all the existing techniques. The MLP is a variant of the original perceptron model proposedby Rosenblatt (1958) in the 1950s. The model consists of a feed-forward, layered network ofMcCulloch and Pitts’ neurons (McCulloch and Pitts, 1943). Each neuron in the MLP model has anonlinear activation function that is often continuously differentiable. Some of the most frequentlyused activation functions for MLP model are the sigmoid and the hyperbolic tangent functions.Basically, a neural network is composed of computer-programming objects called nodes. Thesenodes closely correspond in both form and function to their organic counterparts, neurons.Individually, nodes are programmed to perform a simple mathematical function, or to process asmall portion of data. A node has other components, called weights, which are integral parts of theneural network. Weights are variables applied to the data that each node outputs. By adjusting aweight on a node, the data output is changed, and the behaviour of the neural network can bealtered and controlled. By careful adjustment of weights, the network can learn. Networks learntheir initial behaviour by being exposed to training data. The network processes the data, and acontrolling algorithm adjusts each weight to arrive at the correct or final answer(s) to the data.These algorithms or procedures are called learning algorithms.A key step in applying the MLP model is to choose the weighted matrices. Assuming a layeredMLP structure, the weights feeding into each layer of neurons form a weight matrix of the layer.Values of these weights are found using the error back-propagation method. This leads to anonlinear least square optimization problem to minimize the error. There are numerous nonlinearoptimization algorithms available to solve this problem, and some of the basic algorithms are theSteepest Descend Gradient method, the Newton’s method and the Conjugate-Gradient method.There are two separate modes in which the gradient descent algorithm can be implemented: theincremental mode and the batch mode (Battiti, 1992). In the incremental mode, the gradient iscomputed and the weights are updated after each input is applied to the network. In the batch mode,all the inputs are applied to the network before the weights are updated. The gradient descentalgorithm with momentum converges faster than gradient descent algorithm with non-momentum.Two powerful techniques of gradient descent algorithm with momentum in incremental and batchmodes are online back-propagation and batch back-propagation, respectively.Some researches proposed high-performance algorithms that can converge from ten to onehundred times faster than conventional descend gradient algorithm, for example, the Quasi-Newtonalgorithm (Battiti, 1992), the Resilient Propagation algorithm - RPROP (Riedmiller and Braun,1993), the Levenberg-Marquardt algorithm (Hagan and Menhaj, 1999) and the Quick Propagationalgorithm (Ramasubramanian and Kannan, 2004). The disadvantage of the Quasi-Newtonalgorithm and the Levenberg-Marquardt algorithm is long training time due to complexcalculations in computing the approximate of the Hessian matrix (Battiti, 1992; Hagan and Menhaj,1999).We have considered the mathematical basis of four training techniques, including the onlineback-propagation, the batch back-propagation, the RPROP and the Quick propagation algorithm, asthey are the most suitable techniques. The main difference among these techniques is on themethod of calculating the weights and their updating (Werbos, 1994).The training process starts by initializing all weights with small non-zero values. Often they aregenerated randomly. A subset of training samples (called patterns) is then presented to the network,one at a time. A measure of the error incurred by the network is made, and the weights are updatedin such a way that the error is reduced. One pass through this cycle is called an epoch. This processis repeated as required until the global minimum is reached.
Oil Reservoir Properties Estimation by Fuzzy-Neural Networks123In the online back-propagation algorithm, the weights are updated after each pattern ispresented to the network, otherwise batch back-propagation with weight updates occurring aftereach epoch (Battiti, 1992). The weights are updated as follows; wij t MSE t wij t 1 wij t (3)where wij is the change of the synaptic connection weight from neuron i to neuron j in the nextlayer, MSE is the least mean square error, is the learning rate, t is the step of training and is themomentum that pulls the network out of small local minima. And then,wij (t 1) wij(t) wij(t)(4)The RPROP algorithm is an adaptive learning rate method, where weight updates are basedonly on the signs of the local gradients, not their magnitudes (Riedmiller and Braun, 1993). Eachweight (wij) has its own step size or update value ( ij), which varies with step (t) according to thefollowing equations; Δ ij ( t - 1), ij ( t ) - Δ ij ( t - 1), Δ ( t - 1), ij where 0 - 1 ,if MSE MSE( t - 1).(t ) 0wijwijif MSE MSE( t - 1).(t ) 0wijwij(5)elseand the weights are updated according to: - Δ ij ( t ), Δwij ( t ) Δ ij ( t ), 0 if MSE(t ) 0wijif MSE(t ) 0wij(6)elseThe Quick propagation is a training method based on the following assumptions(Ramasubramanian and Kannan, 2004):1.MSE(w) for each weight can be approximated by a parabola that opens upward, and2.The change in slope of MSE(w) for this weight is not affected by all other weights thatchange at the same time.The weights update rule is wij t Q( t ) wij ( t 1 ) Q( t )Q( t 1 ) Q( t )(7)where Q(t) MSE/ wij(t) is the derivative of the error with respect to the weight and{Q(t-1)-Q(t)}/ wij(t-1) is its finite difference approximation. Together these approximate, Newton’smethod for minimizing a one-dimensional function f(x) is applied as x -f ’(x)/f ’’(x).In general, too low learning rate makes the network learning very slowly, whereas too highlearning rate makes the weights and error function diverge, so there is no learning at all. In thisview, we used fixed values of 0.1 and 0.5 for the learning rate ( ) and the momentum ( ),respectively. Although using these relatively low values may be time-consuming, they giveaccurate results.
124T.L. HO and S. EHARAThe activation function (a) used at each hidden layer and the output layer is logistic, and that isa sigmoid function with smooth step. This is expressed by1(8)a 1 e uwhere u is the output of any neuron in the network (or net function). The derivative of this functionhas a Gaussian shape, which helps to stabilize the network and to compensate for overcorrection ofthe weights.In this study, many paradigms have been tried to find out the most efficient one. And we foundthat batch back-propagation and quick propagation are two most successful paradigms for theporosity/permeability estimation problem; the difference of the two paradigms is the method ofcalculating the weights and their updates using Equations (3) and (7).3.Training and Testing of Fuzzy-Neural Networks3.1 Training data set3.1.1 Well log dataA well log is a record of characteristics of the formation traversed by a measurement in the wellbore. It provides a means to evaluate the formation characteristics and the hydrocarbon productionpotential of a reservoir. Logging tools can be grouped into two categories: conventional andunconventional well logs. Conventional well logs are those that are routinely collected at almost allindustry boreholes. Unconventional well logs are either too specialized, expensive or too recentlydeveloped to be run in every well. For input of training data in this study, we consider eight welllog curves which are measured most fully in the A2-VD prospect, that are caliper, sonic, gamma ray,laterlog deep - LLD, laterlog shallow - LLS, microspherically focused log - MSFL, neutron anddensity logs (Fig. 5).3.1.2 Core samples dataCore analysis is the process of obtaining information about the properties of the subsurface bythe examination of core samples taken from a borehole during drilling. The set of measurementscarried out on cores of this study includes porosity and permeability. Core analysis is one of thetechniques used for identification and characterization of natural fractures. It can providequantification of fracture geometry, fracture frequency and the nature of any filling material.Among the disadvantages of core analysis for naturally fractured reservoirs evaluation are:- It is difficult to assess how representative the core plug is of the reservoir.- Cores that contain fractures of practical significance are often lost in the process ofrecovery.- Mechanical fractures are often induced on the cores during the recovery process as a resultof retrieving the core and stress release as the core is brought to the surface.- Core analysis is costly, labor intensive, and subject to the availability of drilled rocks.These factors have directed the industry to employ well logs that are cost-effective and readilyavailable. Among the advantages of well logs over core analysis are:- Typically cores are obtained over a small portion of the well. Well logs are run
Among fuzzy logic techniques, fuzzy ranking is a tool to select variables that are globally related, it allows ranking the level of the globally relationships. Fuzzy ranking is known as a very efficient tool for removing noise of data by evaluating globally relationship between variables.
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