Atoka and Morrow formations, and the overlying Pennsylvanian sequence of the Buffalo Valley Field in New Mexico. Generalized regression neural network

Today, the major challenge in reservoir characterization is integrating data coming from different sources in varying scales, in order to obtain an accurate and high-resolution reservoir model. The role of seismic data in this integration is often limited to providing a structural model for the reservoir. Its relatively low resolution usually limits its further use. However, its areal coverage and availability suggest that it has the potential of providing valuable data for more detailed reservoir characterization studies through the process of seismic inversion. In this paper, a novel intelligent seismic inversion methodology is presented to achieve a desirable correlation between relatively low-frequency seismic signals, and the much higher frequency wireline-log data. Vertical seismic profile (VSP) is used as an intermediate step between the well logs and the surface seismic. A synthetic seismic model is developed by using real data and seismic interpretation. In the example presented here, the model represents the Atoka and Morrow formations, and the overlying Pennsylvanian sequence of the Buffalo Valley Field in New Mexico. Generalized regression neural network (GRNN) is used to build two independent correlation models between; 1) Surface seismic and VSP, 2) VSP and well logs. After generating virtual VSP’s from the surface seismic, well logs are predicted by using the correlation between VSP and well logs. The values of the density log, which is a surrogate for reservoir porosity, are predicted for each seismic trace through the seismic line with a classification approach having a correlation coefficient of 0.81. The same methodology is then applied to real data taken from the Buffalo Valley Field, to predict interwell gamma ray and neutron porosity logs through the seismic line of interest. The same procedure can be applied to a complete 3D seismic block to obtain 3D distributions of reservoir properties with less uncertainty than the geostatistical estimation methods. The intelligent seismic inversion method should help to increase the success of drilling new wells during field development. Introduction Reservoir characterization requires building a spatial model of the reservoir by using appropriate data gathered from previous studies. This spatial model is then used in flow simulators, which can predict reservoir performance. An accurate and reliable reservoir characterization study is indispensable in reservoir management. The major challenge in today’s reservoir characterization is to integrate all different kinds of data to obtain an accurate and high-resolution reservoir model. The concept of data analysis forms the basis of reservoir characterization. Uncertainty, unreliability, and large variety of scales due to the different origins of the data must be taken into consideration. Together with the immense size of the data sets that must be dealt with, these issues bring complex problems, which are hard to address with conventional tools. That’s why unconventional computation tools have gained much interest in data analysis in recent years. Among those modern tools; intelligent systems, which mimic the mechanism of the human mind, are a way of dealing with imprecision and partial truth. It should not surprise us that using intelligent systems in reservoir characterization studies has become a widely-used method in the petroleum engineering literature. Some previous intelligent reservoir characterization applications include, but are not limited to, synthetic log generation, permeability estimation from logs, and predicting bulk volume of oil. Let us consider different types of data used in reservoir characterization: core samples provide very high resolution information about the reservoir (fraction of inches), while seismic data have a resolution in tens of feet, and well logs have in one of inches. Because of its low resolution, seismic data is routinely used only to attain a structural view of the reservoir. On the other hand, unlike core samples or well logs, which are only available at isolated localities of a reservoir, seismic data frequently provides 3D coverage over a large area. Because of this areal coverage, researchers have always aimed to use seismic data in reservoir description. Inverse modeling of reservoir properties from the seismic data is known as seismic inversion in the literature. The process presented in this paper includes modeling of the well logs from seismic data, which is also an inverse modeling process (Figure 1). This approach attracts a lot of interest and is very important because of the necessary shift from exploration to development of existing fields. Seismic inversion has been applied by several authors with different approaches. Hampson et al. and Leiphart and Hart SPE 98012 Reservoir Characterization Using Intelligent Seismic Inversion Emre Artun, SPE, West Virginia University; Shahab D. Mohaghegh, SPE, West Virginia University; Jaime Toro, West Virginia University; Tom Wilson, West Virginia University; Alejandro Sanchez, Anadarko Petroleum Corporation 2 Reservoir Characterization Using Intelligent Seismic Inversion SPE 98012 have compared different techniques such as multiple linear regression, backpropagation and probabilistic neural networks. They have predicted porosity logs from seismic attributes and both have suggested using probabilistic neural networks in this type of problems considering its mathematical simplicity and success. Balch et al. have used fuzzy ranking to see which type of seismic attribute is related to the target reservoir property. They have modeled correlations between those selected attributes and porosity, water saturation and net pay thickness by using a backpropagation neural network. Chawathe et al. used neural networks to predict gamma ray log from seismic attributes; amplitude, phase, frequency, reflection strength, and quadrature. However, they have used higher-resolution crosswell seismic data instead of surface seismic as a new approach. Soto and Holditch have used the same types of attributes from surface seismic to predict the gamma ray log with neural networks. Reeves et al. introduced a new methodology, which divides the whole seismic inversion problem into two parts. They have considered cross-well tomography as an intermediate step in their procedure, after finding a correlation between surface seismic and cross-well seismic. They have suggested producing virtual cross-well seismic data, before dealing with logs. Giving Chawathe et al.’s work as an example, they stated that well logs can easily be predicted from virtual cross-well seismic data. According to the authors, using crosswell seismic as an intermediate scale data can provide improved vertical resolution, increase constraints and reduce the uncertainty of reservoir description. In this study, a similar methodology is followed. Instead of cross-well seismic which is rather hard to obtain, vertical seismic profile (VSP) is incorporated into the study as the intermediate scale data. This is due to the fact that VSP is available more frequently, and is less expensive to obtain than cross-well tomography. It is a common type of data that can be found in many fields. Together with the integration of a third type of data, another unique feature of this study was developing and integrating a synthetic model to the research, before dealing with real data. Having a synthetic model that we had full control of gave us the opportunity to develop and test the proposed methodology better before applying it to real data. Our synthetic model represents the gas-producing Atoka and Morrow formations and the overlying Pennsylvanian sequence in the Buffalo Valley Field in New Mexico. Surface seismic and VSP responses of this model are computed. Artificial neural networks are used to develop two independent correlation models between; 1) Surface seismic and VSP, 2) VSP and well logs. Density log has been selected as the target log, and is predicted from the seismic line. In the second case, seismic field data have been used to predict gamma ray and neutron porosity distributions through a seismic section. In the following sections a theoretical background, which includes brief explanations of seismic surveys and artificial neural networks -under the light of the methodology of this studyare included. Then, the methodologies followed in the synthetic and the field cases are presented. After that, the results and their discussions are followed by conclusions. Theoretical Background Seismic Surveys. The seismic method is the most widely used tool in the exploration of hydrocarbon reservoirs. It is useful for obtaining a structural view of the subsurface geology. The basic theory of the seismic method is based on the movements of signals through the subsurface. Reflection method is the most widely used seismic method, which is useful in identifying formation tops. A seismic trace is the response of a single seismic detector to the seismic energy propagation through the earth. If these traces are displayed side-by-side, then it is called a seismic record. A processing stage comes after obtaining a seismic record, to enhance the signal, to minimize the noise and increase the resolution. These processed images are than compiled together to produce the final output of the seismic survey: a seismic section. Vertical seismic profiling (VSP) differs from conventional seismic surveys in the location of signal receivers. In VSP surveys, the receivers are located in the borehole instead of at the earth’s surface. Because the earth acts as a low-pass filter, placing of the receivers at depth reduces the distance that the signal has to travel through the earth, thus yielding higher frequency (higher resolution) data. VSP surveys are very similar to velocity surveys in terms of where the sources and receivers are located. However, they differ from each other with two issues: 1) The distance between geophone recording depths (smaller in VSP, every 15-40 meters) 2) Collection of information (Only first break times are collected in velocity surveys. In VSP, upgoing and downgoing events are also collected for several seconds.) Seismic attributes are all the information obtained from seismic data, either by direct measurements or by logical or experience-based reasoning. The attributes used in this study can be briefly defined as; Amplitude: Measure of the strength of the reflected signal. Indicates changes in physical properties of various lithological entities. It can sometimes be used to detect gas presence. Hilbert Transform: This amounts to a 90-degree phase rotation. Amplitude and Hilbert transform are combined as Cartesian components of a trace signal. Instantaneous Phase: Phase angles range from -180 degrees to +180 degrees. Envelope and phase are combined as polar components of a trace signal. Average Energy: This attribute integrates the envelope between paraphase events. It highlights stratigraphic detail through energy fluctuations across traces. Values are in degrees. Envelope: Represents the reflection strength. The envelope is independent of the phase and it relates directly to the acoustic impedance contrasts. Frequency: This attribute describes how long it takes the phase to complete 360 degrees of rotation. Paraphase: This attribute is the instantaneous phase with the predictable trend removed. As such, it assists visualizing the structural picture because phase tracks geologic boundaries. Artificial Neural Networks. Artificial neural networks (ANN) can be broadly defined as information processing systems that mimic the human mind as a mathematical model SPE 98012 Artun, Mohaghegh, Toro, Wilson & Sanchez 3 representation of the biological neural networks. ANN have gained an increasing popularity in different fields of engineering in the past few decades, because of their capability of extracting complex and non-linear relationships. Their mechanism is based on the following assumptions: 1) Information processing occurs in many simple elements that are called neurons (processing elements). 2) Signals are passed between neurons over connection links. 3) Each connection link has an associated weight, which, in a typical neural network, multiplies the signal being transmitted. 4) Each neuron applies an activation function (usually nonlinear) to its net input to determine its output signal. Figure 2 shows a typical neuron (processing element). Outputs (In) coming from another neuron are multiplied by their corresponding weights (Wn), and summed up. An activation function is then applied to the summation, and the output of that neuron is now calculated and ready to be transferred to another neuron. There are many different types of neural network architectures and algorithms available. In this study, a generalized regression neural network (GRNN) is used. GRNN is a modification to probabilistic neural network that has been suggested by authors, who have studied seismic inversion. GRNN has also been successfully used in geological pattern recognition applications such as synthetic log generation and total organic carbon content prediction from logs. Besides, GRNN has been used in finding a correlation between cross-well seismic and surface seismic. Huang et al. described GRNN as an easy-toimplement tool, which has efficient training capabilities, and the ability to handle incomplete patterns. Generalized Regression Neural Network. Introduced by Specht in 1991, GRNN is a one-pass learning algorithm with a highly parallel structure. It is a memory-based network, which provides estimates of continuous variables, and converges to the underlying regression surface. This approach is freed from the necessity of assuming a specific functional form. Instead, the appropriate form is expressed as a probability density function (pdf), which can be determined from the observed data. General regression uses y (a scalar random variable), the X (a particular measured value of a vector random variable x), and the non-parametric estimator of the joint probability density function f(x, y). After defining the scalar Euclidian distance function, Di;