Using Artificial Intelligence to Corellate Multiple Seismic Attributes to Reservoir Properties

Well data gives precise information on reservoir properties at specific field locations with high vertical resolution. 3D seismic surveys cover large areas of the field but reservoir properties are not directly observable due to poor vertical resolution. For this paper, a new methodology has been developed and tested for relating reservoir properties at the well-bore to sets of seismic attributes, in order to predict reservoir properties in two zones of the Nash Draw field in SE New Mexico. Over 350 seismic attributes can be used in regression analyses of reservoir properties. Since using all attributes is computationally unfeasible and labor intensive, fuzzy logic is used to select the most statistically significant attributes for developing regression equations for individual reservoir properties. Non-linear regressions were used, as individual attributes had low correlation coefficients when cross-plotted with reservoir properties, and neural network architectures were developed to relate the selected attributes to each property. In each case the output data used for training was a reservoir property, porosity (φ), water saturation( Sw), or net pay, from 19 wells in the field. Each property was estimated using a neural network trained to CC=0.8 or higher using the highest ranking seismic attributes as inputs. The validity of the solutions were tested by removing three wells from the training data, re-computing the weights, and predicting the three absent points. These tests were applied three times for each reservoir property, with different points removed. Each network accurately predicted these nine test points and the solutions are considered robust. φ, Sw, and net pay maps were generated using the regression relationships and the seismic attributes at each seismic bin location. Pore volume (φh) and hydrocarbon pore volume (hφSo) maps were derived from those reservoir property maps. These new techniques maximize both the well control and seismic data and generated useful maps for targeted drilling programs in the field. Introduction The Nash Draw field in SE New Mexico produces oil and water from two sandstones of the Delaware Mountain group. The field is currently being developed, and overlying Playa lakes and Potash mining concerns require the use of horizontal drilling to target un-drained areas of the reservoir beneath these surface features. Since long horizontal wells are expensive it was decided to pursue advanced reservoir characterization prior to drilling. In 1996 a high quality 3D seismic survey was shot over the field covering an area of about eight square miles. Initially, amplitude alone was used as an indicator of reservoir grade porosity, however, a well drilled on the basis of amplitude data alone was not an economic success. Geostatistics can provide good interpreted estimates of interwell reservoir properties, but existing Nash Draw wells primarily cover the center part of the available seismic survey, so a new technique to extrapolate reservoir properties beyond the area directly constrained by wells was developed. The new technique utilizes non-linear multivariable regression (artificial neural networks) using seismic attributes as inputs and porosity, water saturation, and net pay as outputs. The regression equations allow the prediction of these three reservoir properties in areas without direct well control, using the laterally extensive seismic attribute data, and the computation of related maps such as φh and hφSo. Seismic Attribute Selection The two primary sources of data required for this method are well and seismic attribute data. The well data used in this study is tabulated in Table 1. Over 80 seismic attributes were extracted from the Nash Draw seismic data for the two horizons of interest. Extracted attributes were averaged across the entire interval for each of the horizons of interest (the Brushy Canyon K and L Sands), and the well data from each SPE 56733 Using Artificial Intelligence to Corellate Multiple Seismic Attributes to Reservoir Properties R. S. Balch, SPE, New Mexico Petroleum Recovery Research Center, and B. S. Stubbs, SPE, Pecos Petroleum Engineering, and W. W. Weiss, SPE, and S. Wo, SPE, New Mexico Petroleum Recovery Research Center SPE 56733 USING ARTIFICIAL INTELLIGENCE TO CORELLATE MULTIPLE SEISMIC ATTRIBUTES TO RESERVOIR PROPERTIES 2 of the 19 wells used in the study were also averaged across the respective intervals. Thus the output maps presented later in this paper represent interval-averaged values for the respective reservoir properties. It is both statistically dangerous and not computationally feasable to use all 80 attributes to form regression relationships, therefore we have developed software based on a fuzzy-ranking algorithm to select attributes best suited for predicting individual reservoir properties. The algorithm statistically determines how well a particular input (seismic attribute) could resolve a particular output (reservoir property at the well bore) with respect to any number of other inputs using fuzzy curve analysis. To illustrate the technique a simple example is given. Consider a set of random numbers in the range {0,1} using x={xi}, i=1,2,...,99, and xi=0.01*i, and plot each value (yI= Random(xi)) (Figure 1a). Next add a simple trend to the random data (yi=(xi)^0.5+Random(xi)) and plot those values (Figure1b). For each data (xi, yi) a “fuzzy” membership function is defined using the following relationship Sample fuzzy membership functions are shown in Figures 1a-b. Here, b=0.1, since b is typically taken as about 10% of the length of the input interval of xi. A fuzzy curve is built up using a summation of all individual fuzzy membership functions in (xi, yi), and this final curve can be interpreted for the utility of given inputs for linear or non-linear regressions. The fuzzy curve function is defined below: Where N is the size of the data set or the total number of fuzzy membership functions. Figure 2 shows the curves for the data sets shown in Figures 1a-b. This simple example illustrates the ability of the fuzzy ranking approach to screen apparently random data for obscure trends such as the correlation between seismic attributes and reservoir properties. Based on the deviation from a flat curve, each attribute is assigned a rank, which allows a direct estimation of which attributes would contribute the most to a particular regression. The fuzzy ranking algorithm was applied to select the optimal inputs (attributes) for six output cases: K porosity, K net pay, K water saturation, L porosity, L net pay, and L water saturation. Having selected the most statistically significant attributes, an important question remains. How physically significant are the attributes? A thorough literature review shows some direct relationships between attributes and properties in lab-scale experiments. But, in general relationships are very complex and vary from field to field, and even between formations within a single field so the exact relationship between frequency and porosity, for example, may be ill defined. Ideally, the rigorous use of rock physics could demonstrate fundamental quantitative relationships between seismic attributes and reservoir properties using forward modeling. However, though it seems obvious that all features of seismic signals are a result of changes in rock properties through which the seismic energy is transmitted, these relationships are not straightforward, even for relatively easily computed attributes such as instantaneous frequency. However, individual attributes have been used for a number of years in diverse reservoirs around the world to indicate variations in stratigraphy, porosity and other reservoir properties, and as such are generally accepted as meaningful. At present, any study which uses seismic attributes needs to evaluate individual attributes for statistical significance and thoroughly test results. Multivariable Non-Linear Regression Linear regression for reservoir properties was not feasible for this study, as the relationships between input and outputs were poorly defined by individual attributes (Figure 3). It was decided to use non-linear regressions using software we developed based on the fast-converging, feed-forward, backpropagation conjugate gradient algorithm (neural network). Input attributes were selected using the fuzzy ranking algorithm (Figure 4). Figure 5 shows a sample neural network architecture, circles represent “neurons”, or locations of non-linear functions, while each line represents a coefficient applied to these neurons. A back-propagation feed-forward algorithm such as the conjugate gradient algorithm used here is “trained” using known inputs and outputs in an iteritive fashion, with weights being sequentially adjusted until the desired fit (if possible) is achieved. The sample architecture displayed in Figure 5 is a 2-2-1 architecture, since there are two neurons in the input layer, 2 neurons in the hidden layer, and one output neuron. The regression equation (inverse model) for this network is as follows: Out1=f(v1∗f(w1∗in1+w2∗in2)+v2∗f(w2∗in1+w4∗in2)) Two neural network architectures were utilized in the study, a 3-2-1, and a 4-2-1 (Figure 6), both of which were minimized in order to maintain a satisfactory ratio of training data to weights (coefficients of the regression equation). For this study, reservoir properties are well known at the locations of the well-bore intersections with the K and L intervals. Seismic data that covers a much larger area is also available, and has data at the locations of the well-bore intersections as well. Seismic attribute data from the same seismic bin that contains the well is correlated to well-bore values of porosity, net pay or water saturation in an iterative process using either a 3-2-1, i i i y b x x x F ∗ − − = ) ) ( exp( ) ( 2