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W e saw in Part 1 that when we have 3-D data together with a number of logged wells, we can look at possible relationships between some attributes of the seismic data and various properties measured on the logs. At multiple well locations, where we have both seismic and log data, we can look for trends in these two data types on crossplots. If we see a trend, we can quantify it with a derived or specified functional relationship. This functional relationship can be used to convert the attribute values to log properties, and when followed by a residual correction, provide a means to estimate the distribution of these properties away from the wells.A primer on ANNs. Assume that variables x and y are linearly related, y = ax + b, and are subject to additive noise. In our case, x normally represents the seismic attribute and y is related to the log property to be estimated away from the wells. We are given several observations of the paired data values (x,y) as follows:(2.1, 5.0), (0.6, 1.8), (9.4, 20.2), (6.7, 13.9) and we want to make a prediction for y when x = 4. The best least-squares fit of these known data points to a straight line is Figure 9 ( Figure 6 in Part 1) shows an apparently nonlinear relationship between the instantaneous frequency attribute and the volume fraction of clay log property. In this crossplot, data from 15 wells (both quantities) have been averaged over the vertical extent of the Bravo layer. Although any rock physics relationship between these measurables is obscure at best, the significance value for this crossplot is a compelling 7 1.2 percent.y (x) = 2.06x + 0.54We can postulate various possible mechanisms and argue their credibility. It is possible to imagine geologic settings where instantaneous frequency will be influenced by the shaliness, or volume, of clay, if the clay exists in stacked thin layers. However, let us assume that there is indeed some underlying physical mechanism for this relationship but that we don't know what it is. Rather than trying to derive a functional relationship from approximations to theory, we will estimate the function from the data themselves.which gives y(4) = 8.78 as our estimate. In this example, had we used a neural network to find the best straight line fit, the four given data points would be called the learning set. The basisfunctions would be the two polynomials,fi(x) = x0 and f2( > x = x'; w1 = 0.54 and w2 = 2.06 would be the weights derived from the learning set. Figure 10 shows a neural As evident in Figure 9, we often have to search for a nonlinear function when using seismic attributes to estimate distributions of log properties. Artificial neural networks (ANNS) can help determine nonlinear functions that best fit those relationships.Neural networks are being increasingly used to solve a variety of mathematical problems concerned with unknown and varied functional relationships among measured variables. In this article, we briefly explain the basics of neural networks and then discuss further the principles of one type of neural networ...

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractOne of the classic problems in the development of a reservoir numerical simulation model is the question of scale. Data that are acquired from many different sources give us a view of the reservoir under different constraints. In this paper, we present a technique that integrates data from the core scale to that acquired through logs to well-test pressure transient analysis (PTA) and, finally, to the production history information. A field example from the Neuquen Basin demonstrates this procedure.PTA offers a reasonable estimate of the permeability within the drainage radius of the well.Unfortunately, these measurements usually are not made in every well. Log data typically is acquired in the field from most wells. Using recovered core data and permeability analysis from cores, a probabilistic petrophysical model, honoring that core data, is constructed. The petrophysical model is applied throughout the field and used in constructing a geocellular model. The model can be investigated in positions equivalent to the volumes investigated by the PTA, and the petrophysicallyderived permeability can be iteratively modified to match the permeability derived from the PTA. The geocellular model is upscaled for dynamic fluid-flow simulation. Finally, the production history is compared with the simulation results. The process becomes an iterative loop to achieve the best match of all the available data. This process facilitates the final history match to gas, oil and water production.