--> Abstract: Aspects of Porosity Prediction Using Multivariate Linear Regression, by A. P. Byrnes and M. D. Wilson; #91004 (1991)

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Aspects of Porosity Prediction Using Multivariate Linear Regression

BYRNES, ALAN P., GeoCore, Loveland, CO, and MICHAEL D. WILSON, Wheat Ridge, CO

Highly accurate multiple linear regression models have been developed for sandstones of diverse compositions. Porosity reduction or enhancement processes are controlled by the fundamental variables, Pressure (P), Temperature (T), Time (t), and Composition (X), where composition includes mineralogy, size, sorting, fluid composition, etc. The multiple linear regression equation, of which all linear porosity prediction models are subsets, takes the generalized form:Porosity = C(0) + C(1)(P) + C(2)(T) + C(3)(X) + C(4)(t) + C(5)(PT) + C(6)(PX) + C(7)(Pt) + C(8)(TX) + C(9)(Tt) + C(10)(Xt) + C(11)(PTX) + C(12)(PXt) + C(13)(PTt) + C(14)(TXt) + C(15)(PTXt)

The first four "primary" variables are often interactive, thus requiring terms involving two or more primary variables (the form shown implies interaction and not necessarily multiplication). The final terms used may also involve simple mathematic transforms such as logX, e(T), X(2), or more complex transformations such as the Time-Temperature Index (TTI). The X term in the equation above represents a suite of compositional variables and, therefore, a fully expanded equation may include a series of terms incorporating these variables. Numerous published bivariate porosity prediction models involving P (or depth) or Tt (TTI) are effective to a degree, largely because of the high degree of colinearity between P and TTI. However, all such bivariate models ignore the unique contributions f P and Tt, as well as various X terms. These simpler models become poor predictors in regions where colinear relations change, where important variables have been ignored, or where the database does not include a sufficient range or weight distribution for the critical variables.

 

AAPG Search and Discovery Article #91004 © 1991 AAPG Annual Convention Dallas, Texas, April 7-10, 1991 (2009)