Porosity and lithology are useful indicators of the hydrocarbon potential and productability of a reservoir. In the field, porosity and lithology can be determined using well logs, such as sonic, density. And neutron logs. For rapid processing of a large volume of well log data. Linear matrix algebra algorithms are preferred to iterative search techniques that are slower.
One limitation of the existing linear matrix algebra algorithms is that they sometimes provide unrealistic values (negative or greater than one) of porosity and lithology fractions. Another limitation is that three different algorithms are needed for three log analysis systems: underdetermined, determined, and over determined.
This paper presents a general matrix algebra algorithm based on the Bayesian-type statistical approaches, which combine the prior information (or the "guesses") about the porosity and lithology fractions with the well log data. The algorithm provides fairly accurate values for porosity and lithology fractions along with their uncertainties in all three log analysis systems. Several examples compare the new algorithm with the existing linear matrix algebra algorithms.
Determining porosity and lithology is an important aspect of petroleum reservoir characterization. Porosity is the fraction of reservoir rock volume occupied by hydrocarbons and water. The lower the porosity, the lower the hydrocarbon potential of a reservoir. Porosity generally correlates with rock permeability, a measure of how easily hydrocarbons flow through the rock. Hence, the lower the porosity, the lower the hydrocarbon producibility of a reservoir. Lithology refers to different reservoir rock types, such as sandstone, dolomite, and gypsum. Lithology affects porosity and permeability.
Porosity and lithology can be measured in the laboratory using cored samples, or in the field using well logs core analysis. However, is not sufficient as only a few wells in a given field are cored. For field-wide measurements, well logs, such as sonic, density, and neutron logs, are more suitable as most wells in a field are logged.
Well log responses are related to porosity and lithology through a set of linear equations. Mathematical procedures such as linear matrix algebra algorithms are used to determine porosity and lithology from these equations. Involving only matrix operations(e.g., inversion and multiplication), these algorithms are simple, non-iterative, and fast. Therefore, they are suitable for processing a large volume of well log data.
Existing Linear Matrix Algebra Algorithms Existing matrix algebra algorithms use a set of linear equations relating log responses at a given depth toporosity and lithology fractions: Equation(1) (Available in full paper)
where Li is the i th log response in the reservoir rock at a given depth, and i = 1.2..... n; Xij is the i th log response in the j th porosity or lithology component; Pj IS the volume fraction of the j th unknown porosity or lithology component, and j = 1.2, ..., p. Table 1 shows the "log response" equations for sonic, density, andneutron logs in a carbonate reservoir.
