Mathematical Geology

, Volume 28, Issue 6, pp 791–810

# A statistical adjustment of Haldorsen's conditioned Boolean simulation algorithm

• Roderik J. Berkhout
• Antonio G. Chessa
• Allard W. Martinius
Article

## Abstract

This paper presents a new simulation algorithm for generating realizations of a Boolean model for sandstone reservoirs conditional on sandstone body intersections in wells. It is a statistically corrected version of the conditional simulation algorithm originally proposed by Haldorsen. In previous work it was shown that the conventional algorithm does not reproduce the correct statistics for sandstone body size at the well locations. The simulation of a Boolean model, given grain intersections on line transects, must be in accordance with the conditional distribution of the model, which implies that sandstone bodies intersected by wells and sandstone bodies in the interwell area should be simulated independently. Based on the conditional distribution a simulation algorithm is developed, which is compared to Haldorsen's algorithm by simulating an outcrop section of fluvial sandstone deposits. Simulations are conditioned on data of two fictitious wells. It turns out that the adjusted algorithm gives better results for the sand fraction that is connected to a set of wells, and also for the sand fraction that would be connected to an infill well.

### Key words

point process germ-grain model waiting-time paradox conditional distribution conditional simulation volume fraction

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© International Association for Mathematical Geology 1996

## Authors and Affiliations

• Roderik J. Berkhout
• 1
• Antonio G. Chessa
• 2
• 3
• Allard W. Martinius
• 3
1. 1.Shell U.K. Expro, Brent Field Unit DB/731, Seafield House, Hill of RubislawAberdeenScotland
2. 2.Faculty of Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands
3. 3.Faculty of Mining and Petroleum EngineeringDelft University of TechnologyDelftThe Netherlands