Abstract
Laboratory data on the time-dependent compaction of porous rocks are presented, and various attempts to model this behavior are described. These lead to a discussion of the problems that arise in using laboratory data to estimate long-term effects. A method is suggested for combining laboratory data with information from the geologic record to estimate long term effects.
Introduction
The phenomena of reservoir compaction and subsidence as a result of fluid withdrawal are well known. Particularly well-documented examples include the excessive subsidence at Long Beach, California, resulting from oil production from a thick sequence of sand [1,2] and subsidence at the Wairaki geothermal field in New Zealand where withdrawal of hydrothermal fluids from volcanic rocks is the driving mechanism.[3] Many straightforward attempts to model and predict this behavior have been made,[4,5] none of which have been particularly successful. Typically, such models assume that the reservoir materials are linearly elastic, and compressibilities are obtained from data taken in short-term (1 day) tests on small (typically 50 mm diameter x 100 mm length) samples. Field evidence suggests that the assumptions of elasticity are erroneous. Thus at Long Beach, for example, we can cite the irreversibilty of compaction and subsidence, while at Wairaki, and at many other sites, there is strong evidence that the process of compaction is time-dependent as well. In an earlier study, Schatz, Kasameyer and Cheney[6] indicated a time-dependence in geothermal field compaction based upon a comparison of laboratory compressibilities with those deduced from field porosity measurements. There are a number of factors which will affect the applicability of compressibility measurements in the laboratory to predictions of field values. These include sample disturbance, the effects of fluid/rock interaction if the saturating fluids in the laboratory and in the field are not identical, the temperature and pressure of tests and the fact that small samples may not be representative of a formation which may be heterogeneous and discontinuous on a scale larger than the sample. While these are undoubtedly important factors, we choose to concentrate in this discussion of the aspect of time-dependence of formation rocks. Over the last several years, several investigators have observed time-dependence of porous materials in the laboratory. Some of these observations have been made in relation to the stability of soil-based structure. [8,9] Others have been made in relation to compaction of reservoir formations.[10-17] In this paper we will concentrate on observations made by ourselves and co-workers in relation to three rocks - a siltstone which occurs as a lignite overburden in central Texas, a geopressured-geothermal reservoir sand from the Gulf Coast of Texas, and geothermal reservoir sands from Southern California and Northern Mexi co. A major thrust of the work involved was the development of constitutive relations which would allow the prediction of long-term compaction. In doing this, we have approached the development of constitutive relations both from an empirical standpoint and from the point of phenomonological modelling. A major result of this work has been to highlight the strong possibility of increased compaction occurring over long time periods not usually observable in the laboratory.
