Estimation of In Situ Compaction Modulus from Tidal Response in Well Test Data
Authors: Netland S.O. , Knapstad B. , Holt R.M. 
Published: December 2007

Abstract
Prediction of reservoir compaction and associated compaction drive on petroleum production requires a knowledge of the deformational behavior of the rock (e.g the uniaxial compaction modulus) and of the pore space (e.g. the pore compressibility). These parameters may be derived from different methods such as wireline (primarily acoustic) logs, laboratory measurements, or purely empirical correlations. In weakly cemented reservoirs in particular, large uncertainties are associated with these methods.
Tidal effects observed in well test data from offshore fields offer a possible method for in situ determination of the compaction behavior. If it is assumed that the full load associated with the tidal effect at the sea-bottom is transferred to the reservoir, then the relative pressure amplitude can be calculated by a simple poroelastic model. Models for estimation of pore compressibility from tidal effects have been known since 1940. None of them have however taken proper account of rock stiffness. This Paper presents a corrected model based on Biot's poroelastic theory. Examples are given which show that previously published models might lead to significant overestimation of the compaction modulus, even for relatively soft rocks.
The model was used to estimate compaction modulus and pore compressibility in several North Sea reservoirs. The data were compared to estimates from laboratory tests, from logs, and from empirical correlations. The overall trend shows an expected decrease in compaction modulus with increasing porosity. The reliability of the analysis is significantly improved when the tidal pressure is measured at the sea-bottom simultaneously with the well test.

Introduction
The need to determine the compaction behaviour of a reservoir is essential in cases where reservoir compaction and / or surface subsidence may lead to operational problems. Compaction in itself is also important as it represents a drive mechanism.
Several methods are available for determination of the compaction modulus from field data. Traditionally, the main data sources are core and wireline log data.
Core samples are small, and not necessarily representative of the entire reservoir, so some sort of scale correction should ideally be performed. Furthermore, they may be damaged as a result of the coring process. The most important source of core damage for rock mechanical measurements in reservoir rocks is thought to be the stress release occurring during drill-out of the core plug from the reservoir. Experimental simulations have proven that for relatively weak sandstone, core measurements are likely to overestimate the initial compaction rate significantly.
In order for the data to be valid, the conditions under which laboratory measurements are performed must simulate in situ conditions as close as possible. This means that the (effective) in situ stress state should be known accurately. In addition the stress path followed by the reservoir during depletion must be anticipated. Usually, it is assumed that the vertical stress is fully transferred to the reservoir, i.e. that no shielding takes place. Uniaxial strain (i.e. zero lateral deformation) conditions are also assumed. There are indications that these conditions are not necessarily fulfilled in all cases. Finally, the time scale of a core measurement is very short compared to the time scale on which depletion takes place. Thus, correction for creep effects may also be necessary.
The use of wireline log data is attached with some of the same uncertainties as mentioned above, such as stress path, length and time scale effects. The latter problem is somewhat smaller than with core samples, since logs provide continuous measurements as a function of depth. Normally, the basic log data for compaction prediction are sonic P- and S-wave velocities (vp and vs) and density (), from which dynamic elastic moduli cane be calculated by well known fundamental relationships.
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