Prediction of Formation Compaction from Laboratory Compressibility Data
Authors: Teeuw Dirk 
Published: December 2007

Abstract
This paper presents a new, simple and inexpensive laboratory testing procedure for simulating realistic reservoir compaction behavior both in cemented and friable rocks. Core compaction is measured nowadays by various types of equipment: oedometer, hydrostatic and triaxial cells. Each method has its own shortcomings in the reproduction of subsurface displacement conditions; interpretation of the experimental data is further complicated by the nonlinear compaction behavior of porous rocks. A theoretical expression is derived which interrelates uniaxial and hydrostatic compaction, and which enables the prediction of the in-situ reservoir compaction from hydrostatic cell compaction data. This relation is verified for various types of rock by comparative measurements in oedometer and hydrostatic cells. Based on these results, a new triaxial cell-type compaction measurement for friable rocks has been developed. In addition, this method provides an independent evaluation of Poisson's ratio.

Introduction
In order to predict the compaction behavior of reservoirs due to reduction in pore fluid pressure, it is necessary to know the compaction or compressibility characteristics of the reservoir rock. This paper is concerned with the laboratory measurement of compaction properties of hard and friable rock, allowing for the reservoir boundary conditions. In a theoretical analysis, Geertsma has shown that the compaction of reservoirs depends on reservoir geometry and that reservoirs which show large lateral dimensions compared to their (vertical) thickness deform mainly in the vertical plane. For such reservoirs disregarding lateral deformations, the actual compaction f. according to the linear theory of elasticity amounts to
where Cm = uniaxial compaction coefficientp = reduction in pore fluid pressure. This uniaxial compaction is furthermore related to the hydrostatic bulk deformation by the formula
in which v = Poisson's ratio of the rockCb = rock bulk compressibility= Cma/Cb, the ratio of rock matrix torock bulk compressibility. For such reservoirs showing a measurable compaction Cma Cb, and the factor (1- ) has a negligible influence on Cm. Otherwise the value ofcan be calculated from experimental data on Cb and Cma2. For determining Cm in the laboratory there are two possible methods:1. direct measurement by using equipment which simulates the reservoir boundary condition of zero lateral displacement. There are two ways of doing this, the familiar oedometer cell test, and a modified triaxial cell test - in which lateral deformation of the sample is prevented by the appropriate adjustment of the lateral stress. In addition, this triaxial method enables an independent evaluation of v.2. indirect measurement by measuring Cb under hydrostatic load and estimating v. In view of the nonlinear elastic behavior of porous rock, Eq. 2, which is derived for linear elastic behavior, has to be generalized. This paper reports on an investigation into which one of these different methods provides the most realistic compaction data for the evaluation of in-situ reservoir compaction. For this purpose, the experimental techniques an analyzed and detail, and, as a result, a laboratory testing procedure which enables the determination of realistic laboratory compaction data, is recommended.
JPT
P. 263