Coupling Reservoir and Geomechanics to Interpret Tidal Effects in a Well Test
Authors: Pinilla J.F. , Trevisan O.V. , Tinoco F.L. 
Published: December 2007

Abstract
Variations of hydrostatic pressure over the sea floor, are transmitted through the lithological layers by stress waves. These waves induce changes in the pore pressure, when reaching the subterranean reservoirs. This work models the oceanic tidal effect on a infinite reservoir by coupling geomechanic principles with equations for fluid flow in a deformable porous media. The problem is treated in the context of test analysis, concerning dimensionless form of variables and the inclusion of well effects. The results are incorporated to conventional type curves, and were validated by comparison with real and simulated pressure test data. Alternate practices were suggested to integrate the well test analysis in reservoirs affected by the tidal effect.

Introduction
Tide is a result of the relative displacement of the particles composing a celestial body, caused by gravitational attraction of neighboring bodies. On Earth, comprehended by a gas cap, a water mass and a rock volume, the relative movement of these phases is the base of the known barometric, earth and ocean tides.
At a reservoir located under the sea floor, the three tidal mechanisms are active over the rock-fluid system. The ocean tide is, however, by the magnitude of its effects on the reservoir, the dominant source of perturbation.
The propagation of the pressure perturbations from the ocean floor to the reservoir is not conservative, and the ratio between the pressure variation at these two locations is known as the tidal efficiency.
Though the first observations of the phenomenon are dated of the end of last century, the phenomenon had not been detected in the oil industry until the advent of highly sensitive pressure recorders, about two decades ago. In 1976 Kuruana presented the first work relating the periodical pressure oscillation during testing of wells in Timor sea with the ocean tides.
Hemala and Benalves in 1986 provided an overview of tidal effects from petroleum engineering point of view and proposed some possible applications of the effect to predict fluid heterogeneities in reservoir. Inspired on the Hemala's proposal, Wanell and Morrison presented a practical method of measuring vertical permeability and Dean et al introduced a method to monitor compaction and compressibility changes in offshore chalk reservoir by measuring the tidal effect in the reservoir.
In well test analysis the tidal effect appears as unwelcome perturbations troubling the diagnostic mainly at the late time periods. So far, little has been done to incorporate the theoretical modeling of these effects to the conventional practice of formation evaluation.
In the present work, the tidal effect is addressed according to he interest of well test analysis. The focus is on a infinite reservoir model producing at a single well and being simultaneously affected by the variations in the overburden pressure caused by the ocean tide.
A fundamental study on this topic necessarily involves the basic concepts of geomechanics, the principles governing the tidal phenomena and the theory of fluid flow compressible porous media. The objective of the present paper is to present a model coupling aspects of these three distinct areas, including a theoretical solution given in the form commonly used in well test analysis and finally propose some procedures to help in the diagnostic of pressure records that are affected by tidal waves.

Theoretical Background
To address the problem properly, it is important to begin by stressing on the concept of rock compressibility. Such concept is used both in geomechanics and fluid flow in a nonuniform, and very often mistaken, terminology. P. 301^