Forecasting of Ekofisk Reservoir Compaction and Subsidence by Numerical Simulation
Authors: Boade R.R. , Chin L.Y. , Siemers W.T. 
Published: December 2007

Summary
A finite-element computational procedure for simulating the reservoir compaction and subsidence processes at Ekofisk is described. Data input requirements are considered, and results are presented for selected reservoir management options. Field presented for selected reservoir management options. Field measurements of subsidence, subsidence rates, and subsidence-bowl profiles are shown to be in good agreement with calculated results. profiles are shown to be in good agreement with calculated results. Introduction
The late-1984 discovery of subsidence at the Ekofisk field prompted a variety of technical programs to study physical prompted a variety of technical programs to study physical phenomena bearing on the problem, including an effort to develop phenomena bearing on the problem, including an effort to develop methods to simulate numerically the relevant physical processes. This simulation work was motivated primarily by the need to predict the future course of subsidence so that suitable reservoir management plans could be developed and implemented and required plans could be developed and implemented and required modifications to offshore facilities could be identified and made. Salient features of the simulation procedures developed through this study are reviewed here. Results of selected simulation runs for representative reservoir management options are also presented and, where possible, compared with field measurements,
The Ekofisk reservoir, which lies about 10,000 ft [3 km] below the seafloor, is formed from chalk, most of which was greater than 30% in porosity before the start of production, and some was greater than 40%. The load of the overburden on the reservoir is at any time supported jointly by the overpressured reservoir fluids and the matrix of the porous chalk. As fluids have been removed from the reservoir through production, the pore pressure has been reduced by as much as 3,500 psi [24 MPa] from its initial level of about 7,000 psi [48 MPa]. The decline in pore pressure has led to an increase in the fraction of the load that must be borne by the chalk matrix. Because chalk is structurally weak, the increased load has led to significant reservoir compaction, which in turn has caused the surrounding geological medium, particularly the overburden, to be deformed, with seafloor subsidence being the prominent observed effect.
The compaction and deformation processes are complex, owing in part to the highly nonlinear compaction behavior of chalk and the coupled physical processes. Not only do the mechanical properties of the reservoir affect the deformation of the surrounding properties of the reservoir affect the deformation of the surrounding medium, but the mechanical properties of the surrounding medium also affect reservoir compaction. This coupling makes finite-element computational procedures particularly suitable as numerical simulation tools. When a simulation model is being developed, it is necessary to specify properly the shape and porosity distribution of the reservoir, the mechanical properties of all materials in the modeled zone, and the time dependence and spatial distribution of pore pressure in the reservoir. pore pressure in the reservoir. Two finite-element codes have been used for the Ekofisk problem, ANSYS and DYNAFLOW. The initial work was done with ANSYS, problem, ANSYS and DYNAFLOW. The initial work was done with ANSYS, not because this code is particularly suitable for the problem (in fact, it is not), but because it was being used for another problem and hence was available for immediate application. The principal shortcoming of ANSYS for the reservoir compaction and subsidence problem is that provisions are not available to treat explicitly such problem is that provisions are not available to treat explicitly such fluid-filled porous materials as reservoir rock; because DYNAFLOW has that capability, it was selected for the continuing simulation effort. Most results presented here were obtained with DYNAFLOW, but the basic computational procedures were developed with ANSYS.

Computational Procedures and Input Information

Basic Computational Methodology.
The Ekofisk reservoir is an elongated domal structure (Fig. 1) trending in a north/south direction. Hydrocarbon production from the field is from two separate intervals: the lower in the Tor formation and the upper in the Ekofisk formation. These intervals are often referred to as the Cretaceous and Danian reservoirs, respectively, but here they are called the Tor and Ekofisk formation reservoirs. "Ekofisk reservoir" refers to both reservoirs collectively.
For modeling purposes, the Ekofisk reservoir was assumed to be elliptically shaped and symmetric about the major and minor axes of the ellipse (dashed curve on Fig. 1). This assumption facilitated construction of a three-dimensional (3D) model in which only a single quadrant of the ellipse is considered. Because of large computer-memory and long run-time requirements, however, the 3D model was found to be impractical for routine use. Hence, an alternative procedure, which involves combining results of two 2-dimensional (2D) computations to obtain a single result that is representativeof the result obtained from a 3D computation, was developed. In each 2D run, the reservoir is assumed to be axially symmetric.
The two solid circles in Fig. 1 have radii corresponding to reservoir dimensions assumed for the two axisymmetric calculations. The radius of the smaller circle ([ 1,000 ft (3.35 km]) is representative of the east/west reservoir dimension, while the radius of the larger circle (15,400 ft [4.69 km]) is representative of the north/ south reservoir dimension. The tongue of the reservoir protruding to the south of the larger circle was ignored because it is quite narrow and hence will not be compacted significantly, nor will it contribute significantly to subsidence.
Reservoir compaction and subsidence (vertical displacement) values calculated for the shorter east/west cut are less than those calculated for the longer north/south cut. Logically, the "correct" result (the 3D result) should fall between the results of the two axisymmetric calculations. The procedure to combine vertical displacements from the 2D computations to get pseudo-3D results uses a weighted-averaging function that makes the correct vertical displacement a simple average of the two 2D results along the vertical axis through the reservoir center. Away from this axis in the north/south (or east/west) direction, the correct displacement depends increasingly on the results of the calculation based on the large (small) reservoir radius and decreasingly on those based on the small (large) reservoir radius. These procedures were developed by comparing results of 2D and 3D calculations performed with ANSYS and were verified with similar calculations performed with DYNAFLOW.
The initial step in a computational run with DYNAFLOW is to "turn on" gravity. This step establishes the initial, preproduction state of the reservoir and the surrounding media. Subsequent displacement and changes in stress conditions are related to the initial state. To satisfy convergence criteria and to achieve stable running conditions for the finite-element calculation, the timestep was set at 0. 05 year. Gravity was turned on over a 1-year period starting in 1970, and the first change in reservoir pressure occurred in 1971.
P. 723