Water-Cut Forecasting and Permeability Inversion From Time-Lapse Seismic using a Stream-Line Technique
Authors: de Haan S.C. , Oldenziel T. , Berentsen C.W.J. , van Kruijsdijk C.P.J.W. 
Published: October 2008

Abstract
In this paper, we describe an algorithm, which predicts saturation development through the a-priori unknown permeability field using the saturation history of the field. Furthermore, the algorithm allows estimation of the underlying permeability field. The field's saturation history is derived from time-lapse 3-D seismic data. Time-lapse seismic is used to monitor the reservoir during production. Assuming seismic repeatability, it is possible to couple seismic changes to dynamic reservoir properties changes induced by production. Successive seismic data set give direct information over the speed at which the saturation front propagates through the a-priori unknown permeability field. The propagation speed of the saturation front contains useful information about the fluid flow velocity field in the observed medium. It enables us to forecast the development of the saturation contours in time, which is easily translated into water-cut profiles. In addition, a relation between the velocity map and desired reservoir parameters (e.g. permeability) can be established using an inversion technique.
A streamline technique is used to verify that each simulated saturation contour matches the a-priori known contour it is based on. In a number of test cases we created randomly exponential correlated heterogeneous permeability fields. We verified the algorithm by comparing the forecasted results with the real simulated results. A sensitivity analysis was performed to study the number of saturation fronts (i.e. repeat 3D surveys) required to yield reliable results. The proposed approach offers the advantage of inverting permeability via a rather simple, but reliable method using time-lapse seismic data.

Introduction
Permeability is one of the most important reservoir parameters, because it directly impacts the fluid flow. Accurate permeability maps will result in reliable outcomes from the reservoir simulation and plausible prediction of future oil production. However, estimation of the permeability often turns out to be a difficult task. The heterogeneous character of the reservoir cannot properly be inferred from a few measurements. There are two main methods to measure permeability. One is based on pressure transient analysis using well tests1 or mini-permeameters at outcrops or cores. The spatial or 3-D heterogeneity is inferred by interpolation between the measurement points, most often using geostatistics. In cases, where porosity is assumed to be coupled to permeability, it can be used to improve the actual interpolation. The second method to estimate permeability is based on production data, e.g. monitoring tracers2 or produced fluids3. Inferring the permeability heterogeneity, by matching the production data, is subject to non-uniqueness, because it is constrained only at a few points.
This paper presents a new technique using a streamlinebased approach. This approach offers the advantage of inverting permeability via a rather simple, but reliable method. The technique forecasts the development of saturation through the a-priori unknown permeability field, assuming constant porosity. Time lapse 3D seismic enables us to monitor the changes in the reservoir during production, assuming seismic repeatability. Successive sets of saturation information are used to draw contours of the oil-water contact.