Scale and process dependent model errors in seismic history matching

Time-Lapse (4D) seismic data offers spatial and dynamic information about changes in reservoir fluid properties and can be used to constrain flow simulation models thereby improving confidence in the reservoir characterisation and its predicted behaviour. To address this, we have developed a method of quantitatively integrating 4D seismic data in an automated history matching workflow. Appropriately parameterised flow simulations are converted to predictions of 4D signatures by a petro-elastic transform and suitable rescaling before a misfit is calculated by comparison to observed data. Model parameters are then updated using a quasi-global stochastic inversion method. This process is affected by scale and process dependent model errors. Flow simulations are often created such that computer resources are optimised and some level of accuracy is sacrificed. To speed up simulations, some form of upscaling is required to capture two-phase flow properties such as relative permeability but also to represent geological heterogeneity. The upscaling may be over-simplified or ignored. In addition, simplifications to the flow processes may be made, for example by using streamline methods. Finally, the petro-elastic transform contributes to the model errors due to assumptions about saturation distributions and cross-scaling is required because modelled and observed seismic are obtained for different volumes. We present an analysis of the above model errors that occur using a synthetic geo-model based on a North Sea reservoir. We show that the model error depends on the rock physics parameters as well as the underlying geo-model. When the 4D signature is dominated by pressure effects, the model error is negligible in our case. We describe how the model error affects the history matching process due to biasing. The latter results in a best set of model parameters which may be different from that obtained by upscaling while the uncertainty estimator is also changed. We compare the effect of the model error to other errors such as observed data errors. Finally, we describe how the model error is addressed in the misfit calculation to improve the history matching process and reduce the biasing effect. Copyright © 2007, Institut français du pétrole.