Transmissibility Multipliers Research Articles

Multiple Model Seismic and Production History Matching: A Case Study

Summary Time-lapse (or 4D) seismic is increasingly being used as a qualitative description of reservoir behavior for management and decision-making purposes. When combined quantitatively with geological and flow modeling as part of history matching, improved predictions of reservoir production can be obtained. Here, we apply a method of multiple-model history matching based on simultaneous comparison of spatial data offered by seismic as well as individual well-production data. Using a petroelastic transform and suitable rescaling, forward-modeled simulations are converted into predictions of seismic impedance attributes and compared to observed data by calculation of a misfit. A similar approach is applied to dynamic well data. This approach improves on gradient-based methods by avoiding entrapment in local minima. We demonstrate the method by applying it to the UKCS Schiehallion reservoir, updating the operator's model. We consider a number of parameters to be uncertain. The reservoir's net to gross is initially updated to better match the observed baseline acoustic impedance derived from the RMS amplitudes of the migrated stack. We then history match simultaneously for permeability, fault transmissibility multipliers, and the petroelastic transform parameters. Our results show a good match to the observed seismic and well data with significant improvement to the base case. Introduction Reservoir management requires tools such as simulation models to predict asset behavior. History matching is often employed to alter these models so that they compare favorably to observed well rates and pressures. This well information is obtained at discrete locations and thus lacks the areal coverage necessary to accurately constrain dynamic reservoir parameters such as permeability and the location and effect of faults. Time-lapse seismic captures the effect of pressure and saturation on seismic impedance attributes, giving 2D maps or 3D volumes of the missing information. The process of seismic history matching attempts to overlap the benefits of both types of information to improve estimates of the reservoir model parameters. We first present an automated multiple-model history-matching method that includes time-lapse seismic along with production data, based on an integrated workflow (Fig. 1). It improves on the classical approach, wherein the engineer manually adjusts parameters in the simulation model. Our method also improves on gradient-based methods, such as Steepest Descent, Gauss-Newton, and Levenberg-Marquardt algorithms (e.g., Lépine et al. 1999;Dong and Oliver 2003; Gosselin et al. 2003; Mezghani et al. 2004), which are good at finding local likelihood maxima but can fail to find the global maximum. Our method is also faster than stochastic methods such as genetic algorithms and simulated annealing, which often require more simulations and may have slower convergence rates. Finally, multiple models are generated, enabling posterior uncertainty analysis in a Bayesian framework (as in Stephen and MacBeth 2006a).

The representation of two phase fault-rock properties in flow simulation models

Faults are represented conventionally in production flow simulation models using transmissibility multipliers which capture the single phase, but not the two phase, fault-rock properties. Available data indicate that fault-rocks have similar two phase properties to sediments of the same permeability, hence existing methods can be applied to estimate two phase fault-rock properties from their intrinsic permeabilities. Two methods of representing the two phase fault-rock properties implicitly in the flow simulator are compared, using one-dimensional numerical flow models containing water-wet faults with imbibition capillary pressure curves. The method which is the closer two phase analogue of the single phase transmissibility multiplier is inappropriate, as the implementation is unreasonably unwieldy. A simpler implementation is to derive pseudo-relative permeability functions including the fault-rock properties in the upstream grid block; these properties are then incorporated directly in the simulator. Relative transmissibility multiplier functions can be back-calculated from the pseudo-relative permeability functions, and indicate how closely the single phase multiplier approximates two phase flow through the fault. Implementation in a 3D model with complex fault juxtapositions validates the approach, and a practical workflow for the routine inclusion of two phase fault-rock properties in conventional faulted flow simulation models is outlined.

Fault transmissibility multipliers for flow simulation models

Fault zone properties are incorporated in production flow simulators using transmissibility multipliers. These are a function of properties of the fault zone and of the grid-blocks to which they are assigned. Consideration of the geological factors influencing the content of fault zones allows construction of high resolution, geologically driven, fault transmissibility models. Median values of fault permeability and thickness are predicted empirically from petrophysical and geometrical details of the reservoir model. A simple analytical up-scaling scheme is used to incorporate the influence of likely small-scale fault zone heterogeneity. Fine-scale numerical modelling indicates that variability in fault zone permeability and thickness should not be considered separately, and that the most diagnostic measure of flow through a heterogeneous fault is the arithmetic average of the permeability to thickness ratio. The flow segregation through heterogeneous faults predicted analytically is closely, but not precisely, matched by numerical results. Identical faults have different equivalent permeabilities which depend, in part, on characteristics of the permeability field in which they are contained.

Characterization of Fluvial Sedimentology for Reservoir Simulation Modeling

Summary This paper presents a critical study of a 3D stochastic simulation of a fluvial reservoir and of the transfer of the geological model to a reservoir simulation grid. The stochastic model is conditioned by sand-body thickness and position in wellbores. Geological input parameters—sand-body orientation and width/thickness ratios—are often difficult to determine, and are invariably subject to interpretation. Net/gross ratio (NGR) and sand-body thickness are more easily estimated. Sand-body connectedness varies, depending on the modeling procedure; however, a sedimentary process-related model gives intermediate values for connectedness between the values for a regular packing model and the stochastic model. The geological model is transferred to a reservoir simulation grid by use of transmissibility multipliers and an NGR value for each block. The transfer of data smooths out much of the detailed geological information, and the calculated recovery factors are insensitive to the continuity measured in the geological model. Hence, we propose improvements to the interface between geological and reservoir simulation models. Input for our conditional, statistical, sedimentary, process-related model includes regional geological parameters (rates of subsidence and aggradation and grossly contoured paleotopography) and local values (depth, thickness, and direction and width of sand bodies ascertained from well-test and core analyses). Integration of sedimentological understanding of the reservoir's depositional environment is emphasized.