Efficient Conditioning of 3D Fine-Scale Reservoir Model To Multiphase Production Data Using Streamline-Based Coarse-Scale Inversion and Geostatistical Downscaling

In addition to seismic and well constraints, production data must be integrated into geostatistical reservoir models for reliable reservoir performance predictions. An iterative inversion algorithm is required for such integration and is usually computationally intensive since forward flow simulation must be performed at each iteration. This paper presents an efficient approach for generating fine-scale three dimensional (3D) reservoir models that are conditioned to multiphase production data by combining a recently developed streamline-based inversion technique with a geostatistical downscaling algorithm. Production data can not reveal fine scale details of reservoir heterogeneity. By solving the streamline pressure solution at a coarse scale consistent with the production data we are able to invert numerous geostatistical realizations. Additionally, the streamline method allows fine resolution along the 1D streamlines independent of the coarse grid pressure solution so we do not need to explicitly address multiphase scale-up. Multiple geostatistical fine scale models are up-scaled to a coarse scale used in the inversion process. After inversion, the models are each geostatistically downscaled to multiple fine scale realizations. These fine scale models are now preconditioned to the production data and can be up-scaled to any scale for final flow simulation. A 3D extension of the prior 2D sequential-self calibration method (SSC) is developed for the inversion step. This method updates the coarse models to match production data while preserving as much of geostatistical constraint as possible. A new geostatistical algorithm is developed for the downscaling step. We use Sequential Gaussian Simulation with either block kriging or Bayesian updating to “downscale” the history-matched coarse scale models to fine-scale models honoring fine-scale spatial statistics. Combining these two developments we are able to efficiently generate multiple fine scale geostatistical models constrained to well and production data. Introduction The reliability of geostatistical models increases as more data is included in their construction. Historically only hard data conditioned the models. Now, soft data such as geologic maps or seismic data are included routinely. More recently there has been a growing interest and ability to include dynamic data as a constraint during the construction of reservoir models. The concept of incorporating production data into models by inversion is certainly not new and was commonly termed automatic history matching. These early attempts suffered from poor computer power, early algorithms, and an insufficient appreciation for geologic complexity. These problems are rapidly being overcome and we are now starting to precondition geostatistical models with dynamic data before starting rigorous flow simulation. We use the term "precondition" as a euphemism to avoid the now bitter taste of "automatic history matching" and to more accurately reflect the less ambitious goal of merely dramatically improving the initial flow results as an input to formal history matching and not to replace it entirely. Inversion is both CPU intensive and under-determined because we have so many parameters (cells with unknown properties) to set. Furthermore, the resolution represented by this large number of parameters is typically finer than the spatial resolution of the dynamic data available to us in producer watercut, pressure transient analysis, pressure and/or saturation estimates from 4D seismic. All of these reasons suggest that we reduce the number of parameters before inversion. We can easily reduce the number of parameters before inversion by up-scaling but we want our final model to have fine scale details for flow simulation. The up-scaling process that selectively refines the grid is motivated by observation that fine scale high permeability streaks often dominate breakthrough time and strongly affect ultimate recovery. We want our final geostatistical model to again have high resolution after the coarse scale inversion. SPE 56518 Efficient Conditioning of 3D Fine-Scale Reservoir Model To Multiphase Production Data Using Streamline-Based Coarse-Scale Inversion and Geostatistical Downscaling Thomas T. Tran, SPE, Xian-Huan Wen, SPE, Ronald A. Behrens, SPE, Chevron Petroleum Technology Company 2 T. T. TRAN, X.-H. WEN, R. A. BEHRENS SPE 56518 The resolution of the coarse inversion grid is not necessarily the same as that of the flow simulation grid. Flow simulation grid resolution is typically set to achieve one or two history match runs overnight in a full featured flow simulator. Inversion grid resolution should be governed by the information content of the dynamic data used as constraints and by the CPU constraints of the inversion algorithm and embedded forward model. The embedded forward model in our case is a very efficient coarse grid 3Dstreamline method but in principle it could even be a traditional finite-difference method if we were dealing with complicated flows. There is no reason to expect these grids to have similar resolutions so we can't avoid the final downscaling by simply up-scaling once for both flow simulation and inversion. In this paper we extend a prior method for incorporating production data to 3D models having both saturation data from time lapse seismic (4D seismic) and watercut data at producers. The conditioning is done at a coarse scale consistent with the information content of the data, which both reduces CPU demand and improves the inversion result by making it less under-determined. A downscaling process then takes the coarse inversion grid and restores the fine grid resolution but retains the conditioning from the production data done in the coarse grid inversion. As a result, the final 3D fine-scale model honors both the large-scale features derived from production data and the fine-scale heterogeneity observed at the well logs. We will first present the workflow of our approach with an example, which is followed by a detailed description of the methodology for both the coarse grid inversion and the geostatistical downscaling. Some sensitivities for the inversion and the downscaling are investigated before we conclude with a discussion on limitations and additional work. Basic Workflow Figure 1 shows the basic workflow. We start with any geostatistical technique to incorporate well data and soft spatial data such as from 3D seismic. Commonly multiple realizations are generated consistent with the static data. A fine scale 3D model is upscaled to the coarse grid resolution for inversion and then inverted with the available dynamic data. This coarse grid model is finally downscaled with one of the two new methods presented in this paper to create multiple fine scale realizations all consistent with a given coarse grid inversion result. These fine scale realizations form the basis for a traditional simulation workflow of up-scaling and history matching. The reference field A reference true Ln(k) (natural logarithm of permeability) field was first constructed for testing the proposed approach. This reference field was generated using Sequential Gaussian Simulation at a fine grid consisting of 100x100x20 grid cells. The size of each grid cell is 10x10x5 ft. A spherical variogram was used: the areal direction with maximum spatial continuity is SW-NE with a range of 800 ft, the range in the SE-NW Fine scale k from w ell logs & core Seism ic or other soft data for k Geostatistical method M ultiple fine scale models on uniform grid Scale-up a given fine model to coarse grid and invert w ith SSC using streamlines Single inversion result for each coarse grid input dow nscaling constrained by coarse grid inversion M ultiple fine grid results for each coarse grid inversion result Figure 1: We create an initial fine grid field unconstrained by production data, coarsen grid, constrain to production data, and finally downscale to fine grid. Figure 2: Top: the up-scaled reference (20x20x5) field; Middle: one realization of initial model before inversion; Bottom: SSC Inverted model corresponding to the initial model in the middle. SPE 56518 EFFICIENT CONDITIONING OF 3D FINE-SCALE RESERVOIR MODEL TO MULTIPHASE PRODUCTION DATA USING STREAMLINEBASED COARSE-SCALE INVERSION AND GEOSTATISTICAL DOWNSCALING 3 direction is 200 ft, and the vertical range is 40 ft. The mean and variance of Ln(k) are 5.95 and 2.8, respectively. This reference field was then up-scaled uniformly to a coarse grid consisting of 20x20x5 blocks using an arithmetic average. The top image of Figure 2 shows the up-scaled reference model. Porosity is assumed constant with 0.2 for the entire model. Flow simulation was performed on the fine-scale reference model to generate synthetic production data with the following conditions: • The reservoir is initially saturated with oil. • A nine-well pattern, shown on Figure 2, is used with an injection well at the center and 8 production wells at the edges. All wells are constrained with constant flow rates (3200 RBBL/day for injection well, and 400 RBBL/day for production wells). • No-flow conditions are imposed at the reservoir boundaries. • Standard power-2 relative permeability curves are used. The fractional flow of water at the 8 producers and saturation distribution at 500 days (corresponding to 0.45 PVI) were retained as “truth” production data for inversion. In practical situations, saturation data are usually obtained at a coarser scale. Thus, to make our example more realistic, the fine-scale saturation distribution was up-scaled to the 20x20x5 coarse grid by simple average; this up-scaled saturation distribution was used as input for inversion. SSC Inversion SSC inversion was performed on the 20x20x5 coarse grid. Multiple initial coarse-scale Ln(k) realizations were built using Sequential Gaussian Simulation conditional to data from the nine wells. Since (1) it is difficult to compute a horizontal variogram from only 9 wells, and (2) previous studies by Wen et al. 2 have shown that SSC inversion results are not very sensitive to input variogram model, a variogram model was assumed. This variogram is the same as that used to generate the reference model, except that it has a smaller areal anisotropy ratio of 600:300 ft. The histogram from the upscaled well data was used. These initial permeability models were modified by SSC to match fine-scale fractional flow rates and the coarse-scale saturation distribution. The middle and bottom images of Figure 2 show one realization of the initial SGS-generated coarse-scale Ln(k) and the corresponding SSC-updated model. Next, flow simulation was performed on each initial coarse-grid model and its SSC-updated version with the previously defined initial and boundary conditions. Figure 3 shows the cell-by-cell cross-plots of simulated saturation for the reference vs. the initial and SSC-updated models respectively. Note the significant improvement of saturation matching after inversion. The mismatch at those cells with low saturation is expected because these cells contribute very little Figure 3: Initial and updated water saturation vs. reference results for each block at 0.45 PVI. Figure 4: Water fractional flows of 10 realizations before (top) and after (bottom) SSC inversion on a coarse scale grid. 4 T. T. TRAN, X.-H. WEN, R. A. BEHRENS SPE 56518 mobile water over the entire lower saturation range and hence contribute little to the watercut at the wells. The inversion was weighted more to watercut data than saturation data because of greater uncertainty of saturation data from, e.g., time-lapse (4D) seismic. Comparison between simulated and reference fractional flow at producer 1 (located at top-left corner) for the first 10 initial and SSC-updated realizations is given in Figure 4. Note the improvement of matching and reduction of uncertainty in inverted models. The inversion also improves recovery at this particular well by correctly placing a permeability baffle between it and the injector thus delaying water breakthrough. This water fractional flow delay is seen in the shift of the curves comparing the top and bottom halves of Figure 4. Downscaling The multiple coarse scale Ln(k) permeability models inverted by the SSC method were then downscaled back to the fine scale grid using a geostatistical downscaling method (which will be described in detail in a later section). The downscaled permeability fields honor the well data, variogram and histogram, yet the average of fine scale Ln(k) within a coarse block is preserved as the value inverted by SSC. Multiple downscaled realizations can be generated for each coarse scale model. Figure 5 shows three realizations of Ln(k) downscaled with the Bayesian method from one coarse scale model shown at the bottom of Figure 2. The overall structure of this coarse scale model can be seen in each of the realizations. Only small-scale variations exist between these where the flow response between various realizations is more similar than between unconstrained realizations as expected. The high quality of the fractional flow match to the reference solution of these downscaled models is similar to that of the inverted coarse grid models. In summary, we have demonstrated an efficient workflow to generate highly detailed 3D reservoir models conditioned to (static) geologic data and (dynamic) multiphase production data by an example using a synthetic data set. This workflow consists of a streamline-based coarse-scale inversion and a geostatistically-based downscaling. Detailed description of these two components is given next. SSC Inversion Method The Sequential Self-Calibration (SSC) method, originally proposed by Gomez-Hernandez et al., is an inverse technique that iteratively modifies multiple initial geostatistical reservoir models to match dynamic production data, yet preserves the geostatistical features in the initial models. It utilizes the master point concept coupled with a kriging process to propagate perturbations at master point locations to the entire field. It is computationally efficient and robust. The SSC method has been used previously for integrating single-phase pressure data 1, 2, , and two-phase fractional flow rate data coupled with streamline simulation and fast semi-analytical sensitivity coefficient calculation. In this work, the SSC method is extended to 3-D and includes the inversion of spatially distributed saturation data. The objective function used in this study is: