Calibrate Flow Simulation Models with Well-Test Data to Improve History Matching

Abstract

In this paper we present a methodology to verify and update geostatistically based reservoir models using numerical simulation and automatic history matching of well-test data. A Bayesian estimation technique provides the framework for the inversion procedure used to update reservoir models. A restricted-step Gauss-Newton method and an extension of Carter's method for sensitivity coefficients make the methodology efficient and practical. Reservoir models (permeability, porosity and skin factor) can be updated based on individual simulation cells, geological feathers, or on constant multipliers applied in the well-test radius of investigation. When short-term well-test data is available from many wells, we found it useful to calculate property multipliers around each well and then interpolate the multipliers to unsampled areas in the reservoir. Field examples demonstrate the utility of conditioning reservoir models with well-test data. In the examples, flowing bottomhole pressure mismatches are as high as 2000 psi and core based permeabilities deviate by two orders of magnitude from the well-test results. After conditioning to well-test data, pressure mismatches are significantly reduced, permeabilities are updated to the correct magnitude, and the skin factor closely matches the classic well-test analysis result. We applied our updating methodology to a full-field simulation study on a large carbonate reservoir. Comparisons of historical pressure and production data to the updated full-field model demonstrate good agreement.

Reservoir Characterization and Flow Simulation of a Low-Permeability Gas Reservoir: An Integrated Approach for Modelling the Tommy Lakes Gas Field

“…The deviation between the core/logderived permeability and the in-situ permeability can be two orders of magnitude for a tight gas reservoir. Previous literature has discussed numerical well testing and the linking to the full-field reservoir model (Settari 1990;Puchyr 1991;He and Chambers 1999;Mlacnik and Heinemann 2003;Kamal et al 2005;Al-Thawad et al 2007). An integrated workflow developed in this paper that explains the field-based corner-point grid model is based on matching the well-test buildup data:…”

Mapping of Reservoir Properties and Facies Through Integration of Static and Dynamic Data

“…As shown in Fig. 5.13, the platform is bounded by faults or lithologic breaks and surrounded by gently sloping "flanks" of carbonate debris; see Chambers et al (1997) and He and Chambers (1999) for additional details on the geology. The index on the x and y axes is the number of gridblocks, i.e., the areal grid for the original reservoir model was 90 × 100.…”

“…The correlation coefficients between φ and ln(k), φ and ln(k z ), and ln(k) and ln(k z ), respectively are given by 0.9096, 0.662 and 0.5. These values were determined from the unconditional realization, m uc , and differ somewhat from the variances used by He and Chambers (1999) who used variances of 3.2×10 −4 and 0.225, respectively, for φ and ln(k), but did not specify a variance for ln(k z ) and did not specify values of the correlation coefficients. We use a anisotropic spherical variogram with principle direction coincident with the x axis.…”

“…The correlation ranges in the x, y and z direction, respectively, are given by 6561.6 ft, 4921.3 ft and 164.04 ft. These ranges are same as those used by He and Chambers (1999). Cross covariances are generated using the screening hypothesis Xu et al (1992); Chu et al (1995b).…”