Estimation of Lithofacies Proportions by Use of Well and Well-Test Data
- L.Y. Hu (Inst. Français du Petrole and the HELIOS Reservoir Group) | Georges Blanc (Inst. Français du Petrole and the HELIOS Reservoir Group) | Benoit Noetinger (Inst. Français du Petrole and the HELIOS Reservoir Group)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 1998
- Document Type
- Journal Paper
- 69 - 74
- 1998. Society of Petroleum Engineers
- 5.5.8 History Matching, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 5.6.4 Drillstem/Well Testing, 5.1.1 Exploration, Development, Structural Geology
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A crucial step of the two commonly used geostatistical methods for modeling heterogeneous reservoirs, sequential indicator simulation and truncated Gaussian simulation, is the estimation of the lithofacies local proportion (or probability density) functions. Well-test-derived permeabilities show good correlation with lithofacies proportions around wells. Integrating well and well-test data in estimating lithofacies proportions could permit the building of more realistic models of reservoir heterogeneity. This integration is difficult, however, because of the different natures and measurement scales of these two types of data.
This paper presents a two-step approach to integrating well and well-test data into heterogeneous reservoir modeling. First, we estimate lithofacies proportions in well-test investigation areas with a new kriging algorithm called KISCA. KISCA consists of kriging jointly the proportions of all lithofacies in a well-test investigation area so that the corresponding well-test-derived permeability is respected through a weighted power-averaging of lithofacies permeabilities. For multiple well tests, an iterative process is used in KISCA to account for their interaction. After this, the estimated proportions are combined with lithofacies indicators at wells for estimating proportion (or probability density) functions over the entire reservoir field with a classical kriging method.
We considered some numerical examples to test the proposed method for estimating lithofacies proportions. In addition, we generated a synthetic lithofacies reservoir model and performed a well-test simulation. The comparison between the experimental and estimated proportions in the well-test investigation area demonstrates the validity of the proposed method.
Recent research on stochastic reservoir modeling constrained by well-test data has focused on the approach based on the Bayesian inversion theory and the Markov chain Monte Carlo methods.1-3 This approach is very attractive because it can deal directly with wellpressure data rather than well-test-derived permeability data and because it can be extended to history matching. However, it is limited to gross grid reservoir models in the context of continuous Gaussian-related variables (e.g., log-normal permeability field). In the case of a stabilized well-test, it is possible to define an effective permeability in the corresponding investigation area (well-test-derived permeability). A method based on simulated annealing has been used for conditioning permeability field to well-test derived permeabilities.4 Although the annealing process does not call for fluid-flow simulations, this method still can be very slow. This paper proposes an alternative approach for incorporating well-test-derived permeabilities into lithological reservoir models defined on fine grids.
Consider two commonly used geostatistical methods, truncated Gaussian simulation5 and sequential indicator simulation,6 for building reservoir lithological models. These methods consist of first estimating the local proportion functions [or probability density functions (PDF)] of lithofacies. Then, the lithofacies model is built by truncating a Gaussian random function with the proportion functions (or by randomly drawing lithofacies from the PDF). A realistic modeling of lithofacies distribution with these geostatistical methods depends greatly on the accuracy of the estimation of the lithofacies proportions functions (or PDF). In the case of few well data, the incorporation of other sources of information (including geological knowledge, seismic information, well-test data, and field production data) would improve the estimation of proportion functions (or PDF) significantly.
This paper covers the problem of incorporating well and well-test-derived permeability data into the estimation of lithofacies proportion functions (or PDF). We use a two-step approach: first the lithofacies proportions in well-test investigation areas are estimated with a new kriging algorithm called KISCA, then these estimates are combined with lithofacies indicators at wells for estimating lithofacies proportion functions (or PDF) over the entire reservoir field with a classical kriging method. Ref. 7 describes another method based on the cokriging technique for integrating well and well-test-derived permeability data. Also, there are existing methods for incorporating well and seismic data for estimating lithofacies proportion functions.8
Well and Well-Test Data
The data set is made of a lithofacies description at available wells and a number of well-test-derived permeability values. The continuous lithofacies description on the wells is regularly discretized with a fineness defined according to the lithofacies variability along wells. At each point xa of the well discretization, an indicator is defined for each lithofacies:
We consider that the covariance Cn(h) of each indicator can be inferred from the well data or other sources of information (e.g., analogous outcrop data).
For each well-test-derived permeability, kwt, the investigation area, V, is determined and a power-averaging formula is adopted to relate the well-test-derived permeability to the lithofacies permeabilities:
where kn stands for the permeability of lithofacies n and Pn(V) is its proportion in V. The averaging power ? is calibrated for each well-test9,10 and Pn(V) are to be estimated by the method described next.
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