Streamline-Based Production Data Integration With Gravity and Changing Field Conditions
- Zhong He (Texas A&M U.) | Seongsik Yoon (Texas A&M U.) | Akhil Datta-Gupta (Texas A&M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2002
- Document Type
- Journal Paper
- 423 - 436
- 2002. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 5.3.1 Flow in Porous Media, 5.1 Reservoir Characterisation, 5.6.5 Tracers, 5.5 Reservoir Simulation, 4.3.4 Scale, 7.6.2 Data Integration, 3.3.6 Integrated Modeling, 5.5.7 Streamline Simulation, 5.1.5 Geologic Modeling, 1.6 Drilling Operations, 5.5.8 History Matching, 5.4 Enhanced Recovery, 5.4.2 Gas Injection Methods, 5.1.8 Seismic Modelling, 5.6.1 Open hole/cased hole log analysis, 1.6.9 Coring, Fishing, 5.4.1 Waterflooding
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Recently, streamline-based flow simulation models have offered significant potential in integrating dynamic data into high-resolution reservoir models. A unique feature of the streamline-based production data integration has been the concept of a travel-time match that is analogous to seismic tomography, allowing the use of efficient and proven techniques from geophysics. In this paper, we propose a generalized travel-time inversion method for production data integration that is particularly well-suited for large-scale field applications with gravity and changing conditions. Instead of matching the production data directly, we minimize a travel-time shift derived by maximizing a cross-correlation between the observed and computed production response at each well. There are several advantages of our proposed method. First, it is general and extremely computationally efficient. The travel-time sensitivities can be computed analytically with a single forward streamline simulation that can be much faster than a conventional reservoir simulator. Second, it is robust and the minimization is relatively insensitive to the choice of the initial model. Finally, it is field-proven because we utilize established techniques from geophysical inverse theory.
We demonstrate the power and utility of our proposed method using synthetic and field examples. The synthetic examples include a large-scale 3D example with a quarter-million grid cells involving infill drilling and pattern conversions. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns with 11 injectors and 31 producers. Starting with a reservoir model based on well-log and seismic data, we integrate water-cut history for 20 years in less than 2 hours on a PC.
It is well known that geological models derived from static data only, such as well-log, core, and seismic data, often fail to reproduce the production history. Reconciling geologic models to the dynamic response of the reservoir is critical to building reliable reservoir models. The past few years have seen significant developments in the area of such dynamic data integration through the use of inverse modeling.1-13 Streamline models have shown great promise in this regard.9-13 The key advantages of streamline-based production data integration are its computational efficiency as a "forward" model and analytic computations of sensitivities of the production response with respect to reservoir parameters.9-11 Sensitivities describe the change in production response because of a small perturbation in reservoir properties, such as porosity and permeability, and are a vital part of the dynamic data integration process.
Our previous works on streamline-based production data integration followed directly from seismic waveform inversion and utilized a two-step procedure9,10: (a) a travel-time match that involves matching of the "first arrival" or breakthrough times, and (b) an amplitude match involving matching of the actual production response. The two-step approach has been shown to substantially speed up the computation, and also prevents the solutions from being trapped by secondary peaks in the production response. However, a majority of the production data misfit reduction occurs during the travel-time inversion, and most of the large-scale features of heterogeneity are resolved at this stage.9,10
There are several advantages associated with a travel-time inversion of production data.14,15 First, it is robust and computationally efficient. Unlike conventional "amplitude" matching, which can be highly nonlinear, it has been shown that the travel-time inversion has quasilinear properties.9-11,14,15 As a result, the minimization proceeds rapidly even if the initial model is not close to the solution. Second, the travel-time sensitivities are typically more uniform between wells compared with "amplitude" sensitivities that tend to be localized near the wells. This prevents overcorrection in the near-well regions.14 Finally, during practical field applications, the production data are often characterized by multiple peaks (for example, tracer response). Under such conditions, the travel-time inversion can prevent the solution from converging to secondary peaks in the production response.9,10
In this paper, we utilize concepts from wave-equation traveltime tomography to propose a generalized travel-time inversion method for production data integration into high-resolution reservoir models. Our approach is motivated by the work of Luo and Schuster15 in the context of seismic waveform inversion, and is particularly well-suited for large-scale field applications with gravity and changing field conditions arising from infill drilling, pattern conversions, and other operating constraints, such as rate changes, well shut-in, etc. The approach is very general, robust, and computationally efficient. It actually reduces the previously proposed two-step inversion (travel time and amplitude) into a single-step procedure while retaining most of the desirable features of the travel-time inversion. Most importantly, we can compute the sensitivities of the generalized travel time with respect to reservoir properties analytically using a single forward streamline simulation.
The organization of our paper is as follows. First, we outline the major steps of the proposed generalized travel-time inversion and illustrate the procedure using a synthetic example. Next, we discuss the underlying mathematical formulation, including the concept of a generalized travel time, the sensitivity computations for the generalized travel time, and the production data integration procedure. We also show the relationship between our proposed generalized travel-time inversion and the more traditional amplitude inversion. Finally, we demonstrate the power and computational efficiency of our approach by applications to synthetic and field examples.
|File Size||8 MB||Number of Pages||14|