Integrating Dynamic Data Into High-Resolution Reservoir Models Using Streamline-Based Analytic Sensitivity Coefficients
- D.W. Vasco (Berkeley Laboratory) | Yoon Seongsik (Texas A&M U.) | Akhil Datta-Gupta (Texas A&M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 1999
- Document Type
- Journal Paper
- 389 - 399
- 1999. Society of Petroleum Engineers
- 5.8.7 Carbonate Reservoir, 5.1.8 Seismic Modelling, 5.1.5 Geologic Modeling, 5.3.2 Multiphase Flow, 7.6.2 Data Integration, 5.1.1 Exploration, Development, Structural Geology, 5.5.8 History Matching, 5.7.2 Recovery Factors, 4.3.4 Scale, 5.5 Reservoir Simulation, 5.6.5 Tracers, 5.5.7 Streamline Simulation, 5.1 Reservoir Characterisation, 5.6.1 Open hole/cased hole log analysis, 5.6.4 Drillstem/Well Testing
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One of the outstanding challenges in reservoir characterization is to build high-resolution reservoir models that satisfy static as well as dynamic data. However, integration of dynamic data typically requires the solution of an inverse problem that can be computationally intensive and becomes practically infeasible for fine-scale reservoir models. A critical issue here is computation of sensitivity coefficients, the derivatives of dynamic production history with respect to model parameters such as permeability and porosity.
We propose a new analytic technique that has several advantages over existing approaches. First, the method utilizes an extremely efficient three-dimensional multiphase streamline simulator as a forward model. Second, the parameter sensitivities are formulated in terms of one-dimensional integrals of analytic functions along the streamlines. Thus, the computation of sensitivities for all model parameters requires only a single simulation run to construct the velocity field and generate the streamlines. The integration of dynamic data is then performed using a two-step iterative inversion that involves (i) "lining up" the breakthrough times at the producing wells and then (ii) matching the production history. Our approach follows from an analogy between streamlines and ray tracing in seismology. The inverse method is analogous to seismic waveform inversion and thus, allows us to utilize efficient methods from geophysical imaging.
We have applied the proposed approach to a highly heterogeneous carbonate reservoir in west Texas. The reservoir model consists of 50,000 cells and includes multiple patterns with 42 wells. Water-cut histories from 27 producing wells are utilized to characterize porosity and permeability distribution in the reservoir, a total of 100,000 parameters.
It is now well-recognized that integration of dynamic data is a critical aspect of reservoir characterization. Dynamic data such as transient pressure response, tracer or production history can be particularly effective in identifying preferential flow paths or barriers to flow that can adversely impact sweep efficiency. The past few years have seen significant developments in the area of dynamic data integration through the use of inverse modeling.1-5 However, inverse problems are computationally intensive and require many solutions of the flow and transport problem. Gradient based methods are commonly used to solve the inverse problem and a critical aspect here is the computation of sensitivity coefficients or the state variable derivatives. That is, we must compute the change in the production response induced by small deviation in subsurface properties such as porosity and permeability. Although derivative-free approaches such as simulated annealing and genetic algorithms have been applied to the data integration problem, these methods become computationally prohibitive for large-scale problems involving thousands of parameters.
Recent developments in reservoir characterization have made it fairly routine to generate fine-scale reservoir models consisting of several hundred thousand grid blocks. Integration of dynamic data into such high-resolution models still remains an outstanding challenge. Use of fast streamline-based simulation techniques offers significant potential in this respect.6,7 Our previous work has utilized streamline simulation in conjunction with the pilot point approach to incorporate multiphase production data into reservoir models.8 The model sizes were limited to less than 5,000 grid blocks because of computational costs. Here we extend our approach for dynamic data integration into model sizes that are larger by an order of magnitude without any additional computational efforts.
Streamline models can be advantageous in two ways. First, the streamline simulator can serve as an efficient "forward" model for the inverse problem. Second, and more importantly, we show here that parameter sensitivities can be formulated as one-dimensional integrals of analytic function along streamlines. The computation of sensitivity for all model parameters then requires a single simulation run to construct the model parameter sensitivities. Our approach follows from an analogy between streamlines and ray tracing in seismology since the transport equation can be cast in the form of the Eikonal equation,9 the governing equation for travel time tomography. We can then use efficient inversion techniques from geophysical imaging for integration of dynamic data. We illustrate our approach by application to synthetic and field examples. The synthetic example involves integration of tracer response and multiphase production history into reservoir characterization. The field example is from the North Robertson Unit, a low permeability carbonate reservoir in west Texas. Water-cut histories from 27 producing wells are utilized to characterize porosity and permeability distribution in the reservoir to demonstrate the feasibility of our approach for large-scale field applications.
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