Reservoir simulation

Spatiotemporal Clustering-Based Formulation Aids Multiscale Modeling

In the complete paper, a novel hybrid approach is presented in which a physics-based nonlocal modeling framework is coupled with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs.


In the complete paper, a novel hybrid approach is presented in which a physics-based nonlocal modeling framework is coupled with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. The research adds to the literature by presenting a comprehensive work on spatiotemporal clustering for reservoir-studies applications that considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome.


History matching is the most time-­consuming phase in any reservoir-simulation study. As a means of accelerating reservoir simulations, a 2018 study proposed an approach in which a reservoir is treated as a combination of multiple interconnected compartments that, under a range of uncertainty, can capture the reservoir’s response during a recovery process. In this work, the authors extend that approach to represent a reservoir in a multiscale form consisting of multiple interconnected segments. To identify segments of the reservoir, spatial, temporal, and spatiotemporal unsupervised data-mining clustering techniques are used. Then, a novel nonlocal formulation for flow in porous media is presented in which the reservoir is represented by an adjacency matrix describing the neighbor and non-neighbor connections of comprising compartments. The reservoir is divided automatically into distinct compartments in which direction-dependent multiphase-flow communication is a function of nonlocal phase potential differences. With the segmented reservoir and the uncertain parameters, a robust history-matching technique is used to reproduce the reservoir’s historical response. Finally, for the segmented and history-matched reservoir, forecasting is performed. The complete paper first describes the spatiotemporal clustering framework, followed by an overview of the compartmentalized reservoir simulation framework, in which multitank history material balance and multitank predictive material balance are explained. Next, the history-matching approach is described. These sections are not included in the current synopsis. The complete paper concludes with results of clustering, multitank material balance, and history matching for a real-world reservoir.

Results and Discussion

Case Study Reservoir. In this section of the complete paper, the modeling framework described in the previous sections is applied to a real-world reservoir. The procedures follow the steps presented in Fig. 1. The reservoir considered in this work is a mature field with more than 40 years of recovery. The field has 404 wells (340 producers and 64 injectors). The production from the reservoir includes both gas and oil, and the injections include both water and gas. Because of data-sharing policies, the authors are unable to present more details than those provided in the complete paper and have masked/normalized quantitative information.

Fig. 1—Flow chart showing the order of work flow steps from raw reservoir input data to reservoir history matching and forecast.


Spatiotemporal Clustering. In this section of the complete paper, the clustering framework is presented step by step. Both static and temporal features of both categorical and numerical data types are considered. Also considered are data including well type; wellhead location; number of perforations; history of gas, oil, and water production; history of gas and water injection; and pressure/volume/temperature measurements. Also, geological features are taken into account by the assignment of labels to each well for formation types and sealing faults. An effective separation of scales and behavior is achieved by temporal clustering; the time series in each cluster are similar in terms of the range of values and their overall transient behavior.

Multitank Reservoir’s History Material-Balance Results. The authors next present the multitank history material-balance results for the five-compartment clustered reservoir. Average properties of each block are calculated (e.g., porosity, initial saturations, and formation compressibilities) from available field data and geologists’ reports.

Multitank Reservoir’s History-Matching Results. Because uncertainties attributed to the inputs of the ­material-balance approach exist, global history matching using available production data, injection data, and reservoir pressure is performed. The following are considered to be the uncertain parameters of history matching:

  • Maximum volume of water encroachable from the aquifer in each block
  • Transmissibility between connected blocks
  • Maximum transmissibility used for scaling
  • Initial oil in place for each compartment

The overall mean squared error of the pressure mismatch in each compartment between the multitank material balance and the actual field data is set as the objective function of history matching. The authors consider five to 10 ensembles, each with 50 to 100 ensemble members, and set 0.1 to 1% as the threshold of change for both objective-function and uncertain parameter value between two consecutive iterations as the termination criterion. Also, the ratio of the initial measurement error to the maximum observation is considered to be less than 1%. By starting with a range of uncertainty in each block, as history matching progresses for a few iterations, the original oil in place values converge.
Pressure solutions from the multitank material-balance approach after history matching the uncertain parameters are compared with the field’s historical average pressure in each block. Considerable improvements are gained through history matching the uncertain input parameters in the multitank material-balance approach, which has led to a decrease in the overall pressure mismatch by one order of magnitude.

Multitank Reservoir’s Predictive ­Material-Balance Results. After history matching the uncertain parameters of the multitank history material balance, a forecast is performed on the basis of the future recovery plans for the reservoir. To illustrate the robustness of the forecast approach, a validation test is performed. For the validation test, historical data available from the reservoir are used and a blind test analysis is performed in which the last 10% of the history is masked. The assumption is made that only the first 90% of the history is known. Then, knowing the reservoir parameters in the last timestep of the validation-history region, a forecast is performed with the known recovery plan of the reservoir. For the forecast’s validation test, the authors used the same five-compartment clustered reservoir featured earlier in the complete paper. The Jacobian matrix is dominantly block-diagonal with a few nonzero off-diagonal terms as a result of the nonzero pressure derivatives with respect to neighboring blocks. The compactness of the Jacobian matrix is achieved because of an optimal ordering of unknowns. The complete paper presents the results for the forecast validation test where the last 10% of the historical data is masked and compared with the forecast pressure solution for the five-compartment clustered reservoir. The significant agreement of the forecast results with field data shows the robustness and accuracy of the proposed forecast framework.


In this work, the reservoir is represented as a network of discrete compartments with neighbor and non-neighbor connections for a fast, accurate modeling of oil and gas reservoirs. A key element of such high-level reservoir analysis is the automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties. The authors present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. A nonlocal formulation for flow in porous media is presented in which the reservoir is represented by an adjacency matrix describing the neighbor and non-neighbor connections of comprising compartments. The reservoir is clustered into distinct compartments, in which the direction-dependent multiphase flow communication is a function of nonlocal phase potential differences.

The proposed framework was applied successfully to a major field with hundreds of wells and a long production history. Leveraging the fast-forward model, an efficient ensemble-based history-matching framework was applied to reduce the uncertainty of the global reservoir parameters, such as interblock and aquifer/reservoir communications, fault transmissibilities, and oil-in-place values per block. The ensemble of history-matched models was then used to provide a forecast for different field-development scenarios.

The proposed framework can be applied to fractured reservoirs as a special case of multitank material-balance formulation, where multiple tanks can account for matrix and fracture components with arbitrary connectivity configuration. Furthermore, the proposed framework can be applied to 3D network models where gravity effects are significant, accounting for both pressure-driven and gravity-driven flows.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 195329, “A General Spatiotemporal Clustering-Based Nonlocal Formulation for Multiscale Modeling of Compartmentalized Reservoirs,” by Soheil Esmaeilzadeh, Stanford University, and Amir Salehi and Gill Hetz, Quantum Reservoir Impact, et al., prepared for the 2019 SPE Western Regional Meeting, San Jose, California, 23–26 April. The paper has not been peer reviewed.