The application of the Least-Squares Monte Carlo (LSM) algorithm in the oil and gas industry is increasing. Its use with a production model has been demonstrated to be insightful by Hong et al. (2018) in terms of optimizing the initiation time of an Improved Oil Recovery (IOR) process. This demonstration also reflects the application of decision analysis (DA) in solving the IOR initiation time problem, which is a sequential decision problem in reservoir management. In this context, DA provides a framework that can systematically address the sequential decision problem in reservoir management and generate insights in reservoir decision making.
The production model used in Hong et al. (2018) was the two-factor production model, which is developed by Parra-Sanchez (2010). This production model is a decline curve-based model and thus, it is computationally attractive. Additionally, it is formulated in terms of the recovery factor of a recovery phase. In this context, for each phase, this model depends on two parameters, namely theoretical ultimate recovery factor and time constant (Parra-Sanchez, 2010). Aside from this, pertaining to the use of LSM algorithm, the state variables used are generally modeled as Markovian processes (Longstaff and Schwartz, 2001; Smith, 2005; Willigers and Bratvold, 2009). However, in Hong et al. (2018), the state variable cannot be modeled as a Markovian process (the measured oil production rate is used as a state variable in this case and the details will follow later). Therefore, Hong et al. (2018) have slightly modified the LSM algorithm to handle non-Markovian processes.
The modified LSM algorithm used by Hong et al. (2018) as well as in this work is an approximate dynamic programming (ADP) approach that can provide a near-optimal solution to the IOR initiation time problem. The need for approximation stems from the fact that dynamic programming (DP) suffers from the curse of dimensionality when the state space grows. We call this ADP as a Sequential Reservoir Decision Making (SRDM) approach. SRDM is also referred to as a method in which future learning is considered in reservoir decision making. Besides that, for any sequential decision problem, taking uncertainty and information into account is important to support a person’s decision making. Regarding this, Closed-Loop Reservoir Management (CLRM) has been a state-of-the-art method to solve the IOR initiation time problem. However, in this context, CLRM yields a suboptimal solution as compared to SRDM. This is because CLRM only considers outcomes and decisions based on current information whereas SRDM considers outcomes and decisions based on current and future information (Hong et al., 2018). In other words, as compared to CLRM, SRDM captures the additional value of learning. In this aspect, the value of learning can be estimated by the Value-Of-Information (VOI) framework, which is a robust tool used for decision analysis (Hong et al., 2018).
There are several works done and presented for discussion. These include the replication of the use of the two-factor production model with the modified LSM algorithm as shown in Hong et al. (2018). Its purpose was to develop the present author’s understanding and validate the implementation of the modified LSM algorithm. A sensitivity analysis was conducted to verify if using a richer (more terms as well as nonlinear terms) regression function in the modified LSM algorithm would provide significant improvements to the results. Then, sensitivity analysis on certain parameters related to the algorithm was also performed to generate some useful insights regarding the IOR initiation time problem. This work was also adding to the work by Hong et al. (2018) by including the uncertainties in economic parameters in the modified LSM algorithm that was not done in Hong et al. (2018). Additionally, the application of this modified algorithm with a reservoir simulation model was illustrated. This brief illustration aims at showing the applicability of the modified LSM method with a different type of production model and providing a foundation on which further works can be developed upon.