The Quick Sketch Approach to Manage Complex Systems
Ajay Ganesh, University of Alberta firstname.lastname@example.org
Keywords: complex systems, petroleum reservoirs, proxy/surrogate models, system management
Are you familiar with a crime investigation TV series or a movie where the culprit runs away, leaving behind little clues for the police to trace the crime? I was reading a crime investigation news report in the Canadian Broadcasting Corporation (CBC) website, which reported an incident where the culprit ran away with a big lump sum amount of money stolen from a stall in a Farmers' market in Lancaster. The police used something called the quick sketch made by the professional artists upon hearing the details of the culprit from the eye witnesses and successfully caught the perpetrator. This incident is an example of using a representative model  when the actual one is not available or not feasible to work with .
My research doesn’t deal with culprits but rather petroleum reservoirs. The quick sketch idea can be eloquently extended into the reservoir engineering practice; we refer such engineering models as proxy / surrogate models. My research focuses on developing a proxy model based management strategy  for the petroleum reservoir. Petroleum reservoirs are a multi-phase (solid, liquid and gas), three-dimensional (length, breadth and height) irregular shaped complex system. To model them exactly using physics is a computationally demanding task even in a high end computer. This limits the usage of physics based models in reservoir management. The problem now is to find a suitable alternative mathematical modelling approach  to tackle these problems.
Complex systems can also be modelled using the historical, experimental or computer simulation data. Techniques based on statistical data analysis and artificial intelligence are at the heart of proxy modelling. Proxy modelling is the viable option in complex systems management. Using the available field and production data, a proxy model is built and used in the optimization process to make decisions for the system management. Proxy models are updated as soon as a new set of data is fetched from the complex system to make better future decisions, making it a closed loop interactive process as shown in the Figure.
Proxy modelling finds applications in various fields which include but are not limited to: safety assessment of reservoir operation , ocean modelling , atmosphere modelling for weather forecasting, electrical power transmission network modelling, corporate assets and liability assessment and so on. All these applications are typically large scale and complex in nature and proxy modelling gives a computationally affordable solution in their management.
Quick sketch models are ubiquitous and we have our own quick sketch models of the reality around us. Be it modeling the traffic flow while driving, employing intricate culinary techniques while cooking or while carefully sipping a hot beverage. Using quick sketches and learning to update them is an essential part and parcel of our day today life.
[*] Pump jack and the panel images taken from open source image website unsplash.com.
 Forrester A, Keane A. Engineering design via surrogate modelling: a practical guide. John Wiley & Sons; 2008 Sep 15.
 Zubarev DI. Pros and cons of applying proxy-models as a substitute for full reservoir simulations. InSPE Annual Technical Conference and Exhibition 2009 Jan 1. Society of Petroleum Engineers.
 Vembadi SS, Patel RG, Trivedi JJ, Prasad V. Real‐time feedback control of SAGD wells using model predictive control to optimize steam chamber development under uncertainty. The Canadian Journal of Chemical Engineering. 2018 Jun; 96(6):1290-305.
 Heijn T, Markovinovic R, Jansen JD. Generation of low-order reservoir models using system-theoretical concepts. InSPE Reservoir Simulation Symposium 2003 Jan 1. Society of Petroleum Engineers.
 Azad A, Chalaturnyk R, Movaghati S. Reservoir Characterization: Application of Extended Kalman Filter and Analytical Physics-Based Proxy Models in Thermal Recovery. InProc., International Association for Mathematical Geosciences Conference—IAMG 2011.
 Webster MD, Tatang MA, McRae GJ. Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model.