Optimization of Waterflooding Utilizing Data Driven Models: An Application of the Two-Phase Capacitance Resistance Model
Authors: Ghamdi Ahmed Alghamdi Abdullah , Opoku Daniel , Awotunde Abeeb , Mahmoud Mohamed , Liao Qinzhuo 
Published: October 2021

Abstract
The Capacitance-Resistance Model, commonly known as CRM, is a data-driven model derived from the material balance equation, and only requires production and injection data for history matching and prediction of reservoir performance. The CRM has two model parameters: The input and output are related the first parameter is the connectivity (also called gain, or weight), which is a dimensionless number that quantifies the connectivity between producers and injectors (i.e. how much of the input is supporting the output). The second parameter is the time delay (also called time constant) and is a function of pore volume, total compressibility, and productivity indices, and it represents the time it takes for the input (injection) to result in an output (production). Since the CRM inception in 2005, several authors have further developed it to increase its range of applications. When CRM was first introduced, it was suited most for single-phase reservoirs. A recent improvement of the CRM added two-phase capability. In this project, Two-phase CRM was utilized to test how this tool performed in waterflooding optimization.
The main hypothesis in CRM is that the several reservoir characteristics can be inferred from analyzing production and injection data only. These reservoir characteristics are the connectivity, which can be thought of as an analog to permeability, and the time constant, which is a measure of the pore volume and compressibility. CRM does not require core data, logs, seismic, or any rock or fluids properties. This hypothesis, that reservoir characteristics can be inferred from injection and production data, can be challenged easily since most reservoirs have gradients of fluid properties, multi-porosity systems, and heterogeneous formations with different wettability presences. Regardless, several publications have shown that CRM can result in high certainty output.
To test the two-phase CRM, three synthetic heterogeneous reservoirs were created. Model 1 was developed with nearly stabilized injection and production data. Model 2 had more fluctuations in the injection data than model 1. And model 3 had extreme fluctuations in injection data compared to model 2 with lower rock and fluid compressibilities.
The results presented in this project show that the CRM ability to match field production depends largely on two aspects: first is the compressibility of the system. When the compressibility was lowered in model 3, the CRM achieved excellent results. The second aspect is the degree of the fluctuations in injection rate the CRM is developed upon. Model 2 with a higher degree of injection rate fluctuations than model 1 has achieved a better future prediction performance.
CRM model 3 was used to optimize the field waterflooding injection rates subject to two constraints, The first constraint is a set value for maximum field injection rate at any time step while the second constraint limits each injector maximum injection rate. The optimization of the annual injection rates has added 290,000 bbls of oil produced.