Development of a Fully Coupled Two-phase Flow Based Capacitance Resistance Model CRM

Abstract

The capacitance resistance model (CRM) has become a popular complement to real time reservoir analysis and improved oil recovery in water and CO2 floods. However, the current CRM model is based on a material balance of the total fluid and only the pressure propagation equation is considered. Saturation changes are also important, especially when the water cut is small. To overcome this limitation, this paper proposes a coupled CRM model based on two-phase flow by incorporating an oil material balance and fractional flow theories. In the coupled CRM model, we construct material balances on both total fluid and oil. Pressure and saturation equations are updated at each time step to account for changes of total mobility. By semi-analytically coupling the pressure and saturation in a producer-based control volume and using constrained multivariate nonlinear regression, the new coupled model can quantify the inter-well connection as well as the oil saturation. As a result, the coupled CRM model can be applied to the whole time frame of water and gas floods, not limited to late time (large water cut) cases as was the current CRM model. This new CRM model is validated in heterogeneous synthetic fields using a conventional reservoir simulator. Case studies show that the saturation profile from the coupled CRM model matches very well with the simulation results. The connectivities obtained from the coupled CRM model correspond well with the field geology and the time constant for each producer is also changing reasonably with the total mobility. Validation of both total production and oil production rates showed that relative errors are very small. With estimated parameters from a waterflood, the model found an optimal injection strategy to maximize the field total oil production. By incorporating the saturation variations to model two-phase flow, the coupled CRM model successfully overcomes the limitation of the previous version. It is able to extend the CRM model from mature water floods to immature water floods, which makes the CRM model more adaptable to different field cases. The coupled CRM model also improves the quality of the prediction of the oil rate significantly, especially for immature water floods. This work can lead to a more informed workflow of optimizing injection scheme, and serve the goal of improving ultimate oil recovery.

History Matching and Rate Forecasting in Unconventional Oil Reservoirs With an Approximate Analytical Solution to the Double-Porosity Model

“…The definition of the time constants in the approximate analytical solution is identical in definition to that defined in the capacitance/resistance model (CRM); one can find details about the CRM in Sayapour (2008), Nguyen (2012), and Cao et al (2014). As a result, we conclude that it has a similar physical meaning.…”

“…The parameters in the solution are now time constants and transmissibilities, not pore volumes (PVs) and permeabilities, as in the original problem statement. Cao (2014) presented a detailed discussion of the physical meaning of time constants for immature and mature waterfloods; in this study, these time constants are for primary recovery and, physically, they indicate how fast the volumes in each compartment would be drained. The index n in Eqs.…”

“…As a result, we conclude that it has a similar physical meaning. In the CRM, Nguyen (2012) and Cao et al (2014), following the work of Seborg et al (2003), defined the time constant to be the time it takes for 63.2% of a pressure pulse input to be observed as the output. The input pulse for our model would be the pressure difference that is responsible for flow.…”

“…Since then, many authors (de Swaan-O. 1976;Ozkan et al 1987;Carlson and Mercer 1991;El-Banbi 1998;Mayerhofer et al 2006) have presented applications of the model. All the analytical solutions presented were in Laplace space and have had to be numerically transformed to real-time space with some form of inversion algorithm of which the Stehfest algorithm (Stehfest 1970) is the most popular.…”

An approach to modeling production decline in unconventional reservoirs

“…This definition is identical to that used in the capacitance-resistance model, espoused by Sayarpour et al (2009), Nguyen (2012, Cao et al (2014).…”