CRM-Aquifer-Fractional Flow Model to Characterize Oil Reservoirs with Natural Water Influx
Authors: Parra José E. , Samaniego-V. Fernando , Lake Larry W. 
Published: September 2023

Summary
This work presents a new flow model that uses production data to characterize conventional undersaturated oil reservoirs with natural water influx in primary production. The main application is to estimate the original oil in place (OOIP), but the model also calculates the productivity index (PI), water influx, and heterogeneity factor.
Aquifers are common to many reservoirs and their diagnosis is relevant because they can serve as an important drive mechanism but can also affect well productivity. Discerning between the reservoir and aquifer volumes is also a major challenge in many oil fields.
Reservoir-aquifer systems have been investigated with various dynamic characterization techniques such as the material balance equation (MBE), pressure transient analysis, and production/rate transient analysis. These methods have limitations, for example, requiring shut-in wells and/or very large production histories and high mobility and compressibility ratios to yield distinguishable responses in the diagnostic plots.
The new flow model couples the producer-based capacitance resistance model (CRMP) with the Fetkovich aquifer model (CRMPA). It enables calculating the total instantaneous production flow rate from a well as a function of three mechanisms—reservoir depletion, changes in bottomhole pressure (BHP), and water influx. In addition, CRMPA is coupled with the Koval fractional flow model (capacitance resistance aquifer-fractional flow model, CRMPAF) to calculate the individual oil and water rates and to enhance the OOIP estimation for wells with two-phase production caused by water breakthrough from the aquifer.
The capacitance resistance model (CRM) is a production analysis technique that uses rate and pressure data from typical field surveillance (no dedicated tests) to characterize reservoir properties. It has been widely used to study reservoirs under secondary and tertiary recovery. There are a few applications for primary recovery, and only one reference investigated natural water influx.
There are important differences between the previously published and the new CRMPA formulations. The former estimated the individual water influx to each well in a multiwell reservoir associated with an aquifer. The calculations were performed assuming the reservoir pore volume (PV) was known, whereas the present approach simultaneously calculates the PV and the water influx. The former approach also required a priori knowledge of the average pressure, obtained from buildup tests, whereas the new method uses production data, (i.e., it does not require shut-in wells).
In the new approach, CRMP (without aquifer) is first used to calculate the capacitance/resistance (CR) parameters of the equivalent (reservoir-aquifer) medium. It provides the correct OOIP for volumetric reservoirs; however, CRMPA is used when the PV significantly differs from volumetrics and water influx is detected. CRMPA calculates the reservoir CR parameters using simple relationships between the equivalent and composite mediums. For wells with two-phase production, the Koval factor is an additional parameter. The CRMPA/F solution is obtained by minimizing the errors between the calculated and measured rates over a time window.
The new CRMPA/F approach is compared and validated with several models of single and multiwell synthetic reservoir-aquifer systems with different properties and geometries. It is also used to characterize a field case.