We are starting a new blog post series, on Rate Transient Analysis (RTA) in Spotfire. In this first part we will discuss a mathematical framework to automate the flow regime detection in RTA. Unlike traditional reservoir engineering methods such as Decline Curve Analysis (DCA), RTA incorporates both fluid rates and flowing pressures, where the end goal is to understand the fluid flow in the reservoir. The industry has been doing this with Pressure Transient Analysis (PTA) for many years and RTA is built on the same theory, we are just using the data in a different way. I will refer you to the excellent presentation by Blasingame as a refresher on the fundamental theory for RTA. Following figure represents the important flow regimes in a Multi Fractured Horizontal Wells (MFHW) in conventional/unconventional reservoirs:
Blasingame (2015). Image Source: http://www.pe.tamu.edu/blasingame/data/z_Presentations/20151209_(Blasingame)_Pres_IPTC_Ask_the_Expert_(pdf).pdf
In this blog post we will jump straight to the problem of auto detecting the flow regime change points. We begin by defining the Pressure-normalized rate as a first -order continuous linear piecewise function of time on a log-log scale:
We are trying to estimate the breakpoints tbp1 and tbp2 where the flow regime changes. Also, to ensure first order continuity, we need to satisfy the following conditions:
These continuity conditions allow us to re-parameterize the piecewise function with breakpoints tbp1
and tbp2, now we can define an optimization problem either using a slope-based setup or an intercept-based setup.
Now we want to constrain the m1, m2, m3 to the values of -0.25, -0.5 and -1 representing the flow regimes of Bilinear Flow, Linear/Transition Flow and Boundary Dominated Flow (BDF). Therefore, we will use the slope-based setup.
Also notice the recursion in the above equations, which suggests how this setup could be extended to more segments in a linear piecewise model.
The following graphic shows a great demonstration of how the optimization loop is trying to fit the data in our problem:
We created a Spotfire template which incorporates this methodology to autodetect the flow regime changes mathematically. You can load data for as many wells as you want, run them in batch and visualize the results. You can visit the Exchange.ai website to download the Spotfire template. Shoot us an email if you are not able to access the template.
In the next blog post we will present an analysis using Spotfire on Eagleford wells to show a spatial analysis of the timing when linear flow ends.