Mouin Almasoodi^{1}, Thad Andrews^{1}, Curtis Johnston^{1}, Mark McClure^{2}, and Ankush Singh^{2}

^{1}Devon Energy, ^{2}ResFrac Corporation

**Introduction**

This blog post summarizes a new procedure for interpreting interference tests in shale. The full procedure and a detailed writeup are provided by Almasoodi et al. (2023).

Interference tests are one of the most effective diagnostics for assessing communication between neighboring wells. This information is critical for optimizing completion design and well spacing.

In a typical interference test, one or more wells are progressively put on production, and pressure is measured in one or more shut-in offset wells. After each well is put online, the pressure changes in the offsets well(s) are analyzed to assess the degree of connectivity. If different interference tests are performed between wells at different distances, it is possible to infer the drainage region.

Very often, the Chow Pressure Group (CPG) procedure is used to analyze interference tests (Chu et al., 2020; Miranda et al., 2022). The method fits a power law equation to the deflection in the pressure trend and relates the power law exponent to the “CPG” parameter. The CPG parameter usually varies between 0 and 1, with higher values indicating greater interference.

A drawback to the CPG procedure is that it does not quantitatively relate interference to production interference. If the CPG measurement is 0.65, precisely how much production impact does that imply? Is the answer always the same, or does it depend on reservoir specific parameters?

To address this issue, we took a fresh look at shale interference testing, and devised a new procedure, which we call the ‘Devon Quantification of Interference’ (DQI) method. The procedure starts by estimating the hydraulic diffusivity of the connection between the wells, based on the early-time pressure interference response. Based on the diffusivity, the fracture conductivity is estimated. Finally, based on an appropriate scaling between variables, the fracture conductivity is used to estimate the “Degree of Production Interference (DPI),” which quantitatively predicts the amount that production is reduced because of interference from the offset well. The DQI aims to provide subsurface engineers with a practical procedure to maximize the value of downhole pressure gauges by linking the degree of interference to the DPI.

We ran a large number of simulations, varying reservoir and well spacing parameters, and found that the DQI procedure was able to accurately predict the DPI in all cases. There are a few key reasons why the DQI procedure is effective: (a) it uses the early-time interference response, which is relatively robust to nonlinearities and uncertainties related to flow regime, boundary condition, and physics; and (b) it correctly captures the scaling between fracture conductivity and other variables during production in shale.

**The DQI Procedure**

The figure below shows an actual field interference test. Panel (a) shows how the pressure trend prior to the start of the interference test can be extrapolated to estimate dP. Panels (b) and (c) show log-log derivative plots of dP and t*dP/dt. Panel (c) shows how the hydraulic diffusivity can be estimated from the plot. The black and blue lines correspond to the analytical solution to the 1D diffusivity equation, as seen from an offset observation point.

After the initial response to interference, the pressure trend can be affected by a variety of nonlinearities, by changes in flow regime, and changes in the BHP at the production well over time. However, the initial response is robust to these changes. Thus, the focus is to match the earliest part of the response.

This equation relates hydraulic diffusivity to fracture conductivity:

To perform the conversion, we need an estimate for crack aperture, *W*, and the derivative of aperture with respect to pressure, dW/dp. When performing the calculation, we assume reasonable ranges for these quantities, but this is a potential source of uncertainty.

Once we have estimated conductivity, we can estimate the ‘degree of production interference’ between the wells. We define DPI as:

In other words, we ask – if the offset well was shut-in, what would be the relative impact on production? A DPI of 0.2 implies a 20% increase in production; a DPI of 1.0 implies a doubling of production.

We ran a wide variety of simulations, using different fluid viscosity and compressibility, formation permeability, well spacing, and BHP at the production well over time. For each simulation, we simulated both: (a) a conventional interference test, and (b) shut-in of one of the wells for 20 days to directly observe the DPI. Then, we sought to identify a quantity that would relate fracture conductivity to DPI.

First, we tested the classical definition of ‘dimensionless fracture conductivity,’ *F _{CD}*, using the well half-spacing as the fracture ‘half-length’ in the equation.

*F*is defined as:

_{CD}The figure below shows the result. While there is a relationship between *F _{CD}* and DPI, there is clearly significant scatter. For example, we observe that changing fluid viscosity and compressibility results in large variance in DPI. But fluid properties are not considered in the definition of

*F*.

_{CD}The variance can be explained by considering the underlying meaning and derivation of *F _{CD}*.

First, let’s write Darcy’s law to relate the flow rate and pressure drop down the fracture:

Next, from the analytical solution for radial flow, let’s write the scaling between pressure drop *in the reservoir* and flow rate:

Setting the radial flow rate equal to the fracture flow rate, and solving for the ratio of Δp_{radial} and Δp_{fracture} yields:

Thus, we see that *F _{CD}* can be interpreted as being proportional to the relative pressure drop in the reservoir versus in the fracture. If dimensionless fracture conductivity is low, then most of the pressure drop will occur in the fracture; if it is high, then most of the pressure drop will occur within the formation. However, it is critical to observe:

*this interpretation of F*

_{CD}is only theoretically valid if there is radial flow.If we repeat the derivation assuming *linear* flow geometry in the formation around the fractures, which is appropriate for shale, then we arrive at a different equation:

This equation can be used as the basis for an estimate of DPI in shale.

We set *F _{CD,linear}* to an arbitrary number (1.0) and rearrange the equation to solve for

*L*, and then divide by the actual half-spacing between the wells. This yields a definition for a ‘dimensionless drainage length:’

Then, we run a variety of simulations in order to empirically observe the relationship between *L _{D}* and DPI. The figure below shows a crossplot between DPI and

*L*, using simulations with a variety of different settings.

_{D}With this new scaling, we find that all the simulations collapse onto a single curve!

In practice, we can use this curve to estimate DPI. Once we have estimated hydraulic diffusivity and conductivity from the interference test, we calculate *L _{D}* and then use the figure above the estimate the corresponding value of DPI.

The DPI estimate requires knowledge of formation permeability and fluid properties, which are usually available. Fluid properties must be estimated considering multiphase effects – this topic is addressed in the appendix to Almasoodi et al. (2023).

**Future work**

There are several remaining issues that need to be resolved in future work:

- The simulations performed by Almasoodi et al. (2023), which are used to relate
*L*to DPI (as shown above) assumed only two, unbounded fractures. With different fracture geometries, the actual DPI could be different. We need to determine a more general way of calculating DPI for any geometry._{D} - The simulations relating
*L*to DPI assumed that the conductivity is uniform along the length of each fracture, and is uniform between the various fracture connecting the well. We need to assess the potential impact of conductivity heterogeneity on the quantitative estimation of DPI._{D} - When interference tests are performed when wells are first ‘put on production,’ fracture conductivity is much higher than when they are performed after months of production. Thus, the DPI for early production will be much higher than during long-term production. We need empirical comparison to estimate how much conductivity decreases during long-term production, so that we can relate initial POP interference tests to long-term interference.
- In Almasoodi et al. (2023), we test the DQI procedure on actual interference tests, and the results appear reasonable. Nevertheless, because this is a new procedure, more testing against field data is needed. In particular, we would like to find datasets where wells are shut-in for days to weeks, in order to compare the estimated DPI with the actual observed DPI.

**References**

Almasoodi, Mouin, Thad Andrews, Curtis Johnston, Ankush Singh, Mark McClure. 2023. A new method for interpreting well-to-well interference tests and quantifying the magnitude of production impact: Theory and applications in a multi-basin case study. arXiv:2302.01968.

Chu, W. C., Scott, K. D., Flumerfelt, R., Chen, C., & Zuber, M. D. 2020. A New Technique for Quantifying Pressure Interference in Fractured Horizontal Shale Wells. SPE Reservoir Evaluation & Engineering, 23(01), 143–157.

Miranda, C., Cipolla, C., & Murray, M. 2022. Analysis of Well Interference Tests in the Bakken Shale, a Fully Communicated System. Paper URTeC-3717749-MS presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, TX.