Calibration of Wellbore Pressure During and After Fracturing


The typical ResFrac workflow is: (1) set project goals and scope, (2) gather relevant data, (3) build an ‘initial model’ of fracturing and production, (4) calibrate the model to data, and (5) run alternative scenarios to optimize economic performance. During model calibration, we match to injection pressure (during and after injection), production data, and any other additional calibration data. This ‘additional calibration data’ is often very detailed, and may include fiber optic in the injector well, fiber optic in offset wells, microseismic, geochemistry, interference tests, tracer tests, frac hit data, sealed well pressure responses, and/or downhole imaging.

We recommend history matching to ‘typical’ behavior, rather than trying to ‘match every single wiggle’ in the data from every single stage. We are usually trying to build a calibrated model that is representative of a ‘typical’ stage in order to optimize production of future wells. Small differences between stages probably aren’t important from the perspective of optimizing the design in the next pad, and we risk a nonunique model overfit if we try to calibrate to every little detail.

More broadly, we need to address: which data is important to match and which isn’t? How accurate and precise should we consider different types of data, and how much do the different model parameters matter for the purposes of optimizing fracture design?

I advise calibration to match ISIP, and optionally, calibration to match the trend in pressure versus time during the 5-10 min after shut-in (if available). I typically advise against a detailed match to the entire WHP response versus time during injection. WHP matching has roots in the ‘net pressure analysis’ from Nolte/Smith. Trouble is, in a horizontal well, there are so many different things that could be changing simultaneously to impact WHP. Are the fractures growing into different zones with different stresses? Changes in perf friction from erosion or changes in perf erosion? Changes in near-wellbore tortuosity? Changes in wellbore friction? Changes in net pressure from height growth?  Randomness caused by the idiosyncrasies of fracture geometry during simultaneous propagation of an array of cracks? Lots of possible explanations for subtle trends in WHP – which makes it hard to arrive at a unique interpretation. Nevertheless, I do recommend a loose calibration to WHP during injection, to make sure that the model is in the ballpark.

Remember, when a service company provides BHP during fracturing, this is nearly always a calculated BHP (not measured from a bottomhole pressure gauge). The BHP is calculated from adjusting WHP for hydrostatic and friction. Because of the non-Newtonian properties of the fluid, wellbore friction is a significant uncertainty and could cause significant error in the BHP calculation. Having said that, the service company is in a position to know the properties of the fluid that they are injecting, and so we usually start with the assumption that their BHP calculations are in the ballpark. After shut-in, friction goes to zero, and we can safely assume that the service company’s calculated BHP is accurate.

In this post, I go through basic relationships between variables in a pressure match. I discuss some of the strategies that we use for pressure matching, and try to impart intuition into how different physical processes affect the observations. This post is intended for a fairly informed reader. If you find that this post uses terminology/concepts that you are unfamiliar with, I recommend a general introductory textbook such as Hydraulic Fracturing, by Smith and Montgomery, which goes through the fundamentals. You could also refer to the recorded content from Day 1 of our ResFrac Fundamentals course. For a good discussion specifically on the topic of treating pressure analysis, refer to “Pressure-Based Diagnostics for Evaluating Treatment Confinement” by Cramer and Zhang (in press), or the Cramer et al. (2019) paper “Integrating DAS, Treatment Pressure Analysis and Video-Based Perforation Imaging to Evaluate Limited Entry Treatment Effectiveness.”

Relationships between variables

During injection:

WHP = Shmin + Net pressure + Near wellbore complexity + Perforation pressure drop + Wellbore friction – Hydrostatic head

WHP = BHP + Wellbore friction – Hydrostatic head

BHP = Shmin + Net pressure + Near-wellbore complexity + Perforation pressure drop

BHP = Pressure in the fractures + Near-wellbore complexity + Perforation pressure drop

Pressure in the fractures = Shmin + Net pressure

After shut-in, perforation pressure drop and wellbore friction quickly go to zero (within a couple minutes). Please note that I am using the term ‘near-wellbore complexity’ interchangeably with the term ‘mid-field complexity’. The near-wellbore complexity probably takes at least 10s of minutes after shut-in to dissipate, and so is not yet zero after only a few minutes of shut-in. Therefore, within a few minutes after shut-in:

WHP = Shmin + Net pressure + Near-wellbore complexity – Hydrostatic head

WHP = BHP – Hydrostatic head

BHP = Shmin + Net pressure + Near-wellbore complexity

BHP = Pressure in the fractures + Near-wellbore complexity

If you are trying to match a ResFrac simulation to pressure data, it helps open up the simulation in the 3D viewer and observe the magnitudes of these different parameters. For example, in the screenshot below, I plot WHP, BHP, ‘fracture pressure adjacent to the well’ in one of the fractures, and ‘well pressure adjacent to the fracture’ for that fracture. Both 3D visualization panels show pressure. In the panels, I’ve modified the color scale to emphasize different details of the distribution of pressure within the fractures and within the well. This is a snapshot early in the treatment, and the fractures are still quite small.

The lower left figure shows that there is about 800-1000 psi of pressure difference between the well and the fracture – this is near-wellbore and perforation pressure drop. The upper right figures shows the pressure gradient along part of the lateral. It shows considerable pressure gradient due to friction. The lower right figure shows the pressure distribution within the fractures. The fractures have different pressure – as much as a 500 psi difference. They all accept fluid injection, despite having different pressures, because of the near-wellbore and perforation pressure drop. There is a bit of pressure gradient in the fractures near the wellbore, and pretty minimal pressure gradient along the fractures. Vertical pressure gradient within the fractures is created by hydrostatic head.

After shut-in, it is common to see cross-flow between the fractures through the well. The fractures propagating at higher pressure flow back into the well, and then the fluid flows back out of the well into the fractures with lower pressure. This process allows the pressure to equilibrate. It is also possible to see communication back to the previous stage, either due to plug leakage or flow outside the casing. 

To estimate ‘net pressure’ you can use a stress observation plane to visualize the stress shadowing around the fractures, as shown in the figures below. Because there are multiple fractures, it becomes ambiguous how to define ‘net pressure.’ We could talk about the net pressure of an individual fracture (pressure minus local normal stress) or the net pressure of the fractures overall (pressure minus the initial Shmin prior to injection). In this case, let’s think about the ‘fractures’ as a single system. The ‘net pressure’ is equal to the amount of net stress that the fluid pressure is able to exert outwards to open the fractures. Force balance requires that the net pressure must be matched by the magnitude of the stress shadowing that pushes back on the fractures from the deformation of the rock.

We can estimate the net pressure by looking at a plot that shows stress shadowing (two examples are shown below, with different color scales to show different levels of detail). The stress shadow is reaching about 500-900 psi, and so 500-900 psi is the ‘net pressure’ of the fracture system. Fluid pressure exceeds Shmin by that amount, which is apparent if we compare the pressure in the fractures (8500-9000 psi) to the initial Shmin at the depth of injection (around 8000 psi). Note that because stress and pressure are both spatially variable, the concept ‘net pressure’ is rather approximate and heuristic; it does not have a precise meaning.

Matching to variables

When matching data, first focus on the ISIP and (if available) pressure in the minutes after shut-in. The ISIP at BHP equals Shmin + Net pressure + Near wellbore complexity. You can change one of those three things to get a match.

Changing Shmin linearly translates pressure up and down, the same at all points in time. Shmin should be calibrated by matching to a DFIT performed in a nearby well in the same geologic formation (because of formation dip, this is not necessarily the same depth). If you have a log-based stress estimate that hasn’t been calibrated to a DFIT, then the log estimate should be considered highly uncertain, and feel free to vary Shmin up or down in your model. If you have a DFIT calibration from nearby, then you can still vary Shmin to match data if unavoidable, but the DFIT stress estimate is less likely to be inaccurate. If inaccuracy does exist, this could be due to heterogeneity or because the tests weren’t actually performed in the same geologic interval.

Net pressure should usually be within the range of 500-1000 psi (but not necessarily; could be higher or lower). Net pressure is increased by increasing fracture toughness (either the base toughness or ResFrac’s relative fracture toughness scaling factor). Ideally, you should be to be tuning net pressure (and equivalently, toughness) to an estimate of full fracture length (from frac hits, microseismic, etc.). As a result, because you can constrain toughness/net pressure from these other data sources, it is probably not your best knob for matching ISIP.

If you have reliable Shmin estimates from DFITs (landed in the same zone), and you’ve calibrated toughness to match observed fracture length, then near-wellbore complexity is your best bet for matching ISIP. Very likely, if there is a mismatch after calibrating to fracture length and DFIT-measured Shmin, the observed ISIP is higher than the simulated ISIP, and you add near-wellbore complexity to match the data. The near-wellbore complexity scales with the square root of the flow rate (though you have an option to modify this exponent, if you choose). Even after shut-in, fluid flows out of the wellbore storage, and so there is still an ‘afterflow’ from the well after surface shut-in. This creates the near-wellbore tortuosity pressure drop. The near-wellbore complexity could be in the range of 0 to 2000+ psi – there’s a lot of variability in this parameter. 

In addition to ISIP, take a look at the rate that pressure falls off after shut-in. Even if you have 15 min of pressure data, this can be useful. Is the model matching that falloff rate? If not, the first option is to modify the near-wellbore pressure drop exponent. A lower exponent causes it to last longer. The second option is to modify the rate of fluid leakoff from the fracture. This can be accomplished by increasing the pressure dependent permeability.

After matching to ISIP and post shut-in data, you can modify the wellbore friction to match WHP. This is a bit of a cosmetic change, because changing wellbore friction doesn’t impact the fracture propagation and proppant placement of the simulation (unless it reaches your specified ‘maximum injection wellhead pressure’). So, because detailed matching of WHP during injection isn’t that useful as a model calibration step, I recommend doing the match only loosely and focusing your efforts on other more important things.

Wellbore friction is fairly uncertain. Classical pipe friction calculations are valid for Newtonian fluids, like water. In practice, we use non-Newtonian fluids such as slickwater, which have much lower wellbore friction. We do not have detailed correlations for these fluids (which are dependent on the specific formulation of the chemicals being pumped, and the water salinity). Instead, ResFrac provides a ‘wellbore friction adjustment factor’ that is multiplied by the wellbore friction calculated from a classical pipe friction calculation. This value defaults to 0.19, representing an 81% reduction in friction relative to a Newtonian fluid. This parameter may need to be adjusted to match a particular fluid.

ResFrac also uses a friction adjustment factor that accounts for the proppant concentration. Non-Newtonian pipe flow of proppant slurry is complex, and so this adjustment factor cannot be considered high precision. The code has a special “Wellbore proppant friction adjustment factor” that tunes that correlation up or down. It defaults to 1.0, to use the baseline correlation. But, for example, if you want to weaken the effect of proppant on friction, you could set to a number less than 1.0.

Proppant is denser than water. As proppant concentration increases in the wellbore, the overall slurry density goes up, which increases hydrostatic head. The increasing hydrostatic head tends to make WHP decrease as you inject proppant (if BHP remains constant). However, the increased friction may tend to make WHP increase as you inject proppant. The net effect could be an increase or decrease in WHP when you inject the proppant.

In ‘Pressure-Based Diagnostics for Evaluating Treatment Confinement’ by Cramer and Zhang (in press), they used a downhole pressure gauge during fracturing, and found that the vendor’s BHP calculations were inaccurate by as much as 800 psi. This finding underscores why we focus more effort on matching ISIP and post shut-in pressure data.

At very early time, you may see anomalously high WHP in real data. This happens because the near-wellbore tortuosity can be very high initially, before the fracture fully forms. There is a way to model erosion of NW tortuosity in ResFrac, but really, I recommend not bothering. It is early time, and doesn’t impact the main job, so it’s cosmetic to try to match it.

Perforation pressure drop also affects WHP during injection. But most of the time, this is not the best parameter to vary to match WHP during injection. It is a coarse tool to try to match WHP, and it is less uncertain than wellbore friction. Initial perforation pressure drop is relatively well constrained, although there is some uncertainty about whether the perfs have exactly the same diameter as designed. Perforation erosion is a greater source of uncertainty. But to constrain perf erosion, you would ideally use downhole imaging before and after the frac job (and in a perfect world, you would also have fiber in the injection well to observe flow distribution). For a great case study how to use downhole imaging to measure perf erosion, I recommend the Cramer et al. (2019) paper “Integrating DAS, Treatment Pressure Analysis and Video-Based Perforation Imaging to Evaluate Limited Entry Treatment Effectiveness.”

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