Introducing StageOpt – State-of-the-Art Calculations for Optimizing Perforation Design

Mark McClure, Egor Dontsov, Kevin Torbert, Chris Ponners, Soma Medam, Charles Kang, and Tristen Lawrence

ResFrac Corporation


We have started building web apps! Our company is built around the ResFracPro simulator, which is the only commercial simulator that fully integrates genuine hydraulic fracture modeling and reservoir simulation. Now, we are broadening to build a complementary suite of apps – which we are called ‘ResApps.’ They are cloud-based and run in a web browser. Each ResApp is a focused tool that solves a key problem for engineers and geoscientists. They can be used independently, but as we build them out, our plan is for them to communicate with each other and with our flagship ResFrac simulator.

Licenses to ResApps are available in parallel to the ResFracPro simulator – you do not need to have a license to the simulator to acquire a license for a ResApp. Licenses are available on a per-user, per-year basis. Click here for information about how to log in to the ResApps portal and get set up with a license.

Over the past five and half years, we’ve performed over 90 simulation studies on behalf of clients. We’re using this experience to identify software needs in the industry. But also – we want your feedback! Please let us know your thoughts on what to build next.



Our first ResApp is called StageOpt. It calculates proppant transport from the wellbore and helps optimize perforation design to maximize the uniformity of proppant and slurry transport.

Proppant transport from the wellbore has been a major area of research in recent years because (a) the uniformity of proppant and slurry flow from the wellbore have a direct impact on production and recovery factor, (b) changes to perf design are easy to implement, and (c) new diagnostics such as DarkVision and VA  provide high-fidelity measurements of perforation erosion, which allows calibration and validation of models.

These factors make perforation design a ‘low-hanging fruit’ for improving project economics – design changes are cheap to implement, relatively easy to validate, and they have a significant impact on economics. The ‘missing link’ is that companies need a tool that can calibrate to data and help them identify the optimal perforation design. This is the purpose of StageOpt!

At its core, StageOpt is a fast-running wellbore dynamics simulator. Given a specified injection schedule, perforation design, and other parameters, it predicts where fluid and proppant will exit the well. It has the following features:

  • Simple, easy-to-use user interface with built-in help content and preview plots
  • Cutting-edge correlations on proppant and slurry transport from the well (Dontsov, 2023)
  • Monte Carlo uncertainty quantification
  • Automatic optimization of perforation phasing
  • A wide range of results plots and summary statistics
  • Automatic generation of a pdf summary report for each analysis

Modeling proppant transport from the well is tricky because there are multiple interacting physical processes occurring simultaneously. These include: (a) inertial effects as proppant tries to ‘turn the corner’ into the perforation clusters (Wu and Sharma, 2016 ), (b) gravitational settling of proppant within the lateral, especially towards the toe-side of the stage as velocity decreases (Dontsov, 2023), (c) perforation erosion (Cramer, 1987; Long et al., 2015; Cramer et al., 2020), (d) stress shadowing from fractures in the prior stage and from fractures within the same stage, (e) random variance in perforation phasing and diameter due to practical limitations of perforating tools, (f) fluid properties, (g) proppant properties, (h) fracture breakdown pressure, and (i) perforation plugging.

ResFrac’s Chief Scientist Egor Dontsov developed a comprehensive set of correlations for predicting proppant transport from the well (Dontsov, 2023). To a large extent, his work was based on synthesizing a review of the various experimental and computational fluid dynamics studies that have been presented in the literature (Ahmad and Miskimins, 2019a; Ahmad and Miskimins, 2019b; Ahmad, 2020; Ahmad et al., 2021; Gillies, 1993; Gruesbeck and Collins, 1982; Liu at al., 2021; Ngameni et al., 2017; Snider et al., 2022; Wang et al., 2022; Wu, 2018). However, he found that most studies focused on a relatively narrow range of conditions. He derived the physical equations controlling transport under the full range of conditions and showed that his correlations are consistent across the range of published results (Dontsov, 2023; Dontsov et al., 2023). These correlations form the basis for the StageOpt tool.

However, the Dontsov (2023) correlations are not – on their own – sufficient to evaluate perforation designs. They need to be embedded inside a wellbore dynamics simulator, which timesteps through the injection schedule, calculates the outflow of slurry and proppant from each perforation shot over time, accounts for perforation pressure drop and near-wellbore pressure drop, accounts for stress shadowing between fractures and from the prior stage, calculates erosion, and accounts for heterogeneity in stress along the stage. StageOpt simulates all these physics together into an integrated package. The details are provided in the StageOpt technical writeup.

StageOpt is not a full fracturing and reservoir simulator. It cannot relate changes to production or predict impacts on fracture geometry. For that, you’d need to use the full ResFrac simulator. But specifically for optimization perforation design to maximize uniformity, StageOpt is tailor-made.

StageOpt is most accurate if calibrated to field data. Calibration is required because of two sources of uncertainty: (a) uncertainty in input parameters, and (b) random variance in inputs such as perf phasing and diameter.

As an example of ‘uncertainty in input parameters’, let’s consider perforation erosion. It is widely recognized that erosion is related to the amount of proppant that flows through each shot (Cramer et al., 2020; Long et al., 2015). However, the magnitude of erosion depends on the properties of the steel in the casing, the properties of the proppant, and other factors. Thus, we need measurements of erosion, from which we can calibrate the erosion model. Once calibrated, the model can be applied to predict and optimize proppant placement in neighboring wells completed under similar conditions.

As an example of ‘random variance’, let’s consider the phenomenon that the ‘as placed’ perforation phasing is not exactly the same as the ‘designed’ perf phasing. For example, a company may design for 0° phasing, which means that all the shots should run along the top of the lateral. Most often, a weight bar is used to keep the perf gun towards the bottom of the well, so that it will point upwards when it shoots. But in reality, the gun does not sit exactly at the bottom, and so shots may have significant random variance from their intended orientation.

To consider the effect of random variance in StageOpt, we use Monte Carlo uncertainty quantification. The user specifies uncertainty ranges for the uncertain parameters, and the tool randomly generates 100+ draws for each parameter. An analysis is performed on each of the draws, and then the results are summarized to derive error bars and histograms.


Brief demo

Start by going to This page has general information and FAQs about the ResApps. Then, click the button for “Go to ResApps,” which will take you to the user portal at You need to make an account (click here for a tutorial). Once you have an account, you can sign up for a license to StageOpt.

If you’d prefer to watch a video tutorial, you can check one out here. Also, the StageOpt Technical writeup can be accessed here.

Once you have a license in place, you can start using the tool…

StageOpt is divided into a series of five panels: Welcome, Manage Analyses, Inputs, Perforation Designs, and Results. The Welcome panel has a tutorial movie.

In the Manage Analyses panel, you keep track of your work. All user inputs, such as perforation design, pump schedule, and other properties, are saved as part of an encapsulated “analysis.” From Manage Analyses, you can create, duplicate, and delete analyses, as well as export them to a JSON file that can be shared and imported by someone else.

In the Inputs panel, you enter the injection sequence and other information. Start by inputting the injection sequence:

The “Preview Inj Sequence” button pulls up a preview plot.

Next, input information about the well, such as: (a) inner diameter and dip angle, (b) input uncertainty ranges for phasing and diameter, and (c) calibration parameters related to erosion, the probability of perf plugging, and the effect of orientation on diameter.

Description of the inputs – especially the calibration parameters – is provided in the built-in help content, which is accessible from the orange ‘?’ button at the top of the screen.

The Perforation Designs panel allows specification of the perforation phasing and cluster design.

First define different “Perforation designs.” In the example below, I’ve defined two cluster designs – one with six shots at 60° phasing and another with four shots at 90° phasing. The Perf Design Viewer shows a preview plot of the locations of the shots with the selected design. As shown in the screenshot below, StageOpt takes into account that the perf guns sit on the low-side of the well, and so the actual locations of the holes in the casing are not exactly at the specified phasing.

In the “Cluster configuration” box, we specify the locations of the clusters in each stage, which cluster design to use at each cluster, and optional parameters such as near-wellbore complexity coefficient and stress shadow magnitude at each cluster.

The “Stress Shadow” column can be used to specify either: (a) stress shadow from the prior stage, or (b) stress heterogeneity. To assist with the former, the “Stress Shadow Wizard” allows you to specify the stress shadow magnitude from the prior stage. Then, it uses the Sneddon solution to populate the stress shadow at each cluster, decaying with distance.

Finally, we go to the Results panel and press “Run Analysis.” It takes a few seconds to simulate the 100 Monte Carlo draws for the sensitivity analysis and download the results. The Results panel also has an ‘optimize’ option, in which the algorithm either: (a) identifies the best single, uniform phasing to maximize uniformity, or (b) varies the phasing of each individual shot in order to maximize uniformity. In all cases, it uses the Monte Carlo uncertainty quantification to account for the effect of random variance and find the design that maximizes the expected value of uniformity index.

The Results panel provides a variety of plots. These include: cumulative proppant and slurry flow per shot and per cluster, initial perf diameter, final perf diameter, the ratio of final to initial perf diameter, screenout probability for each shot, perforation pressure drop per shot (both idealized and actual), and histograms giving the distribution of uniformity index and regularized uniformity index (Wehunt et al., 2020) for both slurry and proppant, on a per cluster and a per shot basis. The plots are customizable, with the ability to change font size, axis scales, etc.

In addition, the app generates a screen with summary statistics and tables of the results on a per shot, per cluster, and even per Monte Carlo realization. All the tabular data can be automatically downloaded to CSV files.

Finally, there is a button to generate and download a PDF report that contains all the plots and summary information.

Practical case studies

Let’s go through a few real-life case studies. More detailed descriptions of these case studies will be available in our upcoming paper at the SPE Hydraulic Fracturing Technology Conference.

Case Study 1

This dataset was analyzed for an operator in the Eagle Ford. They had run DarkVision to measure perforation erosion and wanted to apply those measurements to optimize perforation design. The figure below shows the distribution of diameter increase as a position of position along the stage. The data shows a general heel-side bias in erosion.

The wells in this case study used unoriented 120˚  phasing with three shots per cluster, except for the two heel side clusters, which used two shots. Within each cluster, the shots were separated by 120˚. However, because the shots were unoriented, the orientations of these shots could be in any direction.

What causes heel-side bias in perf erosion? Proppant struggles to ‘turn the corner’ and flow into the perforations. But this process should cause a toe-side bias in proppant placement, as proppant preferentially flows past the heel-side clusters where velocity is highest. Why is the opposite often observed?

Wu and Sharma (2016) proposed that heel-side bias may occur because of screenout of toe-side clusters. They hypothesized that proppant inertia initially causes toe-bias, but then the toe-side clusters plug off, causing an eventual heel bias. We do not believe that this is the best explanation. First, DarkVision observations allow identification of plugged perforations, and the toe-side perfs do not preferentially show evidence of plugging (in this dataset, or in general). Second, in many datasets, we have fiber observations of slurry distribution, and we do not consistently observe a dynamic with initial toe-bias, followed by subsequent heel bias.

Another reasonable hypothesis would be that stress shadowing from the prior stage causes a general heel-side bias, as less fluid flows into the toe-side (where stress shadowing is stronger). While plausible, there are two problems with this interpretation. First, in this case study (and in other similar cases where we’ve observed heel-side bias), significant limited-entry completion was utilized. The perforation pressure drop from the limited-entry completion should be sufficient to avoid large differences in flow (to rationalize an average erosion of 10% at the toe-side and 30% at the heel-side). Secondly, stress shadow weakens nonlinearly with distance from the prior stage. Stress shadow ought to cause a particularly severe weakening of flow in the few clusters closest to the toe-side, followed by a relatively more uniform distribution of flow in the clusters further towards the heel. Instead, the data in this case study shows a steady increase in erosion towards the heel, with even the first, second, and third clusters from the heel showing significant differences.

So then, what causes the heel-side bias? The best explanation is that it happens because erosion is a function of lateral fluid velocity. Classically, erosion has been modeled as being proportional only to cumulative proppant flow through each shot (Cramer, 1987; Long et al., 2015). However, as the proppant flows past each shot, the lateral inertia on the downstream side of the shot creates additional abrasion. This can be seen, for example, in the perforation erosion images shown by Cramer et al. (2020).

We model the effect of lateral velocity on perf erosion with the following equation:

Here the overall rate of change of perforation diameter $D$ is proportional to the proppant concentration $C$ and the calibration parameter ∝. Inside the parentheses, the first term is proportional to the squared velocity of slurry in the perforation,$v_p$, while the second term is related to the square of the average slurry velocity in the wellbore, $v_w$. The latter term causes heel bias because the slurry flows faster in the heel, and thus the rate of erosion is higher. Rather than asking the user to specify the erosion parameters $\alpha$ and γ, we give them default values, and ask the user to specify a ‘multiplier’ to the default value:

Setting alpha to zero would turn off perforation erosion of all kinds. Setting gamma to zero (but alpha non-zero) would retain erosion but turn off any effect from lateral fluid velocity.

The fluid velocity is gradually decreasing from heel-to-toe in the stage. This resembles the gradual reduction in perf erosion seen in the actual data. Consequently, when we include the effect of lateral velocity on perf erosion, we readily match the data seen in this case study.

The results are summarized in the figure below. The ratio of ‘final to initial’ diameter is shown on the upper-right panel, matching the trend seen in the actual data. The dots show erosion of each individual perf, while the lines show the average erosion for each cluster.

On a per-shot basis, the proppant flow error bars become increasingly erratic towards the toe. This occurs because – as fluid velocity decreases towards the toe – proppant becomes increasingly concentrated towards the bottom of the well (Dontsov et al., 2023). Thus, on the toe-side of the stage, shots near the top of the well receive relatively less proppant than shots at the bottom. On the heel-side, where velocity is highest, the proppant is entirely suspended by turbulence, and phasing has less effect. The 120˚  shots are unoriented, so because the orientation of each shot varies from stage to stage, they can experience very different proppant flow from stage to stage.

As the heel-side shots erode preferentially, the strength of the limited-entry weakens, causing a heel-side bias in slurry flow.

Despite the uneven distribution of erosion and slurry, the proppant flow distribution is fairly uniform on a per-shot basis from heel to toe. Why? Proppant inertial effects cause proppant to tend to flow past the heel-side clusters, a process that tends to create toe bias. But simultaneously, the overall distribution of slurry has a heel bias because of the erosion processes discussed above. The effects roughly cancel out and proppant is mostly uniform along the stage. This is not a general observation – we do not always observe that these two effects offset. It is coincidental that it occurred in this particular dataset.

We might conclude that the perf design was a success because the proppant flow was roughly uniform on a per-shot basis. However, if you look closely at the figure above, you can observe that the two heel-side clusters have only two shots, as opposed to three shots for the other clusters. Thus, even though the heel-side clusters take roughly the same amount of proppant on a per-shot basis, they take less proppant on a per-cluster basis. This creates an unevenness on a per-cluster basis, and we conclude that the tapered design was not optimal in this case.

To separate the effect of inertia from erosion, we ran calculations with stress shadowing and perf erosion ‘turned off’ so that there would be a uniform distribution of slurry. In this case, we can see that inertial effects are dominant, and there is a tendency for a toe-side bias.

Note that in the figure below, a somewhat different perforation scheme than in the previous figure. This was because the company evaluated various different perforation schemes, and these particular simulations were run a different scenario.

Additional sensitivities were performed to evaluate the effect of adding or subtracting shots per cluster. With too many shots per cluster, limited-entry becomes weak, and the uniformity of stress shadowing between clusters becomes poor. On the other hand, with too few shots per cluster, limited-entry is much stronger. Initially, with a low shot count, slurry flow is highly uniform. However, with fewer shots, velocity through each shot is much higher, exacerbating erosion. The erosion can lead to highly nonuniform diameter distribution, which results in poorer uniformity of slurry flow by the end of pumping than if a larger number of shots with less limited-entry was used. The optimal design used a moderate amount of perforation pressure drop.

Based on the sensitivities in this case study, the operator was able to identify the optimal number of shots per cluster and applied the findings to future wells.


Case Study 2

This second case study is taken from the Montney shale play in Canada. The operator ran three different designs: Design A with five clusters per stage and wider cluster spacing, Design B with the same stage length but seven clusters per stage (tighter cluster spacing than Design A), and Design C with seven clusters per stage and longer stage length (same cluster spacing as Design A). The erosion data, as observed in downhole imaging, is shown below. In all designs, the perforations were generally oriented toward the upper 120˚ of the wellbore.

There is generally a U-shaped erosion distribution, with more erosion towards both the heel and toe. As in the prior case study, the heel bias was partially a consequence of the greater lateral velocity on the heel side. Towards the middle and toe side of the stage, there is a tendency for proppant to ‘flow past’ the top side shots in the clusters closer to the toe, concentrating proppant in the slurry until it reaches the final cluster, when all remaining proppant must flow out of the well.

In the model calibration, we found it useful to increase the magnitude of fracture-to-fracture stress shadow within the stage. This helped create the U-shaped flow distribution since the intra-stage stress shadow is strongest in the middle of the stage.

After the model had been calibrated, we performed an optimization on shot phasing. The figure below compares the ‘regularized’ uniformity index for the three designs with either the original or optimized phasing. The phasing optimization has a minimal effect on the uniformity of slurry but significantly improves the uniformity of proppant.


Changes to perforating strategy can be low-cost or free, and the analyses for the case studies above required only a few hours of work. Yet, the impact of perforation optimization on fracturing efficiency and production is meaningful. This is why we prioritized StageOpt to be our first ResApp! The value of running this analysis and optimizing your perforating strategy is significant, and the cost of implementing the solution is modest.

We would caution – we observe differences in erosion tuning parameters from dataset to dataset. StageOpt has default values that are roughly ‘average,’ but if you have access to downhole imaging, it is best to tune the model to your specific data.

A common question – are all these relations implemented in our full ResFracPro simulator? Not yet, but coming very soon. When the Dontsov (2023) correlations are implemented in ResFrac, you’ll be able to run all the same kinds of analyses inside the fully integrated frac and reservoir simulator. Even so, ResFrac license-holders should find it useful to run StageOpt for standalone perforation design optimizations. It has ease of use, fast runtime, plotting tools, and built-in uncertainty quantification and optimization capabilities.

Please reach out if you would like more details!



We gratefully acknowledge the two operators who provided the data for the case studies. Case Study 1 was provided by an anonymous operator. Case Study 2 was provided by Arc Resources. In particular, thank you to Justin Kitchen, Mani Mehrok, Pierce Anderson, and Farhan Alimahomed.



Ahmad, F., 2020. Experimental Investigation of Proppant Transport and Behavior in Horizontal Wellbores using Low Viscosity Fluids (Ph.D. thesis). Colorado School of Mines.

Ahmad, F.A., Miskimins, J.L., 2019a. An experimental investigation of proppant transport in high-loading friction-reduced systems utilizing a horizontal wellbore apparatus. In: Proceedings of Unconventional Resources Technology Conference. Denver, Colorado, USA, 22–24 July, URTEC-2019-414-MS.

Ahmad, F.A., Miskimins, J.L., 2019b. Proppant transport and behavior in horizontal wellbores using low viscosity fluids. In: Proceedings of Hydraulic Fracturing Technology Resources Conference. 5–7 February 2019, Houston, Texas, USA, SPE-194379-MS.

Ahmad, F.A., Miskimins, J.L., Liu, X., Singh, A., Wang, J., 2021. Experimental investigation of proppant placement in multiple perforation clusters for horizontal fracturing applications. In: Proceedings of Unconventional Resources Technology Conference. Houston, Texas, USA, 26–28 July, URTEC-2021-5298-MS.

Cramer, D.D. 1987. The Application of Limited-Entry Techniques in Massive Hydraulic Fracturing Treatments. In Proceedings of the SPE Production Operations Symposium, Oklahoma City, OK, SPE-16189-MS.

Cramer, D., Friehauf, K., Roberts, K., and Whittaker J., 2020. Integrating distributed acoustic sensing, treatment-pressure analysis, and video-based perforation imaging to evaluate limited-entry-treatment effectiveness. SPE Prod & Oper, 35:0730–0755, SPE 194334–PA.

Dontsov, E.V., 2023. A model for proppant dynamics in a perforated wellbore. International Journal of Multiphase Flow 167, 104552.

Dontsov, E., Hewson, C., McClure, M., 2023. Analysis of Uniformity of Proppant Distribution Between Clusters Based on a Proppant-Wellbore Dynamics Model. Unconventional Resources Technology Conference held in Denver, Colorado, USA, 13-15 June.

Gillies, R.G., 1993. Pipeline Flow of Coarse Particle Slurries (Ph.D. thesis). University of Saskatchewan.

Gruesbeck, C., Collins, R.E., 1982. Particle transport through perforations. Soc. Petrol. Eng. J. 22 (06), 857–865.

Liu, X., Wang, J., Singh, A., Rijken, M., Wehunt, D., Chrusch, L., Ahmad, F., Miskimins, J., 2021. Achieving near-uniform fluid and proppant placement in multistage fractured horizontal wells: a computational fluid dynamics modeling approach. SPE Prod. Oper. 36, 926–945.

Long, G., Liu, S., Xu. G., and Wong, S.-W. , 2015. Modeling of perforation erosion for hydraulic fracturing applications. In Proceedings of SPE Annual Technical Conference and Exhibition held in Houston, Texas, USA, 28–30 September 2015, SPE-174959-MS .

Ngameni, K.L., Miskimins, J.L., Abass adn B. Cherrian, H.H., 2017. Experimental study of proppant transport in horizontal wellbore using fresh water. In: Proceedings of Hydraulic Fracturing Technology Resources Conference. 24–26 January , Houston, Texas, USA, SPE-184841-MS.

Snider, P., Baumgartner, S., Mayerhofer, M., Woltz, M., 2022. Execution and learn- ings from the first two surface tests replicating unconventional fracturing and proppant transport. In: Proceedings of Hydraulic Fracturing Technology Resources Conference. 1–3 February 2022, Houston, Texas, USA, SPE-209141-MS.

Wang, J., Singh, A., Liu, X., Rijken, M., Tan, Y., Naik, S., 2022. Efficient prediction of proppant placement along a horizontal fracturing stage for perforation design optimization. SPE J. 27, 1094–1108.

Wehunt, C. D., Naik, S., and Singh, A. 2020. More bang for the buck – optimized perforating design for unconventional reservoirs. In Proceedings of the Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX, SPE-199730-MS.

Wu, C., 2018. Modeling Particulate Flows in Conduits and Porous Media (Ph.D. thesis). University of Texas at Austin.

Wu, C.-H., Sharma, M.M., 2016. Effect of perforation geometry and orientation on proppant placement in perforation clusters in a horizontal well. In: Proceedings of Hydraulic Fracturing Technology Resources Conference. 9–11 February2016, Houston, Texas, USA, SPE-179117-MS.

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