**Introduction**

ResFrac’s automated optimization tool allows you to quickly and easily identify the economically best well spacing and frac design. This blog post steps through a simple demo.

Prior to performing optimization, you should construct a calibrated numerical model. For details on model construction and history matching, check out Section 8 from the ResFrac “A to Z Guide” (McClure et al., 2022). For a few recent published examples, refer to Pudugramam et al. (2022), Albrecht et al. (2022a,b), Ratcliff et al. (2022), and Fowler et al. (2020).

The automated optimization capability uses a similar user interface as our sensitivity analysis and history matching tools. The user experience is described in a blog post by Kang (2021). The user clicks on parameters to add them to the optimization. Then, the user specifies max/min ranges for each parameter, and organizes them into ‘parameter groups’ (the parameters in each group are varied together). Finally, the user provides instructions to guide the optimization, such as what to use as the ‘objective function.’ Once the algorithm has run, the tool provides a variety of postprocessing/visualization options.

The optimization algorithm uses the same approach as our automated history matching algorithm (Kang et al., 2022). The algorithm generates an initial set of simulations that broadly sample the parameter ranges specified by the user. Then, based on the results, the algorithm fits a proxy model, and runs a second generation of simulations, honing-in on promising areas where the best solution is likely to be located. After this second generation, a proxy model is fit again, and the process is repeated. This algorithm has several advantages: (a) it samples widely, and so it is robust against incorrect convergence local optima; (b) it converges efficiently to the best solution; and (c) it samples broadly and so gives a sense of the overall properties of the solution space.

**Problem setup**

For this demo, I set up a simulation with five wells in a hypothetical formation with two pay zones. In the base simulation, all the wells are landed in the upper pay zone. However, the algorithm is given the option to vary the landing depth of the second and fourth wells. The figures below show the ‘baseline’ simulation. The wells are fractured with a slickwater design and 100 mesh proppant. Limited-entry is used, and so flow is fairly uniform from each perf cluster. However, the simulation permits some cross-flow between clusters outside casing, and so fractures do not necessarily propagate from each perf cluster.

The optimization algorithm is allowed to vary well spacing, landing depth (of the second and fourth wells), and injection duration (which implicitly varies lbs/ft of proppant and bbl/ft of fluid). The objective function is a joint objective function that balances NPV/section (net-present value per section) and DROI (discounted return on investment). The price of oil is assumed to be \$80/bbl, and the discount rate is 10%. Other reasonable values are assumed for the price of drilling, proppant, fluid, etc. The price of land is assumed ‘sunk’ and so is not included in the analysis.

ResFrac uses a built-in economics engine that is similar to those used by commercial software in the industry. It accounts for details such as working interest, different types of taxes, time-varying operations cost, etc.

**Results**

In the cross-plot below, each dot is a single simulation. The figure shows that there is a trade-off between DROI and NPV/section. Designs with tighter well spacing can extract greater NPV/section. However, the overall return on investment decreases. Conversely, designs with wider well spacing achieve greater revenue per well and higher DROI, but extract less NPV per section. The green dashed line shows the approximate position of the Pareto front. The Pareto front shows – for a given value of NPV/section, what is the best possible DROI? Depending on objectives and constraints, a company may rationally decide to use a design with higher or lower NPV/section. However, it is never optimal to select a design that is below the Pareto front.

For example, the figures below show a simulation with well spacing of 685 ft, 1500 lbs/ft proppant, and 34 bbl/ft fluid. The algorithm chose to wine-rack the wells, shifting the second and fourth wells into the lower landing zone. This design achieves an impressive DROI of 8, with an NPV/section of \$247M, and \$35M CAPEX per section.

Alternatively, the design below uses a well spacing of just 240 ft. The DROI is significantly lower – 5 (instead of 8), but the NPV/section is significantly higher – \$396M (instead of \$247M). The CAPEX per section is \$98M (instead of \$35M). The job size is similar – 1600 lbs/ft and 37 bbl/ft. As with the other example, the algorithm chose to wine-rack the wells between the pay zones.

In this case, the optimal job sizes are quite similar between the two values of spacing. However, in many cases, the optimal job size is a strong function of well spacing. All of the frac design parameters interact, and so if a parameter such as spacing is changed, all other parameters must vary simultaneously to compensate.

The figures below show EUR/section and EUR/(5 wells) as a function of well spacing.

The figures below show NPV/section and DROI/section as a function of well spacing. Remember – the cost of land is not included in the analysis. As a result, DROI must increase monotonically with well spacing. Because the land is ‘free,’ the pure DROI analysis does not include a penalty for being inefficient with land.

**Discussion**

The results show that strong tradeoffs exist between maximizing overall return on investment and land efficiency. This naturally raises the question – what should be your objective function? A pure NPV/section optimization versus a pure DROI optimization would arrive at radically different designs.

The answer depends on a company’s priorities and constraints. A company with relatively limited access to land, but easy access to capital, may tend to focus on an NPV/section optimization. Conversely, a company with a huge land position, but relatively limited capital or access to market may focus more heavily on DROI. Companies must also consider practical considerations, such as pipeline constraints and access to drilling rigs and frac crews.

The price of oil has a huge impact on the optimal design. The figure below shows scatterplots of NPV/section versus well spacing for different prices of oil. This figure is taken from a different modeling study than used in this demo, and the axis labels are disguised to obscure the details. We can see that as the price of oil increases, the well spacing that optimizes NPV/section shifts to become tighter.

The current and future-expected prices of oil have dramatically increased over the past 6-18 months. Has your company adjusted its well spacing and frac designs to respond?

Because of these tradeoffs, when performing an economic optimization, it may not be ideal to present one single ‘best’ design. Instead, you may choose a few different designs, to present the range of options available.

I am working on adding more ‘objective function’ options to the economic optimization engine. I have been experimenting with a ‘field development economic model’ that allows you to play out *development of the entire play*, rather than perform optimization on a single pad basis. You can specify your total capital, the maximum number of rigs that you can run simultaneously, the size of the land position, etc., and the algorithm will maximize the entire terminal value of the development. Everything is connected – from asset planning down to granular frac design decisions. The global optimum for a company must consider all of these factors in a closed-loop!

**Conclusions**

The new economic optimization engine is powerful and easy to use. For the demo above, I spent about 15 minutes setting it up. It ran in about a day and a half, and then I spent about 30 minutes making the crossplots and 3D images. Not bad, to get answers that can make a huge positive economic impact! In recent projects using the optimization tool, we have identified opportunities to increase NPV/section and/or DROI by 20-60% (Pudugramam et al., 2022)

**References**

Albrecht, Magdalene, Borchardt, Shannon, and Mark McClure. “Using Geochemical Production Allocation to Calibrate Hydraulic Fracture and Reservoir Simulation Models: A Permian Basin Case Study.” Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, June 2022a.

Albrecht, Magdalene, Borchardt, Shannon, Murphree, Chase, McClure, Mark, and Janz Rondon. “Using Quantitative Tracer Analysis to Calibrate Hydraulic Fracture and Reservoir Simulation Models: A Permian Basin Case Study.” Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, June 2022b.

Fowler, Garrett, Mark McClure, and Craig Cipolla. 2020b. “Making sense out of a complicated parent/child well dataset: a Bakken case study.” Paper SPE-201566-MS presented at the Annual Technical Conference and Exhibition.

Kang, Charles. 2021. “Introducing ResFrac’s Sensitivity Analysis Tools.” ResFrac Blog Post.

Kang, Charles A., Mark W. McClure, Somasekhar Reddy, Mariyana Naidenova, and Zdravko Tynakov. 2022. “Optimizing shale economics with an integrated hydraulic fracturing and reservoir simulator and a Bayesian automated history matching and optimization algorithm.” Paper SPE-209169-MS presented at the Hydraulic Fracturing Technology Conference, The Woodlands, TX.

McClure, Mark, Garrett Fowler, Chris Hewson, and Charles Kang. 2022. “The A to Z Guide to Accelerating Continuous Improvement with ResFrac.” 5^{th} Edition.

Pudugramam, Sriram, Rohan J. Irvin, Mark McClure, Garrett Fowler, Fadila Bessa, Yu Zhao, Jichao Han, Han Li, Arjun Kohli, Mark D. Zoback, Alexei A. Savitski, and Gustavo Ugueto. 2022. “Optimizing Well Spacing and Completion Design Using Simulation Models Calibrated to the Hydraulic Fracture Test Site 2 (HFTS-2) Dataset.” Paper URTeC-3723620 presented at the Unconventional Resources Technology Conference, Houston, Texas.

Ratcliff, Dave, Mark McClure, Garrett Fowler, Brendan Elliot, and Austin Qualls. 2022. “Modelling of Parent Child Well Interactions.” Paper SPE-209152-MS presented at the Hydraulic Fracturing Technology Conference, The Woodlands, TX.** **