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Assisted History Matching Using Bayesian Inference: Application to Multiwell Simulation of a Huff ’n’ Puff Pilot in the Permian Basin

The dynamic nature of unconventional-reservoir developments calls for the availability of fast and reliable history-matching methods for simulation models. In this paper, the authors apply an assisted-history-matching (AHM) approach to a pair of wells in the Wolfcamp B and C formations of the Midland Basin, for which production history is recorded for two periods: primary production and gas injection (huff ’n’ puff, or HNP ). The recorded history of gas injection revealed severe interwell interactions, underscoring the importance of fracture-interference modeling.

Fracture segments are modeled with an embedded discrete fracture model (EDFM). Interwell communication is modeled using long fractures that only become active during gas injection. The authors applied a Bayesian AHM algorithm with a neural-network-proxy sampler to quantify uncertainty and find the best model matches. For each well, they used primary production observations to invert for 13 uncertain parameters that describe fracture properties, initial conditions, and relative permeability. Subsequently, by minimizing pressure- and rate-misfit errors during the HNP period, they evaluated the size and conductivity of interwell fractures. For each AHM study, the objective was to minimize a cost function that is a linear combination of misfit errors between simulation results and observation data for well pressure and production rates of oil, water, and gas. The selected solution samples were used to perform probabilistic forecasts and assess the potential of HNP enhanced oil recovery (EOR) in the area of interest.

From 1,400 total simulation runs, the AHM algorithm generated 100 cases (solutions) that satisfy predefined selection criteria. Even though the parameter prior distributions were the same for the two wells, the marginal posteriors were dissimilar. Relative permeability curves for solution candidates can vary significantly from one another. The prospects of EOR were proven decent for the wells of interest. The authors reported 30 and 81% incremental recovery for the P50 predictions of Wells BH and CH, respectively.

Exploitation activities of tight oil resources (with formation permeability less than 0.1 md) have been increasing as horizontal drilling and hydraulic fracturing technologies continue to improve. According to the Energy Information Administration, in 2018, 61% of total US crude oil production was produced from tight formations. A typical tight oil well will be completed during multiple stages, creating hundreds of fracture clusters along a horizontal wellbore that extends for thousands of feet. This completion forms a large network of fractures that connects the wellbore to a large surface area of the shale formation. The initial well productivity could be quite high; it typically declines very rapidly and remains low during long-term production. Pressure depletion occurs quickly because of the small permeability of tight pores. As a result, recovery factors are only in the 1–10% range of the original oil in place during primary production, leaving significant amounts of unrecovered hydrocarbon in the subsurface.

Two main endeavors are used to maximize recovery, one focusing on optimizing completion, refracturing, and infill drilling and another on EOR techniques. One EOR method that has become frequently used in tight reservoirs is cyclic gas injection (i.e., HNP). One HNP cycle consists of three stages (Fig. 1). First, gas is injected into a well at a high pressure (huff), followed by a period of shut-in to achieve miscibility (soaking), and lastly bringing the well back to production (puff). One advantage of this technique is that it does not involve drilling extra wells because gas is injected into the same producing well. Even though the performance is tied to the properties of injected gas, delivering gas supplies to the field can be costly or impractical. This technique, though, allows produced gas to be recycled back into the formation, and hence becomes particularly attractive if there is adequate availability of produced gas on site.

Fig. 1—Schematic showing stages
of a huff ’n’ puff EOR cycle.

Projections for production and productivity are often made on the basis of numerical simulation runs, especially for low-permeability shale. Across the tight formation pores, flow is more likely to remain in transient conditions for long times, hence the less sophisticated reservoir evaluation techniques would be inaccurate. Many published studies rely on a single geological description that uniquely represents the reservoir. One drawback of this approach is that it does not properly address uncertainty.

We tend to have poor understanding of the geological subsurface because of sampling or a lack of experimental testing. With the added uncertainty arising after hydraulic-fracturing treatments, building representative and reliable static reservoir models is challenging. In addition, it is difficult to assess or quantify the amount of damage incurred to the formation by the fracturing fluid after injection and shut-in periods. The invasion of water into rock matrix alters original fluid-saturation profiles, which largely affect multiphase flow. For the lack of better knowledge, the geologic models will be updated continually in a process known as history matching. History matching is conducted on the basis of prior information to match observations, such as production history or time-lapse seismic. The process involves repetitively altering some uncertain parameters in an attempt to reduce the misfit between simulation results and observed history until achieving satisfactory match. The tedious process could be substituted by systematic algorithms that are designed for the purpose, in a procedure known as assisted history matching (AHM). AHM methods also can provide tools to meaningfully quantify uncertainty; the output is usually an ensemble of equally qualified model candidates as opposed to a unique single solution. Uncertainty, in production forecasts for instance, may be assessed by considering multiple forecasts of the ensemble individual models, as opposed to running one forecast from a single realization.

This paper evaluates the performance of an HNP pilot test in a volatile-oil reservoir in the Midland basin. For developing the AHM method, the authors implemented a systematic modeling approach tailored to typical conditions of shale oil/gas and extended to use in multiwell field applications. In the scarcity of information about the reservoir, the method uses available “noisy” observation data to infer the properties of the subsurface. This can provide a fast first step that leads to further analysis and probabilistic forecast. First, the authors prepared a multiwell base sector model that incorporated the knowledge acquired about the reservoir. They performed a few AHM studies to obtain different realizations with the objective of matching observed history during primary recovery. Then, they incorporated the subsequent EOR phase (i.e., recorded data during first HNP test cycle) into history matching to improve the integrity of the models. Realizations that satisfy a predefined acceptance criterion are used to estimate cumulative oil production probabilistically. For this purpose, the paper reports probabilistic recovery for a 5-year prediction period based on two management scenarios, with extending primary recovery and with continuous HNP cycles.

Find the complete paper on OnePetro here.

This article contains highlights of paper URTeC  2787, “Assisted History Matching Using Bayesian Inference: Application to Multiwell Simulation of a Huff ’n’ Puff Pilot Test in the Permian Basin,” by Esmail Eltahan, SPE, Reza Ganjdanesh, SPE, Wei Yu, SPE, and Kamy Sepehrnoori, SPE, The University of Texas at Austin, et al., prepared for the 2020 Unconventional Resources Technology Conference, Austin, Texas, 20–22 July. The paper has not been peer reviewed and is reprinted with permission from the Unconventional Resources Technology Conference, whose permission is required for further use.


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