# PI Based Forecasting

Traditional decline curve analysis (DCA) does not incorporate pressure data and only strictly works when the operating conditions are constant (e.g., constant bottomhole pressure or choke setting, with limited production interruptions). Also, rate-based forecasting methods do not consider fluid phase behavior (PVT property changes), thereby having no contextual information to capture when a well transitions to saturated conditions and corresponding GOR increases. As there are surface or operational disruptions (e.g., downtime, production constraints, line pressure changes, choke changes, workovers etc.), the rate decline is distorted. In some scenarios, DCA models cannot even be applied as the well may not exhibit any discernable production decline, as illustrated by a sample well in Figure 1 exhibiting flat production as it experiences facility constraints.

We propose using productivity index (PI) as the forecasting variable, as it allows normalizing both surface effects and considers phase behavior, thus reducing noise. It produces cleaner trends that are easier to fit, resulting in more accurate models and generates better predictions. Also, it is possible to generate the forecast with less data, as a clean production decline trend can be established sooner (as highlighted in Figure 1, where a clear production decline trend can be identified at early time even when the rates are flat). This PI decline behavior has also been empirically validated on several wells across multiple shale plays and tight reservoirs with constrained rate production. In comparison, note that pressure normalized rate-based decline methods, though similar, do not handle PVT effects or pressure depletion.

A PI-based production forecasting workflow was introduced in Molinari et al. (2019b), using an ensemble of decline models to generate liquid rate predictions from a base PI forecast, combined with reservoir pressure and flowing BHP extrapolation. The main limitation of that model was the assumption of a constant GOR, which only makes it applicable for scenarios where flowing BHP remains above saturation pressure. Subsequently, the PI-based forecasting method was extended to include saturated flow conditions when the flowing BHP and reservoir pressure drop below bubble point (Molinari and Sankaran 2021).

As discussed in Molinari et al. (2019a and 2019b), productivity index (PI) defines a representative metric of well performance and the true reservoir inflow potential. It normalizes the production volumes by the flowing pressures and incorporates the impact of pressure depletion and PVT. It is an effective diagnostic metric as it allows consistent comparison of wells experiencing different operating conditions, such as different choke openings or artificial lift, mitigating biases often encountered in rate-time based DCA and type curves. Also, by representing the relationship between rates and pressure drawdown, PI can be used for production optimization purposes, to predict current and future production given various operational strategies.

Productivity index depends on the producing rates, flowing bottomhole pressure and average reservoir pressure. For conventional reservoirs, PI can be considered as constant under pseudo-steady state flow. However, we need to treat PI here as a transient quantity that is updated at each timestep.

For a given reservoir condition at any time instance, PI also depends on the actual drawdown and has a constant magnitude only when flowing pressure is above saturation pressure. When flowing pressure drops below saturation pressure, the gas liberation reduces the overall liquid productivity (PI) due to relative permeability changes. Equations (1), (2) and (3), based on the IPR equations defined by Vogel (1968), can be solved to define the liquid PI at any given time step, given the pressure conditions.

When both the reservoir and flowing BHP are above saturation pressure (i.e., undersaturated), the PI is defined as a simple linear equation. Note that all terms on the right-hand side vary with time.

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is calculated based on the algorithms of DDV and average reservoir pressure depletion. Refer to DDV page for more details.

(1)

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If the reservoir is still undersaturated, but the flowing bottomhole pressure drops below saturation pressure (created saturated conditions in the near-wellbore region), the following expression is used.

(2)

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Finally, when the reservoir is fully saturated (average reservoir pressure has depleted below saturation pressure), the PI is represented as follows.

(3)

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For gas systems, a suitable IPR equation is used such as C & n model. Figure 5 illustrates typical PI trends for several wells from a major liquid-rich US shale play

Initially, the liquid PI trend is fitted with a modified hyperbolic equation, following the approach described in Molinari et al. (2019b). Other time series-based forecasting models (ARIMA, RNN etc.) may also be applied based on past values of PI and cumulative volumes.

(4)

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The PI decline model allows extrapolating the PI at future time steps. The key assumption is that the well will remain on primary depletion without sudden changes in productivity index, due to events such as a refrac or offset frac hit.

On the other hand, well interference can also be automatically identified using PI trends more clearly than just using rate or pressure data (Rahman et al. 2019). Figure 2 highlights a breakpoint in the PI trend after 100 days, when a nearby child well was completed and subsequent change in well performance. In such cases, multiple PI segments can be fitted after each valid interference event to create a composite PI decline model. When parent-child interference needs to be included, PI forecast will depend on cumulative volumes of both parent and child wells.

The PI forecast is converted into a liquid rate profile by combining it with reservoir pressure and BHP forecasts, using equations (1), (2) and (3). The average reservoir pressure is extrapolated as a function of cumulative liquid, following the profile defined through material balance in the prior step. The BHP profile is completely controllable by the operator, as it represents the expected operating conditions under the planned production strategy for each well (e.g., choke schedule and artificial lift installs and operational set points). Hence, the BHP profile can be either a smooth profile or a segmented function representing multiple drawdowns corresponding to the application of various production methods. The BHP profile can even become a sensitivity tool to evaluate the production impact of different operational strategies or normalize production conditions to compare different wells using a common BHP profile. The complete forecasting workflow is summarized in the schematic in Figure 2.

Once the liquid rate forecast is generated, as a single-phase forecast, it is necessary to derive a multiphase forecast, obtaining the corresponding oil, gas, and water rate profiles. This is achieved in two steps, first modeling the water cut, and subsequently modeling the gas-oil ratio (GOR). Both the water cut and GOR models are independent and modular, and various mathematical representations can be used as part of the workflow, tailored to a given field specific conditions.

While more complex functional forms could be derived, it is common to represent water cut either as a constant trend, or a linear trend with a gentle slope. Unless a disruptive event happens, such as a frac hit from a neighbor well, typical water cut trends in unconventional wells under primary depletion tend to be smooth and gradual.

The factors that affect GOR trends include flowing BHP, saturation pressure, PVT property suppression, pressure-dependent permeability, changes in critical gas saturation, fracture geometry, pore size distributions and gas-oil relative permeability (Pradhan 2020).

A data-driven approach for GOR forecasting uses a two-segment power law by plotting cumulative oil and cumulative gas in a log-log plot and matching two straight-line models, as illustrated for a sample well in Figure 3.

The method is a combination of physics and data-driven trends. At early time, the cumulative gas is linearly proportional to cumulative oil, as the gas-oil ratio is constant and equal to the initial solution GOR.

(5)

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As the reservoir depletes and reservoir pressure drops below saturation pressure, the well transitions to a second trend, where GOR increases. This is shown as a second linear trend in the log-log plot, with slope larger than 1, representing a power law.

(6)

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The gas-oil ratio is obtained by taking the derivative of equation (6).

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Note that equation (6) is data-driven, and they depend on matching the observed GOR increase after an inflection point has been detected. For young wells, when such transition has not been observed, offset wells can be used as analogs to define expected future GOR trends, provided they are producing under similar drawdown conditions. The two-segment trend has been observed in thousands of wells across various basins (Figure 4), and it is generally adequate to represent most situations. However, when a different GOR model is needed to adapt to specific field trends, such expressions can be implemented without replacing the other parts of the forecasting workflow.

Finally, when both watercut and GOR forecasts are defined, the liquid rate can be decomposed into oil, gas, and water profiles, resulting in a multiphase production forecast which can be extended until the specified abandonment conditions.The proposed PI-based forecasting methodology is a combination of:• Data-driven methods, which are used to extrapolate PI, water cut and GOR trends, and• Physics-based methods, which are PVT-aware, capture pressure depletion, represent PI reduction at low pressures due to multiphase effects, and capture production sensitivity at different pressuredrawdown strategies.

The workflow has been successfully implemented in thousands of wells in major unconventional basins in North America, using scalable and automated algorithms to capture well performance and derive value through fit-for-purpose production optimization and improved field development planning.

- Molinari, D., Sankaran, S., Symmons, D., Perrotte, M., Wolfram, E., Krane, I., Han, J., and N.Bansal. "Implementing an Integrated Production Surveillance and Optimization System in anUnconventional Field." URTEC-2019-41-MS. Paper presented at the SPE/AAPG/SEGUnconventional Resources Technology Conference, Denver, Colorado, USA, July 2019b. doi:https://doi.org/10.15530/urtec-2019-41
- Molinari, D., and S. Sankaran. "A Reduced Physics Modeling Approach to Understand Multiphase Well Production Performance for Unconventional Reservoirs." URTEC-2021-5023-MS. Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, July 2021. doi: https://doi.org/10.15530/urtec-2021-5023
- Molinari, D., Sankaran, S., Symmons, D., and M. Perrotte. "A Hybrid Data and Physics ModelingApproach Towards Unconventional Well Performance Analysis." SPE-196122-MS. Paperpresented at the SPE Annual Technical Conference and Exhibition, Calgary, Alberta, Canada,September 2019a. doi: https://doi.org/10.2118/196122-MS
- Vogel, J.V. "Inflow Performance Relationships for Solution-Gas Drive Wells." J Pet Technol 20(1968): 83–92. doi: https://doi.org/10.2118/1476-PA
- Rahman, M., Gioria, G., Sankaran, S., and D. Molinari. "Automatic Well Interference Identificationand Characterization: A Data-Driven approach to Improve Field Operation." SPE-195813-MS.Paper presented at the SPE Annual Technical Conference and Exhibition, Calgary, Alberta,Canada, September 2019. doi: https://doi.org/10.2118/195813-MS
- Pradhan, Y. "Observed Gas-Oil Ratio Trends in Liquids Rich Shale Reservoirs." URTEC-2020-3229-MS. Paper presented at the SPE/AAPG/SEG Unconventional Resources TechnologyConference, Virtual, July 2020. doi: https://doi.org/10.15530/urtec-2020-3229