Unconventional Well Interference Detection Using Physics Informed Data Driven Model

Abstract

A method of detecting one or more well interference events at a well penetrating a reservoir in a subterranean formation is provided. The method includes: receiving wellhead pressure and flowrates of oil, gas, and water for the well during production; calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and flowrate of oil, gas, and water; calculating an average reservoir pressure based at least on the BHP; determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure; determining a dataset of PI values and corresponding cumulative fluid production values from the well; analyzing the dataset to determine one or more breakpoints in a relationship between PI and cumulative fluid production representing one or more well interference events; and producing fluids from the reservoir based at least on the one or more breakpoints.

Description

TECHNICAL FIELD

This invention relates to detecting well interference in unconventional reservoirs and, more particularly, to methods for well interference detection using a hybrid data-driven and physics informed model.

BACKGROUND

Unconventional reservoirs, such as shale gas and tight oil formations, are becoming increasingly important for the global energy industry. The shale revolution in the U.S. has led to the adoption of multi-staged hydraulic fracturing, allowing for production from ultra-low permeability unconventional reservoirs. However, this practice can result in parent-child well interference under tight well spacing, where fracturing one well can negatively impact the productivity of neighboring wells. An existing producer well (parent) can communicate with tightly spaced, newly completed offset wells (children) through fractures (i.e., inter-well, fracture-driven interference, more commonly called “frac hits”) or encroached drainage volumes. This interference can sometimes cause adverse effects, such as damaging production tubing, casing, or wellheads, or affect the productivity of the invaded (parent) well.

It is now recognized that a need exists for a robust method to detect if a well has undergone frac hit and to forecast the resulting production profile, using limited and readily available input information.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of well interference due to frac hits.

FIG. 2 is a schematic representation of a well performance analysis workflow.

FIG. 3 is a schematic representation of material balance applied to a succession of pseudo-steady-state conditions with expanding drainage volume.

FIG. 4 is a flow chart of an example method for performing productivity index (PI) based forecasting (PIBF) of liquid, oil, water, and gas rates.

FIG. 5 is a process flow diagram of a multi-segment PI-based forecasting (MS-PIBF) workflow calculation method.

FIGS. 6A-6C are plots of cumulative liquid vs liquid productivity index determined using a breakpoint detection algorithm based on dual segment fit at various candidate timesteps.

FIG. 7 is a plot illustrating liquid productivity index increase at the breakpoint of 260 days.

FIG. 8 is a plot illustrating water cut increase at the breakpoint of 260 days.

FIGS. 9A-9D are plots illustrating a multi-segment forecast of liquid productivity index (9A), water cut (9B), average reservoir pressure (9C) and flowing bottom hole pressure (9D) for a single well interference event.

FIGS. 10A-10F are plots illustrating the cumulative rates (oil (10A), water (10B), and liquid (10C)) and rates (oil (10D), water (10E), and liquid (10F)) forecast for all detected segments in a single frac hit event.

FIGS. 11A-11D are plots illustrating a multi-segment forecast of liquid productivity index (11A), water cut (11B), average reservoir pressure (11C) and flowing bottom hole pressure (11D) for multiple well interference events.

FIGS. 12A-12F are plots illustrating the cumulative rates (oil (12A), water (12B), and liquid (12C)) and rates (oil (12D), water (12E), and liquid (12F)) forecast for all detected segments in a multiple frac hit event.

FIGS. 13A-13D are plots illustrating a cumulative density function (CDF) of median absolute percentage error for single-segment PIBF vs multi-segment PIBF results.

FIG. 14 is a process flow diagram of an example method for detecting one or more well interference events at a well penetrating a reservoir in a subterranean formation.

FIG. 15 is a process flow diagram of an example method for analyzing a dataset of production index (PI) values vs. cumulative fluid production values to determine one or more breakpoints representing well interference events.

FIG. 16 is a process flow diagram of an example method for forecasting production in a well penetrating a reservoir in a subterranean formation.

FIG. 17 is a process flow diagram of an example method for forecasting production in a field of a plurality of wells.

FIG. 18 is a block diagram showing an example information handling system in accordance with certain embodiments of the present disclosure.

While embodiments of this disclosure have been depicted and described and are defined by reference to exemplary embodiments of the disclosure, such references do not imply a limitation on the disclosure, and no such limitation is to be inferred. The subject matter disclosed is capable of considerable modification, alteration, and equivalents in form and function, as will occur to those skilled in the pertinent art and having the benefit of this disclosure. The depicted and described embodiments of this disclosure are examples only, and not exhaustive of the scope of the disclosure.

DETAILED DESCRIPTION

Illustrative embodiments of the present disclosure are described in detail herein. In the interest of clarity, not all features of an actual implementation may be described in this specification. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions may be made to achieve the specific implementation goals, which may vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of the present disclosure.

Well interference in unconventional reservoirs has been a pivotal issue due to its significant impact on well productivity, estimated ultimate recovery, and field development economics. Well interference detection and quantification of the future production profile of the frac hit affected well become important to make operational and financial decisions accordingly. However, frac hit detection and production forecasting using a pure physics-based method could be extremely complex, computationally intensive, and significantly demanding in terms of the input information required to create a fit-for-purpose reservoir model.

During a frac hit, some of the child well fractures may intersect or interact with pre-existing fractures or other wells in their reach. Operators typically take preventive or corrective steps to reduce their negative effects. A common approach is to shut down producing wells when fracturing operations are underway in the vicinity. The key goal is to avoid fracturing fluid flow from the child well into a pressure sink (i.e., the parent well). However, this step is not always effective in eliminating fracture-driven interference or preventing mechanical damage of the parent well. Other approaches may include dialing down the treatment volumes or increasing well spacing to reduce frac hits, which may not be an optimal strategy from a field development standpoint.

FIG. 1 illustrates an example of an invasion of completion fluids that may occur during a frac hit event. Sometimes, the invaded fluid may just re-pressurize the drainage area of the parent well and thus boost its productivity (as shown in FIG. 1). This boost in the productivity may be substantial during the initial days of production after the frac hit event (dominated by high water cuts due to invading frac fluid), which becomes a signature to identify that the well has undergone a frac hit. The change in productivity and increase in water cut may also indicate the intensity of the frac hit event.

It is also possible that the well interference may be characterized by a rapid drop in either well's productivity when the well spacing is too tight and the production interference effect is quite strong. The wells drain from a common drainage volume with faster pressure depletion and as a result, the well deliverability may be adversely impacted.

The well production profiles before and after such well interference events may be quite different. As a result, forecasted well rates based on prior well performance will not be accurate after a frac hit. While operators recognize that such events happen in the field regularly, there are no established best practices to characterize and quantify the impact of such events in any standard manner.

Well interference detection is complex and often not easily characterized. Practitioners may detect an event based on criteria such as pressure spikes, changes in water cut or abnormal change in production rates observed in parent wells. Often, these are ad hoc, manual and may not be consistent or comprehensive across the entire field. Real time series analysis of natural flowing wells has been proposed for early frac hit detection. By comparing the well head pressure forecast based on natural decay with actual measurements against a threshold, interference events could be detected and labeled. However, pressure interference does not always translate to production interference as observed in many field cases, and it is likely that the parent well proceeds back on its original production path when put back online.

Other real-time and post-job analyses to calculate the fracture surface area and producing surface area have been proposed. For example, longer fracture length obtained with leakoff data analysis were attributed to parent well depletion and characterized as a hint of well interference based on stage-productivity index. However, this process requires manual stage-wise analysis of the injection treatment data, which is not scalable to entire field. Further, stage-wise analysis cannot be independently verified as the cumulative fracture surface area may not match the well's producing surface area without corresponding stage-wise production data (which is seldom available). It also does not address what happens when the parent well is put back on production to confirm any meaningful change in its original production profile.

The disclosed embodiments address these drawbacks. In particular, the present disclosure provides a workflow to address the following key gaps:

• • 1. Automatically detect well interference events consistently for all wells based on transient well performance and breakpoint identification methods;
  • 2. Forecast the well production rates after such events using a multi-segmented PI-based forecasting procedure; and
  • 3. Quantify impact of interference events based on delta cumulative production during the forecast period.

The disclosed workflow is described step by step in the following sections.

The present disclosure relates to methods for well interference detection, and production forecasting, based on a relationship between production index and cumulative fluid production using a hybrid data-driven and physics informed model.

More specifically, the present disclosure provides a method of detecting one or more well interference events at a well penetrating a reservoir in a subterranean formation, the method comprising: receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production; calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water; calculating an average reservoir pressure of the well based at least on the BHP; determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure; determining a dataset of PI values and corresponding values of cumulative fluid production from the well; analyzing the dataset to determine one or more breakpoints in a relationship between PI and cumulative fluid production representing the one or more well interference events; and producing fluids from the reservoir based, at least in part, on the one or more breakpoints.

In addition, the present disclosure provides a method of forecasting production in a well penetrating a reservoir in a subterranean formation, the method comprising: receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production; calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water; calculating an average reservoir pressure of the well based at least on the BHP; determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure; determining a dataset of PI values and corresponding values of cumulative fluid production from the well; analyzing the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well; and producing fluids from the reservoir based, at least in part, on whether there are any breakpoints representing well interference events at the well.

In addition, the present disclosure provides a method of forecasting production in a field of a plurality of wells, each well penetrating a reservoir in a subterranean formation, the method comprising: for each well of the plurality of wells: receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production; calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water; calculating an average reservoir pressure of the well based at least on the BHP; determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure; determining a dataset of PI values and corresponding values of cumulative fluid production from the well; analyzing the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well; and determining, for each well, one or more production forecasts for the well based on the PI determined for one or more segments of the dataset; and producing fluids via one or more wells of the plurality of wells based, at least in part, on the production forecasts.

Among the many potential advantages to the methods and systems of the present disclosure, only some of which are alluded to herein, the methods of the present disclosure provide a fast, unique, interpretable, and systematic physics-informed data-driven approach to detect well interference events and quantify their resulting impact on future well production. This approach honors the physics of reservoir behavior during transient well-flow, which is represented by a material balance on a closed boundary with expanding control volume, combined with the calculated dynamic drainage volume (DDV) to calculate the average reservoir pressures (Pavg) and well productivity index (PI) profiles as a function of time. This approach requires minimal and routinely available inputs and is computationally robust to scale to the entire field as part of closed-loop reservoir management.

Methodology

Multi-segmented PI-based forecasting (MS-PIBF) is an extension of single segment PI-based forecasting method (PIBF), which is explained below. It may be derived from the potential that transient well productivity index (PI) can be estimated from routine operational data, and PI is a good indicator of well interference.

In general, the following commonly available inputs may be used to compute PI:

• • Multiphase rates (oil, gas, water) and wellhead pressure.
  • Wellbore details (deviation surveys, casing, and tubing information).
  • Black oil PVT (API, solution gas-oil ratio (GOR), gas gravity, water salinity).

Based on the multiphase rates and wellhead pressures, bottomhole pressure is calculated using one of the following methods:

• • Classical steady state multiphase flow pressure models; or
  • Hybrid BHP that combines gauge data collected on a few wells for training within a physics-informed machine learning (PIML) framework.

The disclosed MS-PIBF methods may make use of a transient well performance (TWP) procedure, which is particularly practical in its use at a field scale. This approach is shown in FIG. 2, which blends data-driven techniques with simplified physics to characterize well performance. Material balance may be applied through a succession of pseudo-steady states on the development of a drainage volume in a closed system to approximate transient well performance.

The fluid behavior is first described by computing Pressure-Volume-Temperature (PVT) properties. If PVT data is not available, then flowback data and a non-parametric regression method called Alternating Conditional Expectation (ACE) may be used to estimate saturation pressure and the initial solution gas-oil ratio, corrected for separator conditions. To accurately represent the downhole flowing conditions, flowing bottomhole pressure may be calculated using surface data for the whole production history of the well. Then, using an optimization approach, the TWP may be evaluated using the dynamic drainage volume, average reservoir depletion, and PI. To forecast production under anticipated future operating circumstances, PI may be used as the basis variable.

The key tenet of TWP may be that the drainage volume constantly increases over time, but the exact shape is not known. The reservoir withdrawal may be known through cumulative volume produced and the diffusive time of flight method for drainage volume calculation assures no-flow outer boundary. Material balance may be carried out at each time step with great precision using the succession of pseudo-steady-state (SPSS) assumption (e.g., daily). In the contacted drainage volume at every timestep, this enables the calculation of pressure depletion (i.e., average reservoir pressure).

The TWP method makes use of readily available production rates, PVT, and flowing bottomhole pressure. Additionally, it can simulate both liquid and gas systems that are produced using any lift method (e.g., natural flow, gas lift, ESP, SRP, etc.) and handles variable rate and bottomhole pressure, pressure depletion, variable compressibility, and non-linear pressure-dependent PVT characteristics.

The next few sections will be focused on discussion of the steps for calculating PI.

Average Reservoir Pressure Estimation

The first step in the workflow may be to estimate the average reservoir pressure in the drained volume with time. A dynamic drainage volume may be calculated based on the downhole pressure evolution corresponding to the rate changes. Average Reservoir pressure (p_avg) may be calculated by combining the dynamic drainage volume with static material balance equations to represent an expanding control volume, which simplifies the transient state flow as a succession of pseudo-steady states (SPSS). SPSS may be analogous to an expanding balloon, where the outer boundary continuously expands at the same rate as the pressure contours expand. Based on Reynolds' transport theorem, transient flow may be approximated as “snapshots” or series of instantaneous pseudo-steady states with each steady state lasting for small time periods. Details of this procedure are provided below.

The asymptotic version of the 1D diffusivity equation's boundary condition may be solved to determine the drainage volume. The drainage volume may be determined using the pressure and rate data as follows in the absence of a well and reservoir model:

$\begin{array}{cc}{V}_d\approx \frac{1}{c_t\frac{d}{{\mathrm{dt}}_e}\left(\mathrm{RNP}\right)}& \left(1\right)\end{array}$

• • where:
  • V_d—drainage volume
  • c_t—total compressibility
  • RNP—rate normalized pressure
  • t_e—material balance time

At every given time step in the reservoir, the pressure front's propagation causes the predicted drainage volume in Equation (1) to contact the reservoir's pore volume. Like the idea of radius of investigation in homogeneous fields, it tracks the direct time of flight (DTOF) contour of an irregular geometry brought on by the draining of a lumped fracture system, stimulated matrix, and unstimulated matrix. If the well were producing at a constant reference rate, the production behavior represented by this RNP formulation may be what would be seen.

Only under steady-state or pseudo-steady-state conditions, when the well drains a fixed volume and all reservoir boundaries have been reached, is material balance strictly valid. However, unconventional wells are seldom governed by boundary-dominated circumstances. The low permeability matrix may still be gradually touched even after the well contacts all fractures (loosely referred to as the stimulated rock volume or pseudo-boundary dominated flow).

As shown in FIG. 3, an expanding control volume strategy may remedy the issue. The outside edge of the control volume grows at the same rate as the pressure contours. Transient flow may be approximated using “snapshots” or succession of instantaneous pseudo-steady states. The size of the “container” in each time step may be determined by the drainage volume, which was already estimated in Equation (1). There may be no flow into the container according to the definition of drainage volume based on DTOF at each timestep. However, the amount that is removed from the system due to production at the well may be known. Applying material balance allows for calculating the amount of energy lost in the drainage volume that was contacted and showed up as reservoir depletion. Daily tracking of cumulative output may be done in the field, and these tiny timesteps also aid in increasing the precision of the material balance.

For liquid systems, the general material balance expression represents the following fundamental effects:

(Liquid expansion)+(Liberated gas expansion)+(Change in pore volume due to connate water/residual oil expansion and pore volume reduction)=(Underground withdrawal)

Putting it all together, Equation (2) describes the pressure change representing reservoir depletion for liquid systems:

$\begin{array}{cc}\Delta p=\left(\frac{1}{S_{\mathrm{wc}}{c}_w+S_{\mathrm{or}}{c}_o+c_f}\right)\left\{\frac{N_p\left[B_o+\left(R_p-R_s\right)B_g\right]+W_p{B}_w}{V_d}-\left(\frac{1-S_{\mathrm{wc}}-S_{\mathrm{or}}}{1+\omega }\right)\left[\frac{\left(B_o-B_{\mathrm{oi}}\right)+\left(R_{\mathrm{si}}-R_s\right)B_g}{B_o}+\frac{\omega \left(B_w-B_{\mathrm{wi}}\right)}{B_w}\right]\right\}& \left(2\right)\end{array}$

• • where:
  • B_o—oil formation volume factor at pressure of interest, bbl/STB
  • B_oi—oil formation volume factor at initial reservoir pressure, bbl/STB
  • B_w—water formation volume factor at pressure of interest, bbl/STB
  • B_wi—water formation volume factor at initial reservoir pressure, bbl/STB
  • R_si—initial solution gas-oil ratio, SCF/STB
  • R_s—solution gas-oil ratio at pressure of interest, SCF/STB
  • B_g—gas formation volume factor at pressure of interest, bbl/SCF
  • N_p—cumulative oil production, STB
  • S_wc—connate water saturation
  • S_or—residual oil saturation
  • c_o—oil compressibility, psi⁻¹
  • c_w—water compressibility, psi⁻¹
  • c_f—formation compressibility, psi⁻¹
  • W_p—cumulative water production, STB,
  • ω—Ratio of water in place to oil in place
  • R_p—cumulative gas-oil ratio (calculated as cumulative gas divided by cumulative oil), SCF/STB

Note here,

$V_d=\frac{{\mathrm{NB}}_o+{\mathrm{WB}}_w}{1-S_{\mathrm{wc}}-S_{\mathrm{or}}},$

which is the total pore volume contacted which continuously expands as a function of time.

The delta-pressure in Equation (3) represents the reservoir pressure drop from initial pressure:

$\begin{array}{cc}\Delta p=p_i-p_{\mathrm{avg}}& \left(3\right)\end{array}$

• • where:
  • p_i—Initial Reservoir Pressure (psi)
  • p_avg—Average Reservoir Pressure (psi)

The volumetric-averaged pressure in the contacted drainage volume at any given instant may be represented by the average reservoir pressure, which roughly depicts the reservoir's depletion because of production.

Transient Productivity Index

Finally, based on the average reservoir pressure and operating rates and pressure at any timestep, productivity index (PI) can be calculated.

The productivity index (PI) may be a good predictor of well performance and real reservoir inflow potential. It accounts for the impacts of PVT and pressure depletion and normalizes production volumes by flowing pressures. It may be a useful diagnostic metric because it makes it possible to evaluate wells consistently under a variety of operating situations, such as fluctuating choke openings or artificial lift, hence removing biases present in traditional decline curve analysis (DCA) and type curves that are rate-time based and are frequent. Estimation of transient PI leads to a plethora of applications in production optimization and forecasting phase rates.

Transient PI depends on the producing rates, flowing BHP and average reservoir pressure and may be a transient quantity in unconventional wells that is updated at each timestep. Only when flowing BHP is above saturation pressure does PI have a consistent value for a specific reservoir state at any time instance. Due to relative permeability variations, gas liberation occurs when flowing pressure falls below saturation pressure, which lowers total liquid productivity (PI). Given the pressure circumstances, it may be possible to solve equations (4), (5), and (6) to calculate the liquid PI at any given time step.

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.

$\begin{array}{cc}{q}_l=\mathrm{PI}*\left(p_{\mathrm{avg}}-p_{\mathrm{wf}}\right)& \left(4\right)\end{array}$

• • where:
  • q_l—liquid rate, STB/D
  • PI—Productivity Index, STB/D/psi
  • p_avg—Average Reservoir Pressure (psi)
  • p_wf—Bottomhole Pressure (psi)

If the reservoir is still undersaturated, but the flowing BHP drops below saturation pressure (creating saturated conditions in the near-wellbore region), the following expression may be used:

$\begin{array}{cc}{q}_l=\mathrm{PI}*\left(P_{\mathrm{avg}}-P_{\mathrm{sat}}\right)+\left(\frac{\mathrm{PI}*p_{\mathrm{sat}}}{1.8}\right)*\left[1-0.2\frac{p_{\mathrm{wf}}}{p_{\mathrm{sat}}}-0.8{\left(\frac{p_{\mathrm{wf}}}{p_{\mathrm{sat}}}\right)}^2\right]& \left(5\right)\end{array}$

• • where:
  • q_l—liquid rate, STB/D
  • PI—Productivity Index, STB/D/psi
  • p_avg—Average Reservoir Pressure (psi)
  • p_sat—Saturation Pressure (psi)
  • p_wf—Bottomhole Pressure (psi)

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

$\begin{array}{cc}{q}_l=\left(\frac{\mathrm{PI}*p_{\mathrm{avg}}}{1.8}\right)*\left[1-0.2\frac{p_{\mathrm{wf}}}{p_{\mathrm{avg}}}-0.8{\left(\frac{p_{\mathrm{wf}}}{p_{\mathrm{avg}}}\right)}^2\right]& \left(6\right)\end{array}$

• • where:
  • q_l—liquid rate, STB/D
  • PI—Productivity Index, STB/D/psi
  • p_avg—Average Reservoir Pressure (psi)
  • p_wf—Bottomhole Pressure (psi)

Single Segment PI-Based Forecasting (PIBF)

Traditional DCA only functions when operating conditions are constant and ignores pressure data (e.g., constant bottomhole pressure or choke setting, with limited production interruptions) and fluid phase behavior (e.g., PVT property changes). To normalize both surface impacts and take into account phase behavior and therefore reduce noise, disclosed methods utilize PI as the forecasting variable. This provides clearer patterns that are simpler to fit, which leads to more precise models and better forecasts. Additionally, since a definite production decline trend may be established earlier, it is feasible to produce the forecast with lesser data during early production life of the well.

Liquid rate forecasts are made from a base PI forecast utilizing an ensemble of decline models, reservoir pressure, and flowing BHP extrapolation. Initially, the liquid PI trend may be fitted with a modified hyperbolic equation. Other time series-based forecasting models (e.g., ARIMA, RNN etc.) may also be applied based on past values of PI and cumulative volumes.

$\begin{array}{cc}{\mathrm{PI}}_t=\frac{{\mathrm{PI}}_0}{{\left(1+b\left(N_p+W_p\right)\right)}^{\frac{1}{a}}}=f\left(t,N_p+W_p,{\mathrm{PI}}_{t-k}\right)& \left(7\right)\end{array}$

• • where:
  • N_p—cumulative oil production, STB
  • W_p—cumulative water production, STB
  • PI—Productivity Index, STB/D/psi

The PI forecast may be converted into a liquid rate profile by combining it with reservoir pressure and BHP forecasts, using equations (4), (5), and (6). The history matching process may be used to define the profile, and the material balance formulation as stated in the previous phase may be used to extrapolate the average reservoir pressure as a function of cumulative liquid, according to the profile. Since the BHP profile provides the anticipated operating conditions under the intended production strategy for each well, the operator has entire control over it (e.g., choke schedule, artificial lift installs, and operational set points). As a result, the BHP profile can either be a smooth profile or a segmented function indicating several drawdowns associated with the use of different production techniques. 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 may be summarized in method 400 in FIG. 4.

After a single-phase forecast of the liquid rate has been established, a multiphase forecast may be derived to determine the corresponding oil, gas, and water rate profiles. Two steps are used to do this: first, model the water cut, and then model the gas-oil ratio (GOR). Both the water cut and GOR models are independent and modular, and different mathematical representations may be utilized as part of the process and are customized to a specific field's characteristics.

At step 401, a control unit (such as control unit 1800 as described below in FIG. 18) may calculate liquid PI and average reservoir pressure from dynamic drainage volume. At step 402, the liquid PI trend may be fitted with a modified hyperbolic equation. The PI decline model may allow extrapolating the PI at future time steps. An assumption may be 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. Other time series-based forecasting models (ARIMA, RNN, etc.) may also be applied based on past values of PI and cumulative volumes.

On the other hand, well interference may also be automatically identified using PI trends more clearly than using rate or pressure data. 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.

At step 403, the control unit may convert PI forecast into a liquid rate profile by combining it with reservoir pressure and BHP forecasts. The average reservoir pressure may be extrapolated as a function of cumulative liquid, following the profile defined through material balance in the prior step 402. The BHP profile may be completely controllable by an 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 may be either a smooth profile or a segmented function representing multiple drawdowns corresponding to the application of various production methods. The BHP profile may become a sensitivity tool to evaluate the production impact of different operational strategies.

Once the liquid rate forecast is generated, as a single-phase forecast, a multiphase forecast may also be derived, obtaining the corresponding oil, gas and water rate profiles. This may be achieved in two steps (such as in steps 405 and 407), first modeling the water cut, and subsequently modeling the GOR. The water cut may be modeled in step 404, and the GOR may be modeled in step 406. Both the water cut and GOR models may be independent and modular, and various mathematical representations can be used as part of the workflow, tailored to a given field specific conditions. A person skilled in the art, with the benefit of this disclosure, will understand the appropriate models for water cut and GOR that could be used for given conditions. In certain embodiments, water cut may be modeled as a constant trend, a linear trend with a gentle slope, or more complex functional forms. In certain embodiments, a two-segment power law may be used to model GOR, derived by plotting cumulative oil and cumulative gas in a log-log plot and matching two straight-line models.

Modeling GOR in unconventional reservoirs has been a major challenge as compared to that in conventional reservoirs due to a more complex fluid flow behavior. In unconventional reservoirs, several studies have shown GOR behavior may be driven by BHP schedule, the degree of undersaturation, fracture parameters, gas-oil PVT properties, relative permeabilities, bubble point suppression effects and duration of the transient-flow regime. This can be achieved with the material balance formulation based on the dynamic drainage volume derived above. Rearranging the equation in terms of R_p, which is the cumulative GOR of a well, gives Equation (8). As shown, the formulation depends on PVT properties, production data, reservoir properties, drainage volume, and drawdown at a given time.

$\begin{array}{cc}{R}_p=R_s+\frac{V_d}{N_p{B}_g{B}_{\mathrm{oi}}}\left[\text{⁠}\begin{array}{c}\left(R_{\mathrm{si}}-R_s\right)B_g+\left(B_o-B_{\mathrm{oi}}\right)+\\ \omega \frac{\left(B_w+B_{\mathrm{wi}}\right)B_{\mathrm{oi}}}{B_{\mathrm{wi}}}+\frac{\left(S_{\mathrm{wc}}{c}_w+S_{\mathrm{or}}{c}_o+c_f\right)}{1-S_{\mathrm{wc}}-S_{\mathrm{or}})}\left(1+\omega \right)B_{\mathrm{oi}}\Delta p\end{array}\right]-\frac{W_p{B}_w}{N_p{B}_g}-\frac{B_o}{B_g}& \left(8\right)\end{array}$

• • where:
  • B_o—oil formation volume factor at pressure of interest, bbl/STB
  • B_oi—oil formation volume factor at initial reservoir pressure, bbl/STB
  • B_w—water formation volume factor at pressure of interest, bbl/STB
  • B_w—water formation volume factor at initial reservoir pressure, bbl/STB
  • R_si—initial solution gas-oil ratio, SCF/STB
  • R_s—solution gas-oil ratio at pressure of interest, SCF/STB
  • B_g—gas formation volume factor at pressure of interest, bbl/SCF
  • N_p—cumulative oil production, STB
  • S_wc—connate water saturation
  • S_or—residual oil saturation
  • c_o—oil compressibility, psi⁻¹
  • c_w—water compressibility, psi⁻¹
  • c_f—formation compressibility, psi⁻¹
  • W_p—cumulative water production, STB,
  • ω—Ratio of water in place to oil in place
  • R_p—cumulative gas-oil ratio (calculated as cumulative gas divided by cumulative oil), SCF/STB

Hence, to forecast GOR, all the PVT properties computed at forecasted average reservoir pressure and the forecasted liquid phase rates computed during the previous step are used. This reduced physics formulation for GOR captures complex non-linearities associated with PVT changes as the fluids are produced.

Multiple Segment PI-based Forecasting (PIBF)

Multiple segment PIBF (MS-PIBF) extends the above described forecasting process to multiple segments of time throughout the production life of the well. MS-PIBF may be a hybrid method that performs the following steps:

• • 1. Breakpoint identification—During normal production, the well PI continuously declines during transient flow. However, a production interference event attributed to offset well fracs can lead to significant changes in the well productivity decline trend. The first step in the MS-PIBF method may be to automatically detect any breakpoints in PI decline against cumulative fluid produced and identify it as a segment.
  • 2. Segment verification—Next, the method may include verifying if the PI segmentation is an outcome of a frac hit event or an offset well production interference. Any extraneous effects attributed to parent well workovers (e.g., artificial lift change, stimulation, etc.) or extended shut-ins can also change well productivity and should be identified as such.
  • 3. Impact quantification—Finally, the method may include quantifying the impact of the production interference event to the forecasted future production profile for the pre-frac hit and post-frac hit scenarios. While production interference may be believed to accelerate depletion between competing wells, it is also possible that the parent well may experience a temporary boost in well productivity due to pressurized zones from injecting frac fluids, restimulation of hydraulic fractures, or even opening access to new fractured zones.

The major steps that may be involved in the MS-PIBF workflow are shown in FIG. 5.

Breakpoint Identification

The implicit relationship between PI and cumulative fluid produced may be a transient characteristic of an unconventional well. This relationship can be established using a data-driven approach such as a hyperbolic decline curve, or other decline-based forecasting methods. However, when an interference event occurs, it manifests itself as a sharp change in this trend with a signature jump in the PI magnitude followed by a different declining trend. A breakpoint identification algorithm may be used to detect and identify these discontinuities.

The algorithm may be based on proposing a breakpoint and evaluating the fit with dual segments against a single segment fit (with no breakpoint). The quality of fit may be measured through a Manhattan distance error (∈=|PI_fit−PI_actual|, i.e., L₁ norm of error between actual and calculated PI). The fit errors are computed for a single segment, i.e., with no breakpoint (∈) and dual segments, i.e., with a breakpoint (∈₁+∈₂). This evaluation may be repeated several timesteps using a windowing approach, with results as shown in FIGS. 6A-6C.

The timestep at which minimum value of total fit error (∈₁+∈₂) may be achieved is identified as the ultimate breakpoint position. This algorithm can be easily extended to find more than one breakpoint. For simplicity, we will only discuss the case with a single breakpoint as shown in FIGS. 6A-6C, where the best total fit error is 426 after 260 days (∈₁=309, ∈₁=117) in FIG. 6C.

Segment Verification

Typically, well interference events are also characterized by abnormal changes in fluid ratios (e.g., increase in water cut or water to gas ratio). Also, small changes to PI may be seen due to extended shut-ins that may result in some flush production when the well is restarted. However, such changes often disappear after a few days of production and the well performance continues along its original performance trend. Therefore, it may be desirable to verify and eliminate such false events while determining qualified breakpoints.

The magnitude of changes in PI (FIG. 7) and water cut (FIG. 8) at the break point can be used as valid criteria to confirm if the breakpoint is significant and indeed due to a frac hit event. Note that representative values should be carefully chosen to account for measurement noise and daily operational variations. Additionally, any neighboring child well completion operation(s) immediately before the breakpoint event can be used for further validation.

Impact Quantification

As described above, PI vs. cumulative liquid fit can be forecasted in the future, which may be simply a time-discretized liquid rate and PI equations solved explicitly as shown below in Equations (9) and (10):

$\begin{array}{cc}{q}_l\left(t_j\right)=\mathrm{PI}\left(t_{j-1}\right)\times \left(p_{\mathrm{avg}}\left(t_{j-1}\right)-p_{\mathrm{wf}}\left(t_j\right)\right)& \left(9\right)\end{array}$ $\begin{array}{cc}\mathrm{PI}\left(t_j\right)=\frac{{\mathrm{PI}}_0}{{\left(1+b_{\mathrm{PI}}{d}_{\mathrm{PI}}\left(N_p\left(t_j\right)+W_p\left(t_j\right)\right)\right)}^{\frac{1}{b_{\mathrm{PI}}}}}& \left(10\right)\end{array}$

Equation (10) is applied to each of the segments (for forecast decline in PI), both pre-frac hit and post-frac hit. The method may involve comparing the calculated production profiles for each of the segments to quantify the impact of the frac hit event.

Results

To demonstrate the benefits of the MS-PIBF method discussed above, the workflows were successfully applied to several field cases in the following Examples 1-3.

Example 1—Single Frac Hit Event

In this example, the well may be from a major unconventional basin and has been producing for 610 days with gas lift installed from the beginning of production life. Applying the MS-PIBF method, the algorithm detected one interference event (with 2 segments-seg0 for pre-event and seg1 for post-event). It can be observed that the transient PI trend was established early in the well life consistent with low permeability systems. However, after the detected event (on Oct. 29, 2021), the PI magnitude jumped, and the decline signature also changed, as shown in FIG. 9A. Corresponding to this event, the water cut also increased as shown in FIG. 9B, indicating the invasion of completion fluids from an offset well completion. A multi-segmented forecast was automatically applied based on the detected event for each segment for 1 year after the last production day. This forecast included forecasts for PI (FIG. 9A), water cut (FIG. 9B), average reservoir pressure (FIG. 9C), and flowing bottomhole pressure (FIG. 9D). Note that the flowing bottomhole pressure (FIG. 9D) is a controlled variable, and in this case, the forecasts assumed a hyperbolic decline based on its current trend until it reaches a minimum pressure to predict rates.

The impact of well interference in Example 1 is shown in FIGS. 10A-10F and Table 1. After the frac hit event, the actual oil rate increased from 77.8 STB/d to 310.5 STB/d with an incremental cumulative volume of 150,982 STB at the end of forecast period (on Feb. 22, 2024), which had a positive impact on the well production.

TABLE 1
Multi-segment forecast results based on last day of forecast
(Feb. 22, 2024)
				Cum	Cum	Cum
	Liquid	Oil	Water	Liquid	Oil	Water
	Rate	Rate	Rate	Volume	Volume	Volume
Segment	(STB/d)	(STB/d)	(STB/d)	(STB)	(STB)	(STB)
seg0	106.0	77.8	28.2	469,956	273,994	195,962
seg1	481.4	310.5	170.9	765,827	424,976	340,851
Difference	375.4	232.7	142.7	295,871	150,982	144,889
(seg1 − seg0)

Example 2—Multiple Frac Hit Events with Shut-Ins

In this example, the well may be from a major unconventional basin and has been producing for 1250 days (starting on Aug. 14, 2019) with gas lift (installed on Sep. 12, 2019). There were a series of downtime events observed starting from Dec. 22, 2022, and the production data history is available up to Feb. 22, 2023. Applying the MS-PIBF method, the algorithm detected 2 major interference events (i.e., 3 segments-seg0 for pre-frac hit, seg1 after first frac hit event, seg 2 after second frac hit event). Note that the shut-in events are avoided by the algorithm based on the segment verification criteria. The forecast results for a period of 1 year after last production day (up to Feb. 22, 2024) are shown in FIGS. 11A-11D: multisegmented forecast of average reservoir pressure, water cut, flowing bottom hole pressure and liquid productivity.

The effect of the two frac hit events are shown in FIGS. 12A-12F and Table 2. After the second frac hit event, the forecasted oil rate dropped from 80.1 STB/d to 32.6 STB/d with a net reduced cumulative oil volume of 81,336 STB, indicating a negative impact on the well production.

TABLE 2
Multi-segment forecast results based on last day of forecast
(Feb. 22, 2024)
				Cum	Cum	Cum
	Liquid	Oil	Water	Liq	Oil	Water
	Rate	Rate	Rate	Volume	Volume	Volume
Segment	(STB/d)	(STB/d)	(STB/d)	(STB)	(STB)	(STB)
seg0	318.5	80.1	238.4	1,184,381	288,718	895,663
seg1	108.0	29.9	78.1	819,267	207,755	611,512
seg2	300.3	32.6	267.6	1,065,338	207,381	857,957
Difference	−18.2	−47.4	29.2	−119,043	−81,336	−37,707
(seg2 − seg0)

Example 3—Field-Scale Forecasting

This example illustrates the ability of the MS-PIBF method to be applied at field scale through an automated workflow. This example considered a group of 1303 wells from a major US unconventional play, where several wells suffered field frac hits due to infill well drilling and tight well spacing in certain areas. The forecasts on these wells were compared using single-segment PIBF and multi-segment PIBF, respectively. Errors in forecasting productivity index, liquid rates, oil rates and gas rates are shown in FIGS. 13A-13D using an empirical cumulative density function (CDF) plot of median absolute percentage errors (% MedAE) for each method.

As can be clearly seen, MS-PIBF significantly improves the forecasting accuracy, where the P50 value of the % MedAE is reduced significantly in each case. For example, the P50 value of % MedAE for forecasted oil rate is reduced from 28.9% for single-segment PIBF to 19.0% for multi-segment PIBF.

Methods for Detecting Well Interference Events and Production Forecasting

FIG. 14 is an example process flow diagram illustrating a method 1400 of detecting one or more well interference events at a well penetrating a reservoir in a subterranean formation.

At block 1402, the method 1400 includes receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production. At block 1404, the method 1400 includes calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water. At block 1406, the method 1400 includes calculating an average reservoir pressure of the well based at least on the BHP. At block 1408, the method 1400 includes determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure. At block 1410, the method 1400 includes determining a dataset of PI values and corresponding values of cumulative fluid production from the well. At block 1412, the method 1400 includes analyzing the dataset to determine one or more breakpoints in a relationship between PI and cumulative fluid production, the breakpoints representing one or more well interference events. The one or more breakpoints may indicate one or more times during production at which the one or more well interference events occurred. At block 1414, the method 1400 may include determining multiple production forecasts for the well based on multiple segments of the dataset corresponding to time segments prior to and after each breakpoint. At block 1416, the method 1400 may include quantifying an impact of the one or more well interference events on production of the well based on the multiple production forecasts. At block 1418, the method 1400 includes producing fluids from the reservoir based, at least in part, on the one or more breakpoints. For example, the method 1400 may include producing the fluids from the reservoir based, at least in part, on the multiple production forecasts determined at block 1414.

FIG. 15 is an example process flow diagram illustrating a method 1500 of determining one or more breakpoints representing one or more well interference events experienced by a well. For example, the blocks 1502-1524 shown in FIG. 15 (taken in whole or in part) may be used to perform the analysis of block 1412 in the method 1400 of FIG. 14.

At block 1502, the method 1500 includes determining one or more breakpoints. At block 1504, the method 1500 includes verifying that a proposed breakpoint is representative of a well interference event.

To determine the one or more breakpoints (1502), the method 1500 may include, at block 1506, selecting one or more proposed breakpoints. At block 1508, the method 1500 may include defining two or more segments of the dataset, the segments being separated from each other by the proposed breakpoint(s). At block 1510, the method 1500 may include fitting curves of PI vs. cumulative fluid production for each segment of the dataset defined in block 1508. At block 1512, the method 1500 may include determining a quality of the fit of each of the curves from block 1510 to the dataset. At block 1514, the method 1500 may include selecting another one or more proposed breakpoints 1516 and the process of blocks 1508-1514 repeats for each new one or more proposed breakpoints selected. At block 1518, the method 1500 may include selecting the proposed one or more breakpoints having the highest quality fit of their curves to the dataset. This would be the one or more breakpoints that yield the lowest error fit across the different segments.

As an example, in a well where only one well interference event may be suspected, block 1502 may progress as follows: selecting (1506) a first proposed breakpoint; defining (1508) a first segment and a second segment of the dataset, the first segment having values of PI and cumulative fluid production preceding the first proposed breakpoint and the second segment having values of PI and cumulative fluid production following the first proposed breakpoint; fitting (1510) a first curve representing PI vs. cumulative fluid production to the first segment of the dataset and determining (1512) a quality of fit of the first curve to the first segment of the dataset; fitting (1510) a second curve representing PI vs. cumulative fluid production to the second segment of the dataset and determining (1512) a quality of fit of the second curve to the second segment of the dataset; comparing (1516) the quality of fit of the first and second curves to a quality of fit of one or more other pairs of curves calculated for the dataset using one or more additional proposed breakpoints (1514); and selecting (1518) the proposed breakpoint having the highest quality fit of the first and second curves.

As another example, in a well where multiple well interference events are suspected, block 1502 may progress as follows: selecting (1506) a first set of proposed breakpoints; defining (1508) multiple segments of the dataset, each segment having values of PI and cumulative fluid production, and each pair of adjacent segments of the multiple segments being separated by a proposed breakpoint of the first set of proposed breakpoints; fitting (1510) a curve representing PI vs. cumulative fluid production to each segment of the multiple segments of the dataset to generate a first set of curves; determining (1512) a quality of fit of each curve in the first set of curves to the corresponding segment of the dataset; comparing (1516) the quality of fit of the first set of curves to a quality of fit of one or more additional sets of curves calculated for the dataset using one or more additional sets of proposed breakpoints (1514); and selecting (1518) the set of proposed breakpoints having the highest quality fit of the sets of curves.

Verification (1504) of the suspected breakpoint(s) may be performed based on one or more factors including, but not limited to, a change in water cut or PI at the breakpoint (block 1520), a workover operation performed at the well (block 1522), and/or completion operations performed in neighboring wells (block 1524). For example, verifying (1504) that a proposed breakpoint may be representative of a well interference event may include: calculating a water cut for the well; and determining a change in the water cut and/or the PI at the proposed breakpoint exceeds a threshold (1520). As another example, verifying (1504) that a proposed breakpoint may be representative of a well interference event may include: identifying one or more effects of a workover operation at the well (1522); and determining that one or more proposed breakpoints coinciding with the one or more effects are not representative of a well interference event. As another example, verifying (1504) that a proposed breakpoint may be representative of a well interference event may include identifying one or more completion operations in a neighboring well immediately prior to the proposed breakpoint (1524).

FIG. 16 is an example process flow diagram illustrating a method 1600 of forecasting production in a well penetrating a reservoir in a subterranean formation. At blocks 1602-1610, the method 1600 repeats the same steps described above with reference to blocks 1402-1410 of FIG. 14. At block 1612, the method 1600 includes analyzing the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well. Detection of one or more breakpoints may follow one or more steps discussed above with reference to FIG. 15. Upon determining that there may be no breakpoint representing a well interference event at the well, the method 1600 proceeds to block 1614 then block 1616. At block 1614, the method 1600 may include determining a single production forecast for the well based on the full dataset (e.g., single-segment PIBF). At block 1616, the method 1600 may include producing the fluids from the reservoir based, at least in part, on the single production forecast. Upon determining that there is at least a first breakpoint representing a well interference event at the well, the method 1600 proceeds to block 1618, optionally block 1620, and then block 1616. At block 1618, the method 1600 includes determining multiple production forecasts based on different segments of the dataset on either side of the breakpoint(s) (e.g., MS-PIBF). For example, the block 1618 may include determining a first production forecast for the well based on a first segment of the dataset corresponding to a time segment prior to the first breakpoint; and determining a second production forecast for the well based on a second segment of the dataset corresponding to a time segment after the first breakpoint. At block 1620, the method 1600 may include quantifying an impact of the well interference event on production of the well based on the first production forecast and the second production forecast. At block 1616, the method 1600 may include producing the fluids from the reservoir based, at least in part, on the first production forecast and the second production forecast. As such, the method 1600 allows for production of fluids from the reservoir based, at least in part, on whether there are any breakpoints representing well interference events at the well.

FIG. 17 is an example process flow diagram illustrating a method 1700 of forecasting production in a field of a plurality of wells, each well penetrating a reservoir in a subterranean formation. At block 1702, the method 1700 includes, for each well of the plurality of wells, determining whether there are any breakpoints representative of a well interference event. This block 1702 may involve performing the steps described above with reference to blocks 1602-1612 of FIG. 16 for each well in the field. At block 1704, the method 1700 includes determining, for each well, one or more production forecasts for the well based on the PI determined for one or more segments of the dataset. This block 1704 may involve performing the steps described above with reference to block 1614 of FIG. 16 (if no breakpoint is detected) or block 1618 of FIG. 16 (if one or more breakpoints are detected) for each well in the field. At block 1706, the method 1700 may include quantifying an impact of one or more well interference events on production of one or more wells of the plurality of wells based on the production forecasts of block 1704. At block 1708, the method 1700 may include maintaining an inventory of detected well interference events and the impact of the well interference events on production of the plurality of wells in the field. At block 1710, the method includes producing fluids via one or more wells of the plurality of wells based, at least in part, on the production forecasts.

Hardware Implementation

FIG. 18 illustrates a block diagram of an exemplary control unit 1800 in accordance with some embodiments of the present disclosure. In certain example embodiments, control unit 1800 may be configured to create and maintain one or more databases 1808 that include information concerning one or more reservoirs or reservoir models, one or more wells or well models, or a combination thereof. In some embodiments, control system 1802 may include one or more processors, such as processor 1804. Processor 1804 may include, for example, a microprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), or any other digital or analog circuitry configured to interpret and/or execute program instructions and/or process data. In some embodiments, processor 1804 may be communicatively coupled to memory 1806. Processor 1804 may be configured to interpret and/or execute non-transitory program instructions and/or data stored in memory 1806. Program instructions or data may constitute portions of software for carrying out PI calculations, well interference detection, and MS-PIBF, as described herein. Memory 1806 may include any system, device, or apparatus configured to hold and/or house one or more memory modules; for example, memory 1806 may include read-only memory, random access memory, solid state memory, or disk-based memory. Each memory module may include any system, device or apparatus configured to retain program instructions and/or data for a period of time (e.g., computer-readable non-transitory media).

Although control unit 1800 is illustrated as including two databases 1808, control unit 1800 may contain any suitable number of databases. Control unit 1800 may be communicatively coupled to one or more displays 1810 such that information processed by control system 1802 may be conveyed to operators at or near the well or may be displayed at a location offsite.

Modifications, additions, or omissions may be made to FIG. 18 without departing from the scope of the present disclosure. For example, FIG. 18 shows a particular configuration of components for control unit 1800. However, any suitable configurations of components may be used. For example, components of control unit 1800 may be implemented either as physical or logical components. Furthermore, in some embodiments, functionality associated with components of control unit 1800 may be implemented in special purpose circuits or components. In other embodiments, functionality associated with components of control unit 1800 may be implemented in a general purpose circuit or components of a general purpose circuit. For example, components of control unit 1800 may be implemented by computer program instructions.

CONCLUSIONS

In summary, the disclosed methods provide a physics-informed data-driven approach to detect well interference events and quantify their impact on future well production. The disclosed well interference detection approach is robust, interpretable, systematic, and requires minimal inputs. The MS-PIBF method builds upon a single-segment PIBF approach to further improve forecasting accuracy by identifying breakpoints and using multiple segments for forecasting based on changing well performance. The MS-PIBF method shows improved forecasting accuracy on the field examples, highlighting the need for such a tool to operate at the field-scale. Having an evergreen inventory of automatically detected well interference events and quantifying their impacts systematically can further inform the operator on their field development strategies and asset management.

Modifications, additions, or omissions may be made to the systems and apparatuses described herein without departing from the scope of the disclosure. The components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses may be performed by more, fewer, or other components. Additionally, operations of the systems and apparatuses may be performed using any suitable logic comprising software, hardware, and/or other logic. As used in this document, “each” refers to each member of a set or each member of a subset of a set.

Modifications, additions, or omissions may be made to the methods described herein without departing from the scope of the invention. For example, the steps may be combined, modified, or deleted where appropriate, and additional steps may be added. Additionally, the steps may be performed in any suitable order without departing from the scope of the present disclosure.

Although the present invention has been described with several embodiments, a myriad of changes, variations, alterations, transformations, and modifications may be suggested to one skilled in the art, and it is intended that the present invention encompass such changes, variations, alterations, transformations, and modifications as fall within the scope of the appended claims. Therefore, the present invention is well adapted to attain the ends and advantages mentioned as well as those that are inherent therein. The particular embodiments disclosed above are illustrative only, as the present invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular illustrative embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the present invention. Also, the terms in the claims have their plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. The indefinite articles “a” or “an,” as used in the claims, are each defined herein to mean one or more than one of the element that it introduces.

A number of examples have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other implementations are within the scope of the following claims.

Claims

1. A method comprising: receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production;calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water;calculating an average reservoir pressure of the well based at least on the BHP;determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure;determining a dataset of PI values and corresponding values of cumulative fluid production from the well;analyzing the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well; andproducing fluids from the reservoir based, at least in part, on whether there are any breakpoints representing well interference events at the well.

2. The method of claim 1, wherein the breakpoints indicate one or more times during production at which the well interference events occurred.

3. The method of claim 1, wherein determining whether there are any breakpoints comprises: selecting a first proposed breakpoint;defining a first segment and a second segment of the dataset, the first segment having values of PI and cumulative fluid production preceding the first proposed breakpoint and the second segment having values of PI and cumulative fluid production following the first proposed breakpoint;fitting a first curve representing PI vs. cumulative fluid production to the first segment of the dataset and determining a quality of fit of the first curve to the first segment of the dataset;fitting a second curve representing PI versus cumulative fluid production to the second segment of the dataset and determining a quality of fit of the second curve to the second segment of the dataset;comparing the quality of fit of the first and second curves to a quality of fit of one or more other pairs of curves calculated for the dataset using one or more additional proposed breakpoints; andselecting the proposed breakpoint having a highest quality fit of the first and second curves.

4. The method of claim 1, wherein determining whether there are any breakpoints comprises: selecting a first set of proposed breakpoints;defining multiple segments of the dataset, each segment having values of PI and cumulative fluid production, and each pair of adjacent segments of the multiple segments being separated by a proposed breakpoint of the first set of proposed breakpoints;fitting a curve representing PI versus cumulative fluid production to each segment of the multiple segments of the dataset to generate a first set of curves;determining a quality of fit of each curve in the first set of curves to a corresponding segment of the dataset;comparing the quality of fit of the first set of curves to a quality of fit of one or more additional sets of curves calculated for the dataset using one or more additional sets of proposed breakpoints; andselecting the set of proposed breakpoints having a highest quality fit of the sets of curves.

5. The method of claim 1, wherein determining whether there are any breakpoints comprises: selecting a proposed breakpoint; andverifying that the proposed breakpoint is representative of the well interference event.

6. The method of claim 5, wherein verifying that the proposed breakpoint is representative of the well interference event comprises: calculating water cut for the well; anddetermining that a change in at least one of the water cut at the proposed breakpoint and the PI at the proposed breakpoint exceeds a threshold.

7. The method of claim 5, wherein verifying that the proposed breakpoint is representative of the well interference event comprises: identifying one or more effects of a workover operation at the well; anddetermining that one or more proposed breakpoints coinciding with the one or more effects are not representative of the well interference event.

8. The method of claim 5, wherein verifying that the proposed breakpoint is representative of the well interference event comprises identifying one or more completion operations in a neighboring well immediately prior to the proposed breakpoint.

9. The method of claim 1, further comprising: determining multiple production forecasts for the well based on multiple segments of the dataset corresponding to time segments prior to and after each breakpoint; andproducing the fluids from the reservoir based, at least in part, on the multiple production forecasts.

10. The method of claim 9, further comprising quantifying an impact of one or more well interference events on production of the well based on the multiple production forecasts.

11. The method of claim 1, further comprising, upon determining that there is a first breakpoint representing the well interference event at the well: determining a first production forecast for the well based on a first segment of the dataset corresponding to a time segment prior to the first breakpoint;determining a second production forecast for the well based on a second segment of the dataset corresponding to a time segment after the first breakpoint; andproducing the fluids from the reservoir based, at least in part, on the first production forecast and the second production forecast.

12. The method of claim 11, further comprising quantifying an impact of the well interference event on production of the well based on the first production forecast and the second production forecast.

13. The method of claim 1, further comprising, upon determining that there are no breakpoints representing the well interference event at the well: determining a single production forecast for the well based on a full dataset; andproducing the fluids from the reservoir based, at least in part, on the single production forecast.

14. A non-transitory computer-readable medium comprising instructions that are configured, when executed by a processor, to: receive a wellhead pressure and a flowrate of oil, gas, and water for a well during well production;calculate a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water;calculate an average reservoir pressure of the well based at least on the BHP;determine a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure;determine a dataset of PI values and corresponding values of cumulative fluid production from the well;analyze the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well; andproduce fluids from the reservoir based, at least in part, on whether there are any breakpoints representing well interference events at the well.

15. The non-transitory computer-readable medium of claim 14, wherein the breakpoints indicate one or more times during production at which the well interference events occurred.

16. The non-transitory computer-readable medium of claim 14, wherein the instructions are further configured to: select a proposed breakpoint; andverify that the proposed breakpoint is representative of the well interference event for determining whether there are any breakpoints.

17. The non-transitory computer-readable medium of claim 14, wherein the instructions are further configured to: determine multiple production forecasts for the well based on multiple segments of the dataset corresponding to time segments prior to and after each breakpoint; andproduce the fluids from the reservoir based, at least in part, on the multiple production forecasts.

18. A method of forecasting production in a field of a plurality of wells, each well penetrating a reservoir in a subterranean formation, the method comprising: for each well of the plurality of wells: receiving a wellhead pressure and a flowrate of oil, gas, and water for the well during well production;calculating a bottom hole pressure (BHP) of the well based on the wellhead pressure and the flowrate of oil, gas, and water;calculating an average reservoir pressure of the well based at least on the BHP;determining a productivity index (PI) for the well for a plurality of time steps based at least on the average reservoir pressure;determining a dataset of PI values and corresponding values of cumulative fluid production from the well; andanalyzing the dataset to determine whether there are any breakpoints in a relationship between PI and cumulative fluid production representing a well interference event at the well;determining, for each well, one or more production forecasts for the well based on the PI determined for one or more segments of the dataset; andproducing fluids via one or more wells of the plurality of wells based, at least in part, on the production forecasts.

19. The method of claim 18, further comprising quantifying an impact of one or more well interference events on production of one or more wells of the plurality of wells based on the production forecasts.

20. The method of claim 19, further comprising maintaining an inventory of detected well interference events and the impact of the well interference events on production of the plurality of wells in the field.