Field Production Profiles

Field production profiles model aggregate production from multiple wells drilled over time. These functions are essential for field development planning, where drilling schedules and type curves combine to forecast total field output.

Overview

Field-level production differs from single-well decline in two key ways:

Buildup Phase — Production ramps up as wells are drilled
Aggregation — Total production is the sum of individual well contributions at different ages

Petroleum Office provides two approaches:

Function	Approach	Best For
`BasicFieldProfile`	Parametric (buildup → plateau → decline)	Quick planning estimates
`CombinedFieldProfile`	Discrete convolution	Detailed schedule modeling

Basic Field Profile

Concept

The BasicFieldProfile function models a three-phase production profile:

Rate
  ^
  |        _______ Plateau
  |       /       \
  |      /         \  Exponential Decline
  |     /           \___________
  |    /                         \
  |___/                           \___
  +----------------------------------------> Time
     |<--->|<------>|<--------------->
      t_B     t_P         Decline

Buildup — Linear ramp from 0 to plateau rate over period $t_B$
Plateau — Constant rate $Q_P$ for period $t_P$
Decline — Exponential decline with initial rate $D_i$

Mathematical Model

q(t) = \begin{cases} \displaystyle\frac{Q_P}{t_B} \cdot t & 0 < t \leq t_B \text{ (buildup)} \\[12pt] Q_P & t_B < t \leq t_B + t_P \text{ (plateau)} \\[12pt] Q_P \cdot e^{-D_i(t - t_B - t_P)} & t > t_B + t_P \text{ (decline)} \end{cases}

Cumulative Production

G_p(t) = \begin{cases} \displaystyle\frac{Q_P}{2t_B} \cdot t^2 & 0 < t \leq t_B \\[12pt] \displaystyle\frac{Q_P \cdot t_B}{2} + Q_P(t - t_B) & t_B < t \leq t_B + t_P \\[12pt] \displaystyle\frac{Q_P \cdot t_B}{2} + Q_P \cdot t_P + \frac{Q_P}{D_i}\left(1 - e^{-D_i(t-t_B-t_P)}\right) & t > t_B + t_P \end{cases}

Function

BasicFieldProfile — Rate at time t for parametric profile

Parameters:

Parameter	Description	Units
`time_buildup`	Duration of buildup phase	T
`time_plateau`	Duration of plateau phase	T
`Q_plateau`	Plateau production rate	L³/T
`Di`	Initial decline rate after plateau	1/T
`time`	Evaluation time	T

Returns: Production rate at time t, [L³/T]

Combined Field Profile

Concept

The CombinedFieldProfile function computes field production as a discrete convolution of a type curve with a drilling schedule:

Q_{field}(t) = \sum_{j=0}^{n(t)} S_{t-j} \cdot P_j

Where:

Symbol	Description
$Q_{field}(t)$	Total field rate at time $t$
$S_k$	Number of wells drilled at time $k$ (schedule)
$P_j$	Type curve rate at well age $j$
$n(t)$	Number of time steps elapsed

This is essentially a moving sum where each well follows the same type curve but starts at its drill date.

Visualization

Time →     1   2   3   4   5   6   7   8
Schedule:  2   1   0   3   0   1   0   0   (wells drilled)

Well ages at t=5:
- 2 wells from t=1: age=4, contributing P[4]
- 1 well from t=2:  age=3, contributing P[3]
- 3 wells from t=4: age=1, contributing P[1]

Total Q[5] = 2×P[4] + 1×P[3] + 0×P[2] + 3×P[1] + 0×P[0]

Function

CombinedFieldProfile — Field rate from drilling schedule

Parameters:

Parameter	Description	Type
`timeSeries`	Time grid (e.g., months 1,2,3...)	Range or array
`profile`	Type well production at each age	Range or array
`schedule`	Wells drilled at each time step	Range or array
`time`	Evaluation time point	Number

Returns: Total field production rate at the specified time, [L³/T]

!!! note "Array Alignment" All three arrays (timeSeries, profile, schedule) must have the same length. The time parameter must exactly match a value in timeSeries.

Parameter Selection Guide

Basic Field Profile Parameters

Parameter	Typical Range	Considerations
time_buildup	1-5 years	Depends on drilling pace and well count
time_plateau	2-10 years	Constrained by facilities capacity
Q_plateau	Facility capacity	Often set by surface constraints
Di	5-25%/year	Match to representative well decline

Type Curve Development

For CombinedFieldProfile, the type curve should represent an average or P50 well:

Normalize production histories to common start date
Calculate mean rate at each time step
Use this as the type curve input

Comparison of Methods

Aspect	BasicFieldProfile	CombinedFieldProfile
Input complexity	4 parameters	3 arrays
Drilling schedule	Implicit (buildup rate)	Explicit (per-period)
Well heterogeneity	Single average	Single type curve
Best for	Screening/planning	Detailed development
Cumulative support	Yes (internally)	Yes (trapezoidal)
EUR calculation	TimeToReachRate method	TimeToReachRate method

Field Production Profiles

Overview

Basic Field Profile

Concept

Mathematical Model

Cumulative Production

Function

Combined Field Profile

Concept

Visualization

Function

Parameter Selection Guide

Basic Field Profile Parameters

Type Curve Development

Comparison of Methods

See Also

Related Excel Functions