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:

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

Petroleum Office provides two approaches:

---

Basic Field Profile

Concept

The BasicFieldProfile function models a three-phase production profile:

1. Buildup — Linear ramp from 0 to plateau rate over period $t_B$
2. Plateau — Constant rate $Q_P$ for period $t_P$
3. 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:

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:

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:

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

Type Curve Development

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

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

---

Comparison of Methods

---

See Also

• Decline Overview — Model selection guide
• Arps Decline Models — Individual well decline curves
• Modified Hyperbolic — Terminal decline for type curves