Decline Curve Analysis Overview

Introduction

Decline Curve Analysis (DCA) is the primary method for forecasting well and field production, estimating reserves, and calculating economic metrics. By fitting mathematical models to historical rate-time data, engineers can project future performance and ultimate recovery.

Petroleum Office provides a comprehensive suite of decline models covering both conventional and unconventional reservoirs.

When to Use Decline Curve Analysis

DCA is appropriate when:

• Boundary-dominated flow has been established
• Historical production data shows consistent decline behavior
• Reservoir simulation is impractical or unnecessary
• Quick reserves estimates are needed for economic evaluation

DCA may be insufficient when:

• Flow regimes are still transient (early-time data)
• Significant operational changes affect production
• Complex reservoir heterogeneity dominates behavior

Model Selection Guide

Decision Framework

                        Start Here
                            │
                            ▼
                ┌───────────────────────┐
                │  Reservoir Type?      │
                └───────────────────────┘
                     │           │
            Conventional    Unconventional
                     │           │
                     ▼           ▼
              ┌──────────┐  ┌──────────────────┐
              │   Arps   │  │ Flow Regime?     │
              │  Models  │  └──────────────────┘
              └──────────┘       │        │
                   │        Transient   BDF
                   │             │        │
                   ▼             ▼        ▼
              ┌────────┐   ┌────────┐ ┌────────┐
              │b-value?│   │ Duong  │ │ PLE or │
              └────────┘   │  or    │ │ SEPD   │
                 │         │ PLE    │ └────────┘
        ┌────────┼────────┐└────────┘
        │        │        │
      b=0      0<b{`<`}1     b>1
        │        │        │
        ▼        ▼        ▼
   Exponential Hyperbolic  Use
                          Modified
                          Hyperbolic

Quick Reference Table

Available Decline Models

Arps Decline (1945)

The foundational decline model for conventional reservoirs operating under boundary-dominated flow.

Three Forms:

• Exponential (b = 0): Constant decline rate, most conservative
• Hyperbolic (0 < b < 1): Declining decline rate, most common
• Harmonic (b = 1): Special case of hyperbolic

Best For:

• Conventional oil and gas reservoirs
• Wells with established boundary-dominated flow
• Primary and secondary recovery

Limitations:

• Hyperbolic with b > 1 gives infinite EUR
• Not suitable for transient flow periods

📖 Full Documentation: Arps Decline Models

Modified Hyperbolic Decline

Addresses the infinite EUR problem by transitioning from hyperbolic to exponential decline at a specified terminal decline rate.

Key Concept:

• Follows hyperbolic decline until $D = D_{lim}$
• Transitions to exponential decline thereafter
• Gives finite, realistic EUR values

Best For:

• Conventional reservoirs with b ≥ 1
• Long-term forecasts requiring bounded EUR
• Economic limit calculations

📖 Full Documentation: Modified Hyperbolic Decline

Power Law Exponential (PLE)

Designed for unconventional reservoirs exhibiting power-law decline behavior during extended transient flow.

Rate Equation: $q(t) = q_i \exp\left(-D_\infty t - \frac{D_1}{n} t^n\right)$

Best For:

• Tight gas and shale reservoirs
• Hydraulically fractured horizontal wells
• Extended transient (linear) flow periods

Advantages:

• Captures early steep decline
• Bounded EUR (includes $D_\infty$ term)
• Flexible shape parameter n

📖 Full Documentation: Power Law Exponential Decline

Stretched Exponential (SEPD)

A probabilistic model treating drainage as a statistical distribution of characteristic times.

Rate Equation: $q(t) = q_i \exp\left[-\left(\frac{t}{\tau}\right)^n\right]$

Best For:

• Unconventional reservoirs with heterogeneous drainage
• Wells with gradual transition to BDF
• Probabilistic reserves estimation

Advantages:

• Captures late-time BDF behavior
• Finite EUR without artificial constraints
• Physically meaningful parameters

📖 Full Documentation: Stretched Exponential Decline

Duong Decline

Empirically derived for fracture-dominated flow in unconventional reservoirs.

Rate Equation: $q(t) = q_1 t^{-m} \exp\left[\frac{a}{1-m}(t^{1-m} - 1)\right]$

Best For:

• Shale oil and gas wells
• Early production dominated by fracture flow
• Wells with distinct linear flow signature

Advantages:

• Excellent fit to early unconventional data
• Captures characteristic concave-up log-log behavior
• Two-parameter simplicity

📖 Full Documentation: Duong Decline Model

Model Comparison

Decline Behavior Visualization

log(q)
  │
  │╲
  │ ╲╲                    Duong (steep early decline)
  │  ╲ ╲╲
  │   ╲  ╲╲___           PLE (power-law transition)
  │    ╲    ╲  ╲___
  │     ╲     ╲    ╲___  Hyperbolic
  │      ╲      ╲       ╲___
  │       ╲       ╲         ╲  Exponential
  │        ╲        ╲         ╲
  └─────────────────────────────→ log(t)

EUR Comparison for Same Early Data

Practical Workflow

Step 1: Data Preparation

1. Gather rate-time data (monthly or daily)
2. Normalize for operational effects (choke changes, workovers)
3. Identify flow regime from diagnostic plots

Step 2: Model Selection

1. Determine reservoir type (conventional vs. unconventional)
2. Assess flow regime (transient vs. BDF)
3. Select appropriate model(s) from table above

Step 3: Parameter Estimation

Use fitting functions to determine model parameters:

• Rate functions for point estimates
• Cumulative functions for material balance checks
• Weighted fitting for emphasis on recent data

Step 4: Forecast and EUR

1. Generate rate forecast to economic limit
2. Calculate cumulative production (EUR)
3. Validate with volumetric or simulation estimates
4. Assess uncertainty with multiple scenarios

Function Categories

Rate Calculations

Calculate instantaneous production rate at any time.

Cumulative Calculations

Calculate total production from time zero to any point.

EUR Calculations

Calculate ultimate recovery to economic limit or infinite time.

Time Calculations

Determine time to reach a specific rate or cumulative volume.

Parameter Fitting

Estimate model parameters from historical data.

Related Documentation

Detailed Model Theory

• Arps Decline Models — Exponential, hyperbolic, harmonic
• Modified Hyperbolic Decline — Terminal decline transition
• Power Law Exponential — PLE for unconventional
• Stretched Exponential — SEPD probabilistic model
• Duong Decline — Fracture-dominated flow

Supporting Functions

• Interpolation Functions — For data processing
• Unit Conversions — Rate unit handling

References

1. Arps, J.J. (1945). "Analysis of Decline Curves." Transactions of the AIME, 160(1), pp. 228-247.

2. Ilk, D., Rushing, J.A., Perego, A.D., and Blasingame, T.A. (2008). "Exponential vs. Hyperbolic Decline in Tight Gas Sands." SPE-116731-MS.

3. Valko, P.P. and Lee, W.J. (2010). "A Better Way to Forecast Production from Unconventional Gas Wells." SPE-134231-MS.

4. Duong, A.N. (2011). "Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs." SPE-137748-PA.

5. Fetkovich, M.J. (1980). "Decline Curve Analysis Using Type Curves." Journal of Petroleum Technology, 32(6), pp. 1065-1077.