Material Balance Overview

Introduction

Material Balance Equation (MBE) is a fundamental reservoir engineering tool that applies the conservation of mass to a petroleum reservoir. By accounting for all fluids produced, injected, and remaining in place, the MBE enables:

  • Original fluids in place — estimate OOIP (oil) or OGIP (gas)
  • Drive mechanism identification — depletion, gas cap, water drive, compaction
  • Aquifer characterization — size and strength of water influx
  • Recovery prediction — forecast reservoir performance
  • History matching — validate simulation models

The MBE treats the reservoir as a single "tank" — a zero-dimensional model. Despite this simplification, it provides robust volumetric estimates when sufficient pressure and production data are available.

The General Material Balance Equation

Concept

Production=Expansion+Influx\text{Production} = \text{Expansion} + \text{Influx}

All fluids withdrawn from the reservoir must come from:

  1. Expansion of oil, gas, water, and rock as pressure declines
  2. External influx of water from an aquifer

Reservoir Classification

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Gas Reservoir Material Balance

The p/z Method

For a volumetric gas reservoir (no water influx), the MBE simplifies to:

pz=pizi(1−GpG)\frac{p}{z} = \frac{p_i}{z_i}\left(1 - \frac{G_p}{G}\right)

Where:

  • p/zp/z = pressure divided by gas compressibility factor
  • GG = original gas in place (OGIP)
  • GpG_p = cumulative gas production

A plot of p/zp/z vs. GpG_p yields a straight line:

  • Y-intercept = pi/zip_i/z_i (known)
  • X-intercept = GG (OGIP)

Modified p/z for Geopressured Reservoirs

Abnormally pressured reservoirs require correction for water and rock compressibility:

pz∗=pizi∗(1−GpG)\frac{p}{z^*} = \frac{p_i}{z_i^*}\left(1 - \frac{G_p}{G}\right)

Where z∗z^* incorporates formation and water compressibility terms.

📖 Full Documentation: Gas Reservoirs

Oil Reservoir Material Balance

Havlena-Odeh Straight-Line Method

The general oil MBE is rearranged into linear forms for graphical interpretation:

F=N[Eo+mEg+Efw]+WeF = N[E_o + mE_g + E_{fw}] + W_e

Where:

  • FF = underground withdrawal (production voidage)
  • NN = original oil in place (OOIP)
  • EoE_o = oil and dissolved gas expansion
  • EgE_g = gas cap expansion
  • EfwE_{fw} = connate water and rock expansion
  • mm = gas cap ratio (=GBgi/NBoi= G B_{gi} / N B_{oi})
  • WeW_e = cumulative water influx

Expansion Terms

Term Expression Physical Meaning
EoE_o Bt−BtiB_t - B_{ti} Oil + dissolved gas expansion
EgE_g Bti(Bg/Bgi−1)B_{ti}(B_g/B_{gi} - 1) Gas cap expansion
EfwE_{fw} BticwSwi+cf1−SwiΔpB_{ti}\frac{c_w S_{wi} + c_f}{1 - S_{wi}}\Delta p Water + rock expansion

Underground Withdrawal

F=Np[Bo+(Rp−Rs)Bg]+WpBwF = N_p[B_o + (R_p - R_s)B_g] + W_p B_w

📖 Full Documentation: Oil Reservoirs

Drive Mechanism Identification

Drive Indices

The relative contribution of each drive mechanism is quantified by drive indices:

Index Symbol Expression
Depletion Drive DDI NEo/FN E_o / F
Gas Cap Drive GDI NmEg/FN m E_g / F
Water Drive WDI We/FW_e / F
Compaction Drive CDI NEfw/FN E_{fw} / F

The sum of all drive indices equals 1.0 at each time step:

DDI+GDI+WDI+CDI=1.0DDI + GDI + WDI + CDI = 1.0

Interpretation

Dominant Drive Typical DDI Pressure Behavior Recovery
Solution gas > 0.8 Rapid decline 5-25%
Gas cap > 0.3 Moderate decline 20-40%
Water drive > 0.5 Slow decline, near constant 35-75%
Compaction > 0.3 Slow decline 15-40%

Aquifer Models

Water influx from an aquifer is the most uncertain term in the MBE. Several models with increasing complexity are available:

Model Type Assumptions Best For
Pot Simple tank Finite, instant response Small, active aquifers
Schilthuis Steady-state Constant influx rate per psi Moderate aquifers
Fetkovich Pseudo-steady-state Finite aquifer, declining influx Most field applications
Van Everdingen-Hurst Unsteady-state Rigorous diffusivity solution Large, complex aquifers

📖 Full Documentation: Aquifer Models

MBE Workflow

Step-by-Step Analysis

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Available Calculations

Gas MBE

Function Category Description
p/z and modified p/z Standard and geopressured methods
OGIP estimation From p/z analysis
Pressure prediction Forecast pressure at given cumulative production
Recovery factor Ultimate recovery calculation

Oil MBE

Function Category Description
Havlena-Odeh OOIP estimation (single-point and regression)
Expansion terms EoE_o, EgE_g, EfwE_{fw}, EtE_t, BtB_t
Underground withdrawal FF for oil and gas reservoirs
Drive indices DDI, GDI, WDI, CDI

Aquifer Models

Function Category Description
Pot aquifer Volume and cumulative influx
Schilthuis Influx rate and cumulative
Fetkovich Aquifer properties, pressure, rate, cumulative
Van Everdingen-Hurst Dimensionless influx functions

📖 Full Documentation: Underground Withdrawal

Best Practices

Data Quality

  1. Pressure data must be average reservoir pressure (not flowing pressure)
  2. Use shut-in pressures or correct for pressure gradients
  3. Consistent PVT — use the same correlations throughout
  4. Account for all production — oil, gas, and water

Common Pitfalls

Issue Cause Solution
N varies with time Wrong drive mechanism assumed Re-evaluate m or We
N is negative Aquifer overestimated Reduce aquifer size
Early data scatter Pressure measurement errors Weight later data more
Non-linear p/z plot Water influx present in gas reservoir Use gas MBE with We

MBE Details

Supporting Topics

References

  1. Havlena, D. and Odeh, A.S. (1963). "The Material Balance as an Equation of a Straight Line." Journal of Petroleum Technology, 15(8), 896-900. SPE-559-PA.

  2. Havlena, D. and Odeh, A.S. (1964). "The Material Balance as an Equation of a Straight Line — Part II, Field Cases." Journal of Petroleum Technology, 16(7), 815-822. SPE-869-PA.

  3. Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Elsevier.

  4. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Gulf Professional Publishing.

  5. Craft, B.C. and Hawkins, M.F. (1991). Applied Petroleum Reservoir Engineering, 2nd Edition. Prentice Hall.

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