Derivation of Material Balance Equations

Gas Reservoir Material Balance Equation

5.6.1.1 Dry Gas Reservoir Without Water Influx

Applying the law of conservation of mass on Fig. 5.1, it states that the mass of the

gas initially in place in the reservoir is equal to the amount of gas produced plus the

amount of gas remaining in the reservoir. Recall that gas expands to fill the shape of

its container. Hence, in terms of volume balance, it simply states that the volume of

gas originally in place at the reservoir conditions is equal to the volume of gas

remaining in the reservoir at the new pressure-temperature conditions after some

amount of gas has been produced. Since the pressure of the reservoir has dropped

with a corresponding decrease in the volume of gas due to the amount that have been

produced, therefore the remaining amount of gas in the reservoir would have

expanded to occupy the same volume as that initially in place. Mathematically, we

have that;

A plot of P=z versus Gp gives the x-intercept as the initial gas in place and the

y-intercept as Pi =zi (Fig. 5.2)

Adjustment to Gas Saturation in Water Invaded Zone

The initial gas in place in reservoir volume expressed in terms of pore volume

(PV) is:

GBgi ¼ PVð

 

Material Balance

 Introduction

Globally, there are different techniques applied in the oil and gas industry to estimate

hydrocarbon reserves. These techniques include the analogy, volumetric, decline

curve, material balance and reservoir simulation. The application of these techniques

is dependent on the volume and quality of data available with some level of

uncertainties. In Chap. 2, we have established that the analogy method is applied

by comparing factors for the current field or wells while the volumetric or geologic

method combined the extent of the reservoir (area), the pore volume of the reservoir

rock, the content of fluid within the reservoir pore volume and PVT properties.

When production and pressure data from the field become available, decline

curve analysis and material balance calculations become the predominant methods

of calculating reserves since the hydrocarbon reserve estimation is a continuous

process for a field that is producing. These methods greatly reduce the uncertainties

in reserves estimation; however, during early depletion, caution should be exercised

in using them.

Material balance equation (MBE) makes use of the basic concept of conservation

of mass which states that the cumulative observed production, expressed as an

underground withdrawal, must be equal to the expansion of the fluids in the reservoir

resulting from a finite pressure drop or expressed as the mass of fluids originally in

place equal to mass of fluid remaining plus the mass of fluid produced. MBE is seen

by the Reservoir Engineers as the basic tool for interpreting and predicting the

performance of oil and gas reservoirs. It helps engineers to get a feel of the

reservoir. To better understand this subject, several textbooks and materials were

consultated. these are: Craft & Hawkins (1991), Dake (1978, 1994), Mattar &

Aderson (2005), Numbere (1998), Pletcher (2002), Steffensen (1992), Matter &

McNeil (1998), Tracy (1955) & Tarek (2010).

5.1.1 Assumptions of Material Balance Equation

To apply the material balance equation, there are several assumptions made by the

engineers to successfully carry out an evaluation on oil and gas reservoirs. These are:

• The reservoir is considered to be a tank

• Pressure, temperature, and rock and fluid properties are not space dependent

• Uniform hydrocarbon saturation and pressure distribution (homogenous

reservoir)

• Thermodynamic equilibrium always attained.

• Isothermal condition apply

• Production data is reliable

Limitations of Material Balance Equation

The implication/limitation of the above stated assumptions in evaluating reservoir

performance is that, material balance uses a model that is existing as an imagination

of the reservoir to actually tell or forecast the behaviour of the reservoir. This is

established as a result of the production of hydrocarbon from the reservoir with

natural energy or by gas or water injection. These implications are given below:

• It is considered to be a tank model with a zero dimension which implies that it

does not reflect the area drained

• the shape or geometry of the reservoir

• the manner in which the wells drilled into the reservoirs are positioned and

orientation are not considered

• the dynamic effects of fluid are not considered

• the heterogeneous nature of the reservoir and no time parameters

These implications lead to the statement made by Warner et al. (1979) that the

material balance method has some limitations, though it can be used as a

pre-processing tool to infer fluid in place, drive mechanisms and identify aquifer

for a more sophisticated tool “reservoir simulation”. This sophisticated tool gives an

insight into dynamic rock and fluid properties for evaluation of past reservoir

performance, prediction of future reservoir performance, and reserves estimation.

5.2 Data Requirement in Performing Material Balance

Equation

5.2.1 Production Data

• Cumulative oil, gas and water volume produced

• cumulative gas-oil ratio

5.2.2 PVT Properties

• Oil, gas and water formation volume factor

• Compressibility of water

• Solution Gas-Oil Ratio

5.2.3 Reservoir Properties

• Rock Compressibility

• Connate water saturation

Other Terms

• Initial volume of oil in reservoir

• Initial gas cap

• Water and gas injection if any

5.3 Sources of Data Use for the MBE

Uses of Material Balance Equation

However, despite the assumptions and limitations of the material balance approach,

there some basic uses which could guide reservoir engineers prior to full field

reservoir study. These are:

• Determination of the hydrocarbon in place, gas cap size etc.

• Reservoir pressure estimation from historical production and/or injection

schedule.

• Predict the future performance of the reservoir and the average production of the

wells sunk into the reservoir for a given pressure schedule

• Determine the presence, type and size of an aquifer.

• Estimation of fluid contacts (Gas/Oil, Water/Oil, Gas/Water).

• Material balance equation can be used to calculate fluid saturation as production

increases

5.5 PVT Input Calculation

The PVT properties can either be obtained from the laboratory analysis or generated

from existing correlations. Some of these developed correlations are given below.

Standing Correlations

Glaso Correlations

 Al-Marhouns

Water influx Fetkovich Aquifer Model

 Fetkovich (1971) proposed a model to simplify water influx calculations further.

This method uses a pseudo-steady-state aquifer productivity index (PI) and an

aquifer material balance to represent the system compressibility. Like the Carter￾Tracy method, Fetkovich’s model eliminates the use of superposition and there￾fore, it is much simpler than van Everdingen-Hurst method. However, because

Fetkovich neglects the early transient time period in these calculations, the calcu￾lated water influx will always be less than the values predicted by the previous two

models.

The Fetkovich model applies to finite-acting aquifers; the model is applicable to

both radial and linear aquifers. The Fetkovich aquifer model applies to edge-water

and bottom-water drive reservoirs, while the Carter-Tracy aquifer model applies to

edge-water drive reservoirs. In edge-water drive, water influx occurs around the

flanks of the reservoir. In bottom-water drive, the reservoir is underlain by the

aquifer which encroaches vertically into the reservoir. These are represented in the

Fig. 4.4.

Fetkovich used an inflow equation similar to fluid flow from a reservoir to a well,

to model the water influx to the reservoir. Assuming constant pressure at the original

reservoir/aquifer boundary, the rate of water influx is derived as follow:

The inflow equation is given as:

q ¼

Where qw ¼ water influx rate, j ¼ aquifer productivity index, P ¼ Pressure at the

reservoir fluid contact i.e. inner aquifer boundary pressure, Pa ¼ average pressure in

the aquifer & We ¼ cumulative water influx.

The total aquifer influx due to the total pressure drop is:

The results are plotted in the figure below. This shows that there is a closeness in

value between the Van Everdingen and Fetkovich model with little deviation

from the Carter-Tracy model but that does not mean that Carter-Tracy model cannot

estimate water influx well. In some reservoir, Carter-Tracy model fits the aquifer

model used in matching historical data. Thus, these aquifer models are tested on the

reservoir to see which matches the past field performance with a minimum tolerance

of error.