Petroleum Reserves Estimation Methods

Petroleum Reserves Estimation Methods

The process of estimating oil and gas reserves for a producing field continues throughout the life of the field. There is always uncertainty in making such estimates. The level of uncertainty is affected by the following factors:

1. Reservoir type,

2. Source of reservoir energy,

3. Quantity and quality of the geological, engineering, and geophysical data,

4. Assumptions adopted when making the estimate,

5. Available technology, and

6. Experience and knowledge of the evaluator.

The magnitude of uncertainty, however, decreases with time until the economic limit is reached and the ultimate recovery is realized, see Figure 1.

Figure 1: Magnitude of uncertainty in reserves estimates

The oil and gas reserves estimation methods can be grouped into the following categories:

1. Analogy,

2. Volumetric,

3. Decline analysis,

4. Material balance calculations for oil reservoirs,

5. Material balance calculations for gas reservoirs,

6. Reservoir simulation.

In the early stages of development, reserves estimates are restricted to the analogy and volumetric calculations. The analogy method is applied by comparing factors for the analogous and current fields or wells. A close-to-abandonment analogous field is taken as an approximate to the current field. This method is most useful when running the economics on the current field; which is supposed to be an exploratory field.

The volumetric method, on the other hand, entails determining the areal extent of the reservoir, the rock pore volume, and the fluid content within the pore volume. This provides an estimate of the amount of hydrocarbons-in-place. The ultimate recovery, then, can be estimated by using an appropriate recovery factor. Each of thefactors used in the calculation above have inherent uncertainties that, when combined, cause significant uncertainties in the reserves estimate.

As production and pressure data from a field become available, decline analysis and material balance calculations, become the predominant methods of calculating reserves. These methods greatly reduce the uncertainty in reserves estimates; however, during early depletion, caution should be exercised in using them. Decline curve relationships are empirical, and rely on uniform, lengthy production periods. It is more suited to oil wells, which are usually produced against fixed bottom-hole pressures. In gas wells, however, wellhead back-pressures usually fluctuate, causing varying production trends and therefore, not as reliable.

The most common decline curve relationship is the constant percentage decline (exponential). With more and more low productivity wells coming on stream, there is currently a swing toward decline rates proportional to production rates (hyperbolic and harmonic). Although some wells exhibit these trends, hyperbolic or harmonic decline extrapolations should only be used for these specific cases. Over-exuberance in the use of hyperbolic or harmonic relationships can result in excessive reserves estimates.

Material balance calculation is an excellent tool for estimating gas reserves. If a reservoir comprises a closed system and contains single-phase gas, the pressure in the reservoir will decline proportionately to the amount of gas produced. Unfortunately, sometimes bottom water drive in gas reservoirs contributes to the depletion mechanism, altering the performance of the non-ideal gas law in the reservoir. Under these conditions, optimistic reserves estimates can result.

When calculating reserves using any of the above methods, two calculation procedures may be used: deterministic and/or probabilistic. The deterministic method is by far the most common. The procedure is to select a single value for each parameter to input into an appropriate equation, to obtain a single answer. The probabilistic method, on the other hand, is more rigorous and less commonly used. This method utilizes a distribution curve for each parameter and, through the use of Monte Carlo Simulation; a distribution curve for the answer can be developed. Assuming good data, a lot of qualifying information can be derived from the resulting statistical calculations, such as the minimum and maximum values, the mean (average value), the median (middle value), the mode (most likely value), the standard deviation and the percentiles, see Figures 2 and 3.

Figure 2: Measures of central tendency

Figure 3: Percentiles

The probabilistic methods have several inherent problems. They are affected by all input parameters, including the most likely and maximum values for the parameters. In such methods, one cannot back calculate the input parameters associated with reserves. Only the end result is known but not the exact value of any input parameter. On the other hand, deterministic methods calculate reserve values that are more tangible and explainable. In these methods, all input parameters are exactly known; however, they may sometimes ignore the variability and uncertainty in the input data compared to the probabilistic methods which allow the incorporation of more variance in the data.

A comparison of the deterministic and probabilistic methods, however, can provide quality assurance for estimating hydrocarbon reserves; i.e. reserves are calculated both deterministically and probabilistically and the two values are compared. If the two values agree, then confidence on the calculated reserves is increased. If the two values are away different, the assumptions need to be reexamined.

Volumetric

The volumetric method entails determining the physical size of the reservoir, the pore volume within the rock matrix, and the fluid content within the void space. This provides an estimate of the hydrocarbons-in-place, from which ultimate recovery can be estimated by using an appropriate recovery factor. Each of the factors used in the calculation have inherent uncertainties that, when combined, cause significant uncertainties in the reserves estimate. Figure 4 is a typical geological net pay isopach map that is often used in the volumetric method.

 Figure 4: A typical geological net pay isopach map

 The estimated ultimate recovery (EUR) of an oil reservoir, STB, is given by:

EUR = N(t) RF

Where N(t) is the oil in place at time t, STB, and RF is the recovery factor, fraction. The volumetric method for calculating the amount of oil in place (N) is given by the following equation:

Where:

N(t) = oil in place at time t, STB

Vb = bulk reservoir volume, RB = 7758 A h

7758 = RB/acre-ft

A = reservoir area, acres

h = average reservoir thickness, ft

φ = average reservoir porosity, fraction

So(t) = average oil saturation, fraction

Bo(p) = oil formation volume factor at reservoir pressure p, RB/STB

Similarly, for a gas reservoir, the volumetric method is given by:

EUR = G(t) RF

Where G(t) is the gas in place at time t, SCF, and RF is the recovery factor, fraction. The volumetric method for calculating the amount of gas in place (G) is given by the following equation:

Where:

G(t) = gas in place at time t, SCF

Vb = bulk reservoir volume, CF = 43560 A h

43560 = CF/acre-ft

A = reservoir area, acres

h = average reservoir thickness, ft

φ = average reservoir porosity, fraction

Sg(t) = average gas saturation, fraction

Bg(p) = gas formation volume factor at reservoir pressure p, CF/SCF

Note that the reservoir area (A) and the recovery factor (RF) are often subject to large errors. They are usually determined from analogy or correlations. The following examples should clarify the errors that creep in during the calculations of oil and gas reserves.

Decline Curves

A decline curve of a well is simply a plot of the well’s production rate on the y-axis versus time on the x-axis. The plot is usually done on a semilog paper; i.e. the y-axis is logarithmic and the x-axis is linear. When the data plots as a straight line, it is modeled with a constant percentage decline “exponential decline”. When the data plots concave upward, it is modeled with a “hyperbolic decline”. A special case of the hyperbolic decline is known as “harmonic decline”.

The most common decline curve relationship is the constant percentage decline (exponential). With more and more low productivity wells coming on stream, there is currently a swing toward decline rates proportional to production rates (hyperbolic and harmonic). Although some wells exhibit these trends, hyperbolic or harmonic decline extrapolations should only be used for these specific cases. Over-exuberance in the use of hyperbolic or harmonic relationships can result in excessive reserves estimates. Figure 5 is an example of a production graph with exponential and harmonic extrapolations.

  Figure 5: Decline curve of an oil well

Decline curves are the most common means of forecasting production. They have many advantages:

·         Data is easy to obtain,

·         They are easy to plot,

·         They yield results on a time basis, and

·         They are easy to analyze.

If the conditions affecting the rate of production of the well are not changed by outside influences, the curve will be fairly regular, and, if projected, will furnish useful knowledge as to the future production of the well.

Exponential Decline

As mentioned above, in the exponential decline, the well’s production data plots as a straight line on a semilog paper. The equation of the straight line on the semilog paper is given by:

Where:

q = well’s production rate at time t, STB/day

qi = well’s production rate at time 0, STB/day

D = nominal exponential decline rate, 1/day

t = time, day

The following table summarizes the equations used in exponential decline.

Hyperbolic Decline

Alternatively, if the well’s production data plotted on a semilog paper concaves upward, then it is modeled with a hyperbolic decline. The equation of the hyperbolic decline is given by:

Where:

q = well’s production rate at time t, STB/day

qi = well’s production rate at time 0, STB/day

Di = initial nominal exponential decline rate (t = 0), 1/day

b = hyperbolic exponent

t = time, day

The following table summarizes the equations used in hyperbolic decline:

Harmonic Decline

A special case of the hyperbolic decline is known as “harmonic decline”, where b is taken to be equal to 1. The following table summarizes the equations used in harmonic decline:

 

Material Balance Calculations for Oil Reservoirs

A general material balance equation that can be applied to all reservoir types was first developed by Schilthuis in 1936. Although it is a tank model equation, it can provide great insight for the practicing reservoir engineer. It is written from start of production to any time (t) as follows:

Expansion of oil in the oil zone +

Expansion of gas in the gas zone +

Expansion of connate water in the oil and gas zones +

Contraction of pore volume in the oil and gas zones +

Water influx + Water injected + Gas injected =

Oil produced + Gas produced + Water produced

Mathematically, this can be written as:

 

Where:

N = initial oil in place, STB

Np = cumulative oil produced, STB

G = initial gas in place, SCF

GI = cumulative gas injected into reservoir, SCF

Gp = cumulative gas produced, SCF

We = water influx into reservoir, bbl

WI = cumulative water injected into reservoir, STB

Wp = cumulative water produced, STB

Bti = initial two-phase formation volume factor, bbl/STB = Boi

Boi = initial oil formation volume factor, bbl/STB

Bgi = initial gas formation volume factor, bbl/SCF

Bt = two-phase formation volume factor, bbl/STB = Bo + (Rsoi - Rso) Bg

Bo = oil formation volume factor, bbl/STB

Bg = gas formation volume factor, bbl/SCF

Bw = water formation volume factor, bbl/STB

BIg = injected gas formation volume factor, bbl/SCF

BIw = injected water formation volume factor, bbl/STB

Rsoi = initial solution gas-oil ratio, SCF/STB

Rso = solution gas-oil ratio, SCF/STB

Rp = cumulative produced gas-oil ratio, SCF/STB

Cf = formation compressibility, psia-1

Cw = water isothermal compressibility, psia-1

Swi = initial water saturation

Δpt = reservoir pressure drop, psia = pi - p(t)

p(t) = current reservoir pressure, psia

The MBE as a Straight Line

Normally, when using the material balance equation, each pressure and the corresponding production data is considered as being a separate point from other pressure values. From each separate point, a calculation is made and the results of these calculations are averaged. However, a method is required to make use of all data points with the requirement that these points must yield solutions to the material balance equation that behave linearly to obtain values of the independent variable. The straight-line method begins with the material balance written as:

 

Defining the ratio of the initial gas cap volume to the initial oil volume as:

and plugging into the equation yields:

Let:

Thus we obtain:

The following cases are considered:

1. No gas cap, negligible compressibilities, and no water influx

2. Negligible compressibilities, and no water influx

Which is written as y = b + x. This would suggest that a plot of F/Eo as the y coordinate versus Eg/Eo as the x coordinate would yield a straight line with slope equal to mN and intercept equal to N.

3. Including compressibilities and water influx, let:

Dividing through by D, we get:

 Which is written as y = b + x. This would suggest that a plot of F/D as the y coordinate and We/D as the x coordinate would yield a straight line with slope equal to 1 and intercept equal to N.

Drive Indexes from the MBE

The three major driving mechanisms are:

1. Depletion drive (oil zone oil expansion),

2. Segregation drive (gas zone gas expansion), and

3. Water drive (water zone water influx).

To determine the relative magnitude of each of these driving mechanisms, the compressibility term in the material balance equation is neglected and the equation is rearranged as follows:

 

Dividing through by the right hand side of the equation yields:

 

The terms on the left hand side of equation (3) represent the depletion drive index (DDI), the segregation drive index (SDI), and the water drive index (WDI) respectively. Thus, using Pirson's abbreviations, we write:

DDI + SDI + WDI = 1

The following examples should clarify the errors that creep in during the calculations of oil and gas reserves.

Material Balance Calculations for Gas Reservoirs

Material balance calculation is an excellent tool for estimating gas reserves. It is based on the non-ideal gas law, PV = ZnRT. If a reservoir comprises a closed system and contains single-phase gas, the pressure in the reservoir will decline proportionately to the amount of gas produced. Unfortunately, sometimes bottom water drive in gas reservoirs contributes to the depletion mechanism, altering the performance of the non-ideal gas law in the reservoir. Under these conditions, optimistic reserves estimates can result. Figure 8 is a typical material balance plot for a tank-type reservoir.

 Figure 8: P/z plot of a gas reservoir

 For a single-phase gas reservoir, the MB equation takes the form:

The following cases are considered:

1. Volumetric (Closed) Gas Reservoirs, Neglecting Compressibilities

2. Gas Reservoirs with Water Influx, Neglecting Compressibilities

3. Gas Reservoirs with Water influx, Including Compressibilities

4. Abnormally High-Pressure Gas Reservoirs

5. Abnormally High-Pressure Gas Reservoirs, Including Dissolved Gas in Water (Fetkovitch Technique)

6. Wet Gas Reservoirs

7. Tight Gas Reservoirs

Volumetric (Closed) Gas Reservoirs, Neglecting Compressibilities

The material balance equation for gas reservoirs, when water and rock compressibilities are neglected, is given by:

Since

And

Then

Plugging into the above equation, we obtain:

Which can arranged in a straight line form as follows:

This suggests plotting Gp on the x-axis versus p/z on the y-axis and drawing the best fit line through the set of points. The slope of the best fit line would be -pi/(zi G) and the y-intercept would be pi/zi.

Gas Reservoirs with Water Influx, Neglecting Compressibilities

The material balance equation for gas reservoirs with water influx and negligible water and rock compressibilities, is given by:

Rearranging and dividing all through by Bg yields:

Substituting for Bg = C z/p on the LHS and dividing by G yields:

Solving for p/z yields:

Which suggests plotting (Gp - (We - Wp Bw)/Bg) on the x-axis versus p/z on the y-axis and drawing the best fit line through the set of points. The slope of the best fit line would be -pi/(zi G) and the y-intercept would be pi/zi. The following example would clarify those concepts.

Gas Reservoirs with Water Influx, Including Compressibilities

The material balance equation for gas reservoirs with water influx and water and rock compressibilities is given by:

Let

Dividing all through by Bg and rearranging yields:

Substituting for Bg = C z/p yields:

Rearranging in a straight line form yields:

Which suggests plotting (Gp - (We - Wp Bw)/Bg) on the x-axis versus p/z(1-CeΔpt) on the y-axis and drawing the best fit line through the set of points. The slope of the best fit line would be -pi/(zi G) and the y-intercept would be pi/zi. The following example will clarify this method of solution.

Abnormally High-Pressure Gas Reservoirs

In abnormally high-pressure gas reservoirs, Cf is a strong function of pressure. Thus we set:

Therefore the equation is written as follows:

This is in the form:

y = b + mx

Where:

Abnormally High-Pressure Gas Reservoirs, Including Dissolved Gas in Water (Fetkovitch Method)

For high-pressure gas reservoirs with dissolved gas in water, Fetkovitch et al. expressed the material balance equation as follows:

Where:

"M" is defined as the associated water volume ratio. The associated water and pore volumes external to the net pay include Non-Net Pay (NNP) such as inter-bedded shales and dirty sands plus external water volume found in Aquifers. This volume is expressed as a ratio relative to the pore volume of the net-pay reservoir; i.e.

Wet Gas Reservoirs

In wet gas reservoirs, the stock tank barrels of the liquid condensate produced must be accounted for in the cumulative gas production. This is done as follows:

Where:

(Gp)eff = effective cumulative gas produced, SCF

Gp = cumulative gas produced, SCF

GLc = cumulative liquid condensate produced, STB

KLc = liquid condensate conversion factor, SCF/STB, which is given by:

SGLc = Specific gravity of the liquid condensate which is given by:

MWLc = Molecular weight of the liquid condensate which is given by:

Therefore the effective gas production would be given by:

Tight Gas Reservoirs

The key assumption involved in the P/z plot for gas reservoirs is that the reservoir behaves as a tank. In tight gas reservoirs, however, this assumption is violated; thus the plot fails and can incur greater than 100% error in estimating GIIP. In such a case, the tank assumption does not apply by definition and the method leads to substantial pressure gradients. These gradients manifest themselves in terms of scattered, generally curved, and rate-dependent P/z behavior.

The Communicating Reservoir (CR) model for tight gas reservoirs as suggested by Payne (1) will be considered here. This model consists of subdividing the reservoir into a number of tanks that are allowed to communicate. Such tanks can either be depleted directly by wells, or indirectly via other tanks. Flow rates between tanks are set proportionally to either the difference in the square of tank pressures or the difference in pseudo-pressures. In terms of pressure squared, the flow between two tanks x and y is determined as:

where Cxy is known as the communication factor and qxy is the rate of flow between the two tanks x and y.

Individual tank pressures are determined by assuming straight line P/z versus G behavior where G includes both Gp (gas produced by wells in the tank) and Ge ( gas efflux or influx from connected tanks).

Simulation

The process of simulating petroleum reservoirs has been thoroughly described by Peaceman (24) as the:

“process of inferring the behavior of a real reservoir, the prototype system, from the performance of a model of that reservoir. The model may be physical, such as a scaled laboratory model, or mathematical. A mathematical model of a real reservoir is a set of partial differential equations, together with an appropriate set of boundary conditions, which are believed to adequately describe the significant physical processes taking place in the real reservoir, see Figure 14. The processes taking place in a real reservoir are basically fluid flow and mass transfer. Up to three immiscible phases (gas, oil, and water) may flow simultaneously where gravity, capillary, and viscous forces play an important role in the flow process. Mass transfer may take place between the phases (chiefly between gas and oil phases).

The model equations must account for all forces, and should also take into account an arbitrary reservoir description with respect to heterogeneity and geometry. The equations are obtained by combining the mass conservation equation with the equation of motion (Darcy's law).

To use the mathematical model for predicting the behavior of a real reservoir, it is necessary to solve the model equations subject to the appropriate boundary conditions. The methods of solution are basically divided into two main methods, analytical and numerical. Analytical methods are applicable only to the simplest cases involving homogeneous reservoirs and very regular boundaries. Numerical methods, on the other hand, are extremely general in their applicability and have proved to be highly successful for obtaining solutions to very complex reservoir situations. A numerical model of a reservoir, then, is a computer program that uses numerical methods to obtain an approximate solution to the mathematical model.”

 

 Figure 14: Process of modeling petroleum reservoirs

Due to its simplicity, the finite difference method is the most widely used numerical technique in petroleum industry. Finite differences are easy to understand and to program. In addition, less input is required to construct a finite difference grid.

There are numerous models that were coded using this method. The use of finite difference grids is restricted by the fact that they can not accurately approximate the reservoir boundary as shown by Figure 15.

Figure 15: Finite Difference Method

Reserve estimates are only by-products of the reservoir simulation process. At the end of each time step, the simulator calculates the volume of oil and gas in each cell. Fluid saturations along with pressure values in each cell are updated for the next time step. The process continues until the end of simulation time. The amount of oil and gas in the reservoir is calculated by the summation of oil and gas in all cells.

References:

• S. Naji, Hassan Dr., 2004, Petroleum Reserves Estimation Methods, A Report Submitted to the Energy Studies Department OPEC Secretariat
• www.petrobjects.com