Reservoir performance prediction methods

PREDICTING OILRESERVOIR PERFORMANCE

• Most reservoir engineering calculations involve the use of the material balance equation. Some of the most useful applications of the MBE require the concurrent use of fluid flow equations, e.g., Darcy’s equation.

• Combining the two concepts would enable the engineer to predict the reservoir future production performance as a function of time. Without the fluid flow concepts, the MBE simply provides performance as a function of the average reservoir pressure.

PREDICTING OILRESERVOIR PERFORMANCE

• Prediction of the reservoir future performance is ordinarily performed in the following two phases:

• Phase 1:

Predicting cumulative hydrocarbon production as a function of declining reservoir pressure. This stage is accomplished without regard to:

• Actual number of wells• Location of wells• Production rate of individual wells• Time required to deplete the reservoir

Phase 2: The second stage of prediction is the time-production phase. In these calculations, the reservoir performance data, as calculated from Phase One, are correlated with time. It is necessary in this phase to account for the number of wells and the productivity of each well.

PHASE 1. RESERVOIR PERFORMANCE PREDICTION METHODS

The material balance equation in its various mathematical forms as is designed to provide with estimates of the initial oil in place N, size of the gas cap m, and water influx We. To use the MBE to predict the reservoir future performance, it requires two additional relations:1- Equation of producing (instantaneous) gas-oil ratio2- Equation for relating saturations to cumulative oil productionThese auxiliary mathematical expressions are presented as follows

The produced gas oil ratio (GOR) at any particular time is the ratio of the standard cubic feet of total gas being produced at any time to the stock-tank barrels of oil being produced at that same instant. Hence, the name instantaneous gas-oil ratio.

The following expression describes the GOR mathematically :

Instantaneous Gas-Oil Ratio

The instantaneous GOR equation is of fundamental importance in reservoir analysis. The importance of Equation (1) can appropriately be discussed in conjunction with Figures(1) and (2).These illustrations show the history of the gas-oil ratio of a hypothetical depletion drive reservoir that is typically characterized by the following points:

(1)

Fig-1:Characteristics of solution-gas-drive reservoirs.

Fig-2:History of GOR and Rs for a solution-gas-drive reservoir.

Point 1: When the reservoir pressure p is above the bubble point pressure pb, there is no free gas in the formation, i.e., krg = 0, and therefore:

GOR = Rsi = Rsb (2)

The gas-oil ratio remains constant at Rsi until the pressure reach es the bubble-point pressure at Point 2.

Point 2: As the reservoir pressure declines below pb, the gas begins to evolve from solution and its

• saturation increases. This free gas, however, cannot flow until the gas saturation Sg reaches the critical gas saturation Sgc at Point 3.

From Point 2 to Point 3:

The instantaneous GOR is described by a decreasing

gas solubility as:

GOR = Rs (3)

Point 3:

At Point 3, the free gas begins to flow with the oil and the values of GOR are progressively increasing with the declining reservoir pressure to Point 4. During this pressure decline period, the GOR is described by Equation (1), or:

Point 4:

At Point 4, the maximum GOR is reached due to the

fact that the supply of gas has reached a maximum and

marks the begin ning of the blow-down period to Point 5.

Point 5:

This point indicates that all the producible free gas has

been produced and the GOR is essentially equal to the

gas solubility and continues to Point 6.

There are three types of gas oil ratios, all expressed in scf/STB, which must be clearly distinguished from each other. These are:

1. Instantaneous GOR (defined by Equation (1)

2. Solution GOR

3. Cumulative GOR

The solution gas-oil ratio is a PVT property of the crude oil system. It is commonly referred to as gas solubility and denoted by Rs.

It measures the tendency of the gas to dissolve in or evolve from the oil with changing pressures.

It should be pointed out that as long as the evolved gas remains immobile, i.e., gas saturation Sg is less than the critical gas saturation, the instantaneous GOR is equal to the gas solubility, i.e.:

GOR = Rs

The cumulative gas oil ratio Rp, as defined previously in the material balance equation, should be clearly distinguished from the producing (instantaneous) gas-oil ratio (GOR). The cumulative gas-oil ratio is defined as:

cumulative (TOTAL) gas produced RP = cumulative oil produced or GP

RP = —— (4) Np

where :Rp = cumulative gas-oil ratio, scf/STB Gp = cumulative gas produced, scf Np = cumulative oil produced, STB• The cumulative gas produced Gp is related to the instantaneous GOR and

cumulative oil production by the expression:

• Equation (5) simply indicates that the cumulative gas production at any time is essentially the area under the curve of the GOR versus Np relationship, as shown in Figure 3.

• The above integral can be approximated by using the trapezoidal rule, to give:

(5)

Fig-3:Relationship between GOR and Gp.

• The incremental cumulative gas produced Gp between Np1, and Np2 is then given by:

• The above integral can be approximated by using the trapezoidal rule, to give:

(6)

• Equation (5) can then be approximated as:

(7)

Step 1. Construct the following table:

Solution

The Reservoir Saturation Equations

The saturation of a fluid (gas, oil, or water) in the reservoir is defined as the volume of the fluid divided by the pore volume, or:

oil volumeSo = pore volume

water volumeSw = pore volume

gas volumeSg = pore volume

So + Sw + Sg + 1.0 (11)

(8)

(9)

(10)

• Consider a volumetric oil reservoir with no gas cap that contains N stock-tank barrels of oil at the initial reservoir pressure pi. Assuming no water influx gives:

• Soi = 1 - Swi• where the subscript i indicates initial reservoir

condition. From the defin ition of oil saturation:

If the reservoir has produced Np stock-tank barrels of oil, the remaining oil volume is given by:

remaining oil volume = (N - Np) Bo (12-13)

Substituting Equations 12-13 and 12-12 into Equation 12-8 gives:

• It should be pointed out that the values of the relative permeability ratio krg/kro as a function of oil saturation can be generated by using the actual field production as expressed in terms of Np, GOR, and PVT data. The proposed methodology involves the following steps:

• Step 1. Given the actual field cumulative oil production Np and the PVT data as a function of pressure, calculate the oil and gas saturations from Equations 12-15 and 12-16, i.e.:

Step 2. Using the actual field instantaneous GORs, solve Equation 12-1 for the relative permeability ratio as:

Step 3. Plot (krg/kro) versus So on a semilog paper. Equation 12-15 suggests that all the remaining oil

saturation be distributed uniformly throughout the reservoir. If water influx, gas-cap expansion, or gas-cap shrinking has occurred, the oil saturation equation, i.e., Equation 12-15, must be adjusted to account for oil trapped in the invaded regions.

Oil saturation adjustment for water influxThe proposed oil saturation adjustment methodology

is illustrated in Figure 12-4 and described by the following steps:

Step 1. Calculate the pore volume in the water invaded region, as:

We - Wp Bw = (P.V)water (1 - Swi - Sorw)

Solving for the pore volume of water-invaded zone (P.V)water gives:

Figure 12-4. Oil saturation adjusted for water influx.

Step 2. Calculate oil volume in the water invaded zone,

or:

volume of oil = (P.V)water . Sorw (12-19)

Step 3. Adjust Equation 12-14 to account for the

trapped oil by using Equations 12-18 and 12-19:

Oil saturation adjustment for gas-cap expansion

The oil saturation adjustment procedure is illustrated in Figure 12-5 and

summarized below:

Step 1. Assuming no gas is produced from the gas cap, calculate the net

expansion of the gas cap, from:

Step 2. Calculate the pore volume of the gas-invaded zone,

(P.V)gas, by solving the following simple material balance:

Figure 12-5. Oil saturation adjustment for gas-cap expansion.

• Step 3. Calculate the volume of oil in the gas-invaded zone.

• Step 4. Adjust Equation 12-14 to account for the

trapped oil in the gas expansion zone by using

Equations 12-22 and 12-23, to give:

Oil saturation adjustment for combination drive

• For a combination drive reservoir, i.e., water influx and gas cap, the oil-saturation equation as given by Equation 12-14 can be adjusted to account for both driving mechanisms, as:

Saturated-Oil Reservoirs If the reservoir originally exists at its bubble-point

pressure, the reservoir is referred to as a saturated-oil

reservoir. As the reservoir pressure declines below the

bubble-point, the gas begins to evolve from solution.

The general MBE may be simplified by assuming that the

expansion of the gas is much greater than the expansion

of rock and initial water and, therefore, can be neglected.

For a volumetric and saturated oil reservoir with no fluid

injection, the MBE can be expressed by:

The above material balance equation contains two

unknowns, which are:

• Cumulative oil production ,Np

• Cumulative gas production,Gp

The following reservoir and PVT data must be

available in order to predict the primary recovery

performance of a depletion drive reservoir in terms of

Np and Gp:

(12)

• a. Initial oil-in-place N• b. Hydrocarbon PVT data• c. Initial fluid saturations• d. Relative permeability data

• The above results should be compared with the averaged laboratory relative permeability data.

(13)

• All the techniques that are used to predict the future performance of a reservoir are based on combining the appropriate MBE with the instantaneous GOR using the proper saturation equation. The calculations are repeated at a series of assumed reservoir pressure drops. These calculations are usually based on one stock tank barrel of oil in place at the bubble-point pressure. This avoids carrying large numbers in the calculation procedure and permits calculations to be made on the basis of the fractional recovery of initial oil in place.

• There are several widely used techniques that were specifically developed to predict the performance of solution-gas-drive reservoirs, including:

• Tarner’s method• Tracy’s method• Muskat’s method• These methodologies are presented in the following

section.

Tarner’s Method• Tarner (1944) suggests an iterative technique for predicting

cumulative oil production Np and cumulative gas production Gp as a function of reservoir pressure. The method is based on solving the material balance equation and the instantaneous gas-oil ratio equation simultaneously for a given reservoir pressure drop from p1 to p2. It is accordingly assumed that the cumulative oil and gas production has increased from Np1 and Gp1 to Np2 and Gp2. To simplify the description of the proposed iterative procedure, the stepwise calculation is illustrated for a volumetric saturated-oil reservoir. It should be pointed out that Tarner’s method could be extended to predict the volumetric behavior of reservoirs under different driving mechanisms.

Step 1. Select a future reservoir pressure p2 below the

initial (current) reservoir pressure p1 and obtain the

necessary PVT data. Assume that the cumulative oil

production has increased from Np1 to Np2. It should be

pointed out that Np1 and Gp1 are set equal to zero at the

initial reservoir pressure, i.e., bubble point pressure.

Step 2. Estimate or guess the cumulative oil production

Np2 at p2.

Step 3. Calculate the cumulative gas production Gp2 by

rearranging the MBE, i.e., Equation 12, to give:

(14)

(15)

• Step 4. Calculate the oil and gas saturations at the

assumed cumulative oil production Np2 and the

selected reservoir pressure p2 by applying Equations

(16),(17):

(16)

(17)

• Step 5. Using the available relative permeability data, determine the relative permeability ratio krg/kro that corresponds to the gas saturation at p2 and compute the instantaneous (GOR)2 at p2 from Equation (1), as:

• It should be noted that all the PVT data in the expression must be evaluated at the assumed reservoir pressure p2.

• Step6: Calculate again the cumulative gas production Gp2 at p2 by applying Equation (7), or:

(18)

• in which (GOR)1 represents the instantaneous GOR

at p1. If p1 represents the initial reservoir pressure,

then set (GOR)1 = Rsi.

• Step 7. The total gas produced Gp2 during the first

prediction period as calculated by the material

balance equation is compared to the total gas

produced as calculated by the GOR equation.

(19)

• These two equations provide with two independent

methods required for determining the total gas

produced.

• Therefore, if the cumulative gas production Gp2 as

calculated from Step 3 agrees with the value of Step

6, the assumed value of Np2 is correct and a new

pressure may be selected and Steps 1 through 6 are

repeated.

• Otherwise, assume another value of Np2 and repeat

Steps 2 through 6.

• Step 8. In order to simplify this iterative process,

three values of Np can be assumed, which yield three

different solutions of cumulative gas production for

each of the equations (i.e., MBE and GOR equation).

• When the computed values of Gp2 are plotted versus

the assumed values of Np2, the resulting two curves

(one representing results of Step 3 and the one

representing Step 5) will intersect.

• This intersection indicates the cumulative oil and gas

production that will satisfy both equations.

• It should be pointed out that it may be more

convenient to assume values of NP as a fraction of

the initial oil in place N. For instance, Np could be

assumed as 0.01 N, rather than as 10,000 STB. In

this method, a true value of N is not required.

• Results of the calculations would be, therefore, in

terms of STB of oil produced per STB of oil initially in

place and scf of gas produced per STB of oil initially

in place.

Example 12-6

A saturated oil reservoir has a bubble-point pressure of 2100 psi at 175°F. The initial reservoir pressure is 2925 psi. The following data summarizes the rock and fluid properties of the field:

Original oil in place = 10 MMSTB Connate-water saturation = 15% Porosity = 12 %

cw = 3.6 x 10-6 psi-1

cf = 4.9 x 10-6 psi-1

Predict cumulative oil and gas production at 2100, 1800, and 1500 psi.

Solution

Phase 1: Oil recovery prediction above the bubble-point pressure

Step 1. Arrange the MBE and solve for the cumulative oil as:

Step 2. Calculate the two expansion factors Eo and Ef,w for the pressure declines from 2925 to 2100 psi:

Step 3. Calculate cumulative oil and gas production when the reservoir pressure declines from 2925 to 2100 psi by applying Equation:

to give:

At or above the bubble point pressure, the producing gas oil ratio is equal to the gas solubility at the bubble point and, therefore, the cumulative gas production is given by:

Gp = NP Rsi Gp = (344,656) (1340) =462 MMscf

Step 4. Determine remaining oil in place at 2100 psi.Remaining oil in place = 10,000,000 - 344,656 = 9,655,344 STBThis remaining oil in place is considered as the initial oil in

place during the reservoir performance below the saturation pressure,

Phase 2: Oil recovery prediction below the bubble-point pressure First prediction period at 1800 psi:

1. Assume Np = 0.01 N and apply Equation (15) to solve for Gp:

2. Calculate the oil saturation, to give:

3. Determine the relative permeability ratio krg/kro from the available data to give:

krg/kro = 0.0100

Relative permeability curve

0.01

0.1

1

10

100

0 10 20 30 40 50 60 70 80 90

So

Kg

/Ko

4. Calculate the instantaneous GOR at 1800 psi by applying Equation(18):

to give:

5. Solve again for the cumulative gas production by using the average GOR and applying Equation (19) to yield:

6. Since the cumulative gas production as calculated by the two independent methods (Step 1 and Step 5) do not agree, the calculations must be repeated by assuming a different value for Np and plotting results of the calculation.

GP

Np/N

MB GOR

Actual NP/N

Actual Gp