1. Reservoir performance prediction methods
Formation Evaluation 1
Reservoir performance prediction methods

2. PREDICTING OIL RESERVOIR PERFORMANCE
Formation Evaluation 2
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.

3. PREDICTING OIL RESERVOIR PERFORMANCE
Formation Evaluation 3
PREDICTING OIL RESERVOIR 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

4. PHASE 1. RESERVOIR PERFORMANCE PREDICTION METHODS
Formation Evaluation 4
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 ratio
2- Equation for relating saturations to cumulative oil production
These auxiliary mathematical expressions are presented as follows
So far, we have talked about how reservoirs are created, how petroleum is formed, and how it migrates through permeable rock until it is captured in a trap. We have also discussed how operators explore for hydrocarbons and how wells are drilled.
Since petroleum reservoirs are generally located many thousands of feet below the surface, it is necessary to use sophisticated tools, such as wireline logs, to gather important information about the reservoirs. This information is then interpreted by highly trained industry professionals, using various mathematical and empirical models, to determine fundamental reservoir properties, such as porosity and permeability.
Once estimates of important reservoir parameters have been established, a computer model (a.k.a. reservoir simulation) of the reservoir may be constructed to help engineers predict the production performance of the reservoir. This is very important in the planning stages of the exploitation process, as developing petroleum reservoirs can cost hundreds of millions of dollars. Optimizing the number of wells and production equipment can save the operating company thousands, if not millions of dollars.

5. Instantaneous Gas-Oil Ratio
Formation Evaluation 5
Instantaneous Gas-Oil Ratio
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 :
It is important that an operating company collect as much information about the reservoir as the economics of the project allows. In addition to seismic and wireline logs, core data, geological data, regional data, and information from nearby wells can be extremely valuable in making economic decisions. Obtaining this data requires trained professionals from both the operating company and service companies, such as Schlumberger, working together to get the best possible interpretation.
Over the years, operating companies have found that service companies can offer many of the processes once performed in house at a lower cost and at a highly quality. For example, a Schlumberger wireline expert may have experience with a wide range of reservoirs, as opposed to an operating company engineer who deals only with a limited number of reservoirs. Of course, the operating company engineer will have much more detailed information about his own reservoirs, so it is necessary that the two work closely together.

6. Formation Evaluation 6
(1)
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:

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

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

9. Formation Evaluation 9
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 reach­es 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.
Cores from the reservoir allow direct measurements of important reservoir properties. It is important to gather cores from a representative part of the reservoir, as reservoir properties vary horizontally and vertically. If a reservoir is known to be highly heterogeneous, many core samples will be required to describe the reservoir accurately.

10. 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:

11. Formation Evaluation 11
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 begin­ning 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.
The logs listed above are routinely found in modern log suites. On following slides, each log will be discussed briefly.

12. Instantaneous GOR (defined by Equation (1) Solution GOR Cumulative GOR
Formation Evaluation 12
There are three types of gas oil ratios, all expressed in scf/STB, which must be clearly distinguished from each other. These are:
Instantaneous GOR (defined by Equation (1)
Solution GOR
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.
The Gamma Ray Log is a measurement of the natural radioactivity of the formations. In sedimentary formations the GR log normally reflects the shale content of the formations. This is because the radioactive elements tend to concentrate in shales and clays. Sands have a very low GR measurement.
Gamma rays are bursts of high-energy electromagnetic waves which are emitted spontaneously by some radioactive elements, in particular, the radioactive potassium isotope of atomic weight 40, and the radioactive elements of uranium and thorium series. These radioactive elements tend to concentrate in shales.

13. cumulative (TOTAL) gas produced RP = cumulative oil produced or GP
Formation Evaluation 13
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
The deflections on the SP curve result from electric currents flowing in the mud in the borehole. The SP currents are caused by electromotive forces in the formations, which are of electrochemical and electrokinetic origins.
The movement of ions, which causes the SP phenomenon, is possible only in formations having a certain minimum permeability. But there is no direct relationship between the value of permeability and the magnitude of the SP deflection, nor does the SP deflection have any direct relation to porosity. Accordingly, the SP is used only as a qualitative indication of permeability.

14. Rp = cumulative gas-oil ratio, scf/STB
Formation Evaluation 14
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)

15. Fig-3:Relationship between GOR and Gp.
Formation Evaluation 15
Fig-3:Relationship between GOR and Gp.

16. Formation Evaluation 16
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)

17. Equation (5) can then be approximated as:
Formation Evaluation 17
Equation (5) can then be approximated as:
(7)
1. Mudlogs give a drilling rate, which can be used to determine lithology, cuttings lithology, total gas concentration in air, and gas chromatograph reading.
Cores can give porosity, horizontal permeability, and grain density information, as well as vertical air permeability, relative permeability, capillary pressure, and logging parameters.
2. Gamma ray - used to locate bed boundaries and as a shale indicator; SP - used primary to locate bed boundaries; Resistivity - used to identify fluid type; Neutron, Sonic, and Density - used to calculate porosity and determine lithology.
3. Gamma Ray - same as openhole log; Natural Gamma Ray Spectrometry Log - used to identify clay types and clay volumes, and is a better shale indicator than GR; Neutron Logs - same as open hole log; Long Spaced Sonic tool - longer spacing makes sound waves conducted by casing negligible; Thermal Decay Time log - similar to resistivity logs in open hole; Gamma Ray Spectrometry log - used to calculate lithology, shale volume, porosity, pore fluid types, and saturation.

18. Solution Step 1. Construct the following table:
Formation Evaluation 18
Solution
Step 1. Construct the following table:

19. The Reservoir Saturation Equations
Formation Evaluation 19
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 volume
So =
pore volume
water volume
Sw =
gas volume
Sg =
So + Sw + Sg (11)
(8)
(9)
Assume m = h = 2 and a = 1 in Archie’s equation.
(10)

20. 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 defin­ition of oil saturation:

21. 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 and into Equation 12-8 gives:

22. 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 and 12-16, i.e.:

23. 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 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.

24. Oil saturation adjustment for water influx
The 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:

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

26. Step 2. Calculate oil volume in the water invaded zone, or:
volume of oil = (P.V)water . Sorw (12-19)
Step 3. Adjust Equation to account for the trapped oil by using Equations and 12-19:

27. 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:

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

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

30. Step 4. Adjust Equation to account for the trapped oil in the gas expansion zone by using Equations and 12-23, to give:

31. 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 can be adjusted to account for both driving mechanisms, as:

33. Saturated-Oil Reservoirs
Formation Evaluation 33
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:

34. (12)
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:

35. 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)

36. 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.

37. 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.

38. 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:

39. (14)
(15)

40. 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)

41. 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)

42. (19)
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.

43. 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.

44. 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.

45. 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.

46. 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

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

48. 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:

49. 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

50. Step 4. Determine remaining oil in place at 2100 psi.
= 9,655,344 STB
This 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:

51. Assume Np = 0.01 N and apply Equation (15) to solve for Gp:
Calculate the oil saturation, to give:
3. Determine the relative permeability ratio krg/kro from the available data to give:
krg/kro =

52. Relative permeability curve

53. 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:

54. 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. MB
GOR GP
Actual Gp
Actual NP/N
Np/N