CC BY
89
УДК 553.982.2 О.М. Эхигиатор
Университет Бенсон Айдахоза, Нигерия Р.А. Эхигиатор-Иругхе СГГА, Новосибирск
МОДЕЛИРОВАНИЕ ВОДОНЕФТЯНОГО КОНТАКТА МЕТОДОМ МАТЕРИАЛЬНОГО БАЛАНСА
O.M. Ehigiator
Benson Idahosa University, Nigeria E-mail: [email protected] R.A. Ehigiator-Irughe PhD Student, SSGA, Russian Federation E-mail: [email protected]
MODELLING OF OIL WATER CONTACT BY METHOD OF MATERIAL BALANCE
Abstract
A simple model used for calculation of current oil water contact by simply manipulation of generalized material balance and volumetric method for determination of oil in place are described in this paper. The oil water contact of an oil reservoir is mostly determined using well log data, for example carbon oxygen ratio and geophysical well logs. For cost effectiveness we are using the method of material balance to determine current water contact (cowc) with known reservoir parameters. It allowed us to find the contact to 36.6ft. The result obtained was compared with the method of carbon oxygen ratio and the error was found to be 2.00ft. This equation was used to test series of reservoirs in Niger delta and found to be consistence and we present here only one sample result. This mathematical approach is not affected by water salinity. Therefore, it is a breakthrough in reservoir engineering. This method is more economical, fast and, therefore, affordable by small scale oil and gas industries especially in the acquisition of marginal oil and gas field.
Key words: Material balance, oil water contact.
Numerous procedures have been proposed and employed for estimating of hydrocarbon initial oil in place [3]. The most commonly used method is by volumetric method as stated by [1]. However, it has become both practical and popular to confirm such estimates by material balance equations. The type of material balance equation used in such estimates is similar to that used in many other fields of engineering for quantity and quality estimate and control. In the simplest form, the material balance equation can be written as follows:
Initial volume = volume remaining + volume removed. (1)
A concept of material balance for the estimation of hydrocarbon in underground reservoirs was presented by [5]. The principal improvement in the application of the equation in practice has become possible through processing of measurements and the continuing efforts of reservoir engineers to expand the equation to cover the reservoir rock and its contents. Over the years, well log
interpretation has been based on finding the amount of water in a formation, deducing from that quantity whether or not hydrocarbons are present, and determine the volume.
These techniques have been based on the resistivity and/or pulsed neutron captures contrast between water and oil. In both measurements the contrast are at their minimum when the salinity of the water phase is low. Neither method can accurately determine water saturation when the water salinity is near zero.
What is obviously needed is a logging device that measures the bulk volume of water or oil in a formation without any dependence on the formation water salinity of the formation water. Several types of measurements are available to the industry in theory if not in actual practice.
The theory associated with the carbon and oxygen measurement has been known for many years, but only within the last several years the technology has been improved to allow for reliable measurements outside the laboratory environment [4]. There are only few logging companies having tools, which commercially measure the carbon - oxygen ratio (COR).
We carried out some research the main purpose of which is to estimate the oil water contact using a mathematical approach. This method is more accurate compared to others and cheaper [2]. This mathematical approach is not affected by water salinity. Therefore, it is a breakthrough in reservoir engineering.
The oil water contact is selected on the core or log as the point at which the oil saturation of the sample decreases and the water saturation increases. This is the oil - water contact defined as the level below which the fluid production is 100% water. Unfortunately, not all wells drilled penetrate the water-bearing portion of the formation. Thus, it becomes necessary to determine the limits of the oil-water contact from a merger set of data. The transition between oil and water is defined as the oil water contact (OWC). When defining the oil-water contact position, it is suggested that all open hole drill-stem tests, production and completion tests, core analysis and log data be plotted on the structural map.
We studied Reservoir A, which is slightly silty, gravelly, moderate to well sorted, with loosely consolidated sand. The reservoir is laid down in Bathyal environment and represents a delta prograding Para- sequence whose top paleo-channel sand may have been eroded. The reservoir under study contain only two fluids i.e. water and oil, hence reservoir is described as an under saturated reservoir. Since only two fluids are present (water and oil), their relative rates of flow are determined by their relative viscosity and their relative permeability. The reservoir permeability is 3 - 5 Darcy and the porosity is presented as 0.13.
Below are the methods used for determination of oil in place but we should consider the volumetric and the material balance equation.
1) Volumetric Reservoir
This method is based on log and core analysis data to determine the bulk volume, the porosity and the fluid saturations, and upon fluid analysis to determine the oil volume factor. Let N denote the stock tank oil in place, then
N = 7758AH0(\-SW)
Boi (2)
where: A - cross sectional area of reservoir, H- height (thickness) of reservoir, § - porosity of the reservoir rocks, Sw - water saturation, Boi - initial formation oil volume factor.
2) Material Balance Equation (M.B.E)
The Material balance equation is used to confirm the value obtained from volumetric method. It is simply a volume balance, which equates total production to the difference between the initial volumes of hydrocarbons in the reservoir to the current volume.
3) Generalized Material-Balance Equation
The generalized material-balance equation often is called schilthuis equation [5]. It is simply a volumetric balance, which states that since the volume of a reservoir gas defined by its initial limits is a constant, the algebraic sum of volume oil changes, the free gas, and the water volume in the reservoir must be zero. For example, if both the oil and gas reservoir volume decrease, the sum of these two decreases must be balanced by an increase of equal magnitude in the water volume.
If the assumption is made that complete equilibrium is attained at all time in the reservoir between the oil and its solution gas, it is possible to write a generalized material balance equation relating the quantities of oil, gas and water produced, the average reservoir pressure, the quality of water which may have encroached from the aquifer, and finally the initial oil and gas content of the reservoir.
4) Modification Material Balance Equation
Recalling (2) and multiplying net/gross
7758Ah<fi(\ - S) N
N =-^-z+x- (3)
Ql
where N is the net/gross.
The reserve of still producing reservoir is computed as follows:
N_K = 775Mkm-S„)xN/G ^
Using the method of generalized material balance, the reserve is computed as:
N =
Np[Bt+(Rp-RJBg]-(We-BwWp)
mBH _ _ (5)
B. - B. +--B )
t ti D V g gi J
Combining Eq. (3) and Eq. (4), we have:
Np[Bt+(Rp-Rsl)Bg]-(We-BwWp) J158 Ahr</>(\-Swc)
mB p R
B,-B„ + '^(Bg-Bg,) B°
Np [Bt + (Rp - Rsl )Bg ] - (We -BwWp ) - Nf
mR
B
g
mR
B
g
1158Ahr0(l- Swc)
x
N/G
B0\NP [Bt + (Rp-Rsi)Bg]-(We -BwWp)-Np
mB
B„
= 115%Ahr <f>(\ - Swc )
Bt
" B . g
So
B0[NP [Bt + (R - Rsi ) B ] - (We -BwW ) - N
h=-
■BJxN/G
Bt-Btl + ^(Bg-Bgl)
mp
7758A(p(l-Swc)[Bt-Btl + —A(Bg-Bgl)]xN/G
Bg.
(6)
where: hr - Reservoir thickness, B0 - oil formation volume factor, Np -cumulative oil produced, Rp - producing gas - oil ratio, Rsi - initial solution gas - oil ration, Bg - gas formation volume factor, We - cumulative water influx, Bw - water formation volume factor, WP - cumulative water produces bbl at standard condition, Br - [Bo + (Rsi - RS) Bg ], Bti - Boi - initial oil formation volume factor, M - G Bgi /5.615 NB0i - ratio of initial gas - cap - gas, reservoir volume to initial reservoir oil volume, A - Area in Acres, § - Porosity, SWc - water saturation.
To determine a new fluid contact from a reservoir that has produces for some time, the parameters of Reservoir A were used as shown in Table 1.
By using the above measured reservoir parameter (Reservoir A) and substituting to Eq. (3), we deduce the volume of oil in place equal to 78.8 mmstb.
On the order hand, using Eq. (6), the reservoir thickness was found to be 91.35 ft and the current oil water contact (Cowc) was found to be 36.61ft.
The generalized material-balance equation is simply a volumetric balance, which equates total production balance to the difference between the initial volumes of hydrocarbons in the reservoir to the current volume [1].
p
Parameters STOIIP Np Rp Rsi Bgi Boi Gross Res. Vol.
Reservoil 78.8MMstb 14.1MMstb 429scf/stb 520scf/st 0.006146scf/stb 1.175bbl/stb 51.54mac-ft
Parameters Porosity Net/gross(N/G) Swc(Avg) Bw We W Initial Pressure
Reservoil 0.13 0.97 0.23 1.02 21.53 X 106stb 4.10MMstb 2540psi
Parameters Crest of structure Avg gross sand thickness Current Temperat ure Current Pressure Initial Temperature Bubble point Pressure
Reservoil 5700 ftss 76ft 1670 f 582ft 2280psi 1670 f 2085psi
FIG B (CURRENT OILWATER CONTACT)
OLD OIL WATER CONTACT (Oowc^
FIG A COLD OILWATER CONTACT)
Figure. (A & B) oil water contact of Reservoir A
A direct application of material balance in the determination of current oil water contact will not be possible because in the equation if a reservoir thickness is not included in the equation. To do this, the material balance has to be equated with the volumetric method of computing the oil in place.
It results in the modified material balance equation 6 which was applied to determine the current oil water contact (COwc) revealing reservoir COwc as 36.61ft.
When deriving and applying the modified material-balance equation, the following assumptions were made:
- There is a clear sweep of oil from the reservoir to the surface
- Uniform displacement of reservoir field
- Constant welt ability.
An extensive sensitivity analysis of the numerical simulation to predict the current oil water contact, and the result compared with well log reveal a sensitive result. For Reservoir A, the difference between both methods in the position of
COWC is 2.0 ft. This is an indication that the result was consistent for Reservoir A. It is important to note that one of the most important parameter needed in the computation of COWC is the water influx and the value must be properly estimated.
Conclusion
The result obtained from the logging data by using the material balance method shows the consistency with minimal error. This error can be caused by estimation of relevant computation data used, and care must be taken in the estimation of these relevant data. However, the method of material balance is economical, faster and therefore, affordable by small scale oil and gas industries especially in the acquisition of marginal oil and gas field. This method is recommended to apply either for evaluation of original-hydrocarbons-in-place or the remaining reserves as well. Most of all it depends on the reservoir parameters and accuracy of measurement which are also very important. Some of parameters that may influence on the accuracy:
1. Cumulative water production
2. Water influx
3. Initial solution gas oil ratio
4. Producing gas oil ratio
5. Total oil formation volume factor.
When all relevant parameters are available, the material balance equation can be applied to check for current oil water contact obtained with logging data.
Referenses
1. Craft, B.C. Hawkins, M.F. Reservoir Engineering, Churchill publ., Third Edition, [2004].
2. Ehigiator - Irughe, R. (2002) "Mathematical Methods for Determination of Oil Water Contact". PGD Thesis. Department of Petroleum Engineering, University of Benin, Benin City.
3. Frank Hsieh and Philip, S. Kandel: Material-Balance Method for Production Rejuvenation with Horizontal Wells [2002].
4. (4) Gilchrist, W.A., Rogers, L.T. and Watson, J.T.: Carbon/Oxygen Interpretation-An S.P.E. (Society of Petroleum Engineers), vol. 3, page 66-74 [1983].
5. Schiltius, R, Review of Hydrocarbon Reservoir. Journal of N.A.P.E. (Nigeria Association of Petroleum Explorationist). Vol.1, pp.12.
© O.M. Эхигиатор, P.A. Эхигиатор-Hругхе, 2010
