RU2092691C1 - Method for control of filtration flows created at development of oil deposits with stratified-nonuniform beds - Google Patents

Abstract

FIELD: oil production industry. SUBSTANCE: method implies determination of permeability and capacity of each interlayer, viscosity of substituting agent and substituted liquid, initial and final saturation with substituting agent, and calculation of modified functions of relative phase permeabilities of substituting agent and substituted liquid with subsequent determination of pressure fields of filtration flows and filtration speeds. Schemes of current saturation with substituting agent are drawn according to additionally determined technological information about operation of each well. Basing on thus produced schemes, mathematically simulated is process of filtration in stratified-nonuniform oil bed. Determined for additional information is current content of substituting agent in output of each well in area being investigated. Using these data and modified functions of relative phase permeabilities of substituting agent and substituted liquid calculated for each well, estimated is average value through cross section of multilayer porous medium of saturation with substituting agent around each well, or values of saturation with substituting agent for each well to certain date. EFFECT: high efficiency. 1 cl, 2 tbl, 2 dwg

Description

 The invention relates to the oil industry, namely to study the state of the reservoirs to control the development, in particular to methods for monitoring the filtration flows that are formed during the development of oil fields with layered heterogeneous reservoirs.

 A method for determining the direction of filtration flows of a multiphase incompressible fluid based on the generalized Darcy law in the framework of the Bakleyey-Leverett or Rapoport-Lis model is proposed in [1] (analog). However, in [1], when considering a system simulating the combined flow of phases of displacing and displacing fluids, the dependence of their relative phase permeabilities (RPs) on the permeability of a layered heterogeneous formation is not taken into account, which significantly reduces the applied value of the results.

 According to the prototype [2], to calculate the pressure fields of the filtration flows and filtration rates, the permeability, porosity, power of each layer, the viscosity of the displacement agent and the displaced fluid, the initial and final saturation of the displacement agent are preliminarily determined, and the modified functions of the relative phase permeabilities (MF RPP) of the displacement agent are calculated and displaced fluid.

P\Г=P⁰(x,y,t),
S(x,y,0)=S⁰(x,y),
где

, Г граница области, N число скважин, q_v-расход v-ой скважины, причем при q_v>0 скважина нагнетательная, а если q_v<0, то скважина добывающая. k абсолютная проницаемость, k_в и k_н ОФП или модифицированные функции ОФП воды и нефти соответственно. F функция Баклея-Леверетта. μ_в, μ_н -вязкости воды и нефти; S, S⁰- текущая и начальная водонасыщенность; P текущее поле давлений, P⁰ давление на границе области; x, y пространственные и t - временная переменные.The process of multiphase filtering in the two-dimensional region is described by the following system of differential equations (1) - (4):

P \ T = P ⁰ (x, y, t),
S (x, y, 0) = S ⁰ (x, y),
Where

, G is the boundary of the region, N is the number of wells, q _{v is the} expense of the v-th well, and at q _v > 0 the well is injection, and if q _v <0, then the well is producing. k absolute permeability, k _in and k _n RPP or modified functions RPP of water and oil, respectively. F Buckley-Leverett function. μ _in , μ _n- viscosity of water and oil; S, S ⁰ - current and initial water saturation; P current pressure field, P ⁰ pressure at the boundary of the region; x, y are spatial and t are temporary variables.

 To obtain a picture of the actual watering process when solving system (1) - (2), it is necessary to set the initial value of saturation (4). Moreover, to obtain a stable numerical solution of the boundary value problem (1) - (4), a sufficiently small discrete step in the time variable is required, which significantly increases the amount of computation. The determination of the initial saturation (4) from the data at the time of the drilling of the wells requires solving the problem from the beginning of field development in the entire time range. This also leads to the accumulation of computational errors and to obtain numerical results that are not consistent with real production data. Thus, the disadvantage of the described approach is the huge computational cost with low accuracy of the final output data.

 The purpose of the invention is to increase the reliability of determining pressure fields of filtration flows and filtration rates. Accordingly, the expected technical result is effective control over the development of oil fields.

 The goal is achieved by the fact that according to the additionally determined current production and technological information on the operation of each well, maps of the current saturation with a displacement agent are built, and taking into account the constructed maps, the filtration process is mathematically simulated in a layered heterogeneous formation to calculate the pressure fields of the filtration flows and the filtration rates. It is assumed that either the current content in the production of each well of the studied section of the displacement agent is determined as the additional current production and technological information, according to which the average saturation values of the displacement agent in the vicinity of the cross-section of the multilayer porous medium are calculated using the MF RPF calculated for each well each well; or the saturation values of the displacement agent for each well at a specific date, on which the maps of the current saturation of the displacement agent are built.

 A comparative analysis of the essential features of the proposed technical solution and prototype allows us to conclude that the proposed invention meets the criterion of "novelty."

 As for the "inventive step", until now, in mathematical modeling of filtering processes at the intermediate stages of calculations, saturation maps of the displacement agent, constructed taking into account field data, have not been used. This approach allows you to constantly monitor numerical calculations and coordinate the results with the real technological situation. Thus, the distinguishing features of the proposed technical solutions are new and the entire claimed combination of features meets the criterion of "inventive step".

The method is preferably carried out by the following sequence of operations:
1. Determination, according to geological studies in wells (GIS), of permeability, porosity, viscosities of the displacing agent and displaced fluid, initial and final saturation of the displacing agent, and the thickness of each interlayer of a well that has been discovered by a well over the entire oil field.

 2. Determination of the displacement agent and the displaced fluid for each well of the MF RPF field site, taking into account field information on the viscosities of the filtration components.

 3. Using an additionally determined percentage in the accumulated production of the well of the displacing agent using the MF RPF, calculation of the average saturation values of the displacing agent over the cross section of the multilayer porous medium.

 4. Constructing saturation maps with a displacement agent.

 5. Calculation of pressure fields of filtration flows and filtration rates according to the results of mathematical modeling of filtration processes in a layered inhomogeneous porous medium, taking into account the saturation maps constructed by the displacement agent.

 The above sequence of operations is preferable, since in practice it is difficult to directly determine saturation values of the displacement agent for each well at a specific date for constructing saturation maps.

 An increase in the reliability of determining the velocity field of multiphase filtration flows in layered inhomogeneous porous media is achieved through an adaptive approach, which consists in the constant correction of the calculated data. An important difference from the analogue [1] and prototype [2] is that in mathematical modeling of filtration processes at each stage, maps of the current saturation by the displacement agent are used, constructed taking into account the GIS data and, possibly, the MF OFP.

An example of a specific implementation of the method. Calculation of pressure fields of filtration flows and filtration rates for cell 2-2 of formation BS _{10 of the} Mamontovskoye field.

In the table. Figure 1 shows the averaged characteristics of a layered heterogeneous formation over the entire cell 2-2 of the formation BS _{10 of the} Mamontovskoye field.

The porosity of the interlayers m ⁽ⁱ⁾ was considered constant and equal to 0.2.

The oil and water viscosities in the BS ₁₀ layer of the Mamontovskoye field are 2.4 MPa • s and 0.379 MPa • s, respectively. The initial and final saturations of the displacement agent S _C and S _{T are} determined by the known correlation dependencies.

 Similarly, the parameters of the interlayers are determined for each well of the field site.

где
f $\genfrac{}{}{0ex}{}{\text{0}}{\text{1}}$ (s) = s^3/2, f $\genfrac{}{}{0ex}{}{\text{0}}{\text{2}}$ (s) = (1-s)³ заданные стандартные функции.As a result of the study of a large number of cores of the BS ₁₀ formation of the Mamontovskoye field in a wide range of permeability changes, correlation dependencies were obtained, which determined the characteristics of individual layers:

Where
f $\genfrac{}{}{0ex}{}{\text{0}}{\text{one}}$ (s) = s ^3/2 , f $\genfrac{}{}{0ex}{}{\text{0}}{\text{2}}$ (s) = (1-s) ³ given standard functions.

где
S⁽ⁱ⁾(x, t)- определяется путем решения дифференциальных уравнений гиперболического вида (5).The calculation of the average values of water saturation, RPP of water and oil is made according to the formulas:

Where
S ⁽ⁱ⁾ (x, t) - is determined by solving differential equations of hyperbolic form (5).

по разностной схеме "уголок" [3] для каждого пропластка.

according to the difference scheme “corner” [3] for each layer.

средним по всему разрезу значениям водонасыщенности

в некоторый момент времени t строятся МФ ОФП. Рассчитанные МФ ОФП для всего участка месторождения приведены на фиг.1 (кривые 1, 2 МФ ОФП нефти и воды соответственно). Подобным образом считаются МФ ОФП для всех участков вблизи каждой скважины. По рассчитанным МФ ОФП для каждой скважины строятся кривые обводненности; фиг. 1 (кривая 3).By establishing the correspondence of the average RPP values of oil water

water saturation average over the whole section

at some point in time t, the MF OFP are constructed. The calculated MF OFP for the entire site of the field are shown in Fig. 1 (curves 1, 2 MF OFP of oil and water, respectively). Similarly, the MF RPFs are considered for all sections near each well. According to the calculated MF RPP for each well, water cut curves are constructed; FIG. 1 (curve 3).

Экспериментальным образом определяется обводненность накопленной продукции по всем скважинам ячейки месторождения. Путем установления соответствия обводненности продукции и насыщенности (п. 2), вычисляется средняя по поперечному сечению водонасыщенность участков пласта в районе каждой скважины. Данные обводненности и водонасыщенности по каждой скважине приведены в табл. 2.

The water cut of the accumulated production for all wells of the field cell is determined experimentally. By establishing the correspondence of the water cut of the product and the saturation (Section 2), the average cross section water saturation of the reservoir sections in the area of each well is calculated. Water cut and water saturation data for each well are given in table. 2.

где
r_i расстояние до i-ой скважины.According to the data from table. 2, water saturation maps are constructed over the entire area of the field (Fig. 2). The following dependence was taken as an interpolation formula for restoring the water saturation field at an arbitrary point from the known values in the surrounding wells:

Where
r _{i the} distance to the i-th well.

 Based on the results of mathematical modeling of filtration processes in a layered inhomogeneous porous medium, taking into account the saturation maps of the displacement agent, the pressure fields of the filtration flows and the filtration rates are calculated. In this case, it is necessary to solve only one differential equation of elliptic type (6) with boundary conditions of the first kind (7).

Значение P⁰ на границе принимается равное пластовому давлению и при численных расчетах выбирается исходя из условий технологической эксплуатации ячейки месторождения. В конкретном случае P⁰ 263,9 атм.

The value of P ⁰ at the boundary is assumed to be equal to the reservoir pressure and, in numerical calculations, is selected based on the conditions of technological operation of the field cell. In a specific case, P ⁰ 263.9 atm.

As a method of solving equation (6), it is possible to apply well-known methods: the grid method [4] or the finite element method [5]
The results of calculating the pressure fields of the filtration flows are also shown in FIG. 2. The arrows indicate the directions of the filtration rates.

 The results obtained (figure 2) are in good agreement with the real state of affairs and the data of a comprehensive methodology for checking and monitoring the operation of wells, carried out in practice.

 Thus, the proposed method for determining the direction of movement of the filtration flows in layered inhomogeneous media has high reliability of the results and, therefore, allows more efficient control of the development of the oil field. The invention is industrially applicable, since available laboratory equipment and computers are used.

 Sources of information.

 1. Konovalov A. N. Problems of filtering a multiphase incompressible fluid. Science, Siberian Branch of the Academy of Sciences, Novosibirsk, 1988.168 s.

 2. Halimov E.M. Levy B.I. Dzyuba V.I. Ponomarev S.A. The technology of increasing heat transfer layers. M. Nedra, 1984, p. 271.

 3. Samarsky A. A. Popov Yu.P. Difference methods for solving gas dynamics problems. M. Science, 1980, p. 352.

 4. Samarsky A.A. Andreev V.B. Difference methods for elliptic equations. M. Science, 1976, p. 350.

 5. Bull, Bush. A review of finite element mesh formation methods. Tans, ASME, sec b. 1973-95 N 1.

Claims (2)

 1. A method for monitoring filtration flows formed during the development of oil fields with stratified inhomogeneous formations, including determining the permeability, porosity, thickness of each layer, viscosities of the displacing agent and displaced liquid, initial and final saturation of the displacing agent, and calculating modified functions of the relative phase permeabilities of the displacing agent and displaced fluid with the subsequent determination of the pressure fields of the filtration flows and filtration rates, characterized in further defined by the current industrial-process information about the operation of each well build maps the current saturation and displacement agent with the constructed mathematical model maps filtering process in layered formation for calculating pressure fields seepage flow and filtration rates.  2. The method according to claim 1, characterized in that as an additional current production and technological information, the current content in the production of each well of the studied area of the displacement agent is determined, according to which, using the modified relative phase permeability functions calculated for each well, average values are calculated the cross section of the multilayer porous medium the saturation value of the displacement agent in the vicinity of each well and build maps of the current saturation of the displacement agent, with y a couple of which mathematically modulate the filtration process in a stratified inhomogeneous reservoir to calculate the pressure fields of the filtration flows and the filtration rates.

Images