RU2061221C1 - Method of determination of modified functions of relative phase permeability for nonuniform layer porous media - Google Patents

Abstract

FIELD: study of processes of multi-phase filtration of liquids, displacement processes, in particular, (displacement of oil from porous media by displacement agent) accompanied by determination of modified functions of relative phase permeabilities for nonuniform layer porous media. SUBSTANCE: average saturation by displacement agent, as well as average relative phase permeabilities of displacement agent and relative phase permeability of liquid being displaced are calculated according to permeability, porosity, power, saturation with bonded displacement agent and limiting saturation by displacement agent are determined for each interlayer; then modified functions of relative phase permeabilities are determined through determination of relationship between calculated average magnitudes of relative phase pemeability f displacement agent and relative phase permeability of liquid being displaced and average magnitudes of saturation by displacement agent. To enhanced reliability, viscosities of liquid being displaced and displacement agent, as well as their relative phase permeabilities are additionally determined relative phase permeabilities are additionally determined throughout entire range of change of permeability; average magnitudes of saturation by displacement agent and relative phase permeability of displacement agent and liquid being displaced are calculated according to results of mathematical modelling of filtration in nonuniform layer porous medium taking into account experimental data determined additionally. EFFECT: enhanced reliability. 3 dwg, 1 tbl

Description

 The invention relates to the study of multiphase liquid filtration processes, in particular displacement processes (for example, oil displacement from porous media by a displacing agent) with the definition of modified relative phase permeability functions (MP RPFs) for layered inhomogeneous porous media.

 MF RPFs are important integral filtration characteristics of inhomogeneous porous media, which make it possible to describe such media by quasihomogeneous models, which greatly simplifies the monitoring and control of filtration processes.

 The determination of MF RPF described in [1] is carried out by constructing the distribution function of the effective permeability of the reservoir according to the data of geophysical research of wells. However, in their assumptions, the authors do not take into account such essential points as the dependence of the saturation of the displacement agent on the associated agent, the residual saturation of the displaced fluid and the RPT on the permeability. This leads to an unreliable determination of the MF OFP.

h_i•m⁽ⁱ⁾•S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{T}}$ +

h_i•m⁽ⁱ⁾•S

(1)
относительные фазовые проницаемости:

h_i•k⁽ⁱ⁾,

h_i•k⁽ⁱ⁾,
(2) где S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{с}}$ , S_т(ⁱ⁾ насыщенности связанным агентом вытеснения и предельной насыщенности агентом вытеснения;
k⁽ⁱ⁾ проницаемость i-го прослоя;
m⁽ⁱ⁾ пористость i-го прослоя;
h_i мощность i-го прослоя;
f_1м, f_2м относительные фазовые проницаемости агента вытеснения и вытесняемой жидкости при S S_c и S S_т,
а

h_im⁽ⁱ⁾,

h_ik⁽ⁱ⁾,
Сами МФ ОФП определяют установлением соответствия между рассчитанными средними значениями ОФП агента вытеснения и ОФП вытесняемой жидкости и средними значениями насыщенности агентом вытеснения.In [2] (prototype), a method was proposed for determining the MF of the RPF of a stratified heterogeneous formation by the values of permeability, porosity, power, saturation of the associated displacement agent and the maximum saturation of the displacement agent defined for each layer. Based on the ideas about the piston nature of oil displacement, the average saturation of the displacement agent s is calculated, as well as the average RPT of the displacement agent f ₁ and RPP of the displaced fluid f ₂ at the time of breaking the kth layer using the formulas:
saturation:

h _i • m ⁽ⁱ⁾ • S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{T}}$ +

h _i • m ⁽ⁱ⁾ • S

(one)
relative phase permeability:

h _i • k ⁽ⁱ⁾ ,

h _i • k ⁽ⁱ⁾ ,
(2) where S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{from}}$ , S _t ( ⁱ⁾ saturation of the associated displacement agent and marginal saturation of the displacement agent;
k ^{(i) the} permeability of the i-th layer;
m ⁽ⁱ⁾ porosity of the i-th layer;
h _{i the} power of the i-th layer;
f _1m , f _2m relative phase permeabilities of the displacement agent and the displaced fluid at SS _c and SS _t ,
a

h _i m ⁽ⁱ⁾ ,

h _i k ⁽ⁱ⁾ ,
MF RPFs themselves are determined by establishing a correspondence between the calculated average RPP values of the displacing agent and RPP of the displaced fluid and the average saturation values of the displacing agent.

 The disadvantage of this method is that the assumption of the piston nature of the displacement is valid only at sufficiently large values of the ratio of the viscosities of the displacing agent and the displaced fluid. In addition, it does not take into account the dependence of the RPF of the filtered liquids on the permeability of the interlayers. Due to these reasons, the assessment of MF OFP on the prototype is not sufficiently reliable.

 The purpose of the invention is to increase the reliability of determining the modified functions of relative phase permeabilities for layered inhomogeneous porous media.

 The goal is achieved by the fact that the viscosities of the displaced fluid and the displacement agent are additionally determined, as well as their RPT over the entire range of permeability changes, and the average saturation values of the displacement agent and the RPP of the displacement agent and displaced fluid are calculated from mathematical modeling of filtration in a layered inhomogeneous porous medium, carried out taking into account additionally determined experimental data.

 The proposed method consists in the fact that, based on the solution of a system of differential equations describing the process of liquid displacement by a displacement agent in the framework of the Bakley-Leverett model, taking into account certain physicochemical characteristics of a layered inhomogeneous porous medium, the average values of saturation with a displacement agent and RPP displacing agent and displaced fluid. As calculations show, the MF OFP calculated in this way practically does not change in time t and does not depend on the section x, in which the average saturation of the displacement agent S (x, t), and the average RPP were determined. Therefore, they adequately describe the processes of two-phase filtration in layered-inhomogeneous porous media.

 The method is carried out by the following sequence of actions.

 Determination of permeability, porosity, power, saturation of the associated displacement agent and the maximum saturation of the displacement agent for each interlayer.

 Determination of the viscosities of the displaced fluid and the displacement agent and their RPT in the entire range of permeability changes.

 Calculation of the average saturation values of the displacing agent and the RPT of the displacing agent and the displaced fluid according to the results of mathematical modeling of filtration in a layered inhomogeneous porous medium.

 Establishing the correspondence of the average RPT values of the displacing agent and the displaced liquid to the average saturation values of the displacing agent.

 The reliability of the description of the MF RPF in the proposed method is improved by more accurately determining the average water saturation values along the cross section of the reservoir and the average RPF values of the displacement agent and the displaced fluid by mathematical modeling of filtration processes in a porous medium. An important difference from the analogue [1] and prototype [2] is that the calculations take into account the predetermined physicochemical characteristics of the layered heterogeneous formation and fluids, in particular the viscosity of the displacing agent and the displaced fluid.

 PRI me R. Determination of the MF OFP of oil and water of the BS10 layer of the Mamontovskoye field.

 The table shows the characteristics of the stratified heterogeneous formation for which the MF RPF is calculated.

The porosity of the layers m ⁱ was considered constant and equal to 0.2.

,
f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{2}}$ (s⁽ⁱ⁾)=

,
где стандартные функции f $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ , f $\genfrac{}{}{0ex}{}{\text{o}}{\text{2}}$ имеют вид:
f $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ (s) s^3/2, f $\genfrac{}{}{0ex}{}{\text{o}}{\text{2}}$ (s) (1-s)³
Вязкости нефти и воды в пласте БС10 Мамонтовского месторождения равны 2,4 МПа · с и 0,379 МПа · с соответственно.As a result of the study of a large number of core samples of the BS10 formation of the Mamontovskoye field in a wide range of permeability changes, correlation dependencies were obtained, by which the characteristics of individual layers can be determined:
S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{c}}$ 0.41 0.018 In (k ⁽ⁱ⁾ ),
S $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{t}}$ 0.72 + 0.032 In (k ⁽ⁱ⁾ ),
f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{1}}$ (s ⁽ⁱ⁾ ) 0.07

,
f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{2}}$ (s ⁽ⁱ⁾ ) =

,
where the standard functions f $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ f $\genfrac{}{}{0ex}{}{\text{o}}{}$$\genfrac{}{}{0ex}{}{}{\text{2}}$ have the form:
f $\genfrac{}{}{0ex}{}{\text{o}}{\text{1}}$ (s) s ^3/2 , f $\genfrac{}{}{0ex}{}{\text{o}}{\text{2}}$ (s) (1-s) ³
The oil and water viscosities in the BS10 layer of the Mamontovskoye field are 2.4 MPa · s and 0.379 MPa · s, respectively.

+ ω $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{o}}$ (t)

[F⁽ⁱ⁾(s⁽ⁱ⁾)] i=

, где ω $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{o}}$ (t) скорость фильтрации в i-м пропластке;
а F⁽ⁱ⁾ (s⁽ⁱ⁾ функция Баклея Лаверетта:
F⁽ⁱ⁾(s⁽ⁱ⁾)

μ_o=μ₁/μ₂
Нахождение решения системы дифференциальных уравнений гиперболического вида S⁽ⁱ⁾ (x, t) определяется по разностной схеме "уголок" [3]
Расчет средних значений водонасыщенности и ОФП воды и нефти производится по формулам:

(x,t)

h_im⁽ⁱ⁾S⁽ⁱ⁾(x,t),

h_i•k⁽ⁱ⁾•f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{1}}$ (s⁽ⁱ⁾(x,t)),

h_i•k⁽ⁱ⁾•f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{2}}$ (s⁽ⁱ⁾(x,t)).The system of equations describing the process of oil displacement by water from a linear model of a layered heterogeneous formation has the form:
m

+ ω $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{o}}$ (t)

[F ⁽ⁱ⁾ (s ⁽ⁱ⁾ )] i =

where ω $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{o}}$ (t) filtration rate in the i-th layer;
and F ⁽ⁱ⁾ (s ⁽ⁱ⁾ the Buckley Laverrett function:
F ⁽ⁱ⁾ (s ⁽ⁱ⁾ )

μ _o = μ ₁ / μ ₂
Finding a solution to the system of differential equations of the hyperbolic form S ⁽ⁱ⁾ (x, t) is determined by the difference scheme “corner” [3]
The calculation of the average values of water saturation and RPP of water and oil is made according to the formulas:

(x, t)

h _i m ⁽ⁱ⁾ S ⁽ⁱ⁾ (x, t),

h _i • k ⁽ⁱ⁾ • f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{1}}$ (s ⁽ⁱ⁾ (x, t)),

h _i • k ⁽ⁱ⁾ • f $\genfrac{}{}{0ex}{}{\text{(i)}}{\text{2}}$ (s ⁽ⁱ⁾ (x, t)).

и

средним значением водонасыщенности

в некоторый момент времени t по всему разрезу строятся модифицированные функции ОФП.By establishing the correspondence of the average RPT values of oil and water

and

average water saturation

at some point in time t, modified RPP functions are constructed over the entire section.

 In FIG. Figure 1 shows the graphs of functional dependences (MF OFP of water (curve N 1), MF of RPP of oil (curve N 2); Fig.2 curves of MF RPP of oil and water calculated for vertical sections located at different distances from the discharge gallery. Visually curves The independence of the MF RPF calculations on the time of displacement allows one to determine the MF RPF for a short period of time, almost immediately after the establishment of the filtration flow; in Fig. 3, the dependency graphs in comparison of the MF RPP for oil (curve No. 1) obtained from the prototype and according to the proposed method (curve N 2).

As you can see, the definition of the MF OFP on the prototype leads to large errors. So, for the value S0.52, the relative error in the determination of the MF OFP is 161%
Thus, the proposed method is more reliable than the prototype, using available laboratory equipment and computers.

Claims (1)

 A method for determining the modified relative phase permeability functions (RPFs) for layered inhomogeneous porous media, including determining the permeability, porosity, power, saturation of the displaced agent by the displacement agent and the maximum saturation of the displacement agent of each interlayer, calculation of the average saturation values of the displacement agent and the cross-section of the multilayer porous medium the average RPP of the displacing agent and the displaced fluid with the establishment of a correspondence between the average RPP of the displacing agent and of the displaced liquid and average values of saturation with the displacement agent and the construction of modified RPT functions, characterized in that they additionally determine the viscosities of the displaced liquid and the displacement agent, as well as their RPT in the entire range of permeability changes, mathematically model filtration in a layered inhomogeneous porous medium, taking into account the entire experimental information and calculate the average saturation values of the displacement agent and the RPT of the displacement agent and the displaced fluid according to the results of mathematical simulation of.

Images