AU2020101406A4 - Method for predicting reservoir status based on non-equilibrium anisotropic relative permeability - Google Patents
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Abstract
A method for predicting reservoir status based on non-equilibrium anisotropic relative
permeability. The method includes: updating an initial pressure and an initial fluid flow rate
of a first grid area according to a production pressure and a product rate; sequentially
updating the initial pressure and initial fluid flow rate of remaining grid areas centering on
the first grid area; determining relative permeability in X/Y/Z directions according to an
initial water saturation and the updated initial fluid flow rate of each grid area, and updating
the initial water saturation; obtaining the pressure, fluid flow rate and water saturation of
each grid area at a next moment according to the X/Y/Z relative permeability and the
updated initial pressure, initial fluid flow rate and initial saturation of each grid area;
cyclically calculating to a production time; and determining oil reservoir and pressure
distribution in a fluvial reservoir according to time-varying water saturation and pressure
changes. The present invention accurately predicts the reservoir pressure distribution and
remaining oil distribution.
2/4
Numerical simulation method
based on non-equilibrium
relative permeability
Prepare a sample Input variable flow rate
V1 and saturation S2
Calculate non-equilibrium
Test anisotropic relative anisotropic relative
permeability permeability
II
Replace traditional relative
Testnon-equilibrium ermeability in the oil-phase and
relative permeability water-phase motion equations UpdateV1
Fit non-equilibrium Substitute into a control
anisotropic relative equation, and select a
permeability curves solving process
Fupu e non
equilibrium
anisotropic
relative
permeability of
each step
FIG. 2
Description
2/4
Numerical simulation method based on non-equilibrium relative permeability
Prepare a sample Input variable flow rate V1 and saturation S2
Calculate non-equilibrium Test anisotropic relative anisotropic relative permeability permeability
Replace traditional relative Testnon-equilibrium ermeability in the oil-phase and relative permeability water-phase motion equations UpdateV1
Fit non-equilibrium Substitute into a control anisotropic relative equation, and select a permeability curves solving process
Fupu e non equilibrium anisotropic relative permeability of each step
FIG. 2
TECHNICAL FIELD The present invention relates to the technical field of reservoir development, in particular to a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability.
BACKGROUND The oil-water two-phase numerical simulation method is usually used to predict the reservoir status in the reservoir development process. The existing oil-water two-phase numerical simulation method derives the relative permeability simply by normalizing the laboratory test results. The reservoir with similar physical properties uses only one relative permeability curve, that is, an isotropic relative permeability curve, which has nothing to do with the direction and flow rate. The existing oil-water two-phase numerical simulation method ignores the effects of the production rate and displacement direction on the relative permeability. As a result, there are errors in the pressure propagation and remaining oil saturation change, so the predicted reservoir pressure distribution and remaining oil distribution are inaccurate. Taking the typical fluvial reservoir as an example, when the injection and production are carried out in directions horizontal and perpendicular to the underground river, due to the difference in the pore structures in the two directions, the oil-water two-phase seepage flow laws are different. In addition, the relative permeability curves measured at different flow rates in the same direction are also different.
SUMMARY OF INVENTION An objective of the present invention is to provide a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability. The present invention accurately predicts the reservoir pressure distribution and remaining oil distribution. To achieve the above purpose, the present invention provides the following technical solutions. A method for predicting reservoir status based on non-equilibrium anisotropic relative permeability is provided, including: dividing a three-dimensional geological model into grid areas to obtain well parameters and initial attribute parameters of each grid area, where the well parameters include a well point location, a production rate, a production pressure and a production time; the initial attributes parameters include an initial pressure, an initial fluid flow rate and an initial water saturation; the initial fluid flow rate of one of two adjacent grid areas is calculated based on an initial pressure difference between the two adjacent grid areas and the initial fluid flow rate of the other of the two adjacent grid areas; the three-dimensional geological model is obtained by geological modeling of a structure of a fluvial reservoir in a region to be predicted; determining a grid area of the well point location as a first grid area, and updating the initial pressure and the initial fluid flow rate of the first grid area according to a difference between the production pressure and the initial pressure as well as the production rate, where the updated initial pressure of the first grid area is the difference between the production pressure and the initial pressure, and the updated initial fluid flow rate of the first grid area is the production rate; sequentially updating the initial pressure and initial fluid flow rate of each grid area centering on and adjoining the first grid area, and then sequentially updating the initial pressure and initial fluid flow rate of each grid area centering on and adjoining any updated grid area until the initial pressures and initial fluid flow rates of all grid areas are updated; determining relative permeability of each grid area in X/Y/Z directions according to the initial water saturation and updated initial fluid flow rate of each grid area, and updating the initial water saturation of each grid area according to the X/Y/Z relative permeability and the updated initial pressure and initial fluid flow rate of each grid area; obtaining the pressure, fluid flow rate and water saturation of each grid area at a next moment according to the X/Y/Z relative permeability and the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area; cyclically calculating to the production time based on the pressure, fluid flow rate and water saturation of each grid area at the next moment (as initial attribute parameters) to obtain the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment, and plotting time-varying water saturation and pressure changes of each area of the fluvial reservoir according to the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment; and obtaining oil reservoir and pressure distribution in the fluvial reservoir according to the time-varying water saturation and pressure changes. According to the specific examples provided by the present invention, the present invention discloses the following technical effects. The present invention discloses a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability, which predicts the reservoir pressure distribution and remaining oil distribution by using an oil-water two-phase numerical simulation method. The oil-water two-phase numerical simulation method determines the relative permeability in X/Y/Z directions according to the fluid flow rate, and considers the effects of the production rate and displacement direction on the relative permeability. This method greatly reduces the errors of pressure propagation and remaining oil saturation change, so that the predicted reservoir pressure distribution and remaining oil distribution are accurate.
BRIEF DESCRIPTION OF DRAWINGS To describe the technical solutions in the examples of the present invention or in the prior art more clearly, the accompanying drawings required for the examples are briefly described below. Apparently, the accompanying drawings in the following description show merely some examples of the present invention, and a person of ordinary skill in the art may still derive other accompanying drawings from these accompanying drawings without creative efforts. FIG. 1 is a flowchart of a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to Example 1 of the present invention. FIG. 2 is a general flowchart of a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to Example 2 of the present invention. FIG. 3 shows tabular cross-bedding and sampling directions of an outcrop of a typical fluvial reservoir. FIG. 4 shows X/Y/Z relative permeability curves of a fluvial reservoir with tabular cross-bedding at a displacement rate of 0.05 ml/min. FIG. 5 shows an implementation process of predicting a future reservoir status by a new numerical simulator.
DETAILED DESCRIPTION The technical solutions in the examples of the present invention are clearly and completely described below with reference to the accompanying drawings in the examples of the present invention. Apparently, the described examples are merely a part rather than all of the examples of the present invention. All other examples obtained by a person of ordinary skill in the art based on the examples of the present invention without creative efforts should fall within the protection scope of the present invention. An objective of the present invention is to provide a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability. The present invention accurately predicts the reservoir pressure distribution and remaining oil distribution.
In order to make the above objectives, features and advantages of the present invention more understandable, the present invention will be described in further detail below with reference to the accompanying drawings and detailed examples. Example 1 FIG. 1 is a flowchart of a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to Example 1 of the present invention. Referring to FIG. 1, the method for predicting reservoir status based on non-equilibrium anisotropic relative permeability includes: Step 101: Divide a three-dimensional geological model into grid areas to obtain well parameters and initial attribute parameters of each grid area, where the well parameters include a well point location, a production rate, a production pressure and a production time; the initial attributes parameters include an initial pressure, an initial fluid flow rate and an initial water saturation; the initial fluid flow rate of one of two adjacent grid areas is calculated based on an initial pressure difference between the two adjacent grid areas and the initial fluid flow rate of the other of the two adjacent grid areas; the three-dimensional geological model is obtained by geological modeling of a structure of a fluvial reservoir in a region to be predicted. Step 102: Determine a grid area of the well point location as a first grid area, and update the initial pressure and the initial fluid flow rate of the first grid area according to a difference between the production pressure and the initial pressure as well as the production rate, where the updated initial pressure of the first grid area is the difference between the production pressure and the initial pressure, and the updated initial fluid flow rate of the first grid area is the production rate. Step 103: Sequentially update the initial pressure and initial fluid flow rate of each grid area centering on and adjoining the first grid area, and then sequentially update the initial pressure and initial fluid flow rate of each grid area centering on and adjoining any updated grid area until the initial pressures and initial fluid flow rates of all grid areas are updated. In steps 102 and 103, the first grid area is the location of the well point; the production pressure is the pressure at a wellhead above the ground; the grid pressure (i.e. formation pressure) is an initial state pressure obtained from a pressure gradient, that is, the layer of a depth corresponds to a pressure. As there is a difference between the grid pressure and the wellhead pressure, the fluid flows. The fluid in the first grid area is taken out, and the static balance of the grid system is broken. Due to the pressure difference between the first grid area and other adjacent grid areas, the fluid in the grid system moves from high pressure to low pressure. Step 104: Determine relative permeability of each grid area in X/Y/Z directions according to the initial water saturation and updated initial fluid flow rate of each grid area, and update the initial water saturation of each grid area according to the X/Y/Z relative permeability and the updated initial pressure and initial fluid flow rate of each grid area. In Step 104, the determination of the relative permeability of each grid area in X/Y/Z directions according to the initial water saturation and updated initial fluid flow rate of each grid area specifically includes: determine X/Y/Z relative permeability curves of each grid area according to the updated initial fluid flow rate of each grid area, where the X/Y/Z relative permeability curves take the water saturation as abscissa and the X/Y/Z relative permeability as ordinate; the X/Y/Z relative permeability curves are derived through displacement experiments on an X-direction core sample, a Y-direction core sample and a Z-direction core sample, respectively; the X-direction core sample, the Y-direction core sample and the Z-direction core sample are obtained by drilling in the X/Y/Z directions of a cube-shaped sample of an outcrop of the fluvial reservoir in the region to be predicted, respectively; and determine the X/Y/Z relative permeability of each grid area according to the initial water saturation and the X/Y/Z relative permeability curves of each grid area. In Step 104, the update of the initial water saturation of each grid area according to the X/Y/Z relative permeability and the updated initial pressure and initial fluid flow rate of each grid area specifically includes: replace the relative permeability in a seepage control equation of an oil-water two-phase model of each grid area with the X/Y/Z relative permeability of each grid area to obtain an X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase seepage model of each grid area; substitute the updated initial pressure and initial fluid flow rate of each grid area into the X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase model of each grid area, and calculate the water saturation of each grid area based on a constraint of water saturation and oil saturation, where the constraint of water saturation and oil saturation is: water saturation + oil saturation = 1; and use the water saturation of each grid area to update the initial water saturation thereof Step 105: obtain the pressure, fluid flow rate and water saturation of each grid area at a next moment according to the X/Y/Z relative permeability and the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area. In Step 105, the obtaining of the pressure, fluid flow rate and water saturation of each grid area at a next moment according to the X/Y/Z relative permeability and the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area specifically includes: substitute the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area into the X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase model of each grid area, to calculate the pressure, fluid flow rate and water saturation of each grid area at the next moment. Step 106: Cyclically calculate to the production time based on the pressure, fluid flow rate and water saturation of each grid area at the next moment (as initial attribute parameters) to obtain the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment, and plot time-varying water saturation and pressure changes of each area of the fluvial reservoir according to the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment. Step 107: Obtain the oil reservoir and pressure distribution in the fluvial reservoir according to the time-varying water saturation and pressure changes. Example 2 FIG. 2 is a general flowchart of a method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to Example 2 of the present invention. Referring to FIG. 2, the method for predicting reservoir status based on non-equilibrium anisotropic relative permeability includes: 1. A 30 cm * 30 cm * 30 cm sample with trough or tabular cross-bedding was selected from an outcrop of a typical fluvial reservoir, and core samples were obtained by drilling in X/Y/Z directions respectively. FIG. 3 shows tabular cross-bedding and sampling directions of the outcrop of the typical fluvial reservoir. A novel anisotropic three-dimensional oil-water two-phase experimental device of relative permeability was used to conduct displacement experiments on an X-direction core sample, a Y-direction core sample and a Z-direction core sample obtained by drilling in the X/Y/Z directions. The displacement experiments included: Anisotropic relative permeability test: According to the industry standard (SY/T 5345-2007), a novel non-equilibrium oil-water two-phase experimental device of relative permeability was used to conduct displacement experiments to obtain the oil-water two-phase relative permeability curves of the three core samples. FIG. 4 shows the X/Y/Z relative permeability curves of the fluvial reservoir with tabular cross-bedding at a displacement rate of 0.05 ml/min. FIG. 4 shows that the three relative permeability curves differ significantly, which means that the relative permeability of the oil-water two-phase system in the same reservoir is anisotropic. Non-equilibrium relative permeability test: The on-site injection rate (m 3 /d) was converted to the laboratory displacement rate (ml/min). The relative permeability curves of the same core sample differed significantly at varying displacement rates V, which means that during reservoir development, the relative permeability was not static, but changed with the production rate and showed a non-equilibrium state. The non-equilibrium relative permeability test also included porosity and permeability tests on the X-direction core sample, the Y-direction core sample and the Z-direction core sample to obtain their porosity and permeability. The X/Y/Z relative permeability curves of the fluvial reservoir with tabular cross-bedding at different displacement rates were obtained through the displacement experiments, which are similar as those shown in FIG. 4. 2. The parameters needed to calculate the relative permeability curves were obtained through the displacement experiments in the previous step, including: sample length L (cm), diameter D (cm), cross-sectional area A (cm 2 ), porosity (P (%), permeability k (mD), flow rate q (ml/h), cumulative injection volume V(t) (ml), time-varying change of cumulative volume of each phase of escaping fluid at the output end, cumulative output of the oil phase Vo(t) (ml) and pressure difference AP(t) across the core. The relative permeability curves were calculated based on the one-dimensional two-phase oil-water displacement frontal advance theory of Buckley-Leverett. The capillary pressure and gravity were ignored, and the two-phase immiscible fluids were assumed to be incompressible. The output of each fluid at the core sample outlet and the time-varying changes of the pressure difference across the core sample were recorded. The relationship of the ratio O of two-phase total resistance to single resistance, the apparent viscosity app and the water injection multiple Qi was fit, and the oil-water relative permeability curves were calculated at various directions and displacement rates. FIG. 4 shows the X/Y/Z relative permeability curves of the fluvial reservoir with tabular cross-bedding at a displacement rate of 0.05 ml/min. Specifically, the
Q f AP(L) Ak P'PP(Sw k_ k(kP_ fitting was performed by q(t) pL and ° . The water injection multiple (Q) was measurable cumulative water injection volume of the core sample, which was generally an integer multiple of the pore volume of the core sample. JP was pressure difference, A was cross-sectional area, K was absolute permeability, q(t) was volumetric flow rate, po was oil-phase viscosity, and L was core length, which were obtained by the above displacement experiments. The simplest fitting is fitting in excel. For example, a column of D and a column of Qi are inserted into a chart to select a relational expression that best fits. This method is equivalent to the method of undetermined coefficients to determine the relational expression. There are also professional fitting tools, such as Matlab and 1stOpt. Non-equilibrium anisotropic relative permeability equations and data were input through Matlab to fit the relationship of the displacement rate, water saturation and oil-water relative permeability curves. A Joint-Bayesian-Network (JBN) algorithm was used to calculate the oil-water relative permeability corresponding to the water saturation at various directions and displacement rates. By fitting the oil-water relative permeability corresponding to the water saturation at various directions and displacement rates, the non-equilibrium anisotropic relative permeability equations, K= al*exp(bl*S.)+cl*exp(d*VL) +e*exp(fl*S,*VL)+g 1 and K, =a 2 *exp(b 2 *S.)+c 2 *exp(d 2 *VL) +e2 *exp(f *S*VL)+92 were obtained, 2 where a], bi, 1c , di, e i, fi, g, a2, b 2, C2, d2 , e2, f2 and g2 were undetermined coefficients, S was the water saturation (%), and VL was the injection rate (ml/min).
Then, it was possible to use the oil-water two-phase numerical simulation method based on the non-equilibrium anisotropic relative permeability to calculate the oil-water relative permeability at the current location and current time by the flow rate V and the water saturation S according to the non-equilibrium anisotropic relative permeability equations. The undetermined coefficients in the equations were known by fitting, and only the flow rate and water saturation were needed. According to the relative permeability curves in the three directions shown in FIG. 4, when the sampling direction (that is, the displacement direction) is consistent with the bedding direction (x direction), the residual oil saturation is the highest and the displacement efficiency is the lowest, followed by those in the y direction and the z direction. When the displacement direction is more approximately perpendicular to the bedding direction, lower residual oil saturation leads to higher displacement efficiency. Therefore, the relative permeability has anisotropy, which is related to the displacement direction. The experimental results show that the displacement rate also affects the morphology of the relative permeability curves. The traditional reservoir numerical simulation method ignores the effect of production rate on the relative permeability curves during the entire simulation process. The three conduction directions (sampling directions) are calculated using the same relative permeability curves (an oil-phase relative permeability curve and a water-phase relative permeability curve), resulting errors in pressure propagation and residual oil saturation change. The numerical simulation method based on non-equilibrium anisotropic relative permeability curves accurately characterizes the pressure propagation and remaining oil distribution characteristics of the reservoir. Especially in the remaining oil potential exploitation of high water cut reservoirs in the later stage of development, the numerical simulation method based on non-equilibrium anisotropic relative permeability curves is more accurate to guide the deployment of potential drilling sites.
3. The traditional relative permeability was replaced with the non-equilibrium anisotropic relative permeability in the seepage control equation of the oil-water two-phase model. The traditional oil-water two-phase numerical simulation method ignored that the displacement direction and rate had a significant effect on the relative permeability curve. Therefore, the non-equilibrium anisotropic relative permeability was introduced to replace the isotropic relative permeability in the oil-water two-phase numerical simulation method, thereby improving the traditional method. In this example, based on the oil-water two-phase black-oil model, the static isotropic relative permeability in the water-phase motion equation and the oil-phase motion equation was replaced by the non-equilibrium anisotropic relative permeability, and the established new oil-phase and water-phase motion equations were solved differentially. By introducing the anisotropic relative permeability into the oil-phase control equation and the water-phase control equation of the traditional oil-water two-phase numerical simulation method, the traditional oil-water two-phase numerical simulation method was revised. Specifically: Seepage control equations of oil-water two-phase model: Oil phase:
V. k""'"°'l''' " (Vp 0 - yOVD) -q= (po#So) ]O at(1 In equation (1), k is absolute permeability (md); kronisompic is the oil-phase relative permeability of the non-equilibrium anisotropic relative permeability; po is oil-phase density (g/cm); po is oil-phase viscosity (mPa-s); po is oil-phase pressure (Mp), yo = pog; g is the acceleration of gravity (mIs2); D is the distance from a reference plane (m);e is porosity; So is oil saturation; qo is oil-phase flow rate. Water phase:
V- FkkwanisotropicP '"""''' (Vp,-7y,VD)-q= (p,#fS.) P, at (2)
In equation (2), k is absolute permeability (md); kwanisotropic is the water-phase relative permeability of the non-equilibrium anisotropic relative permeability; p, is water-phase density (g/cm); pw is water-phase viscosity (mPa-s); p, is water-phase pressure (Mp), yw =
pwg; g is the acceleration of gravity (mIs2); D is the distance from a reference plane (m); ' is porosity; S is water saturation; qw is water-phase flow rate. The above experiments determined that the oil-water relative permeability was affected by the anisotropy of the pore structure. Therefore, kroanisotropic in equation (1) was replaced with krox, k, and kroz, where km, was oil-phase relative permeability in the x direction, kroy was oil-phase relative permeability in the y direction, and kroz was oil-phase relative permeability in the z direction. krwanisotpic in equation (2) was replaced with kr., krwy and krwz, where krw. was water-phase relative permeability in the x direction, krwy was water-phase relative permeability in the y direction, and krwz was water-phase relative permeability in the z direction. In this way, the traditional isotropic relative permeability was replaced with the non-equilibrium anisotropic relative permeability. Kroanisotropic in equation (1) ignored the effects of the production system, the displacement direction and rate. krwanisotropic in equation (2) also ignored the effects of the production system, the displacement direction and rate. kroanisotropic was replaced with kro in different directions, namely krox, kroy and kroz, and the variable of the displacement rate was taken into account in the calculation of krox, kroy and kroz. Also, krwanisotropic was replaced with krw in different directions, namely krw., krwy and krwz, and the variable of the displacement rate was taken into account in the calculation of krw., krwy and krwz. Differential discretization was performed on equations (1) and (2). The oil-phase equation was first expanded into a rectangular component:
_[ -k.( yO )]+ -k,( r[ Op 0 ax po ax y PO Yxay ay a po-k (po aD a(#pOS0 + [- -k 0 7 a _ = )
)]+qO Oz po 1z 1z at (3)
Based on the state of point (i,j,k,n+1), namely point (i,j,k) in space at an (n+1)-th time
step, equation (3) was discretized to obtain equation (4). The subscript in equation (4) was
1 .1 i+-=i+-, j,k abbreviated, for example: 2 2
I n--mi1n+ n--i D po-k-k p. -p D -D Ap" ro i 1 11 1 _
[+ -y )+_____ -r. 1 )]
S A1. .A1 .1 .A k2 k2 2 2
n + +
n+1 _p on+1 k kn+[( kn 1 22 DQ-D) p -pk 2 D 2
kpo i 2 1 1 2 1 At 4)-
n1 I 1 =q [(O49S 0)n -_(O49 0Sf] At (4)
Both sides of equation (4) multiplied by V/k *. V/* * was a replacement for simplifying the equation, which had no practical meaning.
Ay; 7,-- k. k -p?" p,AyI-"x P.kpI-pD D,-D -DQ p,"p -pD -p -D D -D O K I[( -r 1 )+( - 1 k o 1 2 1 1, 2 2 2 2
/ PoAz - k-&7 k # A 1 + A 1 D -D. X 1 2AXi n>Ipn+I D-D + o[P~P 1 Ay, AasrAc , - 1 Ay Ap Y a AI Ax2Ax 2 2 2 2 n--i n--i 1+ n-i k+-1 kP +Pkl P k- 1 -D +A-k jPk+lPk 1 2 TZ k- 1 2 1 1 2 2 2 2 2
TX+ -P. +1 P° -I° -.T-i ° - -k +A~iYA~ __I[(0Pz'S 0)n+ 1 -(¼ 0 S 0)n ].xAyAz
P- -- k_ -I-- -k The followingconduction coefficientsweredefinedtosimplifytheequation: p( -k.k Ax~-po ppr-k-k - -k __ __ __ U______, __k (,k k AY Az k p k 01anisotropic+-- kkanisotropic+- knstoi Ax Ax I0 k.+- oilsotp )c- 2I1- k - i7 -\72 x Ix 1 ik- o 2 ia 1 1sm 2 1 2 2 2 2
5t p.- k pk- k () r~k P . ky A A7-kpo k'k PO r Axik oiwsOtMOrC+ Ay, Ay1I Ay1 IJw /t iic Ay, Ay. Ay. ,uO O 2 2 2 2
p0 .-k p0 .-k
Az1 +1k10 , okuiwotropc--I A7 Az Az k, okaisotropc kIA okan 2sk op ok 2 1
2 2 2 2(6
Then equation(5)wassimplified to:
oianuotropiC---2]f oianisotopi1C Lf 2 +~k = [IpS)" kq+"- (p "]
[T(pn7I- p71 )-_y2 D 1 2~- )+IT (Pn7I- P71) r1DD.) ojanisOroPiC- ?j] ojan1uorop1-2Q-L
+IX Lk+. F+I n+I Pp)y +(Dk 0 L<~i2i1)-Pk FP, nl__(D _ LknOrpc (
knisolropic--2 2
-jq 1t E(9Vn-ipS) jk (7)
A second-order difference quotient operator was defined to simplify the equation: x oniotopc 1Pi 1 i)+ TX 1 (p -- pi) oanisotropic+-- oianisotropic 2 oanisoropIC2
AyT anisotropicAP 1 TY - Pk )+ TZ1 (pj-- pj) ojanisotropic+- okanisotropc- 2 2
AzTZoaniYoropcAzP =TZ Il(Pk~l Pk)±+I'Z Il(Pk-l Pk) Lokanisotropic--2 okanisoropic--2 (8)
Similarly:
AxT oanisotropicAxD=TX 1-y 1 (D.-D)+TX 1-y 1 (D1 1 -D) Oianisotropic+- i+ oianisotropic- Oi-
ATY anotropic AD=TY 1. 1 (D 1 1 -D 1 )+TY - I(D_ -Di) ojanisotropic+- 01-2 ojanisotropic- oj 2 2 2 2 2
OaniotropiAzD=TZokanisotropic+- ok+(Dkl- Dk+TZkanisotropic- - (Dk- D 2 2 2 2
(9)
Then equation (7) was simplified to equation (10), where the subscript of Po was omitted:
Ax TX.pj AP"*Y + AT ani,rop AP"*n + ATZ cpoannsoropc ,A 1 -ATX AP .an,,,,,, AD y a #oSo]
--A Y'TY AD-ATZ ADq n 1 jk = Vjk [(OPOS)n~ (OPOSO)n oarnsorropic y' z oanisorropic z 0At
(10)
Then equation (10) was simplified to
T AP" A ,,,A +" = Vij_ [(#p 0S0 )n1 (#pOS )" At (11)
The water-phase equation was written in the same form, and the subscript o in equation (11) was changed to w. The traditional relative permeability krl in the traditional oil-phase control equation and water-phase control equation was replaced with krlanisompic (including kroanisotropic and krwanisotropic), and the anisotropic relative permeability was determined through
experiments. In this way, the anisotropic relative permeability was introduced into the traditional numerical simulation method.
The numerical simulation control equation based on the non-equilibrium anisotropic relative permeability, namely equation (11), was solved by using a fully implicit solution method to obtain the pressure and saturation of each grid at different times. This method could also be used to derive the production data of a well. By revising the numerical simulator through the above steps, a new numerical simulator was obtained. The new numerical simulator iteratively solved the above equations to obtain the calculation results. FIG. 5 shows the implementation process of predicting the future state of the reservoir (pressure distribution, remaining oil distribution, recovery factor and water cut, etc.) by the new numerical simulator. A grid system was established, which was usually converted from a geological model (that is, the digitization of real reservoir morphology). The geological model was established by using petrel software. After the establishment, the basic data required for reservoir numerical simulation, such as GRDECL files could be exported. The parameters were input, including porosity, permeability, initial water saturation and initial bubble point pressure that match each grid of the grid system, as well as the physical parameters of the reservoir fluid such as pressure-volume-temperature (PVT). The PVT parameters included: viscosity, bubble point pressure, solution gas-oil ratio, volume coefficient, water volume coefficient, viscosity, oil density, water density and rock compressibility (ignoring the compressibility of oil and water). These attribute data matching each grid was provided by a geological model, which was also exported through the petrel software. The relative permeability and capillary force function (a relationship between water saturation and capillary force) were input. This relative permeability was the non-equilibrium anisotropic relative permeability, instead of the traditional relative permeability. The traditional oil-water relative permeability was only a function of grid water saturation, that is, the traditional oil-water relative permeability was calculated according to the grid water saturation. The non-equilibrium anisotropic relative permeability was a function of grid water saturation and oil-water flow rate, and was related to the flow direction, that is, the relative permeability curve was selected according to the flow direction, and the water saturation and oil-water flow rates were introduced into the calculation. Well information and production system (the location of oil and water wells, production rate, pressure and time) were input. Then the cycle calculation started. The initial water saturation, pressure distribution and boundary conditions were known. The calculation took a time step as a unit, and each additional time step required the following cycle to be repeated. The oil well production and bottom hole flow pressure were calculated to form the coefficient matrix of the pressure and saturation equation (equation (11)). The system of nonlinear equations was solved by linearizing by using a difference method to obtain the unknowns (i.e. the coefficient matrix). When the accuracy requirements were met, the flow rate, saturation and pressure of the grid system were further calculated according to the Darcy equation and the control equations. The non-equilibrium anisotropic relative permeability of the grid system was calculated to obtain the saturation and pressure distribution of the grid system after a unit time, and this cycle ended. When the calculation cycled to the specified time, the final water saturation and pressure distribution were obtained. Assuming that the reservoir fluid as only water and oil, when the final water saturation was obtained, the final remaining oil saturation was obtained. The residual oil saturation distribution and pressure distribution calculated by the numerical simulation method based on the non-equilibrium anisotropic relative permeability were more accurate than those calculated by the traditional numerical simulation method. The oil-water two-phase numerical simulation method based on the non-equilibrium anisotropic relative permeability proposed by this example achieves the purpose of accurately characterizing the oil-water two-phase seepage flow in the development of the heterogeneous reservoir. The existing traditional numerical simulator ignores the effects of the production rate and displacement direction on the relative permeability curve, so the predicted reservoir pressure distribution and remaining oil distribution are not accurate. This example considers the anisotropy of relative permeability in reservoir simulation, and thus is more accurate to describe the fluid flow law in the reservoir, reflect geological details of the reservoir, evaluate the injection-production effect, and adjust the development plan. In this example, a new numerical simulator is used to conduct the numerical simulation study on the typical fluvial reservoir. The traditional simulator is revised, that is, the oil-water two-phase numerical simulation method in the traditional simulator is revised, so that the simulation process is closer to the actual geological situation. Therefore, the new numerical simulation method more accurately characterizes the oil-water seepage laws under underground conditions, and achieves accurate prediction of the sweep state and various dynamic indicators during the water flooding development of the heterogeneous oil reservoir. This example more accurately characterizes the remaining oil distribution in the typical fluvial reservoir during the high water cut stage, and more clearly explains the reasons for the difference between the drilling production effect and the inherent understanding in the later stage, thereby guiding the extension and providing support for the stable production of the oilfield. In this example, the new numerical simulation method can be used to achieve: (1) simulation of initial reservoir development plans, including: evaluate the development methods, such as depletion mining or water injection development; select reasonable well pattern and spacing and development strata, etc.; select reasonable injection-production methods and injection-production ratios; study the sensitivity of reservoir and fluid properties; (2) historical simulation of developed oilfields, including: verify geological reserves; determine the basic displacement mechanism; determine fluid production and production cycle; determine reservoir and fluid characteristics; determine the location of potential areas; (3) dynamic prediction, including: predict the development indexes and economic benefit; evaluate the methods of enhanced oil recovery (primary oil recovery, water injection, gas injection and chemical flooding, etc.); study the distribution of remaining oil saturation and reproduce the production history; (4) potential evaluation and direction of enhanced recovery factor, including: determine the location of wells including infill wells; determine the effects of maximum fluid production volume and production rate on the oil recovery of the reservoir; and (5) research on special topics and mechanism issues, including: compare water injection, gas injection and natural depletion mining performance; study the effects of various water injection methods; study the effects of well spacing and well pattern on reservoir performance; study the effect of different development strata on reservoir performance; study the effect of water injection rate on oil production and recovery; study the effects of reservoir surface properties and interlayer heterogeneity on reservoir performance; verify the reservoir data. The remaining oil distribution and potential exploitation are the most concerned in the later stage of reservoir development. The effect of infill wells deployed according to the traditional numerical simulation method is not good. The fundamental reason is that the traditional numerical simulation method fails to accurately characterize the heterogeneity of the reservoir, resulting in errors in the prediction of remaining oil distribution. By using the non-equilibrium anisotropic relative permeability instead of the traditional relative permeability, this example more accurately characterizes the heterogeneity of fluid seepage in the reservoir and obtains more accurate remaining oil distribution, which provides important guiding significance for the deployment of wells for exploiting the potential remaining oil. Each example of the present specification is described in a progressive manner, each example focuses on the difference from other examples, and the same and similar parts between the examples may refer to each other. In this disclosure, several examples are used for illustration of the principles and implementations of the present invention. The description of the foregoing examples is used to help illustrate the method of the present invention and the core principles thereof. In addition, those of ordinary skill in the art can make various modifications in terms of specific implementations and scope of application in accordance with the teachings of the present invention. In conclusion, the content of the present specification should not be construed as a limitation to the present invention.
Claims (4)
- CLAIMS 1. A method for predicting reservoir status based on non-equilibrium anisotropic relative permeability, comprising: dividing a three-dimensional geological model into grid areas to obtain well parameters and initial attribute parameters of each grid area, wherein the well parameters comprise a well point location, a production rate, a production pressure and a production time; the initial attributes parameters comprise an initial pressure, an initial fluid flow rate and an initial water saturation; the initial fluid flow rate of one of two adjacent grid areas is calculated based on an initial pressure difference between the two adjacent grid areas and the initial fluid flow rate of the other of the two adjacent grid areas; the three-dimensional geological model is obtained by geological modeling of a structure of a fluvial reservoir in a region to be predicted; determining a grid area of the well point location as a first grid area, and updating the initial pressure and the initial fluid flow rate of the first grid area according to a difference between the production pressure and the initial pressure as well as the production rate, wherein the updated initial pressure of the first grid area is the difference between the production pressure and the initial pressure, and the updated initial fluid flow rate of the first grid area is the production rate; sequentially updating the initial pressure and initial fluid flow rate of each grid area centering on and adjoining the first grid area, and then sequentially updating the initial pressure and initial fluid flow rate of each grid area centering on and adjoining any updated grid area until the initial pressures and initial fluid flow rates of all grid areas are updated; determining relative permeability of each grid area in X/Y/Z directions according to the initial water saturation and updated initial fluid flow rate of each grid area, and updating the initial water saturation of each grid area according to the X/Y/Z relative permeability and the updated initial pressure and initial fluid flow rate of each grid area; obtaining the pressure, fluid flow rate and water saturation of each grid area at a next moment according to the X/Y/Z relative permeability and the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area; cyclically calculating to the production time based on the pressure, fluid flow rate and water saturation of each grid area at the next moment (as initial attribute parameters) to obtain the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment, and plotting time-varying water saturation and pressure changes of each area of the fluvial reservoir according to the pressure, fluid flow rate and water saturation of each grid area corresponding to each moment; and obtaining oil reservoir and pressure distribution in the fluvial reservoir according to the time-varying water saturation and pressure changes.
- 2. The method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to claim 1, wherein the determining relative permeability of each grid area in X/Y/Z directions according to the initial water saturation and updated initial fluid flow rate of each grid area specifically comprises: determining X/Y/Z relative permeability curves of each grid area according to the updated initial fluid flow rate of each grid area, wherein the X/Y/Z relative permeability curves take the water saturation as abscissa and the X/Y/Z relative permeability as ordinate; the X/Y/Z relative permeability curves are derived through displacement experiments on an X-direction core sample, a Y-direction core sample and a Z-direction core sample, respectively; the X-direction core sample, the Y-direction core sample and the Z-direction core sample are obtained by drilling in the X/Y/Z directions of a cube-shaped sample of an outcrop of the fluvial reservoir in the region to be predicted, respectively; and determining the X/Y/Z relative permeability of each grid area according to the initial water saturation and the X/Y/Z relative permeability curves of each grid area.
- 3. The method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to claim 1, wherein the updating the initial water saturation of each grid area according to the X/Y/Z relative permeability and the updated initial pressure and initial fluid flow rate of each grid area specifically comprises: replacing the relative permeability in a seepage control equation of an oil-water two-phase model of each grid area with the X/Y/Z relative permeability of each grid area to obtain an X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase seepage model of each grid area; substituting the updated initial pressure and initial fluid flow rate of each grid area into the X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase model of each grid area, and calculating the water saturation of each grid area based on a constraint of water saturation and oil saturation; and using the water saturation of each grid area to update the initial water saturation thereof
- 4. The method for predicting reservoir status based on non-equilibrium anisotropic relative permeability according to claim 3, wherein the obtaining the pressure, fluid flow rate and water saturation of each grid area at a next moment according to the X/Y/Z relativepermeability and the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area specifically comprises: substituting the updated initial pressure, initial fluid flow rate and initial water saturation of each grid area into the X/Y/Z relative permeability-based seepage control equation of the oil-water two-phase model of each grid area, to calculate the pressure, fluid flow rate and water saturation of each grid area at the next moment.
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