METHOD FOR EVALUATING PRODUCTIVITY OF VERTICALLY HETEROGENEOUS GAS RESERVOIR CONSIDERING INTERLAYER CROSSFLOW

Abstract

A method for evaluating productivity of a heterogeneous gas reservoir considering interlayer crossflow is disclosed in the invention, and includes: (1) dividing a heterogeneous gas reservoir into multiple reservoir sections along the depth of the heterogeneous gas reservoir; (2) obtaining the productivity of each reservoir section according to data obtained through wireline formation test; (3) superimposing the productivity of all reservoir sections based on the water-electricity similarity principle to obtain the superimposed productivity of the heterogeneous gas reservoir; and (4) using an interlayer crossflow correction coefficient considering influence caused by the interlayer crossflow to obtain the corrected productivity of the heterogeneous gas reservoir.

Description

TECHNICAL FIELD

The invention relates to the technical field of oil and gas field exploration and production engineering, and in particular, to a method for evaluating the productivity of a heterogeneous gas reservoir considering interlayer crossflow.

BACKGROUND

Productivity prediction is a crucial link for research of oil and gas field development engineering and determines not only the industrial development value of oil and gas reservoirs but also the investment scale for the development of oil and gas reservoirs. Compared with terrestrial gas reservoirs, deep water gas reservoirs have huge development investments, and high-productivity evaluation or low-productivity prediction affects the exploration and production of gas reservoirs. Preferable selection of high-yield reservoirs through accurate evaluation of the productivity of gas reservoirs is a key technology to achieve the efficient development of deepwater gas fields. In the prior art, drill stem testing (DST) and wireline formation test (WFT) are conventional methods for evaluating the productivity of oil and gas reservoirs, but drill stem testing is expensive in cost, and offshore gas field test is relatively less used. By comparison, the wireline formation test has great advantages in terms of environment, safety, and economy, and the productivity of each reservoir section can be predicted through evaluation on the seepage capability of underground fluid.

An offshore of low-porosity and low-permeability reservoir has the remarkable feature of strong heterogeneity. Generally, under conditions of similar burial depth, lithology, horizon, facies zone, and diagenetic background, the reservoir sections have great difference in physical property and productivity, which brings great difficulty to productivity prediction. For heterogeneous reservoirs, when the productivity prediction is made in the prior art, multiple reservoir sections close to each other are considered as a whole as a seepage unit, and interlayer crossflow caused by heterogeneous differences among different reservoir sections is ignored, which leads to the deviation of productivity evaluation.

SUMMARY

In view of problems in the prior art, the invention provides a method for evaluating the productivity of a heterogeneous gas reservoir considering interlayer crossflow.

The invention is implemented by a method for evaluating the productivity of a heterogeneous gas reservoir considering interlayer crossflow, and the method for evaluating the productivity of a heterogeneous gas reservoir includes the following steps:

• • (1) dividing a heterogeneous reservoir into multiple reservoir sections along the depth of the heterogeneous gas reservoir;
  • (2) obtaining the productivity of each reservoir section according to data obtained through wireline formation test and laboratory test;
  • (3) superimposing the productivity of each reservoir section to obtain the superimposed productivity of the gas reservoir; and
  • (4) using an interlayer crossflow correction coefficient considering influence caused by the interlayer crossflow to obtain the corrected comprehensive productivity of the gas reservoir.

Preferably, Step (1) includes dividing the reservoir into several different reservoir section along the depth of the heterogeneous gas reservoir, according to permeability obtained through logging data, where each of the reservoir section is a relatively homogeneous reservoir section.

Preferably, in Step (1), a first wireline formation tester and a second wireline formation tester are arranged at a first depth and a second depth respectively, where the first depth and second depth belong to the adjacent layer; the pumping speed of the first wireline formation tester is changed, pressure variation of the probe of the second wireline formation tester in another layer is observed, then whether an adjacent layer pertains to a same reservoir section is determined according to the pressure variation of the probe of the second wireline formation tester.

Preferably, determining whether an adjacent layer pertains to the same reservoir section according to the pressure variation of the probe of the second wireline formation tester includes:

• • if pressure measured by the second wireline formation tester is changed along with that measured by the first wireline formation tester, the two layers pertain to the same reservoir section; or
  • if pressure measured by the second wireline formation tester is not changed along with disturbance, the two layers are two independent reservoir sections.

Preferably, Step (2) includes using static permeability K_s obtained through the wireline formation test and permeability K_{g (1−Sw)} obtained through core displacement test from the laboratory to establish a conversion relation K_{g (1−Sw)}=f (K_s), and obtaining effective permeability K_{g (1−Sw)} based on data obtained through the wireline formation test.

Preferably, Step (2) includes establishing a conversion relation of measured productivity Q_i and effective permeability K_{g (1−Sw)} according to the measured productivity relation of the reservoir section.

Preferably, the conversion relation is Q_i=a*K^b_{g (1−Sw)}+c, wherein a, b, and c are fitting coefficients.

Preferably, the conversion relation is validated and corrected using DST data.

Preferably, the productivity of each reservoir section is calculated based on a calculation formula (1):

$q_{\mathrm{sc}}=\frac{-A+\sqrt{A^2-4B\left(\psi \left(p_{\mathrm{wf}}\right)-\psi \left(p_e\right)\right)+C}}{2B}$

Preferably, the superimposed productivity of the gas reservoir is that of all reservoir sections, namely:

$Q_{\mathrm{tol}}=\sum _{i=1}^n{q}_i{Q}_m=\alpha *Q_{\mathrm{tol}}$

• • Where Q_tol is the superimposed productivity of the gas reservoir;
  • q_i is the productivity of the i(th) reservoir section;
  • α is the correction coefficient for the interlayer crossflow; and
  • Q_m is the corrected comprehensive productivity of the gas reservoir.

With reference to all the technical solutions, the invention has the advantages and effective effects that are specific to the heterogeneous characteristics of the gas reservoir, a gas reservoir is divided into several different reservoir sections, such that a complex reservoir with strong heterogeneity is converted into relatively homogeneous reservoir sections, and the productivity of the reservoir sections is determined using data obtained through wireline formation test and laboratory test, considering the influence of the interlayer crossflow in a heterogeneous reservoir on productivity prediction, which has more accurate prediction results.

BRIEF DESCRIPTION OF DRAWINGS

To describe the technical solutions in embodiments of the invention or in the prior art more clearly, the following briefly describes the accompanying drawings required for describing the embodiments or the prior art. Apparently, the accompanying drawings in the following descriptions show some embodiments of the invention, and persons of ordinary skill in the art may still derive other drawings from the accompanying drawings without creative efforts.

FIG. 1 is a flow diagram of a method according to an embodiment of the invention.

FIG. 2 is a schematic diagram of interlayer crossflow in a heterogeneous gas reservoir according to an embodiment of the invention.

FIG. 3 is a schematic diagram of plotting of Lorenz curve when a flow variation coefficient is obtained according to an embodiment of the invention.

FIG. 4 is a schematic diagram of the plotting of permeability along the depth obtained according to an embodiment of the invention.

FIG. 5 is a schematic diagram of multiple reservoir sections in the plotting of permeability along the depth obtained according to an embodiment of the invention.

DESCRIPTION OF EMBODIMENTS

Details of the invention can be more clearly understood with reference to the accompanying drawings and the descriptions of embodiments of the invention. However, the embodiments of the invention described herein are used to explain the invention only but do not constitute any limitation on the invention in any way. Any possible variations based on the invention may be conceived by persons of ordinary skill in the art in the light of the teachings of the invention, and these should be considered to fall within the scope of the invention.

In view of problems in the prior art, as shown in FIG. 1, the invention provides a method for evaluating the productivity of a heterogeneous gas reservoir (may also be referred to as “oil and gas reservoir” or “gas reservoir”) along its depth considering interlayer crossflow, and the method includes the following steps of:

• • (1) dividing a heterogeneous reservoir into multiple reservoir sections along the depth of the heterogeneous gas reservoir;
  • (2) obtaining the productivity of each reservoir section according to data obtained through wireline formation test and laboratory test;
  • (3) superimposing the productivity of all reservoir sections to obtain the superimposed productivity of the gas reservoir; and
  • (4) using an interlayer crossflow correction coefficient considering the influence caused by the interlayer crossflow to obtain the corrected comprehensive productivity of the gas reservoir.

In Step (1), in order to distinguish the reservoir section, the reservoir is divided into several micro-scale lithologic facies units by utilizing logging data obtained through electric imaging and combining diagenesis based on the accurate identification of lithology and sedimentary bedding structure, thereby depicting the heterogeneity characteristics of the reservoir.

Under the restriction of the lithologic facies unit framework, a reservoir quality factor and a flow unit index are used to establish a flow unit (namely reservoir section) model, and the static permeability of each reservoir section is obtained through the multivariate fitting of logging data.

A reservoir whose permeability can be reflected through logging data can be divided into several different reservoir sections (namely flow unit) according to permeability obtained through logging data, where each of the flow units is a relatively homogeneous reservoir section.

For a reservoir with large characteristic differences in pore throat structure and permeability and small logging response among different flow units, logging data cannot accurately reflect whether an adjacent layer pertains to the reservoir in the same reservoir section, so a wireline formation test method can be adopted for such determination. A first wireline formation tester and a second wireline formation tester are arranged at different-depth locations, respectively, where the first wireline formation tester and the second wireline formation tester are set in different layers, respectively; the pumping speed of the first wireline formation tester is changed, such that pressure wave disturbance is generated in the reservoir section, and pressure variation of the probe of the second wireline formation tester in another layer is observed. If pressure measured by the second wireline formation tester is changed along with that measured by the first wireline formation tester, the two layers are interconnected, pertain to the same reservoir section, and can be classified as a same reservoir section. If pressure measured by the second wireline formation tester is not changed along with disturbance, the two reservoir sections are two independent seepage units, instead of being interconnected.

In Step (2), for various reservoir sections obtained by dividing each reservoir in Step (1), static permeability K_s obtained through the wireline formation test and permeability K_{g (1−Sw)} obtained through core displacement test in a laboratory are used to establish a conversion relation K_{g (1−Sw)}=f (K_s), thereby quickly obtaining the effective permeability K_{g (1−Sw)} of the reservoir section based on data obtained through the wireline formation test.

Further, a conversion relation of measured productivity Q_i in the field and effective permeability K_{g (1−Sw)} is established according to the measured productivity relation of the section of the reservoir section, thereby realizing the rapid productivity prediction of untested well sections in the reservoir section. Engineers may use the measured productivity Q_i to validate the corrected comprehensive productivity Q_m of the invention.

In an embodiment, a relational expression obtained through fitting is Q_i-a*K^b_{g (1−Sw)}+c, where a, b, and c are fitting coefficients, and the error of the fitting relation satisfies the requirement through validation of field DST.

In an embodiment, for a single-phase gas seepage vertical well, the productivity can be calculated based on the following calculation:

$q_{\mathrm{sc}}=\frac{-A+\sqrt{A^2-4B\left(\psi \left(p_{\mathrm{wf}}\right)-\psi \left(p_e\right)\right)+C}}{2B}\mathrm{where},A=\frac{6.367\times {10}^{-4}{\mathrm{Te}}^{\left(-b\left(p_e-\stackrel{\_}{p}\right)\right)}}{K_{0}h}\ln \left(\frac{r_e}{r_w}\right)B=\frac{1.0795\times {10}^{-10}{\gamma }_g{\mathrm{Te}}^{\left(-b\left(p_e-\stackrel{\_}{p}\right)\right)}}{K^{1.5}{h}^2\stackrel{\_}{\mu }}\left(\frac{1}{r_w}-\frac{1}{r_e}\right)C=\lambda \left(\frac{p_e+p_{\mathrm{wf}}}{2}\right)\left(r_e-r_w\right)\frac{e^{\left(-b\left(p_e-\stackrel{\_}{p}\right)\right)}}{\stackrel{\_}{\mu }\stackrel{\_}{Z}}$

In the formula, q_sc is the gas production rate under standard conditions, m³/d;

$\psi \left(p\right)={\int }_{p_0}^p\frac{{\mathrm{pe}}^{\left(-b\left(p_e-\stackrel{\_}{p}\right)\right)}}{\mu Z}$

• • is the pseudo-pressure function of single-phase gas;
  • T is reservoir temperature;
  • P_e, p, p_wf, and p are respectively original reservoir pressure, mean reservoir pressure, bottom hole flowing pressure, and pressure at any point in formation, MPa;

K and K₀ are respectively reservoir permeability at pressure of p and permeability at the original reservoir pressure, mD;

• • h is reservoir thickness, m;
  • r_e and r_w are respectively reservoir radius and wellbore radius, m;
  • γ_z is the relative density of natural gas;
  • b is a stress sensitivity coefficient, MPa⁻¹;
  • μ and μ are respectively natural gas viscosity and mean natural gas viscosity, mPa·s;
  • λ is starting pressure gradient, MPa/m; and
  • z and z are respectively a deviation coefficient and a mean deviation coefficient (namely Z-factor).

In Step (3), after the productivity of each reservoir section is obtained by the method in Step (2), based on the equivalent seepage principle, several heterogeneous reservoirs are equivalent resistors connected in parallel, so that the superimposed productivity of the gas reservoir is that of all reservoir sections, namely:

$Q_{\mathrm{tol}}=\sum _{i=1}^n{q}_i$

• • Where Q_tol is the superimposed productivity of the gas reservoir;
  • q_i is the productivity of the i(th) reservoir section.

In Step (4), considering influence caused by the interlayer crossflow, an interlayer crossflow correction coefficient is used to obtain the corrected comprehensive productivity of the gas reservoir.

During the development of heterogeneous gas reservoirs, commingling production is often adopted; with the continuous decrease of the pressure of the gas reservoir, the phenomenon of pressure difference attenuation occurs due to a difference in permeability, fluid property, and other parameters of heterogeneous reservoirs in a specified period of time or a specified local range, which leads to imbalance of pressure among different reservoirs sections and formation of interlayer pressure difference. In case of specified connectivity among the different reservoir sections, gas flows from a high-pressure reservoir section to a low-pressure reservoir section under the drive of the interlayer pressure difference, thereby forming interlayer crossflow in the heterogeneous gas reservoir, as shown in FIG. 2. If influence caused by the interlayer crossflow is ignored when the productivity of the heterogeneous gas reservoirs is evaluated, the calculated productivity is prone to be deviated.

In order to consider the influence caused by the interlayer crossflow of the heterogeneous reservoir, an interlayer crossflow correction coefficient is introduced in this application. The interlayer crossflow correction coefficient is specifically obtained by the following method: calculating corresponding flow coefficients (k h/μ) of various reservoir sections according to the permeability (k), effective thickness (h), and gas viscosity (μ) of various small heterogeneous gas reservoir; arranging the flow coefficients into a sequence from small to large; calculating the cumulative percentages of flow coefficients and effective thicknesses of the various reservoir sections, respectively; plotting Lorenz curve on a rectangular coordinate paper (as shown in FIG. 3); calculating a ratio of an envelope area S_ADCA to a triangle area S_ABC as a flow variation coefficient β (when flow variation coefficient β=0 is satisfied, an interlayer is homogeneous; and when flow variation coefficient β=1 is satisfied, an interlayer is extremely heterogeneous); using a relation curve of an interlayer interference coefficient γ and a flow variation coefficient β to calculate the interlayer interference coefficient γ due to good correlation between them, so it is approximately believed that γ=β; and then calculating the interlayer crossflow correction coefficient according to formula α=1−β=1−γ.

$Q_m=\alpha *Q_{\mathrm{tol}}$

• • Where Q_m is the corrected comprehensive productivity of the gas reservoir.

The permeability of a heterogeneous gas reservoir is measured along different depths via a logging tool. The permeability-depth log obtained by such measurement shows a log and embodies of the heterogeneous gas reservoir. The depths of the oil and gas reservoir that contain oil and gas are determined according to the permeability value in the logging. If the part of the reservoir has high permeability, then there is a high probability of good fluid (oil and gas) content, and these parts are referred to as reservoir sections in the permeability log of oil and gas reservoir. If the part of the reservoir has low permeability and poor oil and gas-bearing properties, then these parts are referred to as interlayers. Accordingly, the reservoir is divided into multiple reservoir sections and interlayers according to the distribution of permeability.

In an exemplary embodiment, the distribution of the permeability of the gas reservoir is obtained along the depth of 3995 m-4035 m via the logging tool. For example, according to the permeability-depth log obtained by logging in FIG. 4, itis clear that section 1 (4003 m-4006 m), section 2 (4009 m-4018 m) and section 3 (4027 m-4030 m) have high permeability, and therefore such sections can be determined as oil and gas reservoirs. However, strata between these sections (namely, 3995 m-4003 m, 4006 m-4009 m, 4018 m-4027 m, and 4030 m-4035 m) have low permeability, so they may be determined as interlayers. The gas reservoir is divided into three reservoir sections as shown in FIG. 5. Section 1 (4003 m-4006 m) is the first reservoir section. Section 2 (4003 m-4006 m) is the second reservoir section. Section 3 (4027 m-4030 m) is the third reservoir section. For the permeability of each reservoir section, a weighted average method is used to obtain average permeability, which is taken as the permeability of the reservoir sections. In the example of this application, the permeability of the first reservoir section is 9.1 mD, the permeability of the second reservoir section is 11.8 mD, and the permeability of the third reservoir section is 6 mD, all which are obtained by the weighted average method. The third reservoir section is taken for calculation of parameters as follows:

$T=350K;p_e=42\mathrm{MPa};\stackrel{\_}{p}=34\mathrm{MPa};p_{\mathrm{wf}}=26\mathrm{MPa};K=K_{0=}6\mathrm{mD};h=3m;r_e=800m,r_w=0.1m;{\gamma }_g=0.5573b=0.005{\mathrm{MPa}}^{-1}\mu =\stackrel{\_}{\mu }=0.027\mathrm{mPa}·s\lambda =0.004\mathrm{MPa}/m;Z=\stackrel{\_}{Z}=0.88.$

The calculation results are as follows:

$A=1.189*{10}^{-2}B=5.664*{10}^{-8}C=4.399*{10}^4{q}_3=1.851*{10}^9{m}^3/d$

The above-mentioned productivity obtained through calculation is the productivity of the third reservoir section. Similarly, the productivity of other reservoir sections (q₁ and q₂) can be obtained, and then Q_tol can be superimposed (Q_tol=q₁+q₂+q₃).

Finally get β=0.25 through Lorenz curve, then can obtained corrected comprehensive productivity Q_m=α*Q_tol=(1−β)*Q_tol.

Although the embodiments of the invention have been detailed with reference to the accompanying drawings, it should not be construed as a limitation on the protection scope of this patent. Within the scope as described in claims, various modifications and variations that may be made by persons of ordinary skill in the art without creative efforts fall within the protection scope of this patent.

Claims

1. A method for evaluating corrected comprehensive productivity of a heterogeneous gas reservoir along its depth considering interlayer crossflow, comprising the following steps: (1) dividing a heterogeneous gas reservoir into multiple reservoir sections along the depth of the heterogeneous gas reservoir;(2) obtaining the productivity of each reservoir section according to data obtained through wireline formation test and laboratory test,wherein the productivity of each of the reservoir sections is calculated based on a calculation formula (1):

2. The method according to claim 1, wherein Step (1) comprises dividing the reservoir into several different reservoir sections according to permeability obtained through logging data, wherein each of the reservoir sections is a relatively homogeneous reservoir section.

3. The method according to claim 1, wherein Step (1) comprises arranging a first wireline formation tester at a first depth and a second wireline formation tester at a second depth, changing the pumping speed of the first wireline formation tester, observing the pressure variation of the probe of the second wireline formation tester in another layer, then determining whether an adjacent layer pertains to a same reservoir section according to the pressure variation of the probe of the second wireline formation tester.

4. The method according to claim 3, wherein the determining whether an adjacent layer pertains to a same reservoir section according to the pressure variation of the probe of the second wireline formation tester comprises: if pressure measured by the second wireline formation tester is changed along with that measured by the first wireline formation tester, the two layers pertain to the same reservoir section; orif pressure measured by the second wireline formation tester is not changed along with disturbance, the two layers are two independent reservoir sections.

5. The method according to claim 1, wherein Step (2) comprises using static permeability Ks obtained through the wireline formation test and permeability Kg (1−Sw) obtained through core displacement test to establish a conversion function relation Kg (1−Sw)=f (Ks), and obtaining effective permeability Kg (1−Sw) based on the data obtained through the wireline formation test.

6. The method according to claim 1, wherein Step (2) comprises establishing a conversion relation of measured productivity Qi and effective permeability Kg (1−Sw) according to the measured productivity relation of the reservoir section.

7. The method according to claim 6, wherein the conversion function relation is Qi=a*Kbg (1−Sw)+c, wherein a, b, and c are fitting coefficients.

8. The method according to claim 7, wherein the conversion function relation is validated and corrected using DST ((Drill stem testing).