﻿ 基于特高含水期相渗规律的含水率预测新模型 A New Model of Water Cut Prediction Based on Relative Permeability Law in Extra-High Water Cut Stage

Journal of Oil and Gas Technology
Vol. 43  No. 03 ( 2021 ), Article ID: 44673 , 9 pages
10.12677/JOGT.2021.433025

A New Model of Water Cut Prediction Based on Relative Permeability Law in Extra-High Water Cut Stage

Jiang Qu, Lianjing Xia

No.4 Oil Production Plant of Daqing Oilfield Co. Ltd., Daqing Heilongjiang

Received: Jun. 22nd, 2021; accepted: Aug. 9th, 2021; published: Aug. 20th, 2021

ABSTRACT

At present, the commonly used water cut prediction methods mainly include Gompertz model, Logistic model and Usher model. These three methods lack theoretical basis and only reflect the statistical law of water cut and time. Although the commonly used water drive law curve can reflect the seepage theory, the oil-water relative permeability ratio and water saturation deviate from the linear relationship on the semi logarithmic curve after entering the extra-high water cut stage, so it cannot be used for the water cut prediction in the extra-high water cut stage. Therefore, this paper deeply studies the change law of relative permeability curve in extra-high water cut stage, and establishes a new water cut prediction model reflecting the relationship between water cut and recovery degree, which can truly reflect the characteristics of oil-water underground seepage in extra-high water cut stage, and the prediction is more accurate. The results show that compared with the other three methods, the prediction accuracy of new water cut prediction model is improved by more than 3 percent, which provides a theoretical basis for the development planning of water drive reservoir in extra-high water cut period.

Keywords:Extra-High Water Cut Stage, Relative Permeability Curve, Water Cut Prediction, Model Establishment, Water Drive Law Curve

1. 引言

2. 目前含水率预测模型

2.1. Gompertz模型

${f}_{w}={\text{e}}^{k\cdot {\text{e}}^{-bt}}$ (1)

$\mathrm{ln}{f}_{w}=k\cdot {\text{e}}^{-bt}$ (2)

2.2. Logistic模型

Logistic模型 [11] 又称Logistic回归分析，该模型在流行病学中应用较多，能够根据危险因素预测某疾病发生的概率。美国地质学家哈伯特King Hubbert于1962年提出将Logistic模型应用于油田开发指标预测中，其一般形式为

${f}_{w}=\frac{1}{1+k\cdot {\text{e}}^{-bt}}$ (3)

$\frac{1}{{f}_{w}}-1=k\cdot {\text{e}}^{-bt}$ (4)

2.3. Usher模型

${f}_{w}=\frac{1}{{\left(1+k\cdot {\text{e}}^{-bt}\right)}^{1/c}}$ (5)

${f}_{w}^{-c}-1=k\cdot {\text{e}}^{-bt}$ (6)

3. 特高含水期相渗规律

(a) (b) (c)

Figure 1. Law of oil-water relative permeability curve. (a) Relative permeability curve; (b) Relative permeability curve law in steady seepage stage; (c) Relative permeability curve law in extra-high water cut stage

$\frac{{k}_{rw}}{{k}_{ro}}=\frac{b{S}_{wd}}{{\left(1-{S}_{wd}\right)}^{n}}$ (7)

${S}_{wd}=\frac{{S}_{w}-{S}_{wc}}{1-{S}_{wc}-{S}_{or}}$ (8)

4. 特高含水期含水率预测新模型

${S}_{wd}=\frac{1-{S}_{wc}}{1-{S}_{wc}-{S}_{or}}\cdot \frac{{S}_{w}-{S}_{wc}}{1-{S}_{wc}}=\frac{R}{{E}_{d}}$ (9)

${f}_{w}=\frac{{Q}_{w}}{{Q}_{w}+{Q}_{o}}=\frac{1}{1+\frac{{\mu }_{w}}{{\mu }_{o}}\cdot \frac{{k}_{ro}}{{k}_{rw}}}$ (10)

${f}_{w}=\frac{1}{1+\frac{{\mu }_{w}}{b{\mu }_{o}}\cdot \frac{{\left(1-{S}_{wd}\right)}^{n}}{{S}_{wd}}}=\frac{1}{1+\frac{{\mu }_{w}}{b{\mu }_{o}}\cdot \frac{{\left(1-R/{E}_{d}\right)}^{n}}{R/{E}_{d}}}=\frac{1}{1+\frac{{\mu }_{w}}{b{\mu }_{o}{E}_{d}^{n-1}}\cdot \frac{{\left({E}_{d}-R\right)}^{n}}{R}}$ (11)

$\left(\frac{1}{{f}_{w}}-1\right)R=m{\left({E}_{d}-R\right)}^{n}$ (12)

$m=\frac{{\mu }_{w}}{b{\mu }_{o}{E}_{d}^{n-1}}$ (13)

${f}_{w}=\frac{1}{1+m\cdot {\left({E}_{d}-R\right)}^{n}/R}$ (14)

5. 实例应用

(a) (b) (c) (d)

Figure 2. Water cut prediction results of each method. (a) Goempertz model; (b) Logistic model; (c) Usher model; (d) A new prediction model of water cut

Table 1. Water cut prediction results of each method

6. 结论

1) 目前常用的含水率预测方法仅反映了含水率与时间的统计规律，缺乏油水渗流理论，而水驱规律曲线虽有理论职称，但特高含水期后油水相对渗透率比值与含水饱和度在半对数曲线上偏离直线关系，不能用于特高含水期含水率预测。

2) 基于特高含水期相渗渗流特征，建立了反映含水率和采出程度变化规律的含水率预测新模型，模型参数求取简单、可靠性高，研究表明与Logistic模型、Usher模型相比，含水率预测精度分别提高了3.85个百分点和3.13个百分点。

A New Model of Water Cut Prediction Based on Relative Permeability Law in Extra-High Water Cut Stage[J]. 石油天然气学报, 2021, 43(03): 16-24. https://doi.org/10.12677/JOGT.2021.433025

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