# Coupled numerical simulation of multi-layer reservoir developed by lean-stratified water injection

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## Abstract

Lean-stratified water injection is one of the most important technologies to increase production and develop potentials for the oilfield with extreme high water content. However, traditional models cannot entirely solve the inner boundary conditions of lean-stratified water injection. Therefore, we established the injection wellbore constraint equations, which were coupled with the oil/water two-phase numerical reservoir models, and then the seven diagonal form sparse coefficient matrix was solved by block precondition of generalized minimal residual algorithm. Considering the specific situation of lean-stratified water injection wells, reservoir geology and production schemes of the middle part of the sixth Oilfield in Xing Shugang, three mechanism models of multi-layer heterogeneous reservoir were constructed to simulate the lean-stratified water injection. The influences of different segments numbers, modes of combination in segment layer and rhythm characteristics of remaining oil reserves and distribution are evaluated.

## Keywords

Lean-stratified water injection Well model Numerical reservoir simulation Remaining oil evaluation Interactive low-permeability reservoir## Introduction

Lean-stratified water injection (LSWI) is a kind of layer targeted water injection to enhance waterflooding recovery of multi-layer reservoirs, which divides wellbore into five or more segments, and every segment injects water for less than six layers. This technology can improve waterflood vertical sweep efficiency, and has been widely used in many multi-layer sandstone reservoirs with high water content (He et al. 2013), such as Chinese Daqing Oilfield with higher than 40 % waterflood recovery. Furthermore, it is required to match the development dynamic history for every oil layer in the process of reservoir numerical simulation during secondary development, for the sake of increasing the prediction precision for remaining oil in each sand body, especially in main sand body (Dakuang 2010).

The water injection rate enters each oil layer cannot follow the mobility allocated principle set in conventional simulation model. This defect leads to inaccuracy for matching the remaining oil distribution and injected water rate in reservoir numerical simulation. Reservoir numerical simulation methods considering LSWI contain injected water deduplication by many injection wells and coupled simulation for water chokes, injection well and reservoir. The former is suitable for reservoir possessed enough injectivity test data, and the water injection rate can be calculated by real-time monitoring test data, and these values can be used as inner boundary condition in model (Dumkwu et al. 2012; Villanueva-Triana et al. 2013; Stone et al. 1989; Ding 2011), practically, injectivity test data are very few, so the complete injection process cannot be represented by them (Gao et al. 2015). The latter needs enough data of injection well devices, such as diameters of water chokes, which should be used to calculate the pressure loss coupled with well bottom pressure (BHP) and reservoir pressure (Zhao et al. 2012; Lin et al. 2011), and this results in quit complex calculation. In this paper, we propose a simple method of modeling LSWI considering inner wellbore constraint condition, and this method can be used to simulate the development effect and remaining oil distribution in reservoir with extreme high water content, so a reliable evidence will be provided for reservoir history matching and project design.

## Well model considering LSWI

- 1.
Injection well is divided into

*N*segments vertically, and every segment contains*M*oil layers. - 2.
The total injected water rate is known, and maintains constant.

- 3.
Every segment is separated by packers in tubing-casing annulus, so there is no fluid flowing through between them.

- 4.
Only oil and water phases are considered in the model, and the capillary is neglected.

## Coupled numerical model

Assuming that the pressure gradient in tubing-casing annulus is constant at different time steps, and then the injected pressure after water chokes and connected reservoir grid flow rate and pressure are given by:

Oil–water two phase flow models are discretized, and pressure and saturation are solved implicitly, residual equations of the reservoir grid with producer or injector contain source and sink terms.

The coefficient of the grid with LSWI becomes more complex as indicated in Eqs. 10 and 11, so every submatrix can be regarded as an integral term when the overall numerical model is solved by block pretreatment of generalized minimal residual algorithm (Baohua et al. 2013).

## Model validation

Figure 1a is the comparative results in 2002, when the LSWI well is divided into four segments by three packers, and Fig. 1b is the comparative results in 2010, when the well is divided into six segments by five packers. It is obviously that conventional heavy oil model cannot simulate the effect of LSWI, but the LSWI model acquires a more accurate injected water ratio close to the injectivity test data in these 2 years.

## Case study

### Geological mechanism model

Considering the specific situation of LSWI wells, reservoir geology and production schemes of the middle part of the sixth Oilfield in Xing Shugang, three mechanism models of multi-layer heterogeneous reservoir were constructed to simulate the LSWI. Each of the models has dimensions of 820 ft × 820 ft × 88 ft, and is discretized equally by 50 × 50 grids horizontally and 54 grids vertically, so it has 135,000 regular grids totally. Generally, there are two kinds of oil layers in the model, and they are high-permeability (100–1000 mD) and interactive low-permeability (5–10 mD) oil layers, which have 22 oil layers totally. One of them is thick high-permeability oil layer (32.8 ft), and 21 of them are interactive low-permeability oil layers, which contain low-permeability oil layers connected with high permeability parts.

### Recovery and vertical sweep efficiency

Six LSWI projects are designed for the three geological mechanism models, and they are totally developed for 20 years with the same injection water rate. In the initial 5 years of production, five-spot waterflood well pattern is used for the development, and the injector with 30 m^{3}/day injection water rate is located at the center of the model. Afterwards, the injector is divided into four segments for waterflooding. 5 years later, it is subdivided into 5–10 segments with LSWI by subdivision and restructuring of original segments, and four producers are added into this waterflood well pattern to enhance the. The injection water rate (100 m^{3}/day) and bottom wellbore pressure of producer keep constant during the 10 years development years with LSWI.

The ultimate recovery of model with different rhythms increases at first, and then become smooth, however, the vertical sweep efficiency increases gradually. When segments number of LSWI increases under subdivision of original segments, ultimate recovery and vertical sweep efficiency both increases with strong fluctuation. However, ultimate recovery increases with smaller fluctuation under segmentation and restructuring, and the vertical sweep efficiency increases gradually. It illustrates that more segments and more complete restructuring of segments may not be effected, so the modes of segmentation and segment numbers need to be optimized.

The variation tendency of recovery and vertical sweep efficiency are the same, and high ultimate recovery will be obtained with high vertical sweep efficiency of interactive low-permeability oil layers, so the key of enhancing production lies in increasing vertical sweep efficiency.

Rhythm characteristics of high-permeability oil layers have little influence for ultimate recovery of interactive low-permeability oil layers, but segmentation modes have more obvious influence. However, vertical sweep efficiency are almost equal for models with reverse rhythm and composite rhythm, and both higher than positive rhythm model.

### Distribution regularity of remaining oil

## Conclusions

Injection pressure adjusted by water chokes, well grid pressure and fluid saturation are made as three unknown parameters, and the source terms of injector wellbore are solved implicitly, and then well model of LSWI is established, which coupled with oil–water two phases model to form the final numerical models. It can also be represented as close linear system with seven diagonal sparse coefficient matrix, and solved by block pretreatment of generalized minimal residual algorithm. According to the theory of LSWI, the numerical model proposed, reservoir stratum distribution and injector segments characterized in the Chinese Daqing Oilfield, three multi-layer reservoir mechanism models are established with positive rhythm, negative rhythm and composite rhythm, respectively in high-permeability oil layers.

Low-permeability oil layers are primary potential for multi-layer reservoirs with extreme high water content, and LSWI will help them to get higher recovery. More segments is not the goal of LSWI, the structure of wellbore segments need to correspond with distribution of remaining oil, and vertical heterogeneity should be weakened. The key of enhancing recovery is to increase vertical sweep efficiency, the remaining oil caused by vertical heterogeneity and poor physical properties can be waterflooded by adjusting structure of segmentation. However, some other stimulating measures are necessary to be used for developing the remaining oil caused by bad connectivity between injectors and producers.

## Notes

### Acknowledgments

This study has been carried out under the framework of the national mega project of science research (2011ZX05010-002) financed by Chinese government, and has been partially supported by Petro-china.

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