Geofluids

Volume 2019, Article ID 6328909, 14 pages

https://doi.org/10.1155/2019/6328909

## A Research on the Effect of Heterogeneities on Sandstone Matrix Acidizing Performance

State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum-Beijing, Karamay Campus, Beijing, China

Correspondence should be addressed to Jianye Mou; nc.ude.puc@eynaijuom

Received 19 December 2018; Revised 31 March 2019; Accepted 15 May 2019; Published 24 July 2019

Guest Editor: Fengshou Zhang

Copyright © 2019 Jianye Mou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Matrix acidizing is one of the common methods to enhance production in sandstone reservoirs. Conventional acidizing designs generally neglected the effect of heterogeneities of mineral and flow field distributions both in areal and vertical directions and assumed that the acid front propagates with a piston-like style. However, sandstone formations inevitably have small-scale heterogeneities of minerals and flow properties that may give rise to acid propagation in a manner much different from what is predicted based on homogeneous assumptions. In this paper, we conduct a research to numerically investigate how the heterogeneities affect acidizing performance under in situ conditions. Firstly, a heterogeneity model is built for mineral and porosity distributions by using the semivariogram model of geological statistics, based on which we generate spatially correlated porosity and mineral distributions. Next, a model of radial acid flooding is developed based on mass balance and the chemical reactions between the acids and minerals occurring during the acidizing process. The model is numerically solved to investigate the permeability response, acid distributions, precipitate distributions, and the effect of the heterogeneities on acidizing. The results show that the heterogeneities both in areal and vertical directions have a significant effect on acidizing. The flow field heterogeneities have a more serious impact than the mineral heterogeneities. In a plane, strong porosity heterogeneity can give rise to acid fingering and even channeling, which make the acid penetration distance longer than the homogeneous cases. The secondary precipitate has a significant effect when fast-reacting mineral content is high. Vertically, several-fold permeability contrast creates the acid break through the high-perm zone leaving the low-perm zone understimulated. Both flow field and mineral heterogeneities make it possible to create high-permeability channels during the acidizing process and to obtain a longer acid penetration distance.

#### 1. Introduction

Drilling, completion, or some other well operations inevitably damage formations, which may seriously decrease the well productivity in sandstone reservoirs. Matrix acidizing is a common method to remove the formation damage and recover well productivity. In acidizing, the acid flows into the porous media, reacts with the minerals, and increase formation porosity as well as permeability. Many researchers conducted studies on acid flooding in experiments. One of the unignorable risks in acidizing in sandstone is the secondary precipitate. Crowe [1], Almond et al. [2], and Underdown et al. [3] investigated the conditions that produce precipitate. They found that silica gel is produced at a slow rate due to the slow reaction at room temperature. When the temperature is higher than 55°C, the fast reaction will generate a lot of precipitate and damage the formation seriously.

Due to the small size of the core sample and the complexity of parallel core flooding, field-scale simulation and design necessitates numerical modeling. Sandstone acidizing models include the capillary model, the microscopic model, the kinetic model, the lumped parameter model, the distributed parameter model, the one-acid two-mineral model, the two-acid three-mineral model, and the generalized geochemistry model [4–10], most of which made the assumption of homogenous formation. The two-acid three-mineral model developed by Bryant [4] takes into account the effect of precipitates and H_{2}SiF_{6} and can simulate well the physical phenomenon of acidizing. At present, the most sophisticated model [9] is the generalized geochemistry model. The model accounts for the reaction of multiple kinds of minerals and the acid and can analyze the effect of mineral content, reactant, product, and reaction kinetics. They found that dissolution and precipitation do not occur simultaneously. Li et al. [11] built a linear acid flooding model to simulate linear core flooding at an experimental scale with the consideration of the heterogeneities of minerals and flow fields. Li et al. [12] built a radial acidizing model and considered the effect of the temperature field on the reaction, but they did not consider the effect of the heterogeneities. Leong et al. [13, 14] did a modeling of the acidizing of HBF_{4} in linear cores with COMSOL.

In this paper, we modeled radial acid flooding based on a two-acid, three-mineral model and considered the heterogeneities of minerals and flow fields in both planar direction and vertical directions. Based on the model, we did extensive numerical simulations to analyze the effect of heterogeneities on acidizing performance. Also considered are multilayer flooding and secondary precipitates.

#### 2. Mathematical Model

In the two-acid three-mineral model, the two acids mean HF and , and the three minerals mean fast-reacting mineral (mineral 1), slow-reacting mineral (mineral 2), and silica gel (mineral 3). The chemical reactions are as follows:

##### 2.1. Governing Equations

Based on material balance, Darcy’s law, and acid-rock reaction kinetics, we establish our governing equations as equations 2–7 with the following assumptions: (1) single-phase flow, (2) Darcy flow, (3) incompressible fluid and rock, and (4) neglecting gravity effect. A 2D model is developed as shown in Figure 1 with the wellbore at the center of the domain. (1)Cylindrical coordinate system is used for the radial flooding(2)Flow equations (3)Hydrofluoric acid concentration distribution equation (4)Fluosilicic acid concentration distribution equation (5)Mineral content equation (6)Porosity variation equation where is the porosity; is the hydrofluoric acid concentration; is fluosilicic acid concentration; is the velocity vector ( is the velocity in the radial direction, and is the velocity in the circumferential direction); is the mineral volume fraction; is the fast-reacting mineral, slow-reacting mineral, and silica gel; is the mole weight of acid, is the specific surface area of minerals, is the hydrofluoric acid or fluosilicic acid; is the reaction rate constant; is the reaction order; is the density of minerals; and is the gravimetric dissolving power.