Numerical simulation and X-ray imaging validation of wormhole propagation during acid core-flood experiments in a carbonate gas reservoir
Graphical abstract
Introduction
Generally, all applied sciences are based on conducting experiments and interpreting their results. These experiments are to investigate the impact of various parameters affecting performance of the system. One of the most common methods is to employ an appropriate mathematical model to evaluate effect of individual system variables and their mutual effects. In this study, we used a model that was developed by Panga (2005) to simulate wormhole propagation in the acid-flood experiments in a carbonate gas reservoir.
Many experimental studies such as Fredd and Fogler, 1998, Bazin, 2001, Safari et al., 2014 investigated the wormholing process and acid efficiency curve. The majority of the studies focused on limestone formation, however, for instance, Fredd and Fogler (1998) showed a significant difference in pore volume to breakthrough curve for the dolomite core used. This kind of difference occurs especially at low temperatures, in which reaction rate in dolomite is much slower than in limestone. The pore scale heterogeneity, which exists because of the different structure of the microbial carbonate, is also reported important by Ziauddin and Bize (2007). Many other experimental studies investigated various parameters that can affect reaction between acid and rock matrix during any acid-based treatment (Mumallah, 1991, Mumallah, 1996, Mumallah, 1998, Sjoeberg and Rickard, 1984, Taylor et al., 2006, Taylor and Nasr-El-Din, 2009).
Since majority of studied core's mineral composition was consisted of calcite (73%) and dolomite (25%) plus very little amount of siderite (>1%), following reactions were the main mechanism of change while acid injection:
Besides the laboratory activities, many other studies were performed to develop models simulating the flow of the acid in porous media.
Steefel and Lasaga (1994) described a numerical model for computing coupled multi-component chemical reactions, multi-species chemical transport, hydrodynamic flow, and heat transfer. Their model employs a new algorithm which solves simultaneously for multi-component reactions and solute transport in one and two dimensions and which uses kinetic formulations for mineral dissolution and precipitation reactions, making the a priori assumption of equilibrium between water and minerals unnecessary.
Liu et al. (2013) used a model which couples a two-scale continuum model simulating wormholing in the invaded zone and a reservoirflow model for the compressed zone was used to study the wormhole propagation behavior under reservoir conditions. Their results showed that the normally distributed porosities simulate wormholing better.
Generally, these models can be categorized into four main groups: namely fractal, capillary tube, pore network, and continuum (average) models.
Relating important dimensionless group to experimental observation is a solution that is followed in fractal models (Fredd and Fogler, 1998, Fredd, 2000, Daccord and Lenormand, 1987, Frick et al., 1994, Pichler et al., 1992).
Capillary tube models are capable of evaluating effect of mass transfer, mutual relation of the wormholes, fluid loss, and reaction on wormhole growth. Interaction and competition between wormholes are key outputs of capillary tube models. Although these models are quite simple, they do not consider the effect of chemical reaction in pore scale as well as transport mechanism. This simplifications may affect the optimum conditions for acidizing (Hung et al., 1989, Huang et al., 1999, Huang et al., 2000, Buijse, 2000).
Pore network model represents porous media in form of many paths that are connected in nodes. Studies performed by Fredd and Fogler (1998) and Hoefner and Fogler (1989) are well-known examples of such modeling. Hagen–Poiseuille relationship describes acid flow in these paths for laminar regime. The acid reaction is considered in form of increase in diameters of these paths. However, scaling up of the result to the field conditions is an issue for these models. Applying such models require large computational power while including heterogeneities effect in pore scale is not usually straightforward.
Due to the deficiencies of first three categories of models, it is generally believed that continuum models are more precise in systematic study of acidizing process. There are three continuum models available: Liu et al., 1997, Golfier et al., 2002, and Panga (2005). While acid is entering the pores, if the reaction rate is very slow compared to the mass-transfer rate, the concentration gradients are negligible. In this case, the reaction is considered to be in the kinetically controlled regime, and a single concentration variable is sufficient to describe this situation. However, if the reaction is very fast compared to the mass transfer, steep gradients develop inside the pores. This regime of reaction is known as the mass-transfer controlled regime. The Liu et al. (1997)’s model does not take account for mass transfer in reaction and considers chemical reaction at local equilibrium. This model has some limitation to the kinetic regime. The developed model by Golfier et al. (2002) is also available in mass transfer controlled regime. Panga et al. (2005) developed a model that overcome drawbacks of two aforementioned models and was infrastructure for many other studies in this area pointed out here. For instance, Izgec et al. (2010) explored the effects of heterogeneity on vuggy carbonate acidizing with high resolution computerized tomography imaging, image processing, geostatistical characterization, acid core-flood experiments, and numerical simulations with a continuum approach modeling. De Oliveira et al. (2012) developed a methodology to numerically represent the acid treatment in a test plug, as well as to reproduce the different existing dissolution patterns and to obtain the corresponding values of pore volumes to breakthrough. They used experimental data published by Fredd and Fogler (1998) to justify their simulation results.
Ratnakar et al. (2013) used an empirical rheological model to describe the relationship between viscosity of in situ cross-linked acids and temperature, shear rate and pH. They presented a two-scale continuum model to describe reactive dissolution of carbonates with in situ cross-linked acids and to analyze wormhole formation in single and dual core set-ups.
Due to the limitations of the first two models, i.e. Liu et al. (1997) and Golfier et al. (2002) that already discussed, we applied Panga's model for our case. This continuum model, extended to a 3D domain, was solved using a finite element based software and tuned by matching the simulation results with output of X-ray imaging of an acid flooded core from a carbonate gas reservoir in Iran.
Section snippets
The experimental study summary and analysis
Fig. 1 illustrates a schematic of the setup used for performing the experiments. Formation water and acid were already put in the accumulators. After putting core sample in Viton sleeves, it was inserted in core-holder. Backpressure, which was supplied by Nitrogen, kept the produced CO2 during reaction in solution. While injecting, injection rate, temperature, overburden pressure, and back-pressure were kept constant and pressure drop along the core was recorded with digital and analog
Numerical approach
The Panga's model simulates the linear acid flow in two dimensions. This two-scale continuum model (TSCM) is extended to radial flow in three dimensions in this study while including both the Darcy and pore scale physics in the model. Fig. 2 illustrates schematics of the different length scales and geometry used in this study. The mathematical model describes the phenomenon of reactive dissolution as a coupling between processes occurring at the Darcy scale and the pore scale. This model is
Simulation outputs
In following sections, some parameters are discussed that could provide great understanding of acid wormholing in the core.
Validations
In this section, using available data and tools we tried to evaluate that whether the simulation is close to the experiment or not.
Summary and conclusion
Pang's model, a continuum model, was used to model acid flow through core samples. Panga's 2D model then was extended to simulate 3D radial behavior of acid wormhole propagation of samples from a carbonated gas reservoir. Different boundary conditions, initial conditions, and core and fluid properties, adopted from the core-flow experiment, were applied to simulate the acid flow behavior using a finite element based software. The flooded core samples were irradiated to x-ray to validate the
Acknowledgment
This work was part of a M.Sc. thesis entitled “Study, Evaluation, and modeling of wormhole propagation during matrix acidizing carbonate reservoirs”. We would like to thank Amirkabir University of Technology and Research Institute of Petroleum Industry (RIPI) for their support and permission to publish the study.
Nomenclature
- a0
- Initial interfacial area per unit volume [1/m]
- av
- Interfacial area per unit volume [1/m]
- Cini
- Initial acid concentration [mole/mˆ3]
- Cf
- Acid concentration [mole/mˆ3]
- Cs
- Acid concentration in liquid–solid interface [mole/mˆ3]
- dh
- Pore hydraulic diameter[m]
- Dm
- Molecular diffusivity of acid [mˆ2/s]
- De
- Dispersivity tensor [mˆ2/s]
- DX
- Longitudinal dispersivity [mˆ2/s]
- DT
- Transversal dispersivity [mˆ2/s]
- kc
- Mass transfer coefficient [m/s]
- ks
- Surface reaction constant [m/s]
- K
- Permeability tensor [mˆ2]
- K0
- Initial permeability of
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