A mathematical model that describes the growth and competition of wormholes during an acidizing treatment in a carbonate formation was developed. The model is initialized with the distribution of largest pores. Wormhole characteristics (size, length, and distribution) were found to be controlled by acid-injection, diffusion, and fluid-loss rates. IntroductionAcidizing in a reservoir formation is a stimulation technique that has been widely used by the oil industry. Acidizing treatments fall into two categories: matrix acidizing and fracture acidizing. Fracture acidizing consists of injecting acid solution into a carbonate formation at a high enough pressure to break down the formation hydraulically. As the acid flows along the crack, it reacts with the rock and etches the face of the crack. These acid-etched patterns remain to provide flow channels when hydraulic pressure is released and the well is placed back on production. In matrix acidizing, acid is injected at a slow enough rate that the fracture pressure is not exceeded. Matrix treatments are generally aimed at the removal of near-wellbore damage; in an optimal treatment, the acid is expended primarily in the damaged region. A relatively strong solution of Hel (typically 15 wt%) is the most common acid system used in treating carbonates.When acid is injected into a carbonate, the acid flows preferentially into the highest-permeability regions-the largest pores, vugs, or natural fractures. The rapid dissolution of the matrix material enlarges these initial flow paths so that the acid has soon formed large, highly conductive flow channels, called wormholes. [1][2][3][4][5] Wormholes are likely to occur in both matrix acidizing and fracture acidizing in carbonate formations. In fracture acidizing, wormholes are usually deleterious and must be minimized for live acid to penetrate deeply along the fracture opening. In a matrixacidizing treatment, these wormholes mayor may not be desired; if a deep damaged zone exists around the wellbore, wormholes enhance stimulation by increasing the acid penetration depth. If, on the other hand, the damaged zone is shallow. wormhole formation leads to an inefficient treatment because most of the acid will be expended beyond the damaged region. To estimate the fluid leakoff rate in an acid fracture or the effect of matrix acidizing in carbonates, a prediction of the distribution, size, and length of wormholes that will be created is needed. Nierode and Williams 5 developed a model to predict the length of a wormhole, but the number of wormholes and their sizes were not addressed. More recently, Hoefner and Fogler 6 used a network model to simulate the growth of wormholes in matrix acidizing. This model illustrates the relationship between reaction rate and diffusion rate in the formation of wormholes but does not account for fluid loss through the walls of the wormholes, which can be the controlling factor limiting their length.To describe the physical process of this wormholing phenomenon, a mathematical model that accounts f...

The results of matrix stimulation in carbonate formation strongly depend on the acid injection condition. Large amounts of lab tests indicate that an optimum acid interstitial velocity, v i-opt , exists, which results in the minimum volume of acid required for wormhole propagation (optimal breakthrough pore volume) and the most efficient stimulation. During the last decade, much progress has been made to identify the factors that affect the optimum conditions of linear coreflood experiments, including temperature, acid type, acid concentration and lithology. However, there lacks a discussion on the effect of core dimensions on the optimal conditions. Experimental results published before show strong evidence that the optimal condition changes as the dimension of core samples changes. Since the optimal condition from experimental studies is the critical information used in treatment design, it is necessary to investigate the relationship between the optimal condition and the core geometry.In this work, a series of coreflood experiments were conducted with Indiana limestone cores at room temperature. The cores selected are relatively homogeneous to eliminate the effect of heterogeneity. The acid used is 15% plain hydrochloric acid. The core lengths range from 1-in. to 10-in. and the core diameters are 1-in., 1.5-in. and 4-in. From the experimental results, the effects of core length and core diameter are examined. The results showed that the v i-opt becomes independent of the core length when the core length reaches a value of 6 inches. These observations can help with the recommendations of the proper core length and core diameter to be used in future laboratory experiments.The core-size dependence is important while scaling up the laboratory results to field applications. The results of this work can give a better understanding of how upscaling works. Also, with these results, the existing wormhole growth models can take into account the core-size dependence, resulting in more accurate upscaling of experimental results.

Interpretation of production logging in multi-phase flow wells is challenging, especially for highly deviated wells or horizontal wells. Flow regime-dependent flow conditions strongly affect the measurements of production logging tools. Segregation and possible back flow of denser phases result in misinterpretation of the inflow distribution. To assess the downhole flow conditions more accurately, logging tools have been developed to overcome the flow regime related issues. Multiple-sensor array tools measure the fluid properties at multiple locations around the cross-sectional area of the wellbore, providing a distributed measurement array that helps to relate the measurements to flow regime and translate the measurement to inflow distribution. This paper present a methodology for using array data from production logging tools to interpret downhole flow conditions. The study uses an example logging tool that consists of 12 resistivity, 12 capacitance probes, and six spinners around the wellbore circumference. The method allows interpretation of phase volumetric flow rates in sub-divided crosssectional areas based on sensor locations. The sub-divided area method divides the wellbore cross-sectional area into several layers depending on the number and arrangement of the sensors with each layer containing at least one sensor. Holdup and velocity outputs from sensors in each wellbore area segment are combined to calculate the volumetric flow rates of each phase in each segment. These results yield a profile of flow of each phase from the high side to the low side of the wellbore, and the overall flow rates of each phase at every location along the well where the interpretation method is applied.The method developed was used to interpret the flow profile of an Eagle Ford well producing gas and water at downhole conditions. A reasonable profile of gas inflow was obtained and the profile was similar to that interpreted with a commercial production log interpretation software package. The interpretation of the water flow profile was complicated by low total water production rate and variations in wellbore inclination.

Guar gum and its derivatives have been the most commonly used polymers to increase the viscosity of fracturing fluids. However, the conductivity of many fractures created with guar-based polymers is low because of residual unbroken polymer gel remaining in the fracture. This residue can cause permeability impairment in the proppant pack resulting in low fracture conductivity and decreased effective fracture length. In this study, we experimentally evaluated two important aspects of the gel damage process - the thickness of the polymer gel filter cake that is created as fracture fluid filtrate leaks off into the formation, and the yield stress of the concentrated polymer gel that accumulates in the fracture. The thickness of the filter cake created during the leakoff process was measured as a function of the polymer loading and the volume of leakoff. We created the filter cake following the procedure described by Ayoub et al. (2006), then measured the filter cake thickness with a precise laserprofilometer. We found that the filter cake thickness varied linearly with leakoff volume, meaning that the gel concentration factor is constant for this guar polymer fluid. The concentrated polymer filter cakes created by leakoff behave rheologically as Herschel-Bulkley fluids having a yield stress. The yield stress of this material is a critical parameter influencing whether or not the gel can be removed from the fracture. We measured the yield stress of borate-crosslinked guar polymer fracture fluids at concentrations up to 200 lb/mgals using a unique flat plate device. The yield stresses of th polymer filter cakes were found to depend strongly on the concentration of both polymer and breaker.