A.D. Hill

A Mechanistic Model of Wormhole Growth in Carbonate Matrix Acidizing and Acid Fracturing

A mathematical model that describes the growth and competition of wormholes during ann 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 too be controlled by acid-injection, diffusion, and fluid-loss rates.

The Effect of Wormholing on the Fluid Loss Coefficient in Acid Fracturing

In most acid fracture designs, a leakoff model developed for proppant fracturing is used to calculate the acid volume lost into the formation. Because wormholing in acid fracturing results in a few large channels near the fracture, the leakoff velocity of the fracturing fluid can be higher in acid fracturing than in proppant fracturing. This paper presents a new leakoff model that includes the effect of wormholing on the overall fluid-loss coefficient. The leakoff model is based on a volumetric model describing wormhole growth in acid fracturing. Conveniently, the leakoff velocity based on the volumetric model for wormholing is still inversely proportional to the square root of treatment time. Laboratory coreflood results are presented that support the use of the volumetric model for the linear flow region near the fracture walls.

Laboratory and Theoretical Modeling of Diverting Agent Behavior

Diverting agents composed of finely ground, oil-soluble resin particles were tested in the laboratory and modeled with a numerical simulator to determine their effectiveness in matrix stimulation treatments. First, the diverting agents were characterized with linear coreflood tests, and then experiments were performed in a physical wellbore model scaled to a typical well completion. A numerical simulator was developed to predict the effect of diverting agent on injected fluid distribution. This paper describes the laboratory and mathematical models of diverting agent behavior and the results obtained with these models. Among the conclusions drawn from this study are: the finely ground, oil-soluble-resin diverting agents are effective for matrix diversion; diverting agent added continuously to treating fluid equalizes the flow to all zones; and diverting agent injected in small stages ahead of treating fluids can cause a highly skewed distribution of injected fluid.

Real-Time Monitoring of Matrix Acidizing Including the Effects of Diverting Agents

Real-time monitoring of the injection rate and pressure during matrix acidizing provides operators with a way to determine the changing skin factor as stimulation proceeds. Current methods are based either on the assumption of steady-state flow in the region around the wellbore affected by acid injection or on computer solution of the transient flow equations describing the unsteady reservoir flow process occurring during acidizing. In this paper, a new method for real-time monitoring of matrix acidizing, the inverse injectivity vs. superposition time function plot, is presented. This new method can be applied with a spreadsheet computer program or a programmable calculator and accounts for the transient flow effects occurring during matrix acidizing at multiple rates and injection pressures. The evolving skin factor during a matrix treatment is readily obtained from the diagnostic plot. Hypothetical examples show how the inverse injectivity plot can be used to assess the efficiency of stimulation and diversion. Comparisons with previously presented field cases show the new method to be a simple and accurate means of monitoring the evolving skin factor during matrix acidizing.

Re-Formation of Xanthan/Chromium Gels After Shear Degradation

Studies were conducted on the re-formability of xanthan-gum/chromium gels that have been degraded by shear. The regelation study of xanthan/chromium gels showed that gels that have been sheared take longer to re-form than to gel initially and that the original gel strength ofter was not recovered after shearing. The weaker the gel at the time of shearing, the more likely it is that it will obtain the ultimate strength of an unsheared gel on the same formulation

Improved Analysis Methods for Radioactive Tracer Injection Logging

Radioactive tracer logging has been used for many years to measure injection profiles. In this study, we analyzed the tracer loss and velocity shot methods of radioactive tracer logging to develop guidelines for improved interpretation of these logs. In addition, tracer logging was simulated experimentally in a test pipeline to check assumptions made in the theoretical analysis. Among the conclusions drawn were that the tracer loss method is imprecise because of poor depth resolution and nonuniform mixing of tracer and that the velocity shot method is subject to significant error when fluid is exiting between detector locations. Finally, a new radioactive tracer logging method is proposed that may offer some advantages over current practices.

An improved method for calculating bottomhole pressures in flowing gas wells with liquid present

A method is presented for calculating bottomhole pressures (BHPs) from wellhead measurements in flowing gas wells with liquid present in the well stream. This method, a modification of existing methods, is based on including the contribution of entrained liquid to gravitational gradients. The study also includes evaluation of effective roughness factors evident from actual flowing pressure data. The proposed method was tested vs. both a two-phase flow model developed by Govier and Fogarasi and currently applied methods based on dry-gas wells. The method was also tested with Govier and Fogarasis data from 94 flowing wells and with data from 50 wells from the public files of the Texas Railroad Commission. The new method compared favorably with the two-phase flow model and was superior to currently applied methods.

Selective matrix acidizing of horizontal wells

The PI of a horizontal well in an anisotropic medium is calculated during a process of partial acidization, in which damage removal occurs over only a fraction of the well length. Two numerical simulators are used in this work: an acidizing simulator, which calculates the permeability distribution around the wellbore; and a reservoir simulator, which calculates the PI of the well. By applying mathematical transformations, it is possible to reduce the acidizing model from a 2D to a 1D problem. By comparing treatment results, it is possible to select the optimal volume of acid, injection rate, and fraction of the length to be acidized for each well. The same procedure also may be applied for vertical wells both with and without anisotropy. Simulation results indicate that the application of a partial acidizing strategy reduces the total amount of acid required for significant improvement in well productivity, substantially reducing the financial, operational, and environmental risks involved in the treatment of a horizontal well. In most cases, the optimal injection rate for sandstone acidizing is the maximum rate that does not fracture the formation.

The Effect of Fluid Diversion on the Acid Stimulation of a Perforation

A previously developed model that considers the effect of acidizing on the productivity of a single perforation penetrating a sandstone reservoir was extended to account for the effect of particulate diverting agents on acid distribution inside the perforation. Cases were run that simulate various types of formation damage, including damage from drilling-mud infiltration and damage caused by perforating itself. The model predicts the evolution of the perforation skin factor as acid dissolves formation minerals in the surrounding region. The primary result of this work is that, for the types of damage simulated, fluid diversion within a perforation has little effect on stimulation performance. Although the diverting agent significantly changes the acid distribution at the perforation surface, the acid tends to migrate rapidly to undamaged regions in the formation. This paper presents results from a series of case studies that emphasized the effect of fluid diversion inside a perforation.

Tracer-Placement Techniques for Improved Radioactive-Tracer Logging

The accuracy of a radioactive-tracer log depends on the tracer rapidly mixing with the wellbore fluid and traveling with the same velocity as the wellbore fluid. In addition, log quality depends on the ability to measure the tracer transit time from the gamma ray detector responses accurately; the tracer must maintain a sharp peak, or sharp leading edge, for reliable transit-time measurement. The authors conducted experiments in a model wellbore to determine the factors affecting tracer slug distribution and the responses at tracer detectors resulting from these factors. Tracer-placement parameters studied included tracer shot velocity, shot duration, wellbore flow rate, and tracer viscosity. When wellbore flow was laminar, the tracer dispersion could be predicted with a theoretical model and the experimental results compared well with the theory. As would be expected, optimal results were obtained when the bulk of the tracer was placed in the high-velocity, central region of the wellbore. In turbulent flow, a fairly low ejection rate and large shot size most consistently yielded sharp slugs that were maintained at both detectors.