Static adsorption isotherm. (Figures courtesy of Halliburton)

The efficiency with which operators “store” scale-inhibiting chemicals (SIC) in producing sandstone formations determines to a great degree how often the formation must be treated to inhibit the formation of scales that limit production and damage tubulars and surface equipment.

An “adsorption isotherm” indicates to the job designer how SIC are stored in the formation matrix. The adsorption isotherm (AI) is a mathematical description (a plot) of the amount adsorbed on a surface as a function of concentration at a fixed temperature. The AI tells how the SIC is stored in the matrix. How well the SIC is stored is dependent on the composition of minerals in the matrix; some minerals store SIC better than others.

It is probably impossible to avoid SIC squeezes to inhibit scale production in formations that have the tendency to form scales; however, it is possible to reduce the frequency of the squeezes.

If an operator can reduce the need to squeeze SIC from once in six months to once in a year or more, a great economy could be realized. If the water flow through the matrix is very slow, the frequency of squeezing could be reduced to five-year intervals. If the water flow is swift, the squeeze might last only a few weeks if the mineralogy and SIC combination is not favorable.

Planning

The following procedures and scenarios help demonstrate the planning process that can lead to a successful plan of scale inhibition:
Step 1. The operator provides mineralogical detail to the service company (SC), or provides a formation core sample to the SC.
Step 2. SC analyzes mineral content to assess the amount of SIC that can be stored (or is stored) in the formation and the concentration profile of the SIC when it comes out of “storage.”
Step 3. SC enters necessary data into a simulator program that predicts how an SIC treatment will perform based on production rate and mineralogy.
Scenario 1. In a very clean sand, SIC storage will be very difficult to achieve.
Scenario 2. If the sand is clean and contains 5% siderite, storage of SIC can be an easy task because siderite is a great surface for SIC storage.
Scenario 3. If the sand has 5% siderite and 30% clay, the siderite provides a good storage surface, but the clays make it difficult to optimize the treatment. The design will have to accommodate the clays.

The above procedures help enable determination of the treatment volume and concentration needed before the operator has finished developing the remainder of the field. As soon as the SC knows the mineralogy and the reservoir engineer provides the expected water production, the SC can return feedback on a job design to deal with the scale problem.

Many operators apply the same scale-prevention measures to all wells. In this process, wells can lose production, treatment frequency can be excessive, and chemical concentrations can be wrong. If the treatment does not consider the rate of water flow, the nature of the storage sites (minerals), and the properties of the SIC, valuable resources can be wasted. The AI, discussed below is a key element of treatment planning.

Adsorption isotherm

The adsorption isotherm correlates the amount of inhibitor adsorbed on the mineral surface to the solution concentration. Because it is determined under equilibrium conditions, it is valid during both adsorption (placement) and desorption (production).

Each mineral has a distinct adsorption behavior with a characteristic shape, strength of adsorption, and capacity, all properties that influence the return profile of the inhibitor. Although the adsorption isotherm for each mineral is unique, for practical application they can be grouped into three main classes: iron carbonates (chiefly siderite), silica-type minerals, and alumina-type minerals. Siderite has the strongest adsorption capability of all the classes. Alumina-type minerals have the weakest binding and consequently release the inhibitor at high concentrations. In general, alumina-type minerals will release the bulk of the inhibitor at concentrations far above the required minimum inhibitor concentration (MIC), resulting in a short squeeze lifetime and waste of inhibitor.

Silica-type minerals have stronger binding to the inhibitor and release it at lower concentrations than the alumina-type minerals. Silica-type surfaces, for brines requiring a high MIC, may provide a reasonably efficient release profile. In most cases, however, the MIC will be far below the concentration released from silica over most of the squeeze lifetime, again resulting in a short lifetime and waste of inhibitor.

Siderite binds inhibitor much more strongly than alumina- and silica-type minerals. In many cases, siderite can provide a very desirable return profile, with the bulk of the inhibitor returning at concentrations close to the MIC. Long squeeze lifetimes and efficient use of inhibitor result from the presence of siderite and other iron carbonates.

By definition, the static adsorption isotherm represents equilibrium conditions. Under some conditions, particularly with small diameter, short-core flow tests, kinetic effects may play a large role in the observed behavior. The adsorption characteristics from these conditions, occasionally referred to as a “dynamic adsorption isotherm,” are valid only under the test conditions. Any change in flow rate will result in a different “isotherm.” This rate-dependent “isotherm” is difficult to extrapolate to different conditions in radial flow. However, if the true equilibrium adsorption isotherm is known, any kinetic effect can be addressed simply as a deviation from equilibrium, thereby allowing the use of a single adsorption isotherm over a wide range of flow conditions.

A thorough understanding of the adsorption isotherms corresponding to the minerals present is essential to design the most cost-effective treatment.

With the knowledge of the adsorption behavior of each mineral, the performance of a squeeze treatment can be predicted from the results of a simple x-ray diffraction analysis of the formation material. Once the mineral composition is known, it is a simple matter to mathematically combine the isotherms of each mineral class in the proper proportions to yield a single composite isotherm.

Using the mineralogy as a guide

The three cases demonstrate the role of each category of surface type on the retention of the common scale inhibitor diethylenetriamine pentamethylenephosphonic acid (DETPMP).

Case 1 is for a mineralogy that was a mixture of silica-type and alumina-type surfaces. The silica-type surfaces, excluding low surface-area sand grains, were feldspars and kaolinite and constituted 20% of the rock composition. The alumina-type surfaces were illite and chlorite and constituted 10% of the rock composition. However, because of the low surface area of feldspar and the low surface coverage on kaolinite, 80% of the composite isotherm was dominated by the alumina-type surfaces. This means that unless an enormous overflush was used to reposition the adsorbed scale inhibitor, most of the inhibitor would desorb at high concentrations from the formation, and the squeeze-life would be short. The formation represented by the mineralogy in Case 1 would not provide highly efficient scale inhibitor squeeze treatments. Typical squeeze treatments in this formation would provide a high level of inhibitor residuals and short “tails” in the few mg/L range.

Case 2 is for a mineralogy dominated by silica-type surfaces. The silica-type surfaces constituted 50% of the rock composition, while alumina-type surfaces constituted only 5% of the composition. In this case, 60% of the composite isotherm was dominated by the silica-type surfaces. However, this still means that most (60 to 90%) of the inhibitor would return at above 3 mg/L as DETPMP, or 6 to 15 mg/L as drummed product depending on the delivered activity level. Only 10% (approximately) of the inhibitor would be available for returning in the long-term “tail” of the squeeze treatment. Still, this would be an improvement over Case 1.

Case 3 is for a mineralogy that was a mixture of alumina-type surfaces and some siderite. The silica-type surface was ignored because of the low surface coverage on kaolinite and the low surface area of feldspars and quartz. In this case, approximately 35% of the composite isotherm was situated below 3 mg/L of DETPMP, with 20% situated in the range of 1 to 3 mg/L. A proper overflush behind the main stage of scale inhibitor could readily reposition the DETPMP from the top 25% of the isotherm and make it available for adsorption and subsequent desorption on the bottom portion of the isotherm. The formation represented by the mineralogy in Case 3 would be an excellent candidate for highly efficient scale inhibitor squeeze treatments.