Software tools for designing downhole scale inhibitor (SI) squeeze treatments are widely available and have been successfully applied in thousands of wells worldwide. Many SPE papers have been published describing such squeeze design case studies from the conceptual modelled design, to implementation and post treatment analysis.These models are based on the fundamental transport equations for the SI in the near well formation. These equations must also include a model describing the SI/rock interaction, regardless of whether it occurs by an adsorption/desorption or by a precipitation (phase separation) mechanism.A number of papers have appeared in the literature on these fundamental equations and on the analytical and numerical models based on them.

In this paper, we present a re-evaluation of the equations that have been proposed to model SI transport and adsorption in porous media.We have analysed the various approaches in terms of two basic aspects:

  1. the mathematical structure of the various equations used to describe transport; and

  2. the surface chemistry assumptions and models used to describe the SI/rock retention mechanism, particularly by adsorption.

We specifically focus on comparing and reconciling our own (Heriot-Watt U. and Halliburton) respective approaches, which have been developed over the last few years.

Background and Introduction

Scale inhibitor (SI) squeeze treatments have been carried out in many reservoirs as a measure for controlling/preventing the formation of oilfield mineral scales such as barium sulphate and calcium carbonate.Such treatments are routine in both onshore and offshore situations and great expertise exists in the service sector and the operator companies in performing these treatments quite successfully.A key feature of the process is the nature of the SI/rock interaction which retains the SI within the formation, allowing it to return to the wellbore in the produced brine over an extended period.However, the mechanism of this retention is open to interpretation and is known to depend on various conditions including the SI type, temperature, pH, [Ca[2+]], nature of mineral substrate, etc. These conditions are either deliberately imposed by the treatment design or they exist in the reservoir.Broadly speaking, it is widely accepted that the two principal mechanisms of SI retention within a reservoir formation are due to adsorption and precipitation.In the general case, a combination of these mechanisms may be involved and this can be described mathematically.Here we focus on where adsorption is the main retention mechanism.

A number of papers have appeared describing the modelling of SI transport and retention during flow through porous media [1–6]. In particular, alternative approaches for modelling adsorption squeeze processes have been developed by the authors [3, 6] and some confusion has arisen as to how these are related.In this paper, we will clarify the similarities and differences between these approaches and point to advantages and disadvantages of each. The main aspects of the models proposed relate to (a) the mathematical structure of the transport/retention equations describing the SI within the porous medium; and (b) the surface chemistry assumptions inherent in the various models that are used to describe the specific details of the SI/rock retention mechanism.Thus, our analysis and comparison will be carried out in the context of the mathematics and the description of the adsorption process.

It will be shown that a unified mathematical model emerges where certain choices or assumptions must be made on the form and kinetics of the actual adsorption model.Depending on these choices/assumptions, the HW (Heriot-Watt) or Halliburton models are recovered.The differences are then those of detail - although this detail may be very important in specific circumstances.Although we focus on adsorption SI treatments in this work, precipitation type models also fit into a similar framework with a modified retention model [7, 8].

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