Simulation of Produced Water Re-Injection Under Fracturing Conditions
Authors: van den Hoek P.J. , Matsuura T. , de Kroon M. , Gheissary G. 
Published: December 2007

Abstract
This paper discusses a number of aspects in relation to simulating unfiltered produced water re-injection (PWRI) under fracturing conditions.
A numerical model has been developed that fully couples the reservoir engineering and fracture mechanics aspects of the problem, and includes features such as finite, non-uniform fracture conductivity, fracture growth, filtercake build-up on the fracture face, formation impairment around the fracture, and backstresses resulting from pore pressure inflation and formation cooling.
An essential difference with simulation of conventional waterflood fracturing is that owing to fracture fill-up with injected solids the fracture conductivity cannot be assumed infinite any more. This relates to the important PWRI issue of where the injected solids go. Using our model, we show that the pressure drop over a finite conductivity fracture can lead to a significant increase in fracture volume without necessarily leading to a significantly higher injection pressure. Thus, a picture emerges in which the fracture conductivity 'adjusts' itself in order to accommodate injected solids. This picture allows the computation of well injectivity as a function of total injected water volume, solids loading, etc. This concept can also be used to qualitatively explain the PWRI field observation that injectivity appears to be partially or fully reversible as a function of water quality.
A field example from the Middle East is presented. The effect of parameters such as water quality, formation stiffness, and filtercake permeability on well injectivity and fracture size is discussed. It is shown that for most practical applications, an approximate analytical formulation for the computation of well injectivity and fracture size provides good results.

Introduction
Mature oil fields with a water drive produce increasing volumes of oily water which require disposal, and so it becomes increasingly important to adopt cost effective, environmentally sound water disposal systems. Re-injection into the subsurface is a potentially attractive option from an environmental view point, but to become the preferred alternative for produced water disposal, re-injection must also be economically competitive and not incur excessive risk.
In a recent study the economics of produced water re-injection (PWRI) was compared with other options for disposal in a North Sea situation. This study shows that declining well-injectivity is the major cost-increasing item in the case of reinjection. In order to maintain injectivity for produced water that has not been fine-filtered, injection above fracture pressure is required. This option, however, offers significant uncertainties, because a reliable prediction of fracture size (containment, sweep) and well-injectivity as a function of water quality cannot be made at this stage. This is caused by a lack of sufficient field experience and insight in the fundamental processes.
Field experience of PWRI under fracturing conditions has shown that well injectivity depends a.o. on injection water quality and temperature. To date, no unambiguous observations exist of well injectivity declining with time for PWRI above fracturing pressure. One key uncertainty in well injectivity relates to the issue of where injected solids go PWRI field experience shows that several fracture volumes of solids can be injected without significant loss of injectivity. Here, the fracture volumes were inferred from hydraulic impedance testing (HIT) and fall-off surveys, assuming infinite conductivity fractures. To date, no explanation exists for this apparent difference.
This paper discusses several aspects of simulating unfiltered produced water re-injection (PWRI) under fracturing conditions.
P. 269