Paper Title: Chemical Placement in Heterogeneous and Long Reach Horizontal Wells

Author list: Robert Stalker (Scaled Solutions Ltd.)Fazrie Wahid (Scaled Solutions Ltd.)Gordon M. Graham (Scaled Solutions Ltd.)

Abstract

The effective placement of chemical squeeze treatments in heterogeneous wells and long reach horizontal wells has proved a significant challenge, with various factors including heterogeneity, crossflow and pressure gradients between otherwise non-communicating zones within the well, all contributing to an uneven placement of the scale squeeze treatment into the reservoir. Current methods to circumvent these problems often rely on extremely expensive coiled tubing operations, staged diversion (temporary shut off) treatments or by designing treatments to deliberately overdose some zones in order to gain placement in other (e.g. low permeability) zones. Moreover for deepwater subsea horizontal wells the costs associated with “spot” treating along the length of horizontal wells by coil tubing tractor operations can often be prohibitively expensive. For other very near wellbore treatments such as acid stimulation a number of self diverting strategies including gelled acid treatments, staged viscoelastic surfactant treatments and foams have been applied in field treatments with some success. However the properties which make such treatments applicable for acid stimulation may also make them inappropriate for bullhead scale squeeze treatments.Recent work by the current authors has however indicated the possible benefits of using modified injection fluids to aid uniform scale inhibitor placement in such wells in order to effect more even placement. In summary this paper will describe the various options available for achieving self diversion and describes the potential drawbacks associated with the viscous placement fluids commonly used for acid simulation techniques. In addition, various simulation packages commonly used for scale related calculations are reviewed and their limitations, primarily due to the inherent assumptions made and input parameters used, for modelling squeeze treatments using such modified fluids are described. The paper therefore presents (i) a review of the limitations and potential benefits of non conventional treatment fluids for scale squeeze operations in heterogeneous and horizontal wells with supporting laboratory and field data (ii) a critique of the utility of the current generation of popular reservoir simulation packages for modelling modified squeeze treatments, and (iii) introduces an alternative model designed specifically for such fluids.

Introduction

The effective treatment of oil wells with scale inhibitor chemicals is often confounded by the presence of a number of factors which act to place the majority of the treatment slug in an undesired region of the well.1-8 For heterogeneous wells and long reach horizontal wells, these factors can include reservoir heterogeneity, fluid crossflow, pressure gradients, wellbore friction and presence of fractures. The presence of some or all of these may result in the majority of the squeeze treatment volume being placed in an inappropriate zone in the near-wellbore, which can result in reduced squeeze lifetimes and inadequate scale protection of vulnerable near-wellbore mixing zones. In this paper, we will briefly summarise the influence of these factors on placement, discuss the advantages of achieving optimum placement and describe the utility of shear thinning fluids in helping to achieve more uniform placement of the treatment slug. The utility of current reservoir simulator packages for modelling the placement of such modified treatment fluids is discussed, and an alternative placement model is described which has been specifically designed to model the placement of these fluids.

Overview of Placement Challenges

In general (considering for example a two-zone well), anything which creates a resistance to fluid flow in one zone will promote fluid placement in the other zone. This resistance to flow may be caused by the rock matrix itself (permeability factors, fluid mobility, the presence of fractures), zonal pressure differences, fluid crossflow in the well etc. As well as these factors, the type of completion used can also affect fluid placement, for example due to wellbore friction effects. In this section, we briefly illustrate how some of these factors can impact fluid placement by bullheaded injection.

Reservoir Heterogeneity: The ease with which injected fluids can enter the reservoir is of course a function of the permeability of the rock matrix, as enshrined in Darcy’s Equation (Equation 1).9

dp = Q—dl............... (1)

where Q is the volumetric flow rate, — is the fluid viscosity, k is the permeability of the matrix and A is the area of the fluid front. If all other factors are equal, then injection of an aqueous fluid into a well consisting of two regions with permeability k1 and k2, will result in fluid placement following the permeability contrast. Another aspect of such ‘Darcy placement’ is that the placement in each zone is also a function of the area of the fluid front A, and hence of the length of the production intervals. This means that for long horizontal wells consisting of predominantly lower permeability production zones and high permeability streaks, significant increases in the total volume of injection fluid placed in the lower permeability regions can be achieved with comparatively smaller amounts of diversion.

Pressure gradients and Crossflow: Pressure gradients or crossflow will also influence the placement of an inhibitor slug, with injection being favoured in the lower pressure zones. In wells with a strong crossflow, injection at lower flow rates may even fail to penetrate the higher pressure zone. Increasing the viscosity of the injected fluid slug has been shown by both modelling and field experience to help overcome the effects of fluid crossflow, allowing more even penetration of the injection slug.

Wellbore Friction: Wellbore friction effects can affect the bullheaded placement of chemical in long horizontal wells, with frictional resistance promoting placement nearer the heel of the well to the detriment of the toe. Wellbore friction is dependent on the diameter of the tubing and the tubing roughness, decreasing with the 5th power of the wellbore radius (Equation 2). Frictional effects become significant as the diameter of the tubing decreases, while completion types such as sand screens will increase the roughness factor and create more frictional resistance.

C.FLpQ2

SP/ = ds (2)

where Cf is a constant, F is the Fanning Friction Factor and the other symbols have their usual meaning.Other factors such as layer pressures, the properties of the fluid in place and differences in mobility ratios between different zones also have an impact on chemical placement but will not be considered in this manuscript.

Chemical Placement Strategies

When chemical treatments are designed for wells containing some or all of the above factors, the challenge is to place the chemical in the optimum manner to obtain adequate protection for the longest possible duration. Current methods to circumvent these problems often rely on extremely expensive coiled tubing operations,2,6,8 staged diversion (temporary shut-off) treatments2,8,10-12 or overdosing some zones to gain placement in other (e.g. low permeability) zones.8 Each of these methods has some potential drawbacks which can limit its applicability. When wells produce from areas of high permeability contrast, with wellbore crossflow or high pressure gradients, coil tubing operations or staged “temporary diversion” treatments can often be the only manner in which effective chemical placement can be guaranteed.

Coiled Tubing: Coiled tubing operations have the advantage, when properly implemented, of injecting chemical at known points of the production interval, and thus (hopefully) decreasing the level of uncertainty regarding where the chemical is placed. However, the costs associated with such treatments are extremely high and are often prohibitive when compared with conventional bullhead operations. As an example, platform based coil tubing pumping operations to ensure effective placement can cost in the region of £2,500K compared with ~ £50K pumping costs associated with conventional bullhead treatments.6 For subsea applications or deepwater treatments, access to wet wellheads can increase the costs more significantly such that squeeze treatments can have a significant impact on field economics.2,4,5,8Staged Diversions: Staged diversion treatments rely on the temporary isolation of more permeable zones using wax divertors or polymer pills, to allow further slugs of injection chemicals to enter the less

permeable zones. In this way, the most permeable zones are treated first, then isolated by application of a temporary blocker to allow effective treatment of the less permeable zones.12Overdosing: A somewhat inelegant solution to the problem of ensuring sufficient chemical placement in lower permeability zones is to simply overdose the higher permeability regions until sufficient treatment volume enters the disfavoured zone. In cases where the placement contrast is reasonably small, such a procedure may be practical. However, as the placement contrast increases significantly larger volumes of fluid must be placed in the higher permeability zones to ensure adequate protection of the lower permeability zone. This results in longer treatment times and larger volumes of fluid to be handled (both during injection and on initial flowback), with associated issues of transport, storage and waste handling. An important consideration is the larger quantity of scale inhibitor which will return with initial flowback following an overdosed treatment, which must be treated appropriately in the face of increasingly stringent environmental protection protocols (zero discharge, reducing quantities of waste generated).

When wells produce from areas of high permeability contrast, with wellbore crossflow or high pressure gradients, coil tubing operations or staged “temporary diversion” treatments can often be the only manner in which effective chemical placement can be guaranteed. However, in the presence of strong crossflow, even achieving good placement may not be sufficient to obtain adequate protection. Fluid crossflow can result in significant redistribution of chemical during shut in, which may be either beneficial or detrimental to squeeze lifetime, depending on the scaling environment and the water production profile in the well.

For each case however the chemical costs remain similar, and as the overall cost of the operation increases the chemical costs contribute an increasingly smaller percentage of the total treatment costs. This therefore creates a strong economic driving force for improving chemical performance both in terms of return lifetimes and also in the potential to improve chemical placement by adjusting the chemical package.2,8 In this case the desire is to place treatment chemicals and retain them in areas of the near wellbore formation designated by the field engineers and production chemists as opposed to where the reservoir itself would “naturally” take in chemicals.

Placement Challenges in Oilfield Acidization Treatments

The problem of appropriate placement of chemicals is not limited to scale inhibitor squeeze treatments. Similar placement problems have been encountered in other oilfield treatments, such as acidization treatments. In such treatments, the challenge is to ensure that sufficient acid contacts the damaged zones to allow reasonable clean-up. However, the injected acid treatment solution will often preferentially enter the least damaged zones which may be where they are least needed.13 For this reason, a variety of methods have been developed to achieve adequate treatment coverage over the whole production interval. Staged diversions,14,15 zonal isolation16 and maximising injection pressures have all been used to ensure uniform clean-up by acidization fluids in heterogeneous wells.17-19 More recently, a number of self-diverting strategies such as viscoelastic surfactants (VES)20-24 or gelled organic acids (GOA)25,26 have been applied in field treatments with some success.

Gelled Organic Acids (GOA’s): Gelled organic acids essentially rely on the increased viscosity of the injection stock to achieve more uniform placement along the zone. The shear thinning nature of the gelled acid solutions help ensure that very rapid increases in zonal pressures are achieved as soon as the chemicals start to penetrate radially into high permeability / low pressure zones.11,27,28 The combination of these two effects ensures effective placement along the length of the well, with the gelled acid contacting other potentially damaged lower permeability / higher pressure areas of the wellbore and perforations. Further self-diversion has been achieved with gelled organic acids by the pH-triggered in situ formation of temporary cross-linked gels in treated zones, thus diverting further acid injection into non-treated zones.29,30 Following treatment, breaking of the remaining polymer gel occurs by acid hydrolysis, which generally occurs rapidly due to the heat from the wellbore. In a squeeze treatment however, strongly acidic conditions are not generally encountered, and significant wellbore cooling can be expected due to the large volumes of injected fluid entering the matrix. The effect of this would be to reduce the rate of hydrolysis of the polymer,25,31 resulting in the need for either significantly longer shut in periods or the addition of oxidative breakers (persulphate, perborate, perchlorate etc.) to ensure breaking, making such highly viscous fluids impractical for squeeze treatments potentially leading to significant levels of formation damage and the risk of killing production altogether.

Viscoelastic Surfactants (VES’s): VES acid treatments rely on the formation of self-organised structures in the water phase following application of the acid treatment to create a temporary impediment to flow in the most permeable zone, forcing the injected acid into neighbouring zones where the process repeats until all the zones have been treated. Such self-diverting VES acid treatments have been used to conduct successful acid stimulation treatments either by staged diversion (using pills of VES acid to temporarily block treated zones)23 or via bullhead application, with unequivocal evidence of diversion occurring.21

Other temporary diversion treatments applied for acid stimulation include foamed acids etc.32-34 These lie beyond the scope of this paper, but have been reviewed elsewhere.7

While both GOA’s and VES’s give more even treatment of production zones in acidization jobs, the techniques may not be directly transferable to squeeze applications. Staged injection of VES / acid results in chemical placement towards non treated (oil bearing) low permeability zones, away from the water-bearing zones which the inhibitor is (normally) intended to treat. Gelled organic acids are designed in such a way as to limit the penetration into the reservoir, whereas for a squeeze job the intention is to place chemical a significant distance away from the wellbore in the near-wellbore region. A typical GOA-type fluid has too high a viscosity to do this easily, and would require extended periods of shut in to break. However, more dilute polymer solutions may be more suitable for achieving better placement in modified scale inhibitor squeeze treatments. In this paper we describe results obtained in an ongoing Joint Industrial Project investigating the design of such modified scale inhibitor squeeze treatments to effect self-diversion for scale inhibitor squeeze treatments (SISQ) in complex wells in the presence of heterogeneity, and other factors impacting placement such as crossflow and pressure gradients etc. After introducing the principle behind these modified placements, we will discuss the challenges faced when attempting to design such a treatment, and discuss the computer simulation of such treatment fluids using both a popular reservoir simulator model and a newly developed near wellbore placement model which has been specifically created to examine the flow behaviour of these modified fluids.

Placement using Shear thinning injection fluids

If we wish to divert chemical injection from its most favoured flow path into a less favoured zone, then we must either restrict fluid flow in the more favoured zone or facilitate flow in the less favoured zone. Examination of Darcy’s Equation suggests that if we were to increase the injection fluid viscosity in the higher permeability zone or decrease the injection fluid viscosity in the lower permeability zone, then more fluid would enter the lower permeability zone than was previously the case (Figure 1). For standard injection fluids, such a scenario is unfeasible. However, shear thinning fluids behave in just such a manner, and so open the possibility of achieving self diversion in bullheaded injections.

The viscosity of a simple fluid such as brine is not dependent on the flow rate - water at 20oC has a viscosity of 1 cP whether it flows at 1 ml/h or 10 bbls/min. However, shear thinning fluids have viscosities which can change with flow rate, or (to be more accurate) with shear rate (Figure 2). At very high and very low shear rates, these shear thinning polymers exhibit Newtonian behaviour, that is their viscosity is independent of shear rate. However, at intermediate shear rates the viscosity of these solutions becomes strongly dependent on shear rate, in a manner which can be described by a Power Law relationship (Equation 3)

— = Kyn 1.......... Equation 3where — is the solution viscosity, y is the shear rate, K is the consistency index of the solution and n is the shear thinning index of the solution. The shear rate in a porous medium (such as a reservoir rock) can be calculated from the bulk reservoir properties using the Kozeny-Carman model (Equation 4)

4auY = , ............Equation 4^8kp

in which a is the shape factor for the rock, u is the superficial flow velocity, k is the permeability and is the porosity of the rock. Equation 4 tells us that as the permeability of the rock decreases, the shear rate experienced by the fluid increases. Similarly, decreasing porosity will result in higher shear rates. Thus, all other factors being equal, the shear rate experienced by a fluid flowing in a lower permeability

zone will be higher than that experienced by a similar fluid flowing in a higher permeability zone. The shape factor a is an empirical factor introduced to correlate the experimentally measured shear rates with those calculated by the relatively simple capillary bundle model. This shape factor is a property of the rock, and in general will increase as the rock permeability decreases.

When a fluid is injected into a heterogeneous reservoir, the fluid will start flowing in both high and low permeability regions and will begin to penetrate the reservoir. If we assume radial displacement occurs, the superficial velocity of the fluid front (Figure 3) and the shear rate experienced by the fluid (Figure 4) can be easily calculated. It is apparent from these two figures that, while the flow velocity of the fluid front is greater in the higher permeability zone, the shear rate experienced by the fluid is lower in the higher permeability zone. Thus a shear thinning fluid will in general display a greater viscosity in the higher permeability zone, promoting fluid diversion into the lower permeability zone. As the shear rate does not affect the viscosity of simple Newtonian fluids, conventional placement simulators are ill- equipped to model these more complex fluids. The consequences of these effects will be discussed in a later section, but first we review some current reservoir simulator and placement packages and assess their suitability for modeling placement of Newtonian and non-Newtonian inhibitor packages.

General Overview of Current Reservoir Simulation Software for Placement

There are various reservoir-type software packages available in the market that deal with flow prediction in the oilfield production industry. These reservoir simulation models are usually employed to predict and track the flow of reservoir fluid throughout the reservoir, for example predicting oil and water production rates, specific well production indices, reservoir performance and mixing zones. Such simulators can be of great benefit for predicting various aspects associated with scale formation and treatments such as water production profiles, potential for reservoir and near-wellbore incompatible water mixing and certain aspects associated with treatment of individual wells such as the impact of crossflow and friction effects in long horizontal wells. Such models are also often used to simulate chemical placement of simple fluids in the near wellbore region. The potential use of several of the more commonly available reservoir simulators lias been reviewed in order to select an appropriate model for further, more detailed evaluation within this work. The various models evaluated are summarised as follows:

REVEAL (Computer Experts): REVEAL is a full field reservoir simulator, specializing in near wellbore effects such as fluid mobility and injectivity, and incorporates the chemical and thermal impact from introducing non-reservoir fluids.35 These are predominantly included to model the impact on the aqueous phase mobility of reservoir fluids of injecting polymers and foam. Additionally, REVEAL can be employed to predict incompatible water mixing which could lead to formation of scale or souring, reaction chemistry, solid precipitation, dissolution and solid transport in the reservoir, and scale inhibitor adsorption/desorption processes.35 The simulator therefore appears to offer some potential for application to examine in detail placement aspects along the near wellbore region although no indication on modelling shear thinning placement calculations were noted for this full field simulator in the literature reviewed.ECLIPSE 100 (Geoquest Schlumberger): ECLIPSE 100 is a black oil simulator, primarily used to simulate reservoir flow processes. Various modules have been incorporated in the current ECLIPSE 100 suite such as local grid refinements, wellbore friction and polymer injections (Newtonian and non- Newtonian fluids), which allow many scale type applications to be examined. ECLIPSE 100 has therefore been used in flow assurance (scale) analysis for predicting chemical placement in near wellbore regions in a number of previous field studies, allowing various aspects to be evaluated in some detail.1"3 In addition, since the software includes the ability to model chemical placement and adsorption/desorption characteristics during placement and return it can also be used effectively to model scale inhibitor treatment and return profiles in complex systems where the simple near wellbore radial squeeze treatment simulators are less effective. Although the Eclipse model does provide an option for modeling shear thinning fluids, this is not suitable for modeling such fluids in the near wellbore region for reasons discussed later in this paper.FrontSim (Geoquest Schlumberger): FrontSim is a three-phase, 3D simulator that models multiphase flow of fluids along streamlines.36 FrontSim traces the injector to producer relationship directly through connecting streamline bundles, hence allowing the user to examine both producer and injector efficiency. Additionally, FrontSim can be used to trace mixing zones of injected and reservoir fluids, allowing a crude analysis of scale formation zones within the reservoir to be examined. Similar to the

other software under review, FrontSim functions as a reservoir flow simulator, rather than a placement or scale prediction tool.STARS (Computer Modelling Group): STARS (Steam, Thermal and Advanced Processes Reservoir Simulator) is a reservoir simulator, which incorporates reaction processes with respect to temperature and chemical mixture.37 STARS can be used to simulate, among other tilings, chemical/polymer flooding, thermal applications, steam injection, horizontal wells, dual porosity/permeability, directional permeabilities, brine tracking and allows flexible gridding. In scale applications, STARS can be employed to predict scale precipitations via its reaction module, although as with other aspects suffers from a degree of numerical dispersion which limits the absolute accuracy of such calculations for real field systems. However, the application of STARS is limited for chemical placement processes, as the polymer and chemical injection modules available are constructed for use in reservoir flooding application. Generally, the polymer flooding (for example, a non-Newtonian fluid) option is used to examine alterations in reservoir fluid mobility. For this application, the viscosity-shear rate dependency is rather low due to the low velocity nature of polymer flooding in the reservoir.38 This is in contrast for near wellbore placement applications, where the shear rate effect is more significant at this relatively higher velocity zone.38 Moreover, recent communication from Computer Modelling Group has indicated that this software does not allow the type of near wellbore shear thinning calculations of the type required for placement analyses.39IMEX (Computer Modelling Group): IMEX (Tmplicit-Explicit Black Oil Simulator) is a 3-phase black oil simulator, similar to ECLIPSE 100, which is able to model ID, 2D and 3D complex heterogeneous reservoir characteristics. It can accurately predict various reservoir processes such as wellbore crossflow, and can be used to examine complex well placement and its implications on reservoir fluid production. By incorporating local grid refinement tools, IMEX can be used to examine near wellbore effects. Similar to ECLIPSE 100, the polymer injection tool in IMEX is primarily designed to handle polymer flooding processes, rather than chemical placement near the wellbore region.Near Wellbore Radial Flow “Squeeze Treatment” Models: Other simpler near wellbore radial treatment models such as SQUEEZE V4" and SqueezeSoftPitzer41 have been used extensively throughout the industry for simulating scale inhibitor squeeze treatments. In essence these models are used to history match field scale inhibitor squeeze returns based upon assumptions relating to the retention and release characteristics of scale inhibitors within the reservoir and therefore allow for some degree of optimisation for future treatments.42 Thus although the models refer to different chemical retention mechanisms (either adsorption/desorption or precipitation/dissolution), their effectiveness relies on their ability to mathematically match field return data and therefore the exact nature of its derivation becomes less important. Both simulators are essentially near wellbore radial simulators which treat different reservoir zones as essentially independent homogeneous sections and therefore do not allow other aspects associated with chemical placement to be examined. In many cases the input data from reservoir simulators such as Eclipse are used in conjunction with these simpler near wellbore scale inhibitor treatment models to assess the impact of various reservoir parameters on scale inhibitor return profiles.27’46 However given that reservoir simulators such as Eclipse incorporate chemical adsorption/desorption properties (or more accurately chemical retention) they can be readily used in complex well systems to model the entire scale inhibitor squeeze placement and chemical return profile directly.

Summary - Initial Evaluation of Placement Simulation Packages

All of the reviewed reservoir simulation software packages (Reveal, Eclipse & FrontSim, Stars and IMEX) offer excellence in technical application, with similar limitations with respect to chemical placement applications near the wellbore region. ECLIPSE was chosen for further study of the predictions for near-wellbore placement of Newtonian and shear thinning fluids. These predictions were compared with those obtained using Place /T, a newly developed near wellbore placement model explicitly designed to model the placement of modified shear thinning injection fluids.

Outline of the Place iT model

As discussed above, while a nmnber of sophisticated full field reservoir models are available, these have not been designed specifically for the near wellbore region and are generally not equipped to handle shear thinning fluids - or even viscous Newtonian fluids - appropriately when examining near wellbore placement for SISQ applications. For this reason, as part of a Joint Industrial Project examining chemical placement we have developed a dedicated near-wellbore placement model capable of appropriate simulation of both non-viscosified and viscosified Newtonian fluids as well as non-

Newtonian fluids. The basis of the model is shown in Figure 5 for the two-zone case, illustrating the injection of fluid with viscosity u2 into a dual core arrangement of length l, containing a Newtonian initial fluid in place of viscosity u The analysis of this system rests on three initial equations, Equations 1, 5 and 6;

kPmj = 4P(U ) + 4P(Ui) Equati°n 5

,1 =^Pi«^' ,2 Equati°n 6

Equation 1 is simply Darcy’s Equation for describing the flow of fluid through a porous medium. Equation 5 states that the differential pressure due to the injection of the fluid can be separated into two parts, the differential pressure arising from the flow of the slug of injected fluid and the differential pressure due to the movement of the slug of initial fluid in place. Finally, Equation 6 states that the injection pressure must be the same in each zone (as they are connected at the wellbore). From these equations, we can analyse the flow behaviour under both linear and radial flow conditions.

Modelling Chemical Placement Using Eclipse 100 simulator & Place iT - Newtonian Fluids

The ability to accurately describe aspects such as local water production along the wellbore and the location of injected water breakthrough (i.e. to identify the areas which require treatment) during production is essential for determining appropriate treatment campaigns in complex wells. In addition, the ability to simulate effects such as pump rates and fluid bulk viscosity, which influence fluid injectivity along the length of the well and into high pressure or low permeability zones, is also of critical importance when designing treatments for complex well systems. Although it is recognised that reservoir simulators such as Eclipse can be used with effect for these calculations, a number of limitations exist which must be considered, particularly when attempting to simulate the effective use of viscous shear thinning solutions into heterogeneous wells or wells with zones of considerable pressure gradients.

Radial Model vs. Cartesian Model: In most cases, fluid injection during the squeeze treatment is best characterized using a radial model. For a simple vertical well, this process can be easily captured using the ECLIPSE suite with a radial model embedded within a global Cartesian grid, which makes up the rest of the reservoir. This provides vital information with respect to chemical placement near the wellbore region, allowing scale inhibitor squeeze treatments to be modelled directly while taking into account the simulated field flow regimes. However, the application of a radial model in most reservoir- type software packages is limited to a vertical well system and cannot be employed for a horizontal well. This limitation can be overcome by modelling the horizontal well as a vertical well within a radial grid, assuming that the flow characteristics are similar. This assumption presents a limitation to the actual process of chemical placement, as various effects are not fully realized. For example, the impact of gravity, absolute permeabilities and the knock-on impact on other reservoir processes are no longer accounted for, making the simulation more similar to the simpler radial models more commonly used for squeeze treatments in conventional vertical wells.When using a Cartesian grid with near wellbore grid block refinement for horizontal wells, although the various reservoir attributes are captured during the simulation stages, further limitations arise when examining near wellbore placement effects, particularly those required in this work. For horizontal wells, there is a requirement to encompass the cross sectional area of the well within a single grid block cross section. This in effects limits the sensitivity to placement calculations in the near wellbore region which represents the most critical area for modeling the placement of viscous shear thinning fluids. In addition, the requirement for relatively large grid blocks introduces numerical dispersion effects which may reduce the accuracy of the predictions. Thus, since the most significant reductions in fluid velocity and associated reduction in viscosity occur in the immediate vicinity of the wellbore, numerical dispersion in this region would have a significant impact on the modelled impact of shear thinning polymers on placement. The inability therefore to accurately model superficial velocity and shear thinning behaviour as the fluids initially move out of the wellbore into the formation in the very near wellbore area represents a relatively major limitation for accurately monitoring the effect of shear thinning behaviour on chemical placement.

Modelling Placement of Newtonian Fluids:

The placement of Newtonian fluids is not dependent on the shear rate experienced, and so the Place iT model and the Eclipse simulator should give good agreement. An extensive series of comparison tests were carried out to ensure that the new model behaved appropriately, of which a sample is presented below.

In the first set of analyses presented here, the validation procedure concentrated on predicting the placement in the presence of varying quality of fluid in place and pump rates. The parameters used for this work are described below:

Parameter Zone 1 Zone 2Permeability (mD) 1000 1000Porosity 0.25 0.25Well length (m) 600 600Viscosity of FIP (cP)

Case 1 1 10 (1 & 20 bpm)Case 2 1 2 (20 bpm)

Boundary length (km) 1 1

Calculations were carried out both in the ECLIPSE suite and via the Place iT software. A graphical picture of the ECLIPSE simple 1-well model is given in Figure 6. The results are shown in Table 1. Good agreement was observed between the placement profiles predicted by the ECLIPSE suite and those predicted by the near-wellbore model. Better convergence between the results obtained by ECLIPSE and Place iT was achieved by increasing the number of time steps used in the in-house near­wellbore model calculation, which increases the model resolution and with it the accuracy of the results.

Case Studies SimulationPlatform Zone 1 (%) Zone 2 (%) Time steps

Case 1 (1 bpm)ECLIPSE 90.4 9.6Place iT 89.9 10.1 18Place iT 90.2 9.8 50

Case 1 (20 bpm)ECLIPSE 90.6 9.4Place iT 89.9 10.1 18Place iT 90.2 9.8 50

Case 2 (20 bpm)ECLIPSE 66.3 33.7Place iT 64.3 35.7 18Place iT 65.0 35.0 50

Table 1: Comparing preliminary validation results between ECLIPSE and Place iT

Further comparison of Newtonian fluid injection predictions were obtained by modeling placement in Well N19z of the Nelson field, operated by Shell UK.43 This long horizontal well contains permeability contrasts and has severe fluid crossflow from the low permeability toe zone towards the high permeability heel region, making it hard to place chemical in the high pressure toe region. When injection of a viscosified injection stock was modelled for this well using the Place iT model, excellent agreement was obtained with the predicted placement using Eclipse (Figure 7), with crossflow effects accounting for the differences.

In conclusion, the validation work demonstrated excellent agreement between Eclipse and Place iT when modeling the injection of Newtonian fluids in radial wellbore systems. Attention then turned to the modeling of shear-thinning fluids using these two models.

Modelling Chemical Placement Using Eclipse 100 simulator & Place iT - Non-Newtonian Fluids

While Eclipse has an option to model the flow of shear thinning fluids, this was designed to simulate polymer flooding operations in a single homogeneous well system. However, although Eclipse can reasonably handle sweep analysis of shear thinning polymer fluids into single permeability zones it is currently unable to accurately simulate shear thinning fluid placement in a heterogeneous reservoir body.44 This is because when Eclipse models shear thinning fluids, it makes an approximation and correlates solution viscosity to flow velocity, rather than to shear rate. While this assumption is reasonable when considering only a single permeability zone, it is inadequate when considering

injection in a heterogeneous system. As described in previous sections, while the superficial velocity of the injected fluid is generally higher in the higher permeability zone relative to a low permeability zone, the shear rate experienced by the injected fluid along the heterogeneous formation is generally higher in the lower permeability formation than in the high permeability zone. The consequences of this approximation can be rather dramatic when Eclipse is asked to model the near-wellbore flow behaviour of a shear thinning fluid, and are illustrated in the following example

Placement of Velocity-thinning fluid (Eclipse) vs. shear thinning fluid (Place iT)

As indicated in Figures 3 and 4, the velocity and shear rate profiles for injection into a two-zone heterogeneous formation differ in important respects. In most cases, the injection front velocity at a given time is predicted to always be higher in the higher permeability zone, whereas the corresponding shear rate is predicted to be lower in the higher permeability zone. Thus, a velocity-thinning fluid (one in which viscosity increases with decreasing velocity, as used by Eclipse to approximate a shear­thinning fluid) will develop an increased viscosity in the lower permeability zone, where it is moving more slowly. This will result in a predicted placement away from the lower permeability zone into the higher permeability zone.However, it should be remembered that in reality, shear-thinning fluids have viscosities which are dependent on shear rate, not on velocity. Does this make a difference to the predicted placement? As illustrated in Figure 4, the shear rate experienced by the fluid in the higher permeability core is generally lower than in the lower permeability core. This means that the shear-thinning fluid will develop a higher viscosity in the higher permeability zone, where it experiences the lower shear rate. Thus a shear thinning fluid will experience diversion from the higher permeability zone into the lower permeability zone - the opposite diversion from that predicted using a viscosity-velocity correlation! The difference this makes to predicted placement is illustrated by the following example from a field case.

Near Well Formation DataThe near wellbore formation data were obtained from well log data and the Full Field Model, as supplied by the Operator. For simplification, the permeability and porosity terms were taken as noted below.

Perforation 1 (heel section - well assumed to be completed across 2 layers)Permeability 200mDPorosity 0.3Total Length: 70ft

Perforation 2Layer 1 Permeability Porosity Length:

(middle section - well assumed to be completed across 3 layers)Layer 2 and Layer 3

70mD Permeability 200mD0.15 Porosity 0.380 ft Combined length: 170 ft

Perforation 3 (Toe section - well assumed to be completed across 2 layers)Layer 1 and Layer 2 Layer 3Permeability 70mD PermeabilityPorosity 0.15 PorosityLength: 100 ft Combined length

200mD 0.3 50 ft

Simulations were conducted to compare the predicted placement when applying a conventional aqueous squeeze (viscosity ~ 0.32 cP at reference reservoir condition) to that predicted when all treatment stages (pre-flush, main treatment and overflush) were viscosified to 5 cP or higher. In addition, to simulate non-Newtonian behaviour, a velocity thinning solution was injected based on the following parameters described in Table 2. For the purposes of this calculation, the methodology for simulating a shear thinning fluid in the ECLIPSE model was approximated accordingly to those proposed in the ECLIPSE manual, by simplifying the correlation to a ‘velocity thinning’ fluid (flow velocity vs. apparent viscosity).

Flow velocity, ft/day Multiplier

viscosity,cP

Flow velocity, ft/day Multiplier

viscosity,cP

0.00 1.000 20.00 160.48 0.044 0.890.32 0.991 19.81 192.58 0.040 0.810.80 0.600 12.0 224.67 0.037 0.751.60 0.443 8.86 256.77 0.035 0.708.02 0.198 3.96 288.87 0.033 0.6616.05 0.140 2.80 320.96 0.031 0.6332.10 0.099 1.98 1604.81 0.014 0.2864.19 0.070 1.40 2407.21 0.011 0.2396.29 0.057 1.14 3209.62 0.010 0.20128.38 0.050 0.99

Table 2: Velocity thinning correlation table for input into the ECLIPSE simulation file for approximating a shear thinning fluid injection

Results for comparing the predicted placement along the near wellbore formation for the aqueous treatment, viscosified treatment and a ‘velocity’ thinning treatment are presented in Figure 8 below. For a standard unviscosified aqueous injection at an injection rate of 7 bpm, the majority of fluid (71% of injected volume) is predicted to enter the higher permeability/lower pressure mid section of the well. Of the remaining injection volume, similar amounts of fluid are predicted to enter the heel (13%) and toe (15%) sections of the well. Similar placement predictions were obtained for a non-viscosified aqueous injection stock using the Place iT model.The predicted placement of a non-Newtonian injection fluid was then examined using both Place iT (modeling true shear thinning behaviour) and Eclipse (using the velocity-thinning approximation of shear thinning behaviour). When the velocity-thinning approximation was used in Eclipse, a substantial improvement in placement was predicted for the high permeability heel region of the well, with 37% of the injected volume entering this zone (176% increase in placement volume in this zone, compared to the placement for an unviscosified brine solution). This increased volume came at the expense of the mid section of the well, where 45% of the injected volume was placed (37% decrease in placement volume), with a slight improvement in placement in the toe region (18.0% of placement volume, 18% increase in fluid placed in this zone). However, a markedly different placement pattern is obtained when the placement of a true shear-thinning fluid is modeled in this well using the purpose- built near wellbore placement model. In this case, the fluid volumes placed in the heel and mid sections of the well are decreased, with 11.9% of the total injected volume entering the heel (10% decrease with respect to unviscosified placement) and 64% entering the mid section (11% decrease in placement volume). The placement in the toe section is predicted to increase using a shear thinning fluid, with 24% of the injected fluid entering this zone (36% increase in placement volume).

Thus, a ‘velocity thinning’ fluid is predicted to divert a substantial amount of fluid into the heel of the well at the expense of the mid section, with little change in placement in the toe. In contrast, the shear thinning injection diverts flow from the mid section to the heel. It must be emphasized again that the velocity thinning fluid is an abstraction used by Eclipse to approximate the behaviour of a shear­thinning fluid. The above example demonstrates that correlating superficial velocity to viscosity to approximate shear thinning fluid behaviour in a heterogeneous formation will in general give misleading results if used to model placement in the near wellbore region.

Summary and Conclusions

In summary, self diversion of injected fluids from the most favoured flow path (higher permeability and/or lower pressure zones) can be achieved by using the shear thinning behaviour of certain polymer solutions. When such fluids penetrate the formation, they experience an in situ viscosity which is in general higher in the lower permeability zone than in the higher permeability zone. This results in a higher in situ viscosity in the higher permeability zone, which promote more fluid flow into the lower permeability zone.While a number of excellent reservoir simulator packages are available, they have in general been designed to model Newtonian fluids and are unable to properly model shear-dependent flow behaviour. While an option for modelling shear-thinning fluids is included in Eclipse, this is designed for use with

EOR polymer flooding studies in homogeneous reservoirs. The approximation used by Eclipse of a ‘velocity-thinning’ fluid is reasonable under these flow conditions, but breaks down when attempting to model flow in the near wellbore region of heterogeneous wells. A new near-wellbore placement model has been constructed as part of an ongoing Joint Industrial Project to model appropriately the behaviour of shear thinning fluids in such squeeze treatments, which has been used to simulate placement in a number of field cases.44 The developed Place iT model is used to predict more accurately the potential benefits of using such fluids, and this has been demonstrated in recent field applications.43,45

ACKNOWLEDGEMENTS

The authors would like to thank the following sponsors of the SIPSS JIP for their support: BP, Champion Technologies, Clariant Oil Services, Nalco, Norsk Hydro A/S, Petrobras, Petronas, Shell and Statoil.

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Figure 1: Schematic of Enhanced Placement Concept: (a) Injected fluid enters high permeability zone (b) In situ viscosification diverts fluid into lower permeability zones (c) Viscosity breaks on resumption of production.

Figure 2: Typical Viscosity-shear rate profile for a shear thinning fluid

Lower Newtonian region (approx, constant viscosity)

Power Law region = K/^5 3000

Upper Newtonian region (approx, constant viscosity)

0.0001 0.001 10000 100000 1000000 10000000 1E+08

Shear rate (s'1)

Shea

r rat

e Fl

ow v

eloc

ity

Figure 3: Superficial flow velocity profile during injection of fluid into a heterogeneous two-zoneformation

------- Higher permeability Zone

— - Lower Permeability Zone

Injection Time

Figure 4: Shear rate profile during injection of fluid into a two-zone heterogeneous reservoir

-----Higher Permeability Zone-----Lower Permeability Zone

Injection time

►

►

►

Figure 5: General dual model for injection of a fluid into porous medium.

Figure 6: Illustrating the 1-well model employed for Eclipse calculations

% of

Tot

al V

ol. in

ject

ed

% of

Tot

al V

olum

e Inj

ecte

d

Figure 7: Comparison of Newtonian fluid placement calculated with 'Place iT in house model and Eclipse,Nelson Well N19z

Injection Rate = 7bpm, permeability contrast @ 70/200 mD, Porosity ratio = 0.15/0.30

□ 7 bpm In-House

□ 7 bpm - ECLIPSE Simulation

Middle

Figure 8 Comparing placement of water (ECLIPSE), Velocity thinning' fluid (ECLIPSE) and shear thinning fluid (Place-IT) at 7bpm injection for well N19z Nelson field.

mixed high l low k zonePredicting increase in

placement along high k zoneixed high 8 low

k zonemixed high 5

low k zone

high k zone

mixed high 5 low k zone

mixed high 5 low k zonemixed high 5

low k zonehigh k zone high k zone

ECLIPSE - water.7bpm ECLIPSE - 'velocity thinning'Jbpm Place-IT Shear Thinning (n=0.4, k-150)

■ heel □ middle □toe