J. Cent. South Univ. Technol. (2008) 15(s1): 362-368

DOI: 10.1007/s11771-008-381-4

Discussion on rheology in petroleum and nature gas teservoir stimulation

LU Yong-jun(卢拥军), LIANG Chong(梁 冲), XU Yun(胥 云), CHEN Yan-dong (陈彦东)

(Research Institute of Petroleum Exploration and Development-Langfang, LangFang 065007, China)

Abstract: Petroleum and nature gas not only are important resources, but also are important strategic materials of our country. All methods the enhancing the producing degree of petroleum and natural gas reservoir, increasing single well production and extending the stimulation period of validity are important stratagem for petroleum and natural gas exploitation. Fracturing and acidizing are the main methods for stimulation as well as one of representative examples of rheology theory application in engineering. Based on analysis of low permeability reservoir characteristics, the fracturing and acidizing stimulation principles and main controlling factors were discussed. And the mechanical characteristics, chemical reaction and rheological behavior in the stimulation process were reviewed. Furthermore research trends afterwards including the material and fluid rheology in oil and natural gas production process, the deep rock fracture initiation and extension rheology, and the fracturing and acidizing application rheology were also proposed in this paper.

Key words: fracturing; fracturing fluids; acid fracturing; acid fluids; low permeability; petroleum; rheology

1 Introduction

Low permeability reservoirs that should be stimulated to exploit economically, are of large proportion of these hard producing reserves in China. Fracturing and acidizing technology originated from 1947, has been applied over 60 years, which now becomes a mature, developmental and effective engineering technology, and has been applied worldwide.

Fracturing and acidizing technology uses characteristics of fluid that can transmit pressure to inject non-Newtonian fluid into porous medium by high pressure, so that the physical or chemical properties of internal structure of porous medium change, the cracks are formed, and the rock permeability changes. As a result, the oil and gas wells production increases and the water wells injection rate increases. The technology is one of representative examples of rheology theory application in engineering^[1], including polymer rheology of new acid fracturing fluid system and acid liquid system^[2-6], rock rheology^[7-8], application rheology, rheological reaction dynamics. As for different exploitation methods of different oil and gas reservoir and different development phases, the selection of liquid system, selection of processing parameters, determination of reconstructing scale are all strictly required. Therefore, it is very necessary for us to understand this technology more deeply from rheology aspect, meanwhile the fracturing and based on acidizing technology applications for a variety of complex reservoirs, the study on reservoir characteristics has furthered from a single layer with low porosity and permeability to the complex lithology and nature fractures as well as igneous rock formation that becomes a hot spot in recent years. From the rheology aspect, modern rheology research of production stimulation has been changed gradually from the traditional theory on the uniform continuous medium to the exploratory study on non-uniform and non-isothermal, multiphase medium.

2 Basic characteristics of low permeability oil and gas reservoirs

Low permeability oil and gas reservoirs are of low porosity, low permeability, low abundance and low production. Their features include following items^[9-10]:

1) Low porosity and permeability, resulting in low natural production of oil and gas wells;

2) Very complex pore structure, making the oil and gas migration process more difficult and the control area of a single well small;

3) Reservoir heterogeneity and anisotropy are obvious, which is hard to predict and describe formations rich in hydrocarbon;

4) High clay content and strong water sensitivity, making particles form pore throat migrate and clay inflate easily;

5) These reservoirs are of high starting pressure, making water injection and gas injection difficult, the formation pressure drops rapidly;

6) Formation damage may occur during fracturing and acidizing process, including water sensitive damage of external fluid, residues damage and severe gas or water breakthrough.

The comprehensive interaction among reservoir lithology, physical properties, temperature and pressure characteristics, pore throat structure, surface wettability of the rocks and oil and gas fluid properties makes low-permeability reservoir unique relative to the middle and high permeability reservoirs. Stimulation  technology, especially the application of fracturing and acidizing technology, is very important for exploiting the low permeability reservoirs economically and effectively.

3 Stimulation principles and main factors controlling production^[11]

Crude oil and natural gas are stored in the formation, the acidizing and hydraulic fracturing of matrix rock can improve or even enhance the natural reservoir connectivity between well bores and reservoirs. During the production process, an equation that expresses productivity of a single well is shown as follows:

＝                         (1)

where  q is oil or gas flow rate; K is absolute permeability; h is the formation thickenss; p is boundary pressure of reservoir; p_wf is bottom hole flowing pressure; r_e is reservoir radius; r_w is effective well bore radius; S is comprehensive skin coefficient.

3.1 Stimulation method of acidizing

Acidizing technology is that the acid liquid is injected into reservoir solves formation minerals near wellbore to relieve formation damage near wells, to vary skin factor of close well bore, to recover and enhance formation permeability near wells, and to enhance oil and gas productivity or water injectivity, under the condition that the bottom operating pressure is smaller than reservoir rock breakdown pressure. Acidizing method can reduce the majority of the skin factors, but the skin factor is a combination of a series of factors, most of which is that the conventional matrix rock stimulation technology cannot change, thus, the deep sand fracturing and acid fracturing technology are required.

3.2 Acid fracturing technology

Acid fracturing technology is that the acid liquid is squeezed into formation, opening the formation. The acid liquid reacts with rock wall forming gaw (Fig.1) so that

Fig.1 Acid liquid etched gaw

channels and fractures are formed after the squeezing stopped, finally, the formation is stimulated and oil and gas production and water injectivity are enhanced, under the condition that pressure is higher than formation breakdown pressure.

In addition, the breakdown of reservoir rock mechanics is involved in the process in this research, and the complex acid rock interaction mechanism is also covered. Understanding degree of acidized fracture conductivity is far behind that of sand fracturing proppant fractures. By the effect of rock heterogeneity and fingering phenomenon that hydrochloric acid behaves as non-Newtonian flow through the formed channels, the non-uniform etching in acidizing forms artificial fracture profile, meanwhile, the earthworm holes occurring on fracture profile make acid etched rock surface uneven, which causes forming a number of “pillars” to support the channels on horizontal direction(Fig.2). Therefore, the fracture conductivity depends on the acid etching patterns, rock strength and closure stress.

Fig.2 Acid liquid etched wormhole mold

3.3 Sand fracturing technology

3.3.1 Changing liquid flow regime under formation

During the producing process, the pressure gradient forces fluids to flow through pore medium(Fig.3). For many reasons, there is an additional pressure drop near well bores, which changes radial (horizontal) direction flow and makes fluids flow toward well bores. The mechanism of radial direction flow is that the pressure difference increase of reservoir is directly proportional to the logarithm of distance. If the permeability near well bores decreases greatly, the majority of total pressure gradient is depleted near well bores. Artificial cracks formed after sand fracturing stimulation alters single radial direction flow, thus fluids flow into artificial cracks first, then flow toward well bottom monodirectionally, greatly reducing energy depletion.

Fig.3 Flow regime diagram plot before and after stimulation

3.3.2 Increasing oil drainage area

Long and high conductive artificial fractures are formed after fracturing and acidizing, PRATS et al proposed the relation between proppant fracture and effective well bore radius considering pore pressure field around fractures as follow:

                                  (2)

CINCO-LEY et al (1978) set up the function between dimensionless conductivity and equivalent well bore radius for pseudo-radial flow. It is apparent that high conductive artificial cracks extend oil drainage area, which can increase single well production(Figs.4 and 5).

Fig.4 Oil drainage area before stimulation

3.3.3 Multi-fracture stimulating mechanism

For hypothetical double-wing shaped symmetrical fractures in current hydraulic fracturing simulation, its stimulating mechanism mainly depends on fracture length or its conductivity. If there are fracture branches, the area that fracture control will extend correspondently, making natural fracture evolved and interconnected, thus quite complex fracture network systems are formed, which extremely improve fluid flow channels in reservoirs and enhance oil well productivity in a great extent. Therefore, oil wells will remain everlasting high productivity after fracturing, making ultralow permeability reservoirs development more economical.

Fig.5 Oil drainage area after stimulation

4 Rheology in reservoir stimulation

4.1 Fracture creation by water horsepower^[12]

Deep stimulation processes with fracturing and acidizing include rock initiation, fracture extension and proppant transport and placing or acid react with rock form heterogenic etched fractures. However, the processes of formation rock initiation and fracture extension is the typical rheology behavior that injected liquid creates fractures with high liquid horsepower. Rock and fluid mechanics and fluid loss theory are the basis to control the created fracture size and geometric shape. The liquid pumping velocity is faster than its diffusion in formation, which forces formation pressure to elevate unavoidably. Thus, the formation starts to break when the formation pressure reaches the value of breakdown, and a definite ‘net pressure’ sustain fractures to extend.

Fracturing rock mechanism includes fracture mechanics and fracture tip effects. Mechanic properties of fracture tip are proposed to explain the effect of rock resistance on fracturing pressure. Tensile strength and shear-resistant rheology of rock influences the horsepower magnitude for creating fractures. Fluid mechanics research includes liquid viscosity, pumping rate and the loss properties of porous medium. During the fracturing extending process, inner facture pressure gradient is determined by rheology of fracturing fluid, liquid flow velocity and fracture width. Theories about controlling fluid flow in fractures are “conservation of momentum” and “lubrication theory”, where the increase of flow resistance will be more serious when the fracture extends to high stress barrier bed. Therefore, keeping up a definite ‘net pressure’ is necessary for fracture extension. In 1970, NOLTE used coefficient β to characterize the effect of pressure gradient and established an Eqn.(3) considering the fluid flow in fracture and rheology which influence pressure to characterize the relationship among well bottom pressure, rock closure pressure and net pressure caused by water horsepower.

                  (3)

4.2 Dispersing, soluting, viscosity increasing and cross-linking properties of polymer in water or acid solution^[13-15]

When estimating liquid performance, we should consider substantially about the compatibility and low damage of pumping liquid, meanwhile we should also consider about the rheology of fracturing fluid and acid liquid. Pipeline friction resistance, liquid leakoff and retarding performance of acidizing system are all related with the rheology of fracturing fluid and acid liquid. The polymer concentration and its relative molecular mass can directly affect the rheology of final fracturing fluid and acid liquid system. Furthermore, the dispersing and soluting properties of polymer solution and acid liquid are affected by temperature, pH value and stirring rate. When the polymer disperses in solution, the non-sequence structures are formed by single molecules gradually grow into random plate entangled shapes whose entangling degree is strengthened as polymer concentration increases. Therefore, solution viscosity can be seen as a function of polymer concentration. Chemical cross-link will occur when the concentration reaches at critical overlapped value while inter-crosslink of polymer will not occur but the inner crosslink of polymer by adding crosslink agent when concentration is lower than critical overlapped value. Crosslinking of polymer solution modifies thess fluid viscoelasticity, which is of great engineering application values for further reducing the leakoff amount of porous medium and flow frictional resistance, increase the fracture fluid efficiency and sand control capacity.

4.3 Flow and friction properties of complex fluid in pipeline and fractures

When fracturing fluid and acid liquid flow through pipeline, perforating holes and artificial fractures, their rheology play important roles, which is the same as frictional resistance plays an important role on wellhead pressure, liquid viscosity plays an important role on fracture width and Qμ value of natural fracture formation plays an important role on eliminating multi-fractures.

4.3.1 Studies on liquid friction properties

Friction values of well bore can be approximately obtained by analyzing liquid rheology and numerical solution of power law fluid flow equation from their theory, however, its discrepancy is large. Foreign and domestic researchers usually use indoor experiment data and in-situ test data to quantitively analyze the liquid friction including indoor multi-function loop test, in-situ pump instant shutoff and step down minifrac test for analyzing perforation holes and near well bores friction.

The value of perforation fraction is affected by the number, diameter of holes and perforating phase. The effect of actual fraction of perforating holes on fracturing pressure is usually neglected, and sand crush, acid erosion can further reduce pore hole fraction. The following Eqn.(4) is used to calculate pore hole fractional resistance.

                       (4)

where  q is the total flow rate; ρ is fluid density; n is the number of perforating holes; D_p is perforating coefficient; C is coefficient of pore holes.

Near-wellbore effect includes well bore connection (perforation), tortuousity (fracture turning and twisting), phasing misalignment, and rock tight and multi-fracture caused by the above factors, whose uncertainty makes it difficult to forecast near-wellbore effect. And fracture turning and multi-fracture are the principal factors that affect the near-wellbore effect. Before turning, fractures first open along the orientation that deviate a big angle from or is vertical to the maximum of principal stress, Fracture width and prevent the opening of the stress difference is inversely proportional, but the pressure within fractures is directly proportional to the stress difference. In addition, frictional resistance increases when sanding liquid flow through fractures with smaller width, all of which can result in that actual observed pressure calculated or during working process is higher than that predict. Mechanism that multi-fractures cause the increase of near-wellbore effect is similar to the above one.

4.3.2 Effect of flow in fractures on fracture width^[16-17]

Liquid viscosity μ and injecting discharge capacity q_i are the central parameters for fluid flow in fractures, which is the key to proppant transportation and affects net pressure as well fracture height and width. Net pressure is expressed by

                       (5)

Based on rock linear-elasticity theory and rheology of Newtonian fluid, the relationship between opened fracture width and fluid flow parameters is given in the following expression:

                              (6)

where  w_max is the maximum of fracture width; p_net is net pressure; d is fracture height; E′ is plane strain modulus, which is expressed as E′=E/(1-v²).

According to the study on viscous force only, net pressure in fractures is a function of modulus, height and (q_iμ)^1/4. Obviously, flow parameters of liquid in fractures affect the net pressure, i.e. fracture width. Discharge capacity can be proximately elevated by twice as before calculated by Eqn.(6), fracture width increases by 20%, and power law value of non-Newtonian fluid is about one third.

4.3.3 Effect of liquid rheology on multi-fracture and ‘fracture network’ formation^[18]

As for the formation that natural fractures are abundant, it is needed to stimulate to form long propped fractures. The effect of main fractures and natural fractures on further extended orientation was studied in WARPINSKI and TEUFEL (1981~1987) work. And BEUGELSDIJK and PATER et al (2000) carried on indoor studies what pointed out how to reasonably select initial fracturing fluid and the value of q_i×μ in stimulation to avoid multi-fracture according to rheological parameters of injecting liquid.

As for low permeability reservoir and particular low permeability reservoir, ability that formation matrix supplies oil and gas to fractures is so poor that it is difficult for a single fracture to obtain expected stimulation effectiveness. Researchers in Langfang developed the ‘fracture network’ technology that analyzes mechanics mechanism of fracture network generation for a definite formation and achieves ‘fracture network’, through which the fluid flow parameters can be controlled to modify stimulating net pressure. Equally it is required to keep on balance between fracturing fluid viscosity and loss when using ‘tip screen-out’ fracturing technology build up ‘fracture network’ system.

4.3.4 Analysis of friction pressure properties of fluids containing proppant

Solid-liquid mixed sand carrier and its rheology are the key elements that affect the transport and placing of hydraulic fracturing proppant in fractures. Friction pressure of fluids containing proppant increases as proppant concentration increases. For both laminar flow state and turbulent flow state, SHAH and LEE (1986) studied the alteration of incremental magnitude of frictional pressure with flow velocity, and established the equation of incremental magnitude of friction pressure caused by proppant for turbulent flow state:

                         (7)

where  is fraction pressure ratio between sand carrier and non-sand carrier; μ_r is apparent viscosity ratio between sand carrier and non-sand carrier; ρ_r is density ratio between sand carrier and non-sand carrier; m is slope of logarithmic plot between fractional resistance and Renault Number (Hannah et al took it as 2).

4.4 Fracturing fluid loss and gel breaking properties at different temperature and pressure^[19]

Fracturing fluid loss influences the created fracture length and fracture shut off time, therefore, controlling fracturing fluid loss can further curtail formation damage. Although waste damage can be eliminated by decreasing guar gum concentration, rheology modification caused by it may lead to more liquid loss. Under in-situ condition, there are three types of fracturing fluid loss: 1) translocation and compression of reservoir fluid; 2) loss liquid or fracturing fluid invasion into formation; 3) the formation of external filter cake. Temperature can change fluid rheology and overlay with pressure increase liquid loss and accelerate the formation of filter cake. The formation of filter cake is proportional to loss volume, but it should be guaranteed that fracturing fluid flow back clean after stimulation, a common way is to add proper scaled gel breaker into fracturing fluid during pumping process. Gel breaker has obvious effect on fracturing fluid viscoelasticity, and increasing temperature accelerate fracturing fluid gel breaking.

4.5 Proppant carrying flow and placing behavior of solid-liquid mixed fracturing fluid^[20]

In fracturing process, slurry proppant transport is mainly affected by gravity, buoyancy and viscous force, and its sand carrying behavior is directly affected by fracturing fluid rheology. Since fracturing fluid is non-Newtonian fluid, their apparent viscosity and viscoelasticity not only depend on the shear stress and forced stress, but also are affected by temperature, fluid loss and chemical gel breaking greatly. The viscosity of fracturing fluid will greatly reduce when flowing through pipeline, tubing and perforation holes, the shear rate slows down after arrival fracture but the temperature increased. The two situations caused fracturing fluid rheological characteristics changed. There is little research about the sand control slurry, which depends on the flow of fracture geometry, temperature, time, proppant size, density and concentration. More recently, proppant transport has been evaluated in large slot-flow devices at commercial testing labotatories, established the relationship between apparent viscosity and shear rate. The studies of GARDNER and EIKERTS (1982) showed that viscosity changes of the liquid for the concentration and shearing affect just the opposite. MEYER et al (1986) carried out a series research by an alternative rheological measurement to calculate settlement rate of proppant, and respectively established laminar and turbulent flow state’s relationship between proppant settling rates and liquid properties, the function of the behavior index.

Proppant has a great effect on rheology of fracturing fluid, whose viscosity of slurry is higher than that of pure fracturing fluid. GARDNER in 1982 found that the viscosity of a crosslinked fracturing fluid increased up to 230% with the addition of 6ppa proppant concentration. Nolte in 1988 found that the equation of power law fluid is similar to the equation of Newtonian fluid, but only power index increases to n:

                 (8)

Rheology of fracturing fluid influences the proppant migration. Under shear gradient conditions in a pipe or fracture slot, proppant particles can move to the center of the fluid for viscoelastic fluids or toward the wall for non-Newtonian fluids that are not viscoelastic. TEHRANI reported the control of particle migration by the elastic properties of the suspending fluid and the shear rate gradient which are characterized by liquid rheology, including shear viscosity and normal stress as functions of the shear rate and G′ and G″ as functions of the frequency.

Particle concentration has the effect of increasing the frequency of interparticle interactions. The bulk viscous stresses that drive particles together are a strong function of the suspension viscosity, which is a function of the particle volume fraction. The main effect is that the resistance encountered by a particle to movement in the suspension increases with the particle volume fraction. Phenomenon that particles migrate away from high concentration zones to low-concentration zones was observed by GADALA et al in 1980 and its mechanism that is referred to as shear-induced self-diffusion was explained by LEIGHTON et al in 1987.

4.6 Reaction between non-Newtonian acid liquid and rock and feature of acidized fractures

Gelled acid, viscoelastic acid and crosslink acid with high viscosity and viscoelasticity are all non-Newtonian fluids. Acid liquid rheology is of great significance in engineering application, can reduce friction pressure and acid filtration and reaction rate, forming long etched fractures(Fig. 6). Effective distance of acid liquid and etched conformation on fracture surface is determined by acid-rock reacting velocity. Mechanisms that determine acid-rock reacting velocity include: 1) ions in the liquid move orientally by concentration difference which force ions to move from high concentration area to low concentration area, and ion transfer is much faster at greater concentration difference; 2) the greater the flow rate of acid liquid, the faster the convection and ion transfer. H⁺ ion’s movement style includes diffusing transfer and convecting transfer which is the key part. The parameters that influence diffusion and convection include temperature, acid liquid concentration, flow rate of acid liquid in fractures, acid liquid viscosity and type, and rock type. Mechanism that rheology affects acid-rock reaction is that acid liquid viscosity relays the transfer of H⁺ ion toward fracture surface and that gelled agents adsorb at fracture surface to retard the connecting degree between acid and rock surface.

Rheology of acid liquid equally affects fracture etched conformation much. We use rheology of acid liquid to control acid-rock reaction to form different fractures and earthworm pores, meanwhile, to make effective acid liquid transport much more distantly. We inject liquids with different viscosity forming fingering phenomenon.

Fig.6 Rotating disk shape after dissolution reaction: (a) 90 ℃ Gelled acid; (b) 90 ℃ ordinary acid

4.7 Fluid surface/interface chemical characteristics and flow-back behavior^[21-22]

Fluid injected into porous medium and artificial fractures should be firstly flown back to ground after fracturing and acidizing stimulation to reduce residual waste in propped fractures, thereby, reservoir permeability is enhanced, as a result that compressed oil and gas are produced subsequently. This flow-back behavior is not only affected by fluid viscosity after fracturing fluid and acid liquid breaking or acid-rock interaction, but also affected by surface/interface chemical characteristics of fluid injected into formation. Fluid characteristics such as surface tension, interfacial tension, dynamic angle and viscosity directly determine the fluid wettability, adsorption and retention on porous medium surface and influence final flow-back efficiency. As for common vegetable gel polymer fracturing fluid, there is waste and residue gel, a kind of visco-elastic micelle fracturing fluid (no polymer) which is developed abroad and inland. Efficient discharge aiding agent decreases the surface tension between fracturing fluid and acid liquid filtrate, which reduces water lock effect greatly, meanwhile that surfactant coalesce dispersing agent can curtail the block of propped fracture/pore throat caused by the coalescence among broken fragments in gel broken liquid.

5 Development direction of rheology in low permeability reservoir stimulation

Low permeability oil reservoir stimulation is considered as the main technology and method to increase reserves and enhance production in oilfield whose research field and contents involve rheology in many aspects. The rules and methods of rheology studies are of great significance to guide the development and production of oil and gas. For petroleum engineering rheology in low permeability oil and gas reservoir stimulation, we should further strengthen and develop the studies on the development of fracturing and acidizing materials and fluid rheology, the deep rock breakdown and extension rheology, and application rheology of fracturing acidizing engineering.

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(Edited by HE Xue-feng)

Foundation item: Projects(10472134, 50490274) supported by the National Natural Science Foundation of China

Received date: 2008-06-25; Accepted date: 2008-08-05

Corresponding author: LU Yong-jun, Doctor candidate; Tel: +86-010-69213437; E-mail: lyj3437@163.com