A Model for Predicting Injectivity Decline in Water-Injection Wells

Abstract

Summary We propose a new method to predict the injectivity decline for water-injection wells. Both internal and external filtration are considered in this method. A transition time from internal to external filtration is calculated by use of the trapping efficiency obtained from Stokesian dynamics simulations. The radius and the permeability of the damage zone are calculated by use of a deep-bed filtration model. Equations are derived that allow us to combine the flow resistance in the external and internal filter cakes to obtain the overall decline in injectivity. Introduction A substantial proportion of oil produced in mature fields is produced by waterflooding. Suspended solids in the injected water will cause the injectivity of the injection well to decline with time. Filtration usually can reduce the concentration of suspended solids, but the cost of water treatment must be balanced against the cost of other alternatives, such as periodic stimulation. The prediction of injectivity decline provides a method to specify the water-quality requirements and determine the degree of well impairment. This method allows an operator to design surface facilities to minimize water-injection and well-treatment costs. To predict the loss in injectivity, we need to know the nature of the impairment and its impact on well injectivity. Previous work shows that external and internal filter-cake formation are the most common causes for well impairment (Fig. 1). Various parameters, such as particle/pore size and distribution, injected solids concentration, formation permeability, and fluid velocity, determine whether or not internal or external filter cakes are formed. Several models are available for predicting injectivity decline by use of these parameters and/or core flow experiments. Our objective is to develop a model that properly accounts for both the infiltration of particles and the buildup of an external filter cake at the rock surface. Literature Review Many published studies relate to well impairment or formation damage caused by suspended particles in injected fluids. They generally can be divided into two categories - experimental studies investigating impairment mechanisms by use of core flow tests and models for the prediction of well-injectivity decline. Previously Reported Experimental Observations. Barkman and Davidson1 proposed four mechanisms of well impairment: wellbore narrowing (external cake formation), particle invasion (internal cake formation or deep-bed filtration), wellbore fillup, and perforation plugging. Donaldson et al.2 conducted experiments by flowing colloidal silica suspensions through three types of core plugs taken from Berea, Noxie, and Cleveland sandstones. Their results show that particles initially pass through the larger openings in the core and are stopped gradually by a combination of the effects of sedimentation, direct interception, and surface deposition. The plugging of the core appears to be a combination of internal blockage of pores and cake buildup. They found that the larger particles initiate cake formation. In most cases, the core itself was only partially plugged, but the external cake formed at the face of the core restricted the flow of the suspension. Davidson3 conducted experiments on the flow of particulate suspensions through porous media. A major finding of this work was that the velocity required to prevent particle deposition is inversely related to the particle size. This conclusion is limited to the particular system that the author tested. However, it is the first indication in the literature that there is a relationship between particle movement through porous media and linear-flow velocity. Todd et al.4 conducted particle-plugging experiments on three different core materials. The results of these studies indicate that significant permeability impairment can be caused by inorganic solids, even in very dilute systems. We did not observe the injectivity decline predicted by core studies in the field. The possible reason for this may be the existence of fractures at the wellbore face. Todd et al.5 used aluminum oxide particles in the size ranges 0 to 3, 4 to 6, and 8 to 10 microns. They found the following:The overall damage is related to the mean pore-throat size;The cores damaged with 0 to 3 micron suspensions exhibit damage throughout their entire length; andAs particle size increases, the damage is gradually shifted toward the injection end of the core and to an external filter cake. Vetter et al.6 provided a critical review of past laboratory studies and conducted particle-filtration tests. Their results show that particles of all sizes (from 0.05 through 7 microns) cause formation damage. The larger particles cause a rapid decline in permeability with the damaged region being shallow. Smaller particles (in the submicron range) enter the core and cause a gradual permeability decline. Fluid flow rate is an important parameter for submicron particles from the point of view of permeability impairment. The higher the linear velocity, the greater the depth of particle penetration. Todd et al.7 reported experiments where permeability measurements were made along the length of a pressure-tapped core, 80 mm in length. The core used was a Clasach sandstone with a permeability of 200 to 1000 md and an average porosity of 14.5%. The flow rates were 0.45 to 1.8 cc/sec, particle sizes were less than 3 microns, and particle concentrations ranged from 1 to 15 ppm. The injection time was chosen to be very large (up to 10,000 core pore volumes) to study the importance of long-time injection tests. The results indicate that in-depth invasion occurs for broken-face plugs as compared to external filter cakes, which often occur with sawn-face plugs. Permeability shows a simple semilog decline with gross flow velocity and particle concentration. Smaller velocities and larger particle concentrations result in larger permeability declines. Pautz8 concluded that the 1/3 to 1/7 rule-of-thumb is upheld by coreflooding results when the formation permeability (square root of k) is used to estimate a minimum particle size that would contribute to permeability reduction. When suspended particles in a carrier fluid are flowed through a porous medium, the operative plugging mechanism depends on the characteristics of the particles, the characteristics of the formation, and the nature of the interaction between the particles and the various reservoir materials. The particle/pore size ratio is the most important parameter in the filtration process. It has been found that larger particle/pore size ratios tend to cause rapid, but shallow, damage. Previously reported core experiments do not demonstrate clearly conditions under which an external or internal filter cake is formed. Permeability decline is sensitive to the linear-flow velocity for only very small (submicron size) particles. Particle concentration has less of an impact on permeability impairment for smaller particles. Previously Reported Experimental Observations. Barkman and Davidson1 proposed four mechanisms of well impairment: wellbore narrowing (external cake formation), particle invasion (internal cake formation or deep-bed filtration), wellbore fillup, and perforation plugging. Donaldson et al.2 conducted experiments by flowing colloidal silica suspensions through three types of core plugs taken from Berea, Noxie, and Cleveland sandstones. Their results show that particles initially pass through the larger openings in the core and are stopped gradually by a combination of the effects of sedimentation, direct interception, and surface deposition. The plugging of the core appears to be a combination of internal blockage of pores and cake buildup. They found that the larger particles initiate cake formation. In most cases, the core itself was only partially plugged, but the external cake formed at the face of the core restricted the flow of the suspension. Davidson3 conducted experiments on the flow of particulate suspensions through porous media. A major finding of this work was that the velocity required to prevent particle deposition is inversely related to the particle size. This conclusion is limited to the particular system that the author tested. However, it is the first indication in the literature that there is a relationship between particle movement through porous media and linear-flow velocity. Todd et al.4 conducted particle-plugging experiments on three different core materials. The results of these studies indicate that significant permeability impairment can be caused by inorganic solids, even in very dilute systems. We did not observe the injectivity decline predicted by core studies in the field. The possible reason for this may be the existence of fractures at the wellbore face. Todd et al.5 used aluminum oxide particles in the size ranges 0 to 3, 4 to 6, and 8 to 10 microns. They found the following:The overall damage is related to the mean pore-throat size;The cores damaged with 0 to 3 micron suspensions exhibit damage throughout their entire length; andAs particle size increases, the damage is gradually shifted toward the injection end of the core and to an external filter cake. Vetter et al.6 provided a critical review of past laboratory studies and conducted particle-filtration tests. Their results show that particles of all sizes (from 0.05 through 7 microns) cause formation damage. The larger particles cause a rapid decline in permeability with the damaged region being shallow. Smaller particles (in the submicron range) enter the core and cause a gradual permeability decline. Fluid flow rate is an important parameter for submicron particles from the point of view of permeability impairment. The higher the linear velocity, the greater the depth of particle penetration. Todd et al.7 reported experiments where permeability measurements were made along the length of a pressure-tapped core, 80 mm in length. The core used was a Clasach sandstone with a permeability of 200 to 1000 md and an average porosity of 14.5%. The flow rates were 0.45 to 1.8 cc/sec, particle sizes were less than 3 microns, and particle concentrations ranged from 1 to 15 ppm. The injection time was chosen to be very large (up to 10,000 core pore volumes) to study the importance of long-time injection tests. The results indicate that in-depth invasion occurs for broken-face plugs as compared to external filter cakes, which often occur with sawn-face plugs. Permeability shows a simple semilog decline with gross flow velocity and particle concentration. Smaller velocities and larger particle concentrations result in larger permeability declines. Pautz8 concluded that the 1/3 to 1/7 rule-of-thumb is upheld by coreflooding results when the formation permeability (square root of k) is used to estimate a minimum particle size that would contribute to permeability reduction. When suspended particles in a carrier fluid are flowed through a porous medium, the operative plugging mechanism depends on the characteristics of the particles, the characteristics of the formation, and the nature of the interaction between the particles and the various reservoir materials. The particle/pore size ratio is the most important parameter in the filtration process. It has been found that larger particle/pore size ratios tend to cause rapid, but shallow, damage. Previously reported core experiments do not demonstrate clearly conditions under which an external or internal filter cake is formed. Permeability decline is sensitive to the linear-flow velocity for only very small (submicron size) particles. Particle concentration has less of an impact on permeability impairment for smaller particles.

Experimental investigation of particle suspension injection and permeability impairment in porous media

“…This cake was studied and characterized by several authors. 3,13,21,22 This is confirmed by the observation of an internal cake formed at the inlet of the column (Fig. 9).…”

“…external and internal filter cakes, wellbore fill-up and perforation plugging are responsible for decline in well injectivity. 3 Pang and Sharma 13 stated that internal and external filter cake formations are the dominant mechanisms. The degree of impairment of porous medium over a period of time depends on the concentration of suspended solids in the injected water, the injection flow rate, the porous rock formation and particles characteristics (types of minerals, grain size, pore access size), and the nature of the interaction between the injected particles and the reservoir rock.…”

Mathematical Modelling of Non-Uniform External Cake Profile in Long Injection Wells

“…Particle penetration into the formation stops at the transition moment, when retained particle concentration reaches the ␣-th fraction of porosity. It results in the following expression for transition time as expressed in pore volumes injected (Pang and Sharma, 1997;Sharma et al, 2000): (B-4) where ␣ is the critical porosity fraction, is filtration coefficient, c 0 is the injected particle concentration and r e is the drainage boundary radius. Let us introduce the well impedance as the ratio between the current dimensionless pressure draw-down and its initial value (B-5) Capture of injected particles with consequent permeability decline and formation of external filter cake yield the impedance growth.…”

Deep-Bed Filtration Under Multiple Particle-Capture Mechanisms

“…1 and 3 for T > X is (Herzig et al 1970;Pang and Sharma 1997): Ahead of the concentration front T < X, both concentrations are zero.…”

“…The explicit formula for suspended concentration allows calculation of the constant filtration coefficient from the constant outlet concentration (Pang and Sharma 1997;Wennberg and Sharma 1997). For the more general case when is not a constant, Λ = Λ(S) and the breakthrough curve C(1, T) determines the filtration coefficient.…”