Chapter 34
Acid Wormholing in Carbonate Reservoirs Validation of Experimental Growth Laws Through Field Data Interpretation Olivier Liétard and Gérard Daccord Dowell Schlumberger, BP 90, 42003 Saint-Etienne Cedex, France Actual responses of two carbonate petroleum reservoirs to matrix injection of hydrochloric acid are compared with a recently proposed experimental model for wormholing. This model i s shown to be applicable i n undamaged primary poro sity reservoirs, and should be useable i n damaged double porosity ones. Formations of no primary porosity are shown to respond very differently. The dissolution channels (wormholes), obtained under certain conditions of attack of carbonate rocks by hydro chloric acid, have been recently proven to have a f r a c t a l geometry. An equation was proposed, relating the increase of the equivalent wellbore radius (i.e. the decrease of the skin) to the amount of acid injected, i n wellbore geometry and i n undamaged primary porosity rocks. This equation i s herein extended to damaged double porosity formations through minor modifications. Two cases of initially undamaged reservoirs have been selected for proper validation of modeling equations. From pressure and rate data recorded all along their treatment, the skin variations during acid attack are derived accor ding to a recently published methodology. Their analysis validates the proposed model. This would mean that wormholes i n reservoirs do scale up with laboratory ones according to the proposed law.
One third of the world production of hydrocarbons originates from carbo nate reservoirs, which, i n addition, are supposed to contain half of the reserves of these compounds (1). The economical importance of such reservoirs i s therefore large enough to j u s t i f y the research of new methods aiming at better producing o i l from these rocks. Most of these reservoirs have natural permeabilities below 10 mD, and the stimulation of their production i s achieved through acid fracturing operations. Viscosified hydrochloric acid i s pumped into wells at pressures larger than formation parting pressure. Irregular etching of the fracture walls by the acid i s expected to create highly 0097-6156/89/0396-0608$06.00/0 © 1989 American Chemical Society
34. LIETARD AND DACCORD
Acid Wormholing in Carbonate Reservoirs
conductive channels which remain open to o i l flow when the injection pressure i s released and the fracture heals up. Some carbonate reservoirs are naturally f a i r l y permeable (more than 10 mD) and are not candidates f o r acid fracturing. Such a treatment would neither be technically feasible (large f l u i d loss rates would prevent fracture propagation) nor boost originally large productivities. However, wells d r i l l e d through such rocks usually demonstrate produc tions lower than one could expect according to their permeability. This is the consequence of the presence, around the wellbore, of a zone of reduced conductivity, refered to as damage. Many causes of damage have been recognized (2). In carbonate reservoirs, the most common ones are invasion by d r i l l i n g muds and precipitation of scales or petroleum heavy ends due to the production pressure drop at wellbore. The damaged zone has variable extension and severity, the l a t t e r being defined as the ratio of undamaged to damaged permeabilities, k and kd respectively. This zone i s responsible for an additional, large resistance to o i l flow, dramatically impairing production. When i n i t i a ting production by imposing a given pressure drawdown AP, part of the latter i s lost through the damaged zone. This results i n lower produc tion rate Q and productivity index Q/AP. The d i f f e r e n t i a l pressure through the damaged zone i s given by : u
where LL i s the viscosity of the flowing f l u i d and h the height of the producing interval. The skin 5 i s a coefficient representative of the characteristics of the damaged zone : [k(r
*
(2)
where r i s the wellbore radius, rj the radial extension of the damaged zone, and k(r) the permeability profile throughout i t . When the seve r i t y i s constant from r to r ^ , Equation 2 reduces to (3) : w
w
'-(s-O-G)
oo
V r with r
w
< r < r , and k(r) = k e
0
V r > r. e
Therefore, the problem reduces to the definition of the relation linking r with the volume V of injected acid. In (9), the following equation was proposed for 3D-radial acid injection into an undamaged primary porosity reservoir : e
34. LIETARD AND DACCORD
It
Acid Wormholing in Carbonate Reservoirs 611
V
l +
A(N „D,Q...)x( -) a
where A i s a slowly varying function. Q, h, r r and V are defined as before, i s the i n i t i a l rock porosity, and D i s the d i f f u s i v i t y constant, df i s the f r a c t a l dimension of the wormholing structure, experimentally determined as being equal to 1.6 ± 0.1 (11)6 i s a constant that reflects the relative conductivity of wormholes compared with the rock permeability. It i s equivalent to the constant B in (10), and was given a value of 1.7xl0 S.I. units i n (9). N, the acid capacity number, i s defined as i n (12) : wt
e
4
ac
_ "
C
~
M-+)P
(
'
where C i s the acid concentration, M the molar weight of the chemical species constituting the rock, p the density of the l a t t e r , and {3 the stoechiometric coefficient of the reaction (2 i n the case of carbonate and hydrochloric acid). One d i f f i c u l t y i n Equation 6 l i e s i n the determination of the d i f f u s i v i t y constant for highly concentrated acids over a broad range of temperature. However, available data (13), combined with viscosity values of hydrochloric acid, lead to estimates shown i n Tables I and II for the f i e l d cases that w i l l be described later on. This wormholing model was shown to agree with previously published experimental data (14). Extension to Damaged Double Porosity Reservoirs Most of the carbonate reservoirs consist i n thick layers of double porosity rocks. There are few limestones, such as chalks, that show primary porosity only (voids being intergranular spaces). On the other hand, there are also some deep dolomites of secondary porosity only : intergranular spaces have disappeared due to large overburden pressures and diagenetic recrystallization. Their secondary porosity consists in cracks, fissures, fractures, faults and vugs. The vast majority of carbonate reservoirs l i e in between these two extremes. The main part of their permeability (50-500 mD) originates from a pattern of diagenetic and/or tectonic fissures (secondary porosity), whereas the permeability of a piece of rock containing no cracks i s much lower, in the order of several milliDarcies. In double porosity carbonate reservoirs, whatever the nature of the damaging materials, the damage i s preferentially located i n the secon dary porosity, and i t s distribution seems f a i r l y regular. Considering a thin s l i c e of reservoir at a given depth, a good approximation of i t s permeability p r o f i l e along any direction perpendicular to the wellbore axis i s the following (Figure 1) : - from r to r«f, a crown of damaged rock wherein the original double-porosity-related permeability fcnp has been reduced to i t s sole primary porosity contribution kpp, natural fissures being almost completely f i l l e d with and sealed by damaging materials (such as d r i l l i n g mud cakes, for instance) ; - from r
