Applications of the Gruesbeck and Collins Model
Gruesbeck and Collins (1982) conducted core flow tests under constant rate and pressure difference conditions and studied the formation damage effects and determined the relevant rate constants. Their data analysis methods and results are presented in the following.
Assuming that ɸ and α essentially remained constant with time during their experiments, Gruesbeck and Collins simplified Eq. 10-119 for a constant injection rate as:
and designed special experiments to verify their model as described in the following.
Case 1 — Particle Deposition and Mobilization in Nonplugging Pathways
First they considered a case where particle mobilization does not occur, and the particle deposition rate is proportional to the particle concentration of the suspension according to
Gruesbeck and Collins (1982) injected a low concentration of a suspension of CaCO3 particles into a column of clean, unconsolidated sand pack. Under these conditions, they assumed that removal of deposited particles was negligible. They measured the concentration of particles in the effluent. Applying Eq. 10-185 with their data given in in this article, Gruesbeck and Collins determined the same |3 value on the average for different flow rates. Therefore, they concluded that the rate law postulated by Eq. 10-180 is valid.
Second, Gruesbeck and Collins neglected the deposition rate and considered that the mobilization phenomena is dominant. Thus, integrating Eq. 10-179 over the length of the porous media and applying the mean value theorem yields:
where Gin = 0 for injection of a particle free solution. In order to test the validity of Eq. 10-186, Gruesbeck and Collins prepared a sand pack by mixing sand and a suspension of CaCO3 particles into a column. Then, a particle free KCl solution was injected into the column. Gruesbeck and Collins, their experimental data and plots of Eq. 10-186 are given, respectively.
Case 2—Particle Deposition in Plugging Pathways
To verify their plugging rate equation, they considered sand packs and suspension of glass particles of various sizes. They estimated the effective pore diameter of the passages between the closest packing of sand grains as the grain diameter, dg, divided by 6.5, dg/6.5. The data of sand grain and glass particle sizes as well as the estimated effective pore diameter to particle diameter ratio. They measured the pressure difference across the sand pack as a function of the pore volume of the suspension of glass beads injected at a constant rate. The deposition process was considered mainly as the pore surface deposition when the variation of the pressure difference was small, and indicated by "5"' in Table 10-2. The deposition was considered due to the porethroat plugging, when the pressure difference indicated a monotonic increase and indicated by "P" in Table 10-2. A rise in pressure difference
to a plateau was an indication of simultaneous pore surface deposition and pore throat plugging, and indicated by "S and P" in Table 10-2. Filter cake deposition was indicated by "FC" in Table 10-2.
Gruesbeck and Collins carried out experiments under conditions favorable for simultaneous surface deposition and pore throat plugging. For this purpose, suspensions of class beads were injected into columns of clean sand packs. The effluent glass beads concentration, pressure difference across the sand pack, and cumulative class bead deposit in the sand pack were measured as a function of the pore volume of suspension of glass beads injected at constant rates. The experimental data are presented in this article. Next, they have solved their model equations, Eqs. 10-121, 111, 112, 114, 115, 116, numerically by assuming trial
values for the various phenomenological parameters to match the measurements. The simulation results are shown in this article. The fact that their model reasonably predicts the experimental observations indicates that their model based on the plugging and nonplugging pathways concept is valid for their experimental systems. When the plugging pathways are eliminated by particle retention, the flow is diverted to the nonplugging pathways. Then the particle retainment continues in the nonplugging pathways as pore surface deposition until a dynamic equilibrium is attained. At this condition, Eq. 10-112 yields the following expression for the equilibrium amount of the deposits in the nonplugging pathways as:
because all flow goes through the plugging pathways. The fact that the cumulative amounts of deposits reach certain limiting values as shown in this article indicative of attainment of such equilibrium conditions. Note, however, that the amounts shown in this article are the cumulative amounts including the amount of deposits in the plugging pathways. Therefore at equilibrium
Constant pressure tests are more representative of the producing well conditions. Gruesbeck and Collins (1982) flowed suspensions of glass particles through sand packs at constant pressure differences by applying relatively high pressure difference to a column of fine sand pack and relatively low pressure difference to a column of coarse sand pack. The results are reported in this article. In the fine sand packs, they observed more deposition near the injection side, and the mean permeability of the sand
pack decreased to zero. Because, in the fine sand pack, almost all the pathways are of the plugging type. Whereas, in coarse sand packs, the deposition tended to occur almost uniformly along the sand pack and the mean permeability of the sand pack decreased to an equilibrium value. Because, in the coarse sand pack, most of the pathways are of the nonplugging types.
Civan et al. (1989), and Ohen and Civan (1990, 1993) also simulated these experiments successfully.
Consolidated Core Tests
Gruesbeck and Collins tested Berea and field cores. First, the Berea cores were tested using
1. 2% KCl brine in a dry core (single phase system)
2. 2% KCl brine and white oil at a 50/50 ratio in a dry core (two phase system)
3. white oil in a dry core (single phase system)
4. white oil in a core at connate 2% KCl brine saturation (two phase)
Cores were tested at various constant injection rates over a period of time determined by a prescribed, cumulative pore volume amount of the injection fluid. During each test, the pressure difference was measured and the permeability was calculated using Darcy's law. As can be seen, the permeability remained unchanged at the low flow rate of 0.0367cm3/-?, while it decreased further at each of the increased high flow rates of 0.0682, 0.1002, 0.1310, and 0.1702cm3/s. The final permeability values attained after each of the high flow rates are used to calculate the permeability reductions from the initial state, which are then plotted against these high flow rates as shown in this article. They stated that the removal of indigeneous particles in the cores from the pore surface and subsequent redeposition at the pore throats caused the permeability reduction. Second, core samples were taken from an oil field, indicating an abnormal decline of productivity in some wells. These cores were tested using
1. white oil in a dry core
2. white oil in a core at connate 2% KCl brine saturation.
This is apparent by the effect of the two phases on the critical velocity values required to initiate particle mobilization. The implication of this is that variation of the fluid system from oil to oil/water can reduce the critical
velocity, induce surface particle mobilization, and increase permeability damage in the near wellbore formation.
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