Hello. Welcome to Just Answer. Please allow me to assist you. Excessive oil consumption (assuming the oil is not leaking out of the engine) is caused by only two things. Both entail the engine oil being 'burned' in the combustion chamber.
At 135,000 miles, it is a high likelihood that the oil control piston rings are either worn, or, there is carbon build up where the oil control rings fit onto the piston. The oil control rings need to rotate around the piston to properly operate as the piston moves. Every time the piston raises in the cylinder, oil is splashed onto the cylinder walls to lubricate the piston's motion. The oil control rings are kind of springy, and their sole function is to scrape the lube oil down as the piston moves downward. If the oil control rings have carbon buildup, the rings wear out. The scraping action is lost, and the oil remains in the cylinder. When the piston rises up again, this oil (that is not supposed to be there) is ignited by the firing of the gasoline mixture, where the oil is burnt.
Also, at 135,000 miles there is a much higher likelihood of the valve seals being worn or heat-hardened (no longer pliable). Ove time, the valve seals (which prevent excess oil from leaking down the stems of the intake and exhaust valves) lost their ability to seal the oil from trickling into the tops of the valves. This leakage is then drawn into the engine (Intake valve) and is then burned. The oil that comes down the exhaust valve is blown out into the exhaust manifold.
Short of removing the engine and replacing the piston rings, and disassembling the head(s), the alternative way to combat oil consumption is as follows:
Start using motor oil that is specifically designed for 'high mileage engines". There are additives in thsi oil that softens hard valve seals, and helps to loosen carbon buildup on the piston rings. Secondly, add a high quality fuel injection cleaner to the fuel tank (we use a product called BG 44-K in our shop). The cleaner is not so much for cleaning the injectors, it is more of a cleaner that will find its way into the oil control rings and clean off the carbon.
This is exactly what we do in the shop for out customer who have this problem. We have had very good results with this regimen, and have noticed a reduction in oil consumption across the board. Oil loss will still happen, but not 1 quart every 500 miles.